Daily Papers

The semantic matching capabilities of neural information retrieval can ameliorate synonymy and polysemy problems of symbolic approaches. However, neural models' dense representations are more suitable for re-ranking, due to their inefficiency. Sparse representations, either in symbolic or latent form, are more efficient with an inverted index. Taking the merits of the sparse and dense representations, we propose an ultra-high dimensional (UHD) representation scheme equipped with directly controllable sparsity. UHD's large capacity and minimal noise and interference among the dimensions allow for binarized representations, which are highly efficient for storage and search. Also proposed is a bucketing method, where the embeddings from multiple layers of BERT are selected/merged to represent diverse linguistic aspects. We test our models with MS MARCO and TREC CAR, showing that our models outperforms other sparse models

Post-training quantization (PTQ) reduces the memory footprint of LLMs by quantizing weights to low-precision datatypes. Since LLM inference is usually memory-bound, PTQ methods can improve inference throughput. Recent state-of-the-art PTQ approaches use vector quantization (VQ) to quantize multiple weights at once, which improves information utilization through better shaping. However, VQ requires a codebook with size exponential in the dimension. This limits current VQ-based PTQ works to low VQ dimensions (le 8) that in turn limit quantization quality. Here, we introduce QTIP, which instead uses trellis coded quantization (TCQ) to achieve ultra-high-dimensional quantization. TCQ uses a stateful decoder that separates the codebook size from the bitrate and effective dimension. QTIP introduces a spectrum of lookup-only to computed lookup-free trellis codes designed for a hardware-efficient "bitshift" trellis structure; these codes achieve state-of-the-art results in both quantization quality and inference speed.

Product search is a crucial component of modern e-commerce platforms, with billions of user queries every day. In product search systems, first-stage retrieval should achieve high recall while ensuring efficient online deployment. Sparse retrieval is particularly attractive in this context due to its interpretability and storage efficiency. However, sparse retrieval methods suffer from severe vocabulary mismatch issues, leading to suboptimal performance in product search scenarios. With their potential for semantic analysis, large language models (LLMs) offer a promising avenue for mitigating vocabulary mismatch issues and thereby improving retrieval quality. Directly applying LLMs to sparse retrieval in product search exposes two key challenges:(1)Queries and product titles are typically short and highly susceptible to LLM-induced hallucinations, such as generating irrelevant expansion terms or underweighting critical literal terms like brand names and model numbers;(2)The large vocabulary space of LLMs leads to difficulty in initializing training effectively, making it challenging to learn meaningful sparse representations in such ultra-high-dimensional spaces.To address these challenges, we propose PROSPER, a framework for PROduct search leveraging LLMs as SParsE Retrievers. PROSPER incorporates: (1)A literal residual network that alleviates hallucination in lexical expansion by reinforcing underweighted literal terms through a residual compensation mechanism; and (2)A lexical focusing window that facilitates effective training initialization via a coarse-to-fine sparsification strategy.Extensive offline and online experiments show that PROSPER significantly outperforms sparse baselines and achieves recall performance comparable to advanced dense retrievers, while also achieving revenue increments online.

In this paper, we introduce LangSplatV2, which achieves high-dimensional feature splatting at 476.2 FPS and 3D open-vocabulary text querying at 384.6 FPS for high-resolution images, providing a 42 times speedup and a 47 times boost over LangSplat respectively, along with improved query accuracy. LangSplat employs Gaussian Splatting to embed 2D CLIP language features into 3D, significantly enhancing speed and learning a precise 3D language field with SAM semantics. Such advancements in 3D language fields are crucial for applications that require language interaction within complex scenes. However, LangSplat does not yet achieve real-time inference performance (8.2 FPS), even with advanced A100 GPUs, severely limiting its broader application. In this paper, we first conduct a detailed time analysis of LangSplat, identifying the heavyweight decoder as the primary speed bottleneck. Our solution, LangSplatV2 assumes that each Gaussian acts as a sparse code within a global dictionary, leading to the learning of a 3D sparse coefficient field that entirely eliminates the need for a heavyweight decoder. By leveraging this sparsity, we further propose an efficient sparse coefficient splatting method with CUDA optimization, rendering high-dimensional feature maps at high quality while incurring only the time cost of splatting an ultra-low-dimensional feature. Our experimental results demonstrate that LangSplatV2 not only achieves better or competitive query accuracy but is also significantly faster. Codes and demos are available at our project page: https://langsplat-v2.github.io.

Most recent exciting experimental advances introduced buckled and flat borophene nanomembranes as new members to the advancing family of two-dimensional (2D) materials. Borophene, is the boron atom analogue of graphene with interesting properties suitable for a wide variety of applications. In this investigation, we conducted extensive first-principles density functional theory simulations to explore the application of four different flat borophene films as anode materials for Al, Mg, Na or Li-ion batteries. In our modelling, first the strongest binding sites were predicted and next we gradually increased the adatoms coverage until the maximum capacity was reached. Bader charge analysis was employed to evaluate the charge transfer between the adatoms and the borophene films. Nudged elastic band method was also utilized to probe the ions diffusions. We calculated the average atom adsorption energies and open-circuit voltage profiles as a function of adatoms coverage. Our findings propose the flat borophene films as electrically conductive and thermally stable anode materials with ultra high capacities of 2480 mAh/g, 1640 mAh/g and 2040 mAh/g for Mg, Na or Li-ion batteries, respectively, which distinctly outperform not only the buckled borophene but also all other 2D materials. Our study may provide useful viewpoint with respect to the possible application of flat borophene films for the design of high capacity and light weight advanced rechargeable ion batteries.

In the era of large foundation models, the quality of embeddings has become a central determinant of downstream task performance and overall system capability. Yet widely used dense embeddings are often extremely high-dimensional, incurring substantial costs in storage, memory, and inference latency. To address these, Contrastive Sparse Representation (CSR) is recently proposed as a promising direction, mapping dense embeddings into high-dimensional but k-sparse vectors, in contrast to compact dense embeddings such as Matryoshka Representation Learning (MRL). Despite its promise, CSR suffers severe degradation in the ultra-sparse regime, where over 80% of neurons remain inactive, leaving much of its efficiency potential unrealized. In this paper, we introduce CSRv2, a principled training approach designed to make ultra-sparse embeddings viable. CSRv2 stabilizes sparsity learning through progressive k-annealing, enhances representational quality via supervised contrastive objectives, and ensures end-to-end adaptability with full backbone finetuning. CSRv2 reduces dead neurons from 80% to 20% and delivers a 14% accuracy gain at k=2, bringing ultra-sparse embeddings on par with CSR at k=8 and MRL at 32 dimensions, all with only two active features. While maintaining comparable performance, CSRv2 delivers a 7x speedup over MRL, and yields up to 300x improvements in compute and memory efficiency relative to dense embeddings in text representation. Extensive experiments across text and vision demonstrate that CSRv2 makes ultra-sparse embeddings practical without compromising performance, where CSRv2 achieves 7%/4% improvement over CSR when k=4 and further increases this gap to 14%/6% when k=2 in text/vision representation. By making extreme sparsity viable, CSRv2 broadens the design space for real-time and edge-deployable AI systems where both embedding quality and efficiency are critical.

The advancement of artificial intelligence toward agentic science is currently bottlenecked by the challenge of ultra-long-horizon autonomy, the ability to sustain strategic coherence and iterative correction over experimental cycles spanning days or weeks. While Large Language Models (LLMs) have demonstrated prowess in short-horizon reasoning, they are easily overwhelmed by execution details in the high-dimensional, delayed-feedback environments of real-world research, failing to consolidate sparse feedback into coherent long-term guidance. Here, we present ML-Master 2.0, an autonomous agent that masters ultra-long-horizon machine learning engineering (MLE) which is a representative microcosm of scientific discovery. By reframing context management as a process of cognitive accumulation, our approach introduces Hierarchical Cognitive Caching (HCC), a multi-tiered architecture inspired by computer systems that enables the structural differentiation of experience over time. By dynamically distilling transient execution traces into stable knowledge and cross-task wisdom, HCC allows agents to decouple immediate execution from long-term experimental strategy, effectively overcoming the scaling limits of static context windows. In evaluations on OpenAI's MLE-Bench under 24-hour budgets, ML-Master 2.0 achieves a state-of-the-art medal rate of 56.44%. Our findings demonstrate that ultra-long-horizon autonomy provides a scalable blueprint for AI capable of autonomous exploration beyond human-precedent complexities.

Millimeter-wave (mmWave) and Terahertz (THz)-band communications hold great promise in meeting the growing data-rate demands of next-generation wireless networks, offering abundant bandwidth. To mitigate the severe path loss inherent to these high frequencies and reduce hardware costs, ultra-massive multiple-input multiple-output (UM-MIMO) systems with hybrid beamforming architectures can deliver substantial beamforming gains and enhanced spectral efficiency. However, accurate channel estimation (CE) in mmWave and THz UM-MIMO systems is challenging due to high channel dimensionality and compressed observations from a limited number of RF chains, while the hybrid near- and far-field radiation patterns, arising from large array apertures and high carrier frequencies, further complicate CE. Conventional compressive sensing based frameworks rely on predefined sparsifying matrices, which cannot faithfully capture the hybrid near-field and far-field channel structures, leading to degraded estimation performance. This paper introduces DiffPace, a diffusion-based plug-and-play method for channel estimation. DiffPace uses a diffusion model (DM) to capture the channel distribution based on the hybrid spherical and planar-wave (HPSM) model. By applying the plug-and-play approach, it leverages the DM as prior knowledge, improving CE accuracy. Moreover, DM performs inference by solving an ordinary differential equation, minimizing the number of required inference steps compared with stochastic sampling method. Experimental results show that DiffPace achieves competitive CE performance, attaining -15 dB normalized mean square error (NMSE) at a signal-to-noise ratio (SNR) of 10 dB, with 90\% fewer inference steps compared to state-of-the-art schemes, simultaneously providing high estimation precision and enhanced computational efficiency.

The astonishing breakthrough of multimodal large language models (MLLMs) has necessitated new benchmarks to quantitatively assess their capabilities, reveal their limitations, and indicate future research directions. However, this is challenging in the context of remote sensing (RS), since the imagery features ultra-high resolution that incorporates extremely complex semantic relationships. Existing benchmarks usually adopt notably smaller image sizes than real-world RS scenarios, suffer from limited annotation quality, and consider insufficient dimensions of evaluation. To address these issues, we present XLRS-Bench: a comprehensive benchmark for evaluating the perception and reasoning capabilities of MLLMs in ultra-high-resolution RS scenarios. XLRS-Bench boasts the largest average image size (8500times8500) observed thus far, with all evaluation samples meticulously annotated manually, assisted by a novel semi-automatic captioner on ultra-high-resolution RS images. On top of the XLRS-Bench, 16 sub-tasks are defined to evaluate MLLMs' 10 kinds of perceptual capabilities and 6 kinds of reasoning capabilities, with a primary emphasis on advanced cognitive processes that facilitate real-world decision-making and the capture of spatiotemporal changes. The results of both general and RS-focused MLLMs on XLRS-Bench indicate that further efforts are needed for real-world RS applications. We have open-sourced XLRS-Bench to support further research in developing more powerful MLLMs for remote sensing.

While diffusion models excel at generating images with conventional dimensions, pushing them to synthesize ultra-high-resolution imagery at extreme aspect ratios (EAR) often triggers catastrophic structural failures, such as object repetition and spatial fragmentation. This limitation fundamentally stems from a lack of robust spatial priors, as static text-to-image models are primarily trained on image distributions with conventional dimensions. To overcome this bottleneck, we present ScrollScape, a novel framework that reformulates EAR image synthesis into a continuous video generation process through two core innovations. By mapping the spatial expansion of a massive canvas to the temporal evolution of video frames, ScrollScape leverages the inherent temporal consistency of video models as a powerful global constraint to ensure long-range structural integrity. Specifically, Scanning Positional Encoding (ScanPE) distributes global coordinates across frames to act as a flexible moving camera, while Scrolling Super-Resolution (ScrollSR) leverages video super-resolution priors to circumvent memory bottlenecks, efficiently scaling outputs to an unprecedented 32K resolution. Fine-tuned on a curated 3K multi-ratio image dataset, ScrollScape effectively aligns pre-trained video priors with the EAR generation task. Extensive evaluations demonstrate that it significantly outperforms existing image-diffusion baselines by eliminating severe localized artifacts. Consequently, our method overcomes inherent structural bottlenecks to ensure exceptional global coherence and visual fidelity across diverse domains at extreme scales.

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a 'geometric unification' endeavour, in the spirit of Felix Klein's Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.

Hot carriers, inheriting excess kinetic energy from high-energy photons, underpin numerous optoelectronic applications involving non-equilibrium transport processes. Current research on hot carriers has predominantly focused on inorganic materials, with little attention paid to organic-based systems due to their ultrafast energy relaxation and inefficient charge transport. Here, we overturn this paradigm by demonstrating highly mobile hot carriers in solution-processable, highly crystalline two-dimensional conjugated coordination polymer (2D c-CP) Cu3BHT (BHT = benzenehexathiol) films. Leveraging a suite of ultrafast spectroscopic and imaging techniques, we unravel the microscopic charge transport landscape in Cu3BHT films following non-equilibrium photoexcitation across temporal, spatial, and frequency domains, revealing two distinct high-mobility transport regimes. In the non-equilibrium transport regime, hot carriers achieve ultrahigh mobility of ~2,000 cm2 V-1 s-1, traversing grain boundaries up to 300 nm within a picosecond. In the quasi-equilibrium transport regime, free carriers exhibit Drude-type band-like transport with a remarkable mobility of ~400 cm2 V-1 s-1 and an intrinsic diffusion length exceeding 1 micrometer. These findings establish 2D c-CPs as versatile platforms for exploring high-mobility non-equilibrium transport, unlocking new opportunities for organic-based hot carrier applications.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain poorly understood, as universality is traditionally studied for models accepting inputs of a fixed size, defined on a compact subset of their domain. In sharp contrast, any-dimensional models can be viewed as sequences of functions defined on growing-sized inputs, and it is not clear in which sense they can be universal. We develop a systematic approach to establish any-dimensional universality, by identifying any-dimensional functions with a unique function taking inputs in a suitable infinite-dimensional limit space containing inputs of all finite sizes as well as their limits. Using the symmetries of these inputs and relations between inputs of different sizes, we show that this limit space admits a natural topology with rich families of compact sets on which any-dimensional universality can be established. We illustrate our approach by showing that several existing architectures fail to be universal, and we propose simple modifications that restore universality.

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used to preserve the grouping properties of the data distribution on multiple levels. The core of the proposal is an optimization-free projection that is competitive with the latest versions of t-SNE and UMAP in performance and visualization quality while being an order of magnitude faster in run-time. Furthermore, its interpretable mechanics, the ability to project new data, and the natural separation of data clusters in visualizations make it a general purpose unsupervised dimension reduction technique. In the paper, we argue about the soundness of the proposed method and evaluate it on a diverse collection of datasets with sizes varying from 1K to 11M samples and dimensions from 28 to 16K. We perform comparisons with other state-of-the-art methods on multiple metrics and target dimensions highlighting its efficiency and performance. Code is available at https://github.com/koulakis/h-nne

Ultra-High-Definition (UHD) image restoration is trapped in a scalability crisis: existing models, bound to pixel-wise operations, demand unsustainable computation. While state space models (SSMs) like Mamba promise linear complexity, their pixel-serial scanning remains a fundamental bottleneck for the millions of pixels in UHD content. We ask: must we process every pixel to understand the image? This paper introduces C^2SSM, a visual state space model that breaks this taboo by shifting from pixel-serial to cluster-serial scanning. Our core discovery is that the rich feature distribution of a UHD image can be distilled into a sparse set of semantic centroids via a neural-parameterized mixture model. C^2SSM leverages this to reformulate global modeling into a novel dual-path process: it scans and reasons over a handful of cluster centers, then diffuses the global context back to all pixels through a principled similarity distribution, all while a lightweight modulator preserves fine details. This cluster-centric paradigm achieves a decisive leap in efficiency, slashing computational costs while establishing new state-of-the-art results across five UHD restoration tasks. More than a solution, C^2SSM charts a new course for efficient large-scale vision: scan clusters, not pixels.

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schrödinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in 100,000 effective dimensions in 12 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

Visual generation with discrete tokens has gained significant attention as it enables a unified token prediction paradigm shared with language models, promising seamless multimodal architectures. However, current discrete generation methods remain limited to low-dimensional latent tokens (typically 8-32 dims), sacrificing the semantic richness essential for understanding. While high-dimensional pretrained representations (768-1024 dims) could bridge this gap, their discrete generation poses fundamental challenges. In this paper, we present Cubic Discrete Diffusion (CubiD), the first discrete generation model for high-dimensional representations. CubiD performs fine-grained masking throughout the high-dimensional discrete representation -- any dimension at any position can be masked and predicted from partial observations. This enables the model to learn rich correlations both within and across spatial positions, with the number of generation steps fixed at T regardless of feature dimensionality, where T ll hwd. On ImageNet-256, CubiD achieves state-of-the-art discrete generation with strong scaling behavior from 900M to 3.7B parameters. Crucially, we validate that these discretized tokens preserve original representation capabilities, demonstrating that the same discrete tokens can effectively serve both understanding and generation tasks. We hope this work will inspire future research toward unified multimodal architectures. Code is available at: https://github.com/YuqingWang1029/CubiD.

Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in fully-connected layers with Hamilton products of Quaternions, both enjoy parameter savings with only 1/4 learnable parameters and achieve comparable performance in various applications. However, one key caveat is that hypercomplex space only exists at very few predefined dimensions (4D, 8D, and 16D). This restricts the flexibility of models that leverage hypercomplex multiplications. To this end, we propose parameterizing hypercomplex multiplications, allowing models to learn multiplication rules from data regardless of whether such rules are predefined. As a result, our method not only subsumes the Hamilton product, but also learns to operate on any arbitrary nD hypercomplex space, providing more architectural flexibility using arbitrarily 1/n learnable parameters compared with the fully-connected layer counterpart. Experiments of applications to the LSTM and Transformer models on natural language inference, machine translation, text style transfer, and subject verb agreement demonstrate architectural flexibility and effectiveness of the proposed approach.

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis introduces robust and computationally efficient methods to address several common challenges associated with high-dimensional data. In my first manuscript, I propose a coherent approach to variable screening that accommodates nonlinear associations. I develop a novel variable screening method that transcends traditional linear assumptions by leveraging mutual information, with an intended application in neuroimaging data. This approach allows for accurate identification of important variables by capturing nonlinear as well as linear relationships between the outcome and covariates. Building on this foundation, I develop new optimization methods for sparse estimation using nonconvex penalties in my second manuscript. These methods address notable challenges in current statistical computing practices, facilitating computationally efficient and robust analyses of complex datasets. The proposed method can be applied to a general class of optimization problems. In my third manuscript, I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power-law entropy maximization and discussed the theoretical properties of such distribution. This model surpasses the constraints of conventional Gaussian models by accommodating a broader class of distributions with enhanced robustness to outliers. Additionally, I develop a proximal nonlinear conjugate gradient algorithm that accelerates convergence while maintaining numerical stability, along with rigorous statistical properties for the proposed framework.

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension n=8, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions 4-16, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

Recent advances in sparse voxel representations have significantly improved the quality of 3D content generation, enabling high-resolution modeling with fine-grained geometry. However, existing frameworks suffer from severe computational inefficiencies due to the quadratic complexity of attention mechanisms in their two-stage diffusion pipelines. In this work, we propose Ultra3D, an efficient 3D generation framework that significantly accelerates sparse voxel modeling without compromising quality. Our method leverages the compact VecSet representation to efficiently generate a coarse object layout in the first stage, reducing token count and accelerating voxel coordinate prediction. To refine per-voxel latent features in the second stage, we introduce Part Attention, a geometry-aware localized attention mechanism that restricts attention computation within semantically consistent part regions. This design preserves structural continuity while avoiding unnecessary global attention, achieving up to 6.7x speed-up in latent generation. To support this mechanism, we construct a scalable part annotation pipeline that converts raw meshes into part-labeled sparse voxels. Extensive experiments demonstrate that Ultra3D supports high-resolution 3D generation at 1024 resolution and achieves state-of-the-art performance in both visual fidelity and user preference.

Deep learning based methods have achieved significant success in the task of single image reflection removal (SIRR). However, the majority of these methods are focused on High-Definition/Standard-Definition (HD/SD) images, while ignoring higher resolution images such as Ultra-High-Definition (UHD) images. With the increasing prevalence of UHD images captured by modern devices, in this paper, we aim to address the problem of UHD SIRR. Specifically, we first synthesize two large-scale UHD datasets, UHDRR4K and UHDRR8K. The UHDRR4K dataset consists of 2,999 and 168 quadruplets of images for training and testing respectively, and the UHDRR8K dataset contains 1,014 and 105 quadruplets. To the best of our knowledge, these two datasets are the first largest-scale UHD datasets for SIRR. Then, we conduct a comprehensive evaluation of six state-of-the-art SIRR methods using the proposed datasets. Based on the results, we provide detailed discussions regarding the strengths and limitations of these methods when applied to UHD images. Finally, we present a transformer-based architecture named RRFormer for reflection removal. RRFormer comprises three modules, namely the Prepossessing Embedding Module, Self-attention Feature Extraction Module, and Multi-scale Spatial Feature Extraction Module. These modules extract hypercolumn features, global and partial attention features, and multi-scale spatial features, respectively. To ensure effective training, we utilize three terms in our loss function: pixel loss, feature loss, and adversarial loss. We demonstrate through experimental results that RRFormer achieves state-of-the-art performance on both the non-UHD dataset and our proposed UHDRR datasets. The code and datasets are publicly available at https://github.com/Liar-zzy/Benchmarking-Ultra-High-Definition-Single-Image-Reflection-Removal.

The rapid advancement of high-throughput sequencing has led to large, high-dimensional omics datasets. Deep unsupervised learning architectures, particularly Autoencoders (AEs), are increasingly used for dimensionality reduction and representation learning in this domain. However, AEs are highly sensitive to architectural choices and hyperparameters, and unsupervised optimization typically relies on reconstruction loss, which may be a poor proxy for downstream utility. Exhaustive hyperparameter optimization (HPO) is computationally expensive, leading researchers to frequently rely on suboptimal default configurations. To democratize access to large-scale unsupervised HPO research, we introduce BBOmix, the first open-source tabular benchmark for unsupervised representation learning on real-world biological data. Our benchmark includes 105,000 evaluations across four AE architectures and seven multi-omics modalities from the TCGA and SCHC datasets. We quantify the correlation between reconstruction loss and downstream task performance and provide an extensive evaluation of state-of-the-art single-fidelity, multi-fidelity, and transfer learning HPO methods, establishing a rigorous baseline for future research in unsupervised biological representation learning.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

By classifying infinite-width neural networks and identifying the *optimal* limit, Tensor Programs IV and V demonstrated a universal way, called muP, for *widthwise hyperparameter transfer*, i.e., predicting optimal hyperparameters of wide neural networks from narrow ones. Here we investigate the analogous classification for *depthwise parametrizations* of deep residual networks (resnets). We classify depthwise parametrizations of block multiplier and learning rate by their infinite-width-then-depth limits. In resnets where each block has only one layer, we identify a unique optimal parametrization, called Depth-muP that extends muP and show empirically it admits depthwise hyperparameter transfer. We identify *feature diversity* as a crucial factor in deep networks, and Depth-muP can be characterized as maximizing both feature learning and feature diversity. Exploiting this, we find that absolute value, among all homogeneous nonlinearities, maximizes feature diversity and indeed empirically leads to significantly better performance. However, if each block is deeper (such as modern transformers), then we find fundamental limitations in all possible infinite-depth limits of such parametrizations, which we illustrate both theoretically and empirically on simple networks as well as Megatron transformer trained on Common Crawl.

Machine-learning datasets labelled "4D" universally denote three spatial dimensions plus time. We introduce HyperShadow, the first public benchmark in which the fourth, fifth, and sixth dimensions are spatial: the task is to decide whether a 3D point cloud is a native three-dimensional shape or the projection, the "shadow", of a rigid object living in R^N (N = 4-6). We show this task is fundamentally distinct from intrinsic-dimension estimation: a shadow is still at-most-3-dimensional data, and standard estimators (TwoNN, Levina-Bickel MLE) reach only 71-73% accuracy. Detection instead requires projection signatures, density folds, filled volumes with characteristic radial profiles, and topology changes, which a 190k-parameter point network recovers at 96.6% accuracy across four corruption tiers, generalizing at 79-91% to object families never seen in training. On a temporal track of rigidly rotating objects we introduce a zero-parameter rigidity witness: the residual of the optimal rigid 3D alignment (Kabsch) between consecutive frames, which must vanish for any rigid 3D motion but cannot vanish for the shadow of a rigid rotation in R^N. This single interpretable statistic separates the classes at AUROC 0.982. All data are generated reproducibly from seeds; the dataset, models, and code are released publicly. HyperShadow makes no claim about physical reality; it is a controlled instrument for studying which observable statistics can certify incompatibility with a purely three-dimensional explanation.

The manifold hypothesis posits that high-dimensional data often lies on a lower-dimensional manifold and that utilizing this manifold as the target space yields more efficient representations. While numerous traditional manifold-based techniques exist for dimensionality reduction, their application in self-supervised learning has witnessed slow progress. The recent MSimCLR method combines manifold encoding with SimCLR but requires extremely low target encoding dimensions to outperform SimCLR, limiting its applicability. This paper introduces a novel learning paradigm using an unbalanced atlas (UA), capable of surpassing state-of-the-art self-supervised learning approaches. We investigated and engineered the DeepInfomax with an unbalanced atlas (DIM-UA) method by adapting the Spatiotemporal DeepInfomax (ST-DIM) framework to align with our proposed UA paradigm. The efficacy of DIM-UA is demonstrated through training and evaluation on the Atari Annotated RAM Interface (AtariARI) benchmark, a modified version of the Atari 2600 framework that produces annotated image samples for representation learning. The UA paradigm improves existing algorithms significantly as the number of target encoding dimensions grows. For instance, the mean F1 score averaged over categories of DIM-UA is ~75% compared to ~70% of ST-DIM when using 16384 hidden units.

Large language models (LLMs) often need to incorporate external knowledge to solve theme-specific problems. Retrieval-augmented generation (RAG) has shown its high promise, empowering LLMs to generate more qualified responses with retrieved external data and knowledge. However, most RAG methods retrieve relevant documents based on either sparse or dense retrieval methods or their combinations, which overlooks the essential, multi-dimensional, and structured semantic information present in documents. This structured information plays a critical role in finding concise yet highly relevant information for domain knowledge-intensive tasks, such as scientific question-answering (QA). In this work, we introduce a multi-dimensional (cube) structure, Hypercube, which can index and allocate documents in a pre-defined multi-dimensional space. Built on the hypercube, we further propose Hypercube-RAG, a novel RAG framework for precise and efficient retrieval. Given a query, Hypercube-RAG first decomposes it based on its entities, phrases, and topics along with pre-defined hypercube dimensions, and then retrieves relevant documents from cubes by aligning these decomposed components with corresponding dimensions. Experiments on three datasets across different domains demonstrate that our method improves response accuracy by 3.7% and retrieval accuracy by 5.3% over the strongest RAG baseline. It also boosts retrieval efficiency (speed) by one or two magnitudes faster than graph-based RAG. Notably, our Hypercube-RAG inherently offers explainability by revealing those underlying dimensions used for retrieval. The code and data are available at https://github.com/JimengShi/Hypercube-RAG.

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

Why does the low dimensionality of representations, typically dapprox 1000, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin embeddings in the following retrieval model, classically studied in communication complexity [PS86] and more recently in embedding-based retrieval [WBNL26]. Let Ain {0,1}^{Ntimes n} be a matrix indicating whether each of N queries is relevant to each of n documents. We are interested in the largest margin m>0, denoted by m^{rd}(d, A), for which there exist unit norm embeddings of the queries and documents {U_j}_{j = 1}^N, {V_i}_{i = 1}^n with the following property. langle U_j, V_irangle ge m whenever A_{ji} = 1 and langle U_j, V_irangle le -m otherwise. A large margin is a key proxy for representation quality: it controls both robustness to perturbations and compositional generalization across queries. Our main theorem establishes that the best possible margin without a restriction on the dimension, m^{rd}(+infty, A), can be nearly achieved in dimension d = O(m^{rd}(+infty, A)^{-2}log n) which improves a theorem of [BDES02]. Together with a matching lower bound in Theorem 1.5, we conclude that when Ain {0,1}^{n{k}times n} is the matrix containing all possible k-sparse rows once, dimension d = O(klog (n/k)) is necessary and sufficient for the maximal possible margin m^{rd}(+infty, A) = Θ(k^{-1/2}) in this setting. This fully resolves the setup of [WBNL26]. We also give several constructions for large margins when d = o(klog (n/k)). Finally, we empirically test the InfoNCE and sigmoid losses for producing large margin embeddings and demonstrate a clear advantage of the sigmoid loss.

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such as images. Yet, we lack a quantitative understanding of how such structure affects performance, e.g., the rate of decay of the generalisation error with the number of training samples. In this paper, we study infinitely-wide deep CNNs in the kernel regime. First, we show that the spectrum of the corresponding kernel inherits the hierarchical structure of the network, and we characterise its asymptotics. Then, we use this result together with generalisation bounds to prove that deep CNNs adapt to the spatial scale of the target function. In particular, we find that if the target function depends on low-dimensional subsets of adjacent input variables, then the decay of the error is controlled by the effective dimensionality of these subsets. Conversely, if the target function depends on the full set of input variables, then the error decay is controlled by the input dimension. We conclude by computing the generalisation error of a deep CNN trained on the output of another deep CNN with randomly-initialised parameters. Interestingly, we find that, despite their hierarchical structure, the functions generated by infinitely-wide deep CNNs are too rich to be efficiently learnable in high dimension.

Deep neural networks (DNNs) have been shown to outperform traditional machine learning algorithms in a broad variety of application domains due to their effectiveness in modeling complex problems and handling high-dimensional datasets. Many real-life datasets, however, are of increasingly high dimensionality, where a large number of features may be irrelevant for both supervised and unsupervised learning tasks. The inclusion of such features would not only introduce unwanted noise but also increase computational complexity. Furthermore, due to high non-linearity and dependency among a large number of features, DNN models tend to be unavoidably opaque and perceived as black-box methods because of their not well-understood internal functioning. Their algorithmic complexity is often simply beyond the capacities of humans to understand the interplay among myriads of hyperparameters. A well-interpretable model can identify statistically significant features and explain the way they affect the model's outcome. In this paper, we propose an efficient method to improve the interpretability of black-box models for classification tasks in the case of high-dimensional datasets. First, we train a black-box model on a high-dimensional dataset to learn the embeddings on which the classification is performed. To decompose the inner working principles of the black-box model and to identify top-k important features, we employ different probing and perturbing techniques. We then approximate the behavior of the black-box model by means of an interpretable surrogate model on the top-k feature space. Finally, we derive decision rules and local explanations from the surrogate model to explain individual decisions. Our approach outperforms state-of-the-art methods like TabNet and XGboost when tested on different datasets with varying dimensionality between 50 and 20,000 w.r.t metrics and explainability.

It is widely acknowledged that the performance of Transformer models is exponentially related to their number of parameters and computational complexity. While approaches like Mixture of Experts (MoE) decouple parameter count from computational complexity, they still face challenges in inference due to high memory access costs. This work introduces UltraMem, incorporating large-scale, ultra-sparse memory layer to address these limitations. Our approach significantly reduces inference latency while maintaining model performance. We also investigate the scaling laws of this new architecture, demonstrating that it not only exhibits favorable scaling properties but outperforms traditional models. In our experiments, we train networks with up to 20 million memory slots. The results show that our method achieves state-of-the-art inference speed and model performance within a given computational budget.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

Although pretrained language models can be fine-tuned to produce state-of-the-art results for a very wide range of language understanding tasks, the dynamics of this process are not well understood, especially in the low data regime. Why can we use relatively vanilla gradient descent algorithms (e.g., without strong regularization) to tune a model with hundreds of millions of parameters on datasets with only hundreds or thousands of labeled examples? In this paper, we argue that analyzing fine-tuning through the lens of intrinsic dimension provides us with empirical and theoretical intuitions to explain this remarkable phenomenon. We empirically show that common pre-trained models have a very low intrinsic dimension; in other words, there exists a low dimension reparameterization that is as effective for fine-tuning as the full parameter space. For example, by optimizing only 200 trainable parameters randomly projected back into the full space, we can tune a RoBERTa model to achieve 90\% of the full parameter performance levels on MRPC. Furthermore, we empirically show that pre-training implicitly minimizes intrinsic dimension and, perhaps surprisingly, larger models tend to have lower intrinsic dimension after a fixed number of pre-training updates, at least in part explaining their extreme effectiveness. Lastly, we connect intrinsic dimensionality with low dimensional task representations and compression based generalization bounds to provide intrinsic-dimension-based generalization bounds that are independent of the full parameter count.

The quality of the video dataset (image quality, resolution, and fine-grained caption) greatly influences the performance of the video generation model. The growing demand for video applications sets higher requirements for high-quality video generation models. For example, the generation of movie-level Ultra-High Definition (UHD) videos and the creation of 4K short video content. However, the existing public datasets cannot support related research and applications. In this paper, we first propose a high-quality open-sourced UHD-4K (22.4\% of which are 8K) text-to-video dataset named UltraVideo, which contains a wide range of topics (more than 100 kinds), and each video has 9 structured captions with one summarized caption (average of 824 words). Specifically, we carefully design a highly automated curation process with four stages to obtain the final high-quality dataset: i) collection of diverse and high-quality video clips. ii) statistical data filtering. iii) model-based data purification. iv) generation of comprehensive, structured captions. In addition, we expand Wan to UltraWan-1K/-4K, which can natively generate high-quality 1K/4K videos with more consistent text controllability, demonstrating the effectiveness of our data curation.We believe that this work can make a significant contribution to future research on UHD video generation. UltraVideo dataset and UltraWan models are available at https://xzc-zju.github.io/projects/UltraVideo.

We introduce the Nemotron 3 family of models - Nano, Super, and Ultra. These models deliver strong agentic, reasoning, and conversational capabilities. The Nemotron 3 family uses a Mixture-of-Experts hybrid Mamba-Transformer architecture to provide best-in-class throughput and context lengths of up to 1M tokens. Super and Ultra models are trained with NVFP4 and incorporate LatentMoE, a novel approach that improves model quality. The two larger models also include MTP layers for faster text generation. All Nemotron 3 models are post-trained using multi-environment reinforcement learning enabling reasoning, multi-step tool use, and support granular reasoning budget control. Nano, the smallest model, outperforms comparable models in accuracy while remaining extremely cost-efficient for inference. Super is optimized for collaborative agents and high-volume workloads such as IT ticket automation. Ultra, the largest model, provides state-of-the-art accuracy and reasoning performance. Nano is released together with its technical report and this white paper, while Super and Ultra will follow in the coming months. We will openly release the model weights, pre- and post-training software, recipes, and all data for which we hold redistribution rights.

Real-world data is high-dimensional: a book, image, or musical performance can easily contain hundreds of thousands of elements even after compression. However, the most commonly used autoregressive models, Transformers, are prohibitively expensive to scale to the number of inputs and layers needed to capture this long-range structure. We develop Perceiver AR, an autoregressive, modality-agnostic architecture which uses cross-attention to map long-range inputs to a small number of latents while also maintaining end-to-end causal masking. Perceiver AR can directly attend to over a hundred thousand tokens, enabling practical long-context density estimation without the need for hand-crafted sparsity patterns or memory mechanisms. When trained on images or music, Perceiver AR generates outputs with clear long-term coherence and structure. Our architecture also obtains state-of-the-art likelihood on long-sequence benchmarks, including 64 x 64 ImageNet images and PG-19 books.

Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for instance to understand the organization of different cell types. However, clustering is known to scale poorly to high dimensions, even though the exact impact of dimensionality is unclear as current benchmark datasets are mostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets that share a key property of real-world datasets, namely that individual samples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained by training mixture variational autoencoders with 2 to 64 latent dimensions on MNIST, resulting in six datasets with comparable structure but varying dimensionality. It thus offers the chance to disentangle the impact of dimensionality on clustering. Preliminary common clustering algorithm benchmarks on MNIST-Nd suggest that Leiden is the most robust for growing dimensions.

Recent advances in video generation have made it possible to produce visually compelling videos, with wide-ranging applications in content creation, entertainment, and virtual reality. However, most existing diffusion transformer based video generation models are limited to low-resolution outputs (<=720P) due to the quadratic computational complexity of the attention mechanism with respect to the output width and height. This computational bottleneck makes native high-resolution video generation (1080P/2K/4K) impractical for both training and inference. To address this challenge, we present UltraGen, a novel video generation framework that enables i) efficient and ii) end-to-end native high-resolution video synthesis. Specifically, UltraGen features a hierarchical dual-branch attention architecture based on global-local attention decomposition, which decouples full attention into a local attention branch for high-fidelity regional content and a global attention branch for overall semantic consistency. We further propose a spatially compressed global modeling strategy to efficiently learn global dependencies, and a hierarchical cross-window local attention mechanism to reduce computational costs while enhancing information flow across different local windows. Extensive experiments demonstrate that UltraGen can effectively scale pre-trained low-resolution video models to 1080P and even 4K resolution for the first time, outperforming existing state-of-the-art methods and super-resolution based two-stage pipelines in both qualitative and quantitative evaluations.

Ultra-high-resolution image generation poses great challenges, such as increased semantic planning complexity and detail synthesis difficulties, alongside substantial training resource demands. We present UltraPixel, a novel architecture utilizing cascade diffusion models to generate high-quality images at multiple resolutions (e.g., 1K to 6K) within a single model, while maintaining computational efficiency. UltraPixel leverages semantics-rich representations of lower-resolution images in the later denoising stage to guide the whole generation of highly detailed high-resolution images, significantly reducing complexity. Furthermore, we introduce implicit neural representations for continuous upsampling and scale-aware normalization layers adaptable to various resolutions. Notably, both low- and high-resolution processes are performed in the most compact space, sharing the majority of parameters with less than 3% additional parameters for high-resolution outputs, largely enhancing training and inference efficiency. Our model achieves fast training with reduced data requirements, producing photo-realistic high-resolution images and demonstrating state-of-the-art performance in extensive experiments.

We study the memorization power of feedforward ReLU neural networks. We show that such networks can memorize any N points that satisfy a mild separability assumption using Oleft(Nright) parameters. Known VC-dimension upper bounds imply that memorizing N samples requires Omega(N) parameters, and hence our construction is optimal up to logarithmic factors. We also give a generalized construction for networks with depth bounded by 1 leq L leq N, for memorizing N samples using O(N/L) parameters. This bound is also optimal up to logarithmic factors. Our construction uses weights with large bit complexity. We prove that having such a large bit complexity is both necessary and sufficient for memorization with a sub-linear number of parameters.

Contemporary models of high dimensional physical systems are constrained by the curse of dimensionality and a reliance on dense data. We introduce KHRONOS (Kernel Expansion Hierarchy for Reduced Order, Neural Optimized Surrogates), an AI framework for model based, model free and model inversion tasks. KHRONOS constructs continuously differentiable target fields with a hierarchical composition of per-dimension kernel expansions, which are tensorized into modes and then superposed. We evaluate KHRONOS on a canonical 2D, Poisson equation benchmark: across 16 to 512 degrees of freedom (DoFs), it obtained L_2-square errors of 5e-4 down to 6e-11. This represents a greater than 100-fold gain over Kolmogorov Arnold Networks (which itself reports a 100 times improvement on MLPs/PINNs with 100 times fewer parameters) when controlling for the number of parameters. This also represents a 1e6-fold improvement in L_2-square error compared to standard linear FEM at comparable DoFs. Inference complexity is dominated by inner products, yielding sub-millisecond full-field predictions that scale to an arbitrary resolution. For inverse problems, KHRONOS facilitates rapid, iterative level set recovery in only a few forward evaluations, with sub-microsecond per sample latency. KHRONOS's scalability, expressivity, and interpretability open new avenues in constrained edge computing, online control, computer vision, and beyond.

Diffusion models have shown remarkable performance in image generation in recent years. However, due to a quadratic increase in memory during generating ultra-high-resolution images (e.g. 4096*4096), the resolution of generated images is often limited to 1024*1024. In this work. we propose a unidirectional block attention mechanism that can adaptively adjust the memory overhead during the inference process and handle global dependencies. Building on this module, we adopt the DiT structure for upsampling and develop an infinite super-resolution model capable of upsampling images of various shapes and resolutions. Comprehensive experiments show that our model achieves SOTA performance in generating ultra-high-resolution images in both machine and human evaluation. Compared to commonly used UNet structures, our model can save more than 5x memory when generating 4096*4096 images. The project URL is https://github.com/THUDM/Inf-DiT.

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width w^*_{min}=max(d_x,d_y), where d_x and d_y are the dimensions of the input and output, respectively. Recently, cai2022achieve shows that a leaky-ReLU NN with this critical width can achieve UAP for L^p functions on a compact domain K, i.e., the UAP for L^p(K,R^{d_y}). This paper examines a uniform UAP for the function class C(K,R^{d_y}) and gives the exact minimum width of the leaky-ReLU NN as w_{min}=max(d_x+1,d_y)+1_{d_y=d_x+1}, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding. Traditional methods, such as principal component analysis (PCA) and autoencoders (AE), operate in an unsupervised manner, ignoring label information even when it is available. In this work, we introduce a unified method capable of learning latent spaces in both unsupervised and supervised settings. We formulate the problem as a nonlinear multiple-response regression within an index model context. By applying the generalized Stein's lemma, the latent space can be estimated without knowing the nonlinear link functions. Our method can be viewed as a nonlinear generalization of PCA. Moreover, unlike AE and other neural network methods that operate as "black boxes", our approach not only offers better interpretability but also reduces computational complexity while providing strong theoretical guarantees. Comprehensive numerical experiments and real data analyses demonstrate the superior performance of our method.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

We introduce Hyperdimensional Graph Learner (HDGL), a novel method for node classification and link prediction in graphs. HDGL maps node features into a very high-dimensional space (hyperdimensional or HD space for short) using the injectivity property of node representations in a family of Graph Neural Networks (GNNs) and then uses HD operators such as bundling and binding to aggregate information from the local neighborhood of each node yielding latent node representations that can support both node classification and link prediction tasks. HDGL, unlike GNNs that rely on computationally expensive iterative optimization and hyperparameter tuning, requires only a single pass through the data set. We report results of experiments using widely used benchmark datasets which demonstrate that, on the node classification task, HDGL achieves accuracy that is competitive with that of the state-of-the-art GNN methods at substantially reduced computational cost; and on the link prediction task, HDGL matches the performance of DeepWalk and related methods, although it falls short of computationally demanding state-of-the-art GNNs.

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into "supervertices" which are arranged according to a d-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification.

The ability to control multidimensional quantum systems is key for the investigation of fundamental science and for the development of advanced quantum technologies. Here we demonstrate a multidimensional integrated quantum photonic platform able to robustly generate, control and analyze high-dimensional entanglement. We realize a programmable bipartite entangled system with dimension up to 15 times 15 on a large-scale silicon-photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality and controllability of our multidimensional technology, and further exploit these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides a prominent experimental platform for the development of multidimensional quantum technologies.

Energy-efficient medical data classification is essential for modern disease screening, particularly in home and field healthcare where embedded devices are prevalent. While deep learning models achieve state-of-the-art accuracy, their substantial energy consumption and reliance on GPUs limit deployment on such platforms. We present Hyperdimensional Computing with Class-Wise Clustering (HD3C), a lightweight classification framework designed for low-power environments. HD3C encodes data into high-dimensional hypervectors, aggregates them into multiple cluster-specific prototypes, and performs classification through similarity search in hyperspace. We evaluate HD3C across three medical classification tasks; on heart sound classification, HD3C is 350times more energy-efficient than Bayesian ResNet with less than 1% accuracy difference. Moreover, HD3C demonstrates exceptional robustness to noise, limited training data, and hardware error, supported by both theoretical analysis and empirical results, highlighting its potential for reliable deployment in real-world settings. Code is available at https://github.com/jianglanwei/HD3C.

Grid-based approaches to approximate nearest neighbor (ANN) search have been absent from modern scaling analyses. We present a systematic characterization of a multiprobe grid algorithm with respect to dataset size N and dimensionality d. Our experiments reveal a previously unreported d-scaling crossover on the GloVe embedding family, in which multiprobe grid search maintains an approximately constant dimensional scaling exponent while other graph-, tree-, and partitioning-based methods exhibit degrading throughput. The advantage comes with near-linear query scaling in N, but also with lower indexing cost than competing ANN methods. Our results suggest that grid-based methods such as multiprobe grid may be competitive in rebuild-heavy or high-dimensional settings where indexing cost and dimensional robustness dictate performance. More broadly, recent work has formalized self-attention as an ANN operation. Thus, the N- and d-scaling properties of ANN algorithms may guide cost analysis of efficient transformer architectures. Code is available at: https://github.com/weiz345/MultiProbeANN.

Ultra-high-resolution (UHR) remote sensing imagery couples kilometer-scale context with query-critical evidence that may occupy only a few pixels. Such vast spatial scale leads to a quadratic explosion of visual tokens and hinders the extraction of information from small objects. Previous works utilize direct downsampling, dense tiling, or global top-k pruning, which either compromise query-critical image details or incur unpredictable compute. In this paper, we propose UHR-BAT, a query-guided and region-faithful token compression framework to efficiently select visual tokens under a strict context budget. Specifically, we leverage text-guided, multi-scale importance estimation for visual tokens, effectively tackling the challenge of achieving precise yet low-cost feature extraction. Furthermore, by introducing region-wise preserve and merge strategies, we mitigate visual token redundancy, further driving down the computational budget. Experimental results show that UHR-BAT achieves state-of-the-art performance across various benchmarks. Code will be available at https://github.com/Yunkaidang/UHR.

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings, often in the range of hundreds to thousands of dimensions, can present scalability challenges in terms of storage and latency, especially when processing massive financial text corpora. This paper investigates the use of Principal Component Analysis (PCA) to reduce embedding dimensionality, thereby mitigating computational bottlenecks without incurring large accuracy losses. We experiment with a real-world dataset and compare different similarity and distance metrics under both full-dimensional and PCA-compressed embeddings. Our results show that reducing vectors from 3,072 to 110 dimensions provides a sizeable (up to 60times) speedup in retrieval operations and a sim 28.6times reduction in index size, with only moderate declines in correlation metrics relative to human-annotated similarity scores. These findings demonstrate that PCA-based compression offers a viable balance between retrieval fidelity and resource efficiency, essential for real-time systems such as Zanista AI's Newswitch platform. Ultimately, our study underscores the practicality of leveraging classical dimensionality reduction techniques to scale RAG architectures for knowledge-intensive applications in finance and trading, where speed, memory efficiency, and accuracy must jointly be optimized.

In this study, we examine the potential of one of the ``superexpressive'' networks in the context of learning neural functions for representing complex signals and performing machine learning downstream tasks. Our focus is on evaluating their performance on computer vision and scientific machine learning tasks including signal representation/inverse problems and solutions of partial differential equations. Through an empirical investigation in various benchmark tasks, we demonstrate that superexpressive networks, as proposed by [Zhang et al. NeurIPS, 2022], which employ a specialized network structure characterized by having an additional dimension, namely width, depth, and ``height'', can surpass recent implicit neural representations that use highly-specialized nonlinear activation functions.

Foundation models in language and vision have the ability to run inference on any textual and visual inputs thanks to the transferable representations such as a vocabulary of tokens in language. Knowledge graphs (KGs) have different entity and relation vocabularies that generally do not overlap. The key challenge of designing foundation models on KGs is to learn such transferable representations that enable inference on any graph with arbitrary entity and relation vocabularies. In this work, we make a step towards such foundation models and present ULTRA, an approach for learning universal and transferable graph representations. ULTRA builds relational representations as a function conditioned on their interactions. Such a conditioning strategy allows a pre-trained ULTRA model to inductively generalize to any unseen KG with any relation vocabulary and to be fine-tuned on any graph. Conducting link prediction experiments on 57 different KGs, we find that the zero-shot inductive inference performance of a single pre-trained ULTRA model on unseen graphs of various sizes is often on par or better than strong baselines trained on specific graphs. Fine-tuning further boosts the performance.

Scalar quantization of large language models (LLMs) is fundamentally limited by information-theoretic bounds. While vector quantization (VQ) overcomes these limits by encoding blocks of parameters jointly, practical implementations must avoid the need for expensive lookup mechanisms or other explicit codebook storage. Lattice approaches address this through highly structured and dense packing. This paper explores the Leech lattice, which, with its optimal sphere packing and kissing configurations at 24 dimensions, is the highest dimensional lattice known with such optimal properties. To make the Leech lattice usable for LLM quantization, we extend an existing search algorithm based on the extended Golay code construction, to i) support indexing, enabling conversion to and from bitstrings without materializing the codebook, ii) allow angular search over union of Leech lattice shells, iii) propose fully-parallelisable dequantization kernel. Lastly, we provide a geometric reinterpretation of combining shape--gain quantization with GPTQ-style Hessian corrections: the standard scale-correction step of shape--gain acts as a retraction onto a product of spheres, yielding a Spherical GPTQ primarily acting on directions. We find that low-angular-distortion LLVQ reduces sensitivity to Hadamard/rotation preprocessing, and enables a strong Hadamard-free PTQ in practice. LLVQ delivers state-of-the-art LLM quantization performance, outperforming recent methods such as Quip\#, QTIP, and PVQ. The results highlight the effectiveness of high-dimensional lattices for scalable, theoretically grounded model compression.

Transductive few-shot learning has recently triggered wide attention in computer vision. Yet, current methods introduce key hyper-parameters, which control the prediction statistics of the test batches, such as the level of class balance, affecting performances significantly. Such hyper-parameters are empirically grid-searched over validation data, and their configurations may vary substantially with the target dataset and pre-training model, making such empirical searches both sub-optimal and computationally intractable. In this work, we advocate and introduce the unrolling paradigm, also referred to as "learning to optimize", in the context of few-shot learning, thereby learning efficiently and effectively a set of optimized hyper-parameters. Specifically, we unroll a generalization of the ubiquitous Expectation-Maximization (EM) optimizer into a neural network architecture, mapping each of its iterates to a layer and learning a set of key hyper-parameters over validation data. Our unrolling approach covers various statistical feature distributions and pre-training paradigms, including recent foundational vision-language models and standard vision-only classifiers. We report comprehensive experiments, which cover a breadth of fine-grained downstream image classification tasks, showing significant gains brought by the proposed unrolled EM algorithm over iterative variants. The achieved improvements reach up to 10% and 7.5% on vision-only and vision-language benchmarks, respectively.

The primary aim of single-image super-resolution is to construct high-resolution (HR) images from corresponding low-resolution (LR) inputs. In previous approaches, which have generally been supervised, the training objective typically measures a pixel-wise average distance between the super-resolved (SR) and HR images. Optimizing such metrics often leads to blurring, especially in high variance (detailed) regions. We propose an alternative formulation of the super-resolution problem based on creating realistic SR images that downscale correctly. We present an algorithm addressing this problem, PULSE (Photo Upsampling via Latent Space Exploration), which generates high-resolution, realistic images at resolutions previously unseen in the literature. It accomplishes this in an entirely self-supervised fashion and is not confined to a specific degradation operator used during training, unlike previous methods (which require supervised training on databases of LR-HR image pairs). Instead of starting with the LR image and slowly adding detail, PULSE traverses the high-resolution natural image manifold, searching for images that downscale to the original LR image. This is formalized through the "downscaling loss," which guides exploration through the latent space of a generative model. By leveraging properties of high-dimensional Gaussians, we restrict the search space to guarantee realistic outputs. PULSE thereby generates super-resolved images that both are realistic and downscale correctly. We show proof of concept of our approach in the domain of face super-resolution (i.e., face hallucination). We also present a discussion of the limitations and biases of the method as currently implemented with an accompanying model card with relevant metrics. Our method outperforms state-of-the-art methods in perceptual quality at higher resolutions and scale factors than previously possible.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad or an item, is critical to many online applications such as online advertising and recommender systems. The problem is very challenging since (1) the input features (e.g., the user id, user age, item id, item category) are usually sparse and high-dimensional, and (2) an effective prediction relies on high-order combinatorial features (a.k.a. cross features), which are very time-consuming to hand-craft by domain experts and are impossible to be enumerated. Therefore, there have been efforts in finding low-dimensional representations of the sparse and high-dimensional raw features and their meaningful combinations. In this paper, we propose an effective and efficient method called the AutoInt to automatically learn the high-order feature interactions of input features. Our proposed algorithm is very general, which can be applied to both numerical and categorical input features. Specifically, we map both the numerical and categorical features into the same low-dimensional space. Afterwards, a multi-head self-attentive neural network with residual connections is proposed to explicitly model the feature interactions in the low-dimensional space. With different layers of the multi-head self-attentive neural networks, different orders of feature combinations of input features can be modeled. The whole model can be efficiently fit on large-scale raw data in an end-to-end fashion. Experimental results on four real-world datasets show that our proposed approach not only outperforms existing state-of-the-art approaches for prediction but also offers good explainability. Code is available at: https://github.com/DeepGraphLearning/RecommenderSystems.

High-dimensional vector embeddings are widely used in retrieval systems, yet dimensionality reduction (DR) is seldom applied due to its tendency to distort nearest-neighbor (NN) structure critical for search. Existing DR techniques such as PCA and UMAP optimize global or manifold-preserving criteria, rather than retrieval-specific objectives. We present MPAD: Maximum Pairwise Absolute Difference, an unsupervised DR method that explicitly preserves approximate NN relations by maximizing the margin between k-NNs and non-k-NNs under a soft orthogonality constraint. This design enables MPAD to retain ANN-relevant geometry without supervision or changes to the original embedding model. Experiments across multiple domains show that MPAD consistently outperforms standard DR methods in preserving neighborhood structure, enabling more accurate search in reduced dimensions.

With the rapid development of mobile devices, modern widely-used mobile phones typically allow users to capture 4K resolution (i.e., ultra-high-definition) images. However, for image demoireing, a challenging task in low-level vision, existing works are generally carried out on low-resolution or synthetic images. Hence, the effectiveness of these methods on 4K resolution images is still unknown. In this paper, we explore moire pattern removal for ultra-high-definition images. To this end, we propose the first ultra-high-definition demoireing dataset (UHDM), which contains 5,000 real-world 4K resolution image pairs, and conduct a benchmark study on current state-of-the-art methods. Further, we present an efficient baseline model ESDNet for tackling 4K moire images, wherein we build a semantic-aligned scale-aware module to address the scale variation of moire patterns. Extensive experiments manifest the effectiveness of our approach, which outperforms state-of-the-art methods by a large margin while being much more lightweight. Code and dataset are available at https://xinyu-andy.github.io/uhdm-page.

Ultra-High Field MRI (UHF-MRI) is increasingly used in large-scale neuroimaging studies, yet automatic brain segmentation and cortical parcellation remain challenging due to signal inhomogeneities, heterogeneous contrasts and resolutions, and the limited availability of tools optimized for UHF data. Standard software packages such as FastSurferVINN and SynthSeg+ often yield suboptimal results when applied directly to UHF images, thereby restricting region-based quantitative analyses. To address this need, we introduce GOUHFI 2.0, an updated implementation of GOUHFI that incorporates increased training data variability and additional functionalities, including cortical parcellation and volumetry. GOUHFI 2.0 preserves the contrast- and resolution-agnostic design of the original toolbox while introducing two independently trained 3D U-Net segmentation tasks. The first performs whole-brain segmentation into 35 labels across contrasts, resolutions, field strengths and populations, using a domain-randomization strategy and a training dataset of 238 subjects. Using the same training data, the second network performs cortical parcellation into 62 labels following the Desikan-Killiany-Tourville (DKT) protocol. Across multiple datasets, GOUHFI 2.0 demonstrated improved segmentation accuracy relative to the original toolbox, particularly in heterogeneous cohorts, and produced reliable cortical parcellations. In addition, the integrated volumetry pipeline yielded results consistent with standard volumetric workflows. Overall, GOUHFI 2.0 provides a comprehensive solution for brain segmentation, parcellation and volumetry across field strengths, and constitutes the first deep-learning toolbox enabling robust cortical parcellation at UHF-MRI.

We present X^3 (pronounced XCube), a novel generative model for high-resolution sparse 3D voxel grids with arbitrary attributes. Our model can generate millions of voxels with a finest effective resolution of up to 1024^3 in a feed-forward fashion without time-consuming test-time optimization. To achieve this, we employ a hierarchical voxel latent diffusion model which generates progressively higher resolution grids in a coarse-to-fine manner using a custom framework built on the highly efficient VDB data structure. Apart from generating high-resolution objects, we demonstrate the effectiveness of XCube on large outdoor scenes at scales of 100mtimes100m with a voxel size as small as 10cm. We observe clear qualitative and quantitative improvements over past approaches. In addition to unconditional generation, we show that our model can be used to solve a variety of tasks such as user-guided editing, scene completion from a single scan, and text-to-3D. More results and details can be found at https://research.nvidia.com/labs/toronto-ai/xcube/.

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.

In the last three years, the largest dense deep learning models have grown over 1000x to reach hundreds of billions of parameters, while the GPU memory has only grown by 5x (16 GB to 80 GB). Therefore, the growth in model scale has been supported primarily though system innovations that allow large models to fit in the aggregate GPU memory of multiple GPUs. However, we are getting close to the GPU memory wall. It requires 800 NVIDIA V100 GPUs just to fit a trillion parameter model for training, and such clusters are simply out of reach for most data scientists. In addition, training models at that scale requires complex combinations of parallelism techniques that puts a big burden on the data scientists to refactor their model. In this paper we present ZeRO-Infinity, a novel heterogeneous system technology that leverages GPU, CPU, and NVMe memory to allow for unprecedented model scale on limited resources without requiring model code refactoring. At the same time it achieves excellent training throughput and scalability, unencumbered by the limited CPU or NVMe bandwidth. ZeRO-Infinity can fit models with tens and even hundreds of trillions of parameters for training on current generation GPU clusters. It can be used to fine-tune trillion parameter models on a single NVIDIA DGX-2 node, making large models more accessible. In terms of training throughput and scalability, it sustains over 25 petaflops on 512 NVIDIA V100 GPUs(40% of peak), while also demonstrating super linear scalability. An open source implementation of ZeRO-Infinity is available through DeepSpeed, a deep learning optimization library that makes distributed training easy, efficient, and effective.

We present Pangu Ultra, a Large Language Model (LLM) with 135 billion parameters and dense Transformer modules trained on Ascend Neural Processing Units (NPUs). Although the field of LLM has been witnessing unprecedented advances in pushing the scale and capability of LLM in recent years, training such a large-scale model still involves significant optimization and system challenges. To stabilize the training process, we propose depth-scaled sandwich normalization, which effectively eliminates loss spikes during the training process of deep models. We pre-train our model on 13.2 trillion diverse and high-quality tokens and further enhance its reasoning capabilities during post-training. To perform such large-scale training efficiently, we utilize 8,192 Ascend NPUs with a series of system optimizations. Evaluations on multiple diverse benchmarks indicate that Pangu Ultra significantly advances the state-of-the-art capabilities of dense LLMs such as Llama 405B and Mistral Large 2, and even achieves competitive results with DeepSeek-R1, whose sparse model structure contains much more parameters. Our exploration demonstrates that Ascend NPUs are capable of efficiently and effectively training dense models with more than 100 billion parameters. Our model and system will be available for our commercial customers.

Information Retrieval using dense low-dimensional representations recently became popular and showed out-performance to traditional sparse-representations like BM25. However, no previous work investigated how dense representations perform with large index sizes. We show theoretically and empirically that the performance for dense representations decreases quicker than sparse representations for increasing index sizes. In extreme cases, this can even lead to a tipping point where at a certain index size sparse representations outperform dense representations. We show that this behavior is tightly connected to the number of dimensions of the representations: The lower the dimension, the higher the chance for false positives, i.e. returning irrelevant documents.

Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.

High-resolution (HR) magnetic resonance imaging (MRI) is crucial for many clinical and research applications. However, achieving it remains costly and constrained by technical trade-offs and experimental limitations. Super-resolution (SR) presents a promising computational approach to overcome these challenges by generating HR images from more affordable low-resolution (LR) scans, potentially improving diagnostic accuracy and efficiency without requiring additional hardware. This survey reviews recent advances in MRI SR techniques, with a focus on deep learning (DL) approaches. It examines DL-based MRI SR methods from the perspectives of computer vision, computational imaging, inverse problems, and MR physics, covering theoretical foundations, architectural designs, learning strategies, benchmark datasets, and performance metrics. We propose a systematic taxonomy to categorize these methods and present an in-depth study of both established and emerging SR techniques applicable to MRI, considering unique challenges in clinical and research contexts. We also highlight open challenges and directions that the community needs to address. Additionally, we provide a collection of essential open-access resources, tools, and tutorials, available on our GitHub: https://github.com/mkhateri/Awesome-MRI-Super-Resolution. IEEE keywords: MRI, Super-Resolution, Deep Learning, Computational Imaging, Inverse Problem, Survey.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

Hyperdimensional computing (HD), also known as vector symbolic architectures (VSA), is a framework for computing with distributed representations by exploiting properties of random high-dimensional vector spaces. The commitment of the scientific community to aggregate and disseminate research in this particularly multidisciplinary area has been fundamental for its advancement. Joining these efforts, we present Torchhd, a high-performance open source Python library for HD/VSA. Torchhd seeks to make HD/VSA more accessible and serves as an efficient foundation for further research and application development. The easy-to-use library builds on top of PyTorch and features state-of-the-art HD/VSA functionality, clear documentation, and implementation examples from well-known publications. Comparing publicly available code with their corresponding Torchhd implementation shows that experiments can run up to 100x faster. Torchhd is available at: https://github.com/hyperdimensional-computing/torchhd.

Pre-training (PT) followed by fine-tuning (FT) is an effective method for training neural networks, and has led to significant performance improvements in many domains. PT can incorporate various design choices such as task and data reweighting strategies, augmentation policies, and noise models, all of which can significantly impact the quality of representations learned. The hyperparameters introduced by these strategies therefore must be tuned appropriately. However, setting the values of these hyperparameters is challenging. Most existing methods either struggle to scale to high dimensions, are too slow and memory-intensive, or cannot be directly applied to the two-stage PT and FT learning process. In this work, we propose an efficient, gradient-based algorithm to meta-learn PT hyperparameters. We formalize the PT hyperparameter optimization problem and propose a novel method to obtain PT hyperparameter gradients by combining implicit differentiation and backpropagation through unrolled optimization. We demonstrate that our method improves predictive performance on two real-world domains. First, we optimize high-dimensional task weighting hyperparameters for multitask pre-training on protein-protein interaction graphs and improve AUROC by up to 3.9%. Second, we optimize a data augmentation neural network for self-supervised PT with SimCLR on electrocardiography data and improve AUROC by up to 1.9%.

We consider the problem of computing persistent homology (PH) for large-scale Euclidean point cloud data, aimed at downstream machine learning tasks, where the exponential growth of the most widely-used Vietoris-Rips complex imposes serious computational limitations. Although more scalable alternatives such as the Alpha complex or sparse Rips approximations exist, they often still result in a prohibitively large number of simplices. This poses challenges in the complex construction and in the subsequent PH computation, prohibiting their use on large-scale point clouds. To mitigate these issues, we introduce the Flood complex, inspired by the advantages of the Alpha and Witness complex constructions. Informally, at a given filtration value rgeq 0, the Flood complex contains all simplices from a Delaunay triangulation of a small subset of the point cloud X that are fully covered by balls of radius r emanating from X, a process we call flooding. Our construction allows for efficient PH computation, possesses several desirable theoretical properties, and is amenable to GPU parallelization. Scaling experiments on 3D point cloud data show that we can compute PH of up to dimension 2 on several millions of points. Importantly, when evaluating object classification performance on real-world and synthetic data, we provide evidence that this scaling capability is needed, especially if objects are geometrically or topologically complex, yielding performance superior to other PH-based methods and neural networks for point cloud data. Source code and datasets are available on https://github.com/plus-rkwitt/flooder.

Exploiting sparsity underlying neural networks has become one of the most potential methodologies to reduce the memory footprint, I/O cost, and computation workloads during inference. And the degree of sparsity one can exploit has become higher as larger model sizes have been considered along with the trend of pre-training giant models. On the other hand, compared with quantization that has been a widely supported option, acceleration through high-degree sparsity is not supported in most computing platforms. In this work, we introduce the first commercial hardware platform supporting high-degree sparsity acceleration up to 32 times -- S4. Combined with state-of-the-art sparse pruning techniques, we demonstrate several-times practical inference speedup on S4 over mainstream inference platforms such as Nvidia T4. We also show that in practice a sparse model of larger size can achieve both higher accuracy and higher throughput on S4 than a dense model of smaller size.

Why do even the most powerful 7B-parameter embedding models struggle with simple retrieval tasks that the decades old BM25 handles with ease? Recent theory suggests that this happens because of a dimensionality bottleneck. This occurs when we force infinite linguistic nuances into small, fixed-length learned vectors. We developed NUMEN to break this bottleneck by removing the learning process entirely. Instead of training heavy layers to map text to a constrained space, NUMEN uses deterministic character hashing to project language directly onto high-dimensional vectors. This approach requires no training, supports an unlimited vocabulary, and allows the geometric capacity scale as needed. On the LIMIT benchmark, NUMEN achieves 93.90 % Recall@100 at 32,768 dimensions. This makes it the first dense retrieval model to officially surpass the sparse BM25 baseline 93.6 %. Our findings show that the real problem in dense retrieval isn't the architecture, but the embedding layer itself. The solution isn't necessarily smarter training, but simply providing more room to breathe.

This paper presents a novel approach for similarity search with complex filtering capabilities on billion-scale datasets, optimized for CPU inference. Our method extends the classical IVF-Flat index structure to integrate multi-dimensional filters. The proposed algorithm combines dense embeddings with discrete filtering attributes, enabling fast retrieval in high-dimensional spaces. Designed specifically for CPU-based systems, our disk-based approach offers a cost-effective solution for large-scale similarity search. We demonstrate the effectiveness of our method through a case study, showcasing its potential for various practical uses.

Transformer models encounter challenges in scaling hidden dimensions efficiently, as uniformly increasing them inflates computational and memory costs while failing to emphasize the most relevant features for each token. For further understanding, we study hidden dimension sparsity and observe that trained Transformers utilize only a small fraction of token dimensions, revealing an "activation flow" pattern. Notably, there are shared sub-dimensions with sustained activation across multiple consecutive tokens and specialized sub-dimensions uniquely activated for each token. To better model token-relevant sub-dimensions, we propose MoHD (Mixture of Hidden Dimensions), a sparse conditional activation architecture. Particularly, MoHD employs shared sub-dimensions for common token features and a routing mechanism to dynamically activate specialized sub-dimensions. To mitigate potential information loss from sparsity, we design activation scaling and group fusion mechanisms to preserve activation flow. In this way, MoHD expands hidden dimensions with negligible increases in computation or parameters, efficient training and inference while maintaining performance. Evaluations across 10 NLP tasks show that MoHD surpasses Vanilla Transformers in parameter efficiency and task performance. It achieves 1.7% higher performance with 50% fewer activation parameters and 3.7% higher performance with a 3x parameter expansion at constant activation cost. MOHD offers a new perspective for scaling the model, showcasing the potential of hidden dimension sparsity to boost efficiency

We introduce Uncommon Objects in 3D (uCO3D), a new object-centric dataset for 3D deep learning and 3D generative AI. uCO3D is the largest publicly-available collection of high-resolution videos of objects with 3D annotations that ensures full-360^{circ} coverage. uCO3D is significantly more diverse than MVImgNet and CO3Dv2, covering more than 1,000 object categories. It is also of higher quality, due to extensive quality checks of both the collected videos and the 3D annotations. Similar to analogous datasets, uCO3D contains annotations for 3D camera poses, depth maps and sparse point clouds. In addition, each object is equipped with a caption and a 3D Gaussian Splat reconstruction. We train several large 3D models on MVImgNet, CO3Dv2, and uCO3D and obtain superior results using the latter, showing that uCO3D is better for learning applications.

Ultra-high-resolution (UHR) text-to-image (T2I) generation has seen notable progress. However, two key challenges remain : 1) the absence of a large-scale high-quality UHR T2I dataset, and (2) the neglect of tailored training strategies for fine-grained detail synthesis in UHR scenarios. To tackle the first challenge, we introduce UltraHR-100K, a high-quality dataset of 100K UHR images with rich captions, offering diverse content and strong visual fidelity. Each image exceeds 3K resolution and is rigorously curated based on detail richness, content complexity, and aesthetic quality. To tackle the second challenge, we propose a frequency-aware post-training method that enhances fine-detail generation in T2I diffusion models. Specifically, we design (i) Detail-Oriented Timestep Sampling (DOTS) to focus learning on detail-critical denoising steps, and (ii) Soft-Weighting Frequency Regularization (SWFR), which leverages Discrete Fourier Transform (DFT) to softly constrain frequency components, encouraging high-frequency detail preservation. Extensive experiments on our proposed UltraHR-eval4K benchmarks demonstrate that our approach significantly improves the fine-grained detail quality and overall fidelity of UHR image generation. The code is available at https://github.com/NJU-PCALab/UltraHR-100k{here}.

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces (d=128), transformer training trajectories rapidly collapse onto low-dimensional execution manifolds of dimension 3--4. This dimensional collapse is robust across random seeds and moderate task difficulties, though the orientation of the manifold in parameter space varies between runs. We demonstrate that this geometric structure underlies several empirically observed phenomena: (1) sharp attention concentration emerges as saturation along routing coordinates within the execution manifold, (2) SGD commutators are preferentially aligned with the execution subspace (up to 10times random baseline) early in training, with >92% of non-commutativity confined to orthogonal staging directions and this alignment decreasing as training converges, and (3) sparse autoencoders capture auxiliary routing structure but fail to isolate execution itself, which remains distributed across the low-dimensional manifold. Our results suggest a unifying geometric framework for understanding transformer learning, where the vast majority of parameters serve to absorb optimization interference while core computation occurs in a dramatically reduced subspace. These findings have implications for interpretability, training curriculum design, and understanding the role of overparameterization in neural network learning.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We validate these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP=BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

Recent advances in volumetric super-resolution (SR) have demonstrated strong performance in medical and scientific imaging, with transformer- and CNN-based approaches achieving impressive results even at extreme scaling factors. In this work, we show that much of this performance stems from training on downsampled data rather than real low-resolution scans. This reliance on downsampling is partly driven by the scarcity of paired high- and low-resolution 3D datasets. To address this, we introduce VoDaSuRe, a large-scale volumetric dataset containing paired high- and low-resolution scans. When training models on VoDaSuRe, we reveal a significant discrepancy: SR models trained on downsampled data produce substantially sharper predictions than those trained on real low-resolution scans, which smooth fine structures. Conversely, applying models trained on downsampled data to real scans preserves more structure but is inaccurate. Our findings suggest that current SR methods are overstated - when applied to real data, they do not recover structures lost in low-resolution scans and instead predict a smoothed average. We argue that progress in deep learning-based volumetric SR requires datasets with paired real scans of high complexity, such as VoDaSuRe. Our dataset and code are publicly available through: https://augusthoeg.github.io/VoDaSuRe/

Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

Retrieval-Augmented Generation enhances language models by retrieving relevant information from external knowledge bases, relying on high-dimensional vector embeddings typically stored in float32 precision. However, storing these embeddings at scale presents significant memory challenges. To address this issue, we systematically investigate on MTEB benchmark two complementary optimization strategies: quantization, evaluating standard formats (float16, int8, binary) and low-bit floating-point types (float8), and dimensionality reduction, assessing methods like PCA, Kernel PCA, UMAP, Random Projections and Autoencoders. Our results show that float8 quantization achieves a 4x storage reduction with minimal performance degradation (<0.3%), significantly outperforming int8 quantization at the same compression level, being simpler to implement. PCA emerges as the most effective dimensionality reduction technique. Crucially, combining moderate PCA (e.g., retaining 50% dimensions) with float8 quantization offers an excellent trade-off, achieving 8x total compression with less performance impact than using int8 alone (which provides only 4x compression). To facilitate practical application, we propose a methodology based on visualizing the performance-storage trade-off space to identify the optimal configuration that maximizes performance within their specific memory constraints.

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very high-dimensionality --exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for every patient), necessitating models that can process large, high-dimensional point-clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric and topological information. In contrast, HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We show that geometric and topological information is preserved in this framework both theoretically and empirically. We showcase the utility of HiPoNet on point-cloud level tasks, involving classification and regression of entire point-clouds in data cohorts. Experimentally, we find that HiPoNet outperforms other point-cloud and graph-based models on single-cell data. We also apply HiPoNet to spatial transcriptomics datasets using spatial coordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.

We propose HyperSteiner -- an efficient heuristic algorithm for computing Steiner minimal trees in the hyperbolic space. HyperSteiner extends the Euclidean Smith-Lee-Liebman algorithm, which is grounded in a divide-and-conquer approach involving the Delaunay triangulation. The central idea is rephrasing Steiner tree problems with three terminals as a system of equations in the Klein-Beltrami model. Motivated by the fact that hyperbolic geometry is well-suited for representing hierarchies, we explore applications to hierarchy discovery in data. Results show that HyperSteiner infers more realistic hierarchies than the Minimum Spanning Tree and is more scalable to large datasets than Neighbor Joining.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of Obigl(NKD^3bigr) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this paper, we manage to reduce this complexity to Obigl(NKD^2bigr) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.

In this work, we aim to discretize the high-dimensional visual representations to bridge the gap with language models - a non-trivial challenge, as existing quantization methods suffer from codebook collapse, failing to scale while preserving semantic coherence. We identify the root cause as metric mismatch: standard Euclidean codebook objectives are fundamentally misaligned with the anisotropic geometry of representation space, leading to codebook embeddings with high-variance magnitude scales and uneven angular distributions that hinder scalability. To address this, we propose Hyper-Spherical Quantization (HSQ), which decouples semantic content from feature magnitude via angular routing, preventing code assignment from being dominated by scale rather than meaning. The resulting discrete Representation Autoencoder (dRAE) achieves high-fidelity reconstruction while preserving semantic integrity and supporting scalable codebook budget. Extensive experiments demonstrate consistent performance gains as the vocabulary size scales to 131{,}072, along with 100\% codebook utilization, simplified training pipeline, and strong performance across understanding and generation tasks.

Minwise hashing is a fundamental and one of the most successful hashing algorithm in the literature. Recent advances based on the idea of densification~Proc:OneHashLSH_ICML14,Proc:Shrivastava_UAI14 have shown that it is possible to compute k minwise hashes, of a vector with d nonzeros, in mere (d + k) computations, a significant improvement over the classical O(dk). These advances have led to an algorithmic improvement in the query complexity of traditional indexing algorithms based on minwise hashing. Unfortunately, the variance of the current densification techniques is unnecessarily high, which leads to significantly poor accuracy compared to vanilla minwise hashing, especially when the data is sparse. In this paper, we provide a novel densification scheme which relies on carefully tailored 2-universal hashes. We show that the proposed scheme is variance-optimal, and without losing the runtime efficiency, it is significantly more accurate than existing densification techniques. As a result, we obtain a significantly efficient hashing scheme which has the same variance and collision probability as minwise hashing. Experimental evaluations on real sparse and high-dimensional datasets validate our claims. We believe that given the significant advantages, our method will replace minwise hashing implementations in practice.

Recent advancements in large language models and their multi-modal extensions have demonstrated the effectiveness of unifying generation and understanding through autoregressive next-token prediction. However, despite the critical role of 3D structural generation and understanding ({3D GU}) in AI for science, these tasks have largely evolved independently, with autoregressive methods remaining underexplored. To bridge this gap, we introduce Uni-3DAR, a unified framework that seamlessly integrates {3D GU} tasks via autoregressive prediction. At its core, Uni-3DAR employs a novel hierarchical tokenization that compresses 3D space using an octree, leveraging the inherent sparsity of 3D structures. It then applies an additional tokenization for fine-grained structural details, capturing key attributes such as atom types and precise spatial coordinates in microscopic 3D structures. We further propose two optimizations to enhance efficiency and effectiveness. The first is a two-level subtree compression strategy, which reduces the octree token sequence by up to 8x. The second is a masked next-token prediction mechanism tailored for dynamically varying token positions, significantly boosting model performance. By combining these strategies, Uni-3DAR successfully unifies diverse {3D GU} tasks within a single autoregressive framework. Extensive experiments across multiple microscopic {3D GU} tasks, including molecules, proteins, polymers, and crystals, validate its effectiveness and versatility. Notably, Uni-3DAR surpasses previous state-of-the-art diffusion models by a substantial margin, achieving up to 256\% relative improvement while delivering inference speeds up to 21.8x faster. The code is publicly available at https://github.com/dptech-corp/Uni-3DAR.

Supervised machine learning methods for geological mapping via remote sensing face limitations due to the scarcity of accurately labelled training data that can be addressed by unsupervised learning, such as dimensionality reduction and clustering. Dimensionality reduction methods have the potential to play a crucial role in improving the accuracy of geological maps. Although conventional dimensionality reduction methods may struggle with nonlinear data, unsupervised deep learning models such as autoencoders can model non-linear relationships. Stacked autoencoders feature multiple interconnected layers to capture hierarchical data representations useful for remote sensing data. We present an unsupervised machine learning-based framework for processing remote sensing data using stacked autoencoders for dimensionality reduction and k-means clustering for mapping geological units. We use Landsat 8, ASTER, and Sentinel-2 datasets to evaluate the framework for geological mapping of the Mutawintji region in Western New South Wales, Australia. We also compare stacked autoencoders with principal component analysis (PCA) and canonical autoencoders. Our results reveal that the framework produces accurate and interpretable geological maps, efficiently discriminating rock units. The results reveal that the combination of stacked autoencoders with Sentinel-2 data yields the best performance accuracy when compared to other combinations. We find that stacked autoencoders enable better extraction of complex and hierarchical representations of the input data when compared to canonical autoencoders and PCA. We also find that the generated maps align with prior geological knowledge of the study area while providing novel insights into geological structures.

Recently, several models based on deep neural networks have achieved great success in terms of both reconstruction accuracy and computational performance for single image super-resolution. In these methods, the low resolution (LR) input image is upscaled to the high resolution (HR) space using a single filter, commonly bicubic interpolation, before reconstruction. This means that the super-resolution (SR) operation is performed in HR space. We demonstrate that this is sub-optimal and adds computational complexity. In this paper, we present the first convolutional neural network (CNN) capable of real-time SR of 1080p videos on a single K2 GPU. To achieve this, we propose a novel CNN architecture where the feature maps are extracted in the LR space. In addition, we introduce an efficient sub-pixel convolution layer which learns an array of upscaling filters to upscale the final LR feature maps into the HR output. By doing so, we effectively replace the handcrafted bicubic filter in the SR pipeline with more complex upscaling filters specifically trained for each feature map, whilst also reducing the computational complexity of the overall SR operation. We evaluate the proposed approach using images and videos from publicly available datasets and show that it performs significantly better (+0.15dB on Images and +0.39dB on Videos) and is an order of magnitude faster than previous CNN-based methods.

Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling gates scales quadratically with the dimension of the dataset and the number of qubits. In this work, we introduce a quantum feature map designed to handle high-dimensional data with a significantly reduced number of qubits and entangling operations. Our approach preserves essential data characteristics while promoting computational efficiency, as evidenced by extensive experiments on benchmark datasets that demonstrate a marked improvement in both accuracy and resource utilization when using our feature map as a kernel for characterization, as compared to state-of-the-art quantum feature maps. Our noisy simulation results, combined with lower resource requirements, highlight our map's ability to function within the constraints of noisy intermediate-scale quantum devices. Through numerical simulations and small-scale implementation on a superconducting circuit quantum computing platform, we demonstrate that our scheme performs on par or better than a set of classical algorithms for classification. While quantum kernels are typically stymied by exponential concentration, our approach is affected with a slower rate with respect to both the number of qubits and features, which allows practical applications to remain within reach. Our findings herald a promising avenue for the practical implementation of quantum machine learning algorithms on near future quantum computing platforms.

We present LRM-Zero, a Large Reconstruction Model (LRM) trained entirely on synthesized 3D data, achieving high-quality sparse-view 3D reconstruction. The core of LRM-Zero is our procedural 3D dataset, Zeroverse, which is automatically synthesized from simple primitive shapes with random texturing and augmentations (e.g., height fields, boolean differences, and wireframes). Unlike previous 3D datasets (e.g., Objaverse) which are often captured or crafted by humans to approximate real 3D data, Zeroverse completely ignores realistic global semantics but is rich in complex geometric and texture details that are locally similar to or even more intricate than real objects. We demonstrate that our LRM-Zero, trained with our fully synthesized Zeroverse, can achieve high visual quality in the reconstruction of real-world objects, competitive with models trained on Objaverse. We also analyze several critical design choices of Zeroverse that contribute to LRM-Zero's capability and training stability. Our work demonstrates that 3D reconstruction, one of the core tasks in 3D vision, can potentially be addressed without the semantics of real-world objects. The Zeroverse's procedural synthesis code and interactive visualization are available at: https://desaixie.github.io/lrm-zero/.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence without increasing the computational effort for inference.

We report a flexible language-model based deep learning strategy, applied here to solve complex forward and inverse problems in protein modeling, based on an attention neural network that integrates transformer and graph convolutional architectures in a causal multi-headed graph mechanism, to realize a generative pretrained model. The model is applied to predict secondary structure content (per-residue level and overall content), protein solubility, and sequencing tasks. Further trained on inverse tasks, the model is rendered capable of designing proteins with these properties as target features. The model is formulated as a general framework, completely prompt-based, and can be adapted for a variety of downstream tasks. We find that adding additional tasks yields emergent synergies that the model exploits in improving overall performance, beyond what would be possible by training a model on each dataset alone. Case studies are presented to validate the method, yielding protein designs specifically focused on structural proteins, but also exploring the applicability in the design of soluble, antimicrobial biomaterials. While our model is trained to ultimately perform 8 distinct tasks, with available datasets it can be extended to solve additional problems. In a broader sense, this work illustrates a form of multiscale modeling that relates a set of ultimate building blocks (here, byte-level utf8 characters) to complex output. This materiomic scheme captures complex emergent relationships between universal building block and resulting properties via a synergizing learning capacity to express a set of potentialities embedded in the knowledge used in training, via the interplay of universality and diversity.

Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the simple case of a one-dimensional (scalar) hyperparameter. This leaves the practically important, multi-dimensional hyperparameter tuning setting unresolved. We address this open question by establishing the first general framework for establishing generalization guarantees for tuning multi-dimensional hyperparameters in data-driven settings. Our approach strengthens the generalization guarantee framework for semi-algebraic function classes by exploiting tools from real algebraic geometry, yielding sharper, more broadly applicable guarantees. For completeness, we also instantiate the first lower bound for this general setting. We further extend the analysis to hyperparameter tuning using the validation loss under minimal assumptions, and derive improved bounds when additional structure is available. Finally, we demonstrate the scope of the framework with new learnability results, including data-driven weighted group lasso and weighted fused lasso.

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.

Ultra-high-resolution (UHR) remote sensing (RS) imagery offers valuable data for Earth observation but pose challenges for existing multimodal foundation models due to two key bottlenecks: (1) limited availability of UHR training data, and (2) token explosion caused by the large image size. To address data scarcity, we introduce SuperRS-VQA (avg. 8,376times8,376) and HighRS-VQA (avg. 2,000times1,912), the highest-resolution vision-language datasets in RS to date, covering 22 real-world dialogue tasks. To mitigate token explosion, our pilot studies reveal significant redundancy in RS images: crucial information is concentrated in a small subset of object-centric tokens, while pruning background tokens (e.g., ocean or forest) can even improve performance. Motivated by these findings, we propose two strategies: Background Token Pruning and Anchored Token Selection, to reduce the memory footprint while preserving key semantics.Integrating these techniques, we introduce GeoLLaVA-8K, the first RS-focused multimodal large language model capable of handling inputs up to 8Ktimes8K resolution, built on the LLaVA framework. Trained on SuperRS-VQA and HighRS-VQA, GeoLLaVA-8K sets a new state-of-the-art on the XLRS-Bench.

Scientific datasets present unique challenges for machine learning-driven compression methods, including more stringent requirements on accuracy and mitigation of potential invalidating artifacts. Drawing on results from compressed sensing and rate-distortion theory, we introduce effective data compression methods by developing autoencoders using high dimensional latent spaces that are L^1-regularized to obtain sparse low dimensional representations. We show how these information-rich latent spaces can be used to mitigate blurring and other artifacts to obtain highly effective data compression methods for scientific data. We demonstrate our methods for short angle scattering (SAS) datasets showing they can achieve compression ratios around two orders of magnitude and in some cases better. Our compression methods show promise for use in addressing current bottlenecks in transmission, storage, and analysis in high-performance distributed computing environments. This is central to processing the large volume of SAS data being generated at shared experimental facilities around the world to support scientific investigations. Our approaches provide general ways for obtaining specialized compression methods for targeted scientific datasets.

Ultra-low-field (ULF) MRI offers portable and accessible neuroimaging but suffers from reduced signal-to-noise ratio and limited spatial resolution compared to high-field (HF) systems. Acquiring paired ULF-HF data for supervised enhancement is often difficult, particularly in resource-limited settings. We introduce ULF-Synth, a framework that combines: (i) acquisition-based synthesis of realistic ULF images from HF volumes to create large-scale paired training data, (ii) a spatial-frequency domain objective that prioritizes recovery of high-frequency anatomical detail. This formulation is architecture-agnostic, consistently improving structural similarity and perceptual fidelity across encoder-decoder, adversarial, and diffusion-based translation models. When trained exclusively on synthetic data, the resulting models generalize effectively to real 64mT ULF acquisitions, improving downstream multiclass brain segmentation and achieving higher radiologist preference and diagnostic acceptability in a blinded reader study. These findings demonstrate that synthetic paired supervision provides a practical and scalable pathway for enhancing ULF MRI without requiring real paired acquisitions. Code, Models and Dataset: https://github.com/toufiqmusah/ULF-Synth

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

Hyper-Connections (HC) expand the residual stream of Transformers into N parallel streams, providing a form of memory scaling beyond model width and depth. Manifold-Constrained HC (mHC) stabilizes this formulation at scale. The large gains from N{=}1 to N{=}4 suggest residual-stream expansion as a promising scaling axis. However, existing HC-family methods typically stop at N{=}4. Our experiments reveal why: scaling mHC beyond this point yields diminishing performance gains and rapidly increasing training cost. We attribute this limitation to two bottlenecks: insufficient write-back information for an expanding number of streams and residual-mixing generation whose cost scales cubically with N. To address both bottlenecks, we propose xHC (Expanded Hyper-Connections), the first HC-family method to achieve meaningful expansion beyond N{=}4. xHC combines temporal feature augmentation for richer write-back with a sparse residual-stream architecture that updates only k=4 of the N=16 streams while retaining dense access to the full residual state. Across 18B and 28B MoE models, xHC delivers strong and consistent downstream improvements. On an 18B MoE model, xHC improves the average downstream score by 4.0 points over mHC, while adding only modest training FLOPs over the vanilla baseline. Scaling-law experiments show that the vanilla and mHC require 1.50times and 1.19times the compute of xHC, respectively, to reach the same loss. Practical large-N training also requires controlling memory traffic from the expanded residual state. We therefore introduce xHC-Flash, which reduces the per-sublayer memory traffic from 73.5C to 40C, comparable to the 34C required by mHC at N{=}4, while retaining the gains of full xHC. Together, xHC and xHC-Flash make large-N residual-stream expansion effective and practical for LLM pre-training.

This paper concludes a series of studies on the polyharmonic cascade, a deep machine learning architecture theoretically derived from indifference principles and the theory of random functions. A universal initialization procedure is proposed, based on symmetric constellations in the form of hyperoctahedra with a central point. This initialization not only ensures stable training of cascades with tens and hundreds of layers (up to 500 layers without skip connections), but also radically simplifies the computations. Scalability and robustness are demonstrated on MNIST (98.3% without convolutions or augmentations), HIGGS (AUC approximately 0.885 on 11M examples), and Epsilon (AUC approximately 0.963 with 2000 features). All linear algebra is reduced to 2D operations and is efficiently executed on GPUs. A public repository and an archived snapshot are provided for full reproducibility.

Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learning rate along with its scheduling, we systematically investigate the impact of scale on CBS. Then we fit scaling laws with respect to model and data sizes to decouple their effects. Overall, our results demonstrate that CBS scales primarily with data size rather than model size, a finding we justify theoretically through the analysis of infinite-width limits of neural networks and infinite-dimensional least squares regression. Of independent interest, we highlight the importance of common hyper-parameter choices and strategies for studying large-scale pre-training beyond fixed training durations.

Dual encoders perform retrieval by encoding documents and queries into dense lowdimensional vectors, scoring each document by its inner product with the query. We investigate the capacity of this architecture relative to sparse bag-of-words models and attentional neural networks. Using both theoretical and empirical analysis, we establish connections between the encoding dimension, the margin between gold and lower-ranked documents, and the document length, suggesting limitations in the capacity of fixed-length encodings to support precise retrieval of long documents. Building on these insights, we propose a simple neural model that combines the efficiency of dual encoders with some of the expressiveness of more costly attentional architectures, and explore sparse-dense hybrids to capitalize on the precision of sparse retrieval. These models outperform strong alternatives in large-scale retrieval.