Daily Papers

Many biological processes involve numerous coupled degrees of freedom, yet free-energy estimation is often restricted to one-dimensional profiles to mitigate the high computational cost of multidimensional sampling. In this work, we extend Fokker--Planck Score Learning (FPSL) to efficiently reconstruct two-dimensional free-energy landscapes from non-equilibrium molecular dynamics simulations using different types of collective variables. We show that explicitly modeling orthogonal degrees of freedom reveals insights hidden in one-dimensional projections at negligible computational overhead. Additionally, exploiting symmetries in the underlying landscape enhances reconstruction accuracy, while regularization techniques ensure numerical robustness in sparsely sampled regions. We validate our approach on three distinct systems: the conformational dynamics of alanine dipeptide, as well as coarse-grained and all-atom models of solute permeation through lipid bilayers. We demonstrate that, because FPSL learns a smooth score function rather than histogram-based densities, it overcomes the exponential scaling of grid-based methods, establishing it as a data-efficient and scalable tool for multidimensional free-energy estimation.

Accurate free-energy estimation is essential in molecular simulation, yet the periodic boundary conditions (PBC) commonly used in computer simulations have rarely been explicitly exploited. Equilibrium methods such as umbrella sampling, metadynamics, and adaptive biasing force require extensive sampling, while non-equilibrium pulling with Jarzynski's equality suffers from poor convergence due to exponential averaging. Here, we introduce a physics-informed, score-based diffusion framework: by mapping PBC simulations onto a Brownian particle in a periodic potential, we derive the Fokker-Planck steady-state score that directly encodes free-energy gradients. A neural network is trained on non-equilibrium trajectories to learn this score, providing a principled scheme to efficiently reconstruct the potential of mean force (PMF). On benchmark periodic potentials and small-molecule membrane permeation, our method is up to one order of magnitude more efficient than umbrella sampling.

Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides a roadmap for advancing quantum algorithms and hardware toward achieving quantum advantage in molecular modeling.

Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground and excited-state energies of a quantum many-body system. While QKSD algorithms typically rely on using the Hadamard test for estimating Krylov subspace matrix elements of the form, langle ϕ_i|e^{-iHτ}|ϕ_j rangle, the associated quantum circuits require an ancilla qubit with controlled multi-qubit gates that can be quite costly for near-term quantum hardware. In this work, we show that a wide class of Hamiltonians relevant to condensed matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test. We propose a multi-fidelity estimation protocol that can be used to compute such quantities showing that our approach, when combined with efficient single-fidelity estimation protocols, provides a substantial reduction in circuit depth. In addition, we develop a unified theory of quantum Krylov subspace algorithms and present three new quantum-classical algorithms for the ground and excited-state energy estimation problems, where each new algorithm provides various advantages and disadvantages in terms of total number of calls to the quantum computer, gate depth, classical complexity, and stability of the generalized eigenvalue problem within the Krylov subspace.

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation -- a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates improvements over existing learning-based methods.

Spiking Transformers have recently emerged as promising architectures for combining the efficiency of spiking neural networks with the representational power of self-attention. However, the lack of standardized implementations, evaluation pipelines, and consistent design choices has hindered fair comparison and principled analysis. In this paper, we introduce STEP, a unified benchmark framework for Spiking Transformers that supports a wide range of tasks, including classification, segmentation, and detection across static, event-based, and sequential datasets. STEP provides modular support for diverse components such as spiking neurons, input encodings, surrogate gradients, and multiple backends (e.g., SpikingJelly, BrainCog). Using STEP, we reproduce and evaluate several representative models, and conduct systematic ablation studies on attention design, neuron types, encoding schemes, and temporal modeling capabilities. We also propose a unified analytical model for energy estimation, accounting for spike sparsity, bitwidth, and memory access, and show that quantized ANNs may offer comparable or better energy efficiency. Our results suggest that current Spiking Transformers rely heavily on convolutional frontends and lack strong temporal modeling, underscoring the need for spike-native architectural innovations. The full code is available at: https://github.com/Fancyssc/STEP

Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on a quantum device. To guide the selection of measurement methods designed for this observable estimation problem, we propose a benchmark called CSHOREBench (Common States and Hamiltonians for ObseRvable Estimation Benchmark) that assesses the performance of these methods against a set of common molecular Hamiltonians and common states encountered during the runtime of hybrid quantum-classical algorithms. In CSHOREBench, we account for resource utilization of a quantum computer through measurements of a prepared state, and a classical computer through computational runtime spent in proposing measurements and classical post-processing of acquired measurement outcomes. We apply CSHOREBench considering a variety of measurement methods on Hamiltonians of size up to 16 qubits. Our discussion is aided by using the framework of decision diagrams which provides an efficient data structure for various randomized methods and illustrate how to derandomize distributions on decision diagrams. In numerical simulations, we find that the methods of decision diagrams and derandomization are the most preferable. In experiments on IBM quantum devices against small molecules, we observe that decision diagrams reduces the number of measurements made by classical shadows by more than 80%, that made by locally biased classical shadows by around 57%, and consistently require fewer quantum measurements along with lower classical computational runtime than derandomization. Furthermore, CSHOREBench is empirically efficient to run when considering states of random quantum ansatz with fixed depth.

Sampling from discrete distributions with multiple modes and energy barriers is fundamental to machine learning and computational physics. Recent discrete neural samplers like MDNS suffer from mode collapse and fail to sample high-energy barrier regions between modes, which is critical for free energy estimation and understanding phase transitions. We propose Metadynamics Discrete Neural Sampler (MetaDNS), a general framework integrating well-tempered metadynamics into discrete diffusion or autoregressive samplers. By maintaining an adaptive, history-dependent bias potential along selected low-dimensional coordinates, MetaDNS forces exploration of previously inaccessible regions, enabling free energy reconstruction infeasible with standard neural samplers due to a lack of high-energy samples. On challenging low-temperature benchmarks including Ising, Potts, and the copper-gold binary alloy, MetaDNS reproduces the thermodynamic distribution. Compared to MCMC-based metadynamics, MetaDNS also achieves comparable exploration requiring fewer bias deposition steps.

Diffusion-based samplers learn to sample complex, high-dimensional distributions using energies or log densities alone, without training data. Yet, they remain impractical for molecular sampling because they are often slower than molecular dynamics and miss thermodynamically relevant modes. Inspired by enhanced sampling, we encourage exploration by introducing a sequential bias along bespoke, information-rich, low-dimensional projections of atomic coordinates known as collective variables (CVs). We introduce a repulsive potential centered on the CVs from recent samples, which pushes future samples towards novel CV regions and effectively increases the temperature in the projected space. Our resulting method improves efficiency, mode discovery, enables the estimation of free energy differences, and retains independent sampling from the approximate Boltzmann distribution via reweighting by the bias. On standard peptide conformational sampling benchmarks, the method recovers diverse conformational states and accurate free energy profiles. We are the first to demonstrate reactive sampling using a diffusion-based sampler, capturing bond breaking and formation with universal interatomic potentials at near-first-principles accuracy. The approach resolves reactive energy landscapes at a fraction of the wall-clock time of standard sampling methods, advancing diffusion-based sampling towards practical use in molecular sciences.

Spiking Neural Networks (SNNs) have been widely praised for their high energy efficiency and immense potential. However, comprehensive research that critically contrasts and correlates SNNs with quantized Artificial Neural Networks (ANNs) remains scant, often leading to skewed comparisons lacking fairness towards ANNs. This paper introduces a unified perspective, illustrating that the time steps in SNNs and quantized bit-widths of activation values present analogous representations. Building on this, we present a more pragmatic and rational approach to estimating the energy consumption of SNNs. Diverging from the conventional Synaptic Operations (SynOps), we champion the "Bit Budget" concept. This notion permits an intricate discourse on strategically allocating computational and storage resources between weights, activation values, and temporal steps under stringent hardware constraints. Guided by the Bit Budget paradigm, we discern that pivoting efforts towards spike patterns and weight quantization, rather than temporal attributes, elicits profound implications for model performance. Utilizing the Bit Budget for holistic design consideration of SNNs elevates model performance across diverse data types, encompassing static imagery and neuromorphic datasets. Our revelations bridge the theoretical chasm between SNNs and quantized ANNs and illuminate a pragmatic trajectory for future endeavors in energy-efficient neural computations.

This paper addresses the problem of ranking pre-trained models for object detection and image classification. Selecting the best pre-trained model by fine-tuning is an expensive and time-consuming task. Previous works have proposed transferability estimation based on features extracted by the pre-trained models. We argue that quantifying whether the target dataset is in-distribution (IND) or out-of-distribution (OOD) for the pre-trained model is an important factor in the transferability estimation. To this end, we propose ETran, an energy-based transferability assessment metric, which includes three scores: 1) energy score, 2) classification score, and 3) regression score. We use energy-based models to determine whether the target dataset is OOD or IND for the pre-trained model. In contrast to the prior works, ETran is applicable to a wide range of tasks including classification, regression, and object detection (classification+regression). This is the first work that proposes transferability estimation for object detection task. Our extensive experiments on four benchmarks and two tasks show that ETran outperforms previous works on object detection and classification benchmarks by an average of 21% and 12%, respectively, and achieves SOTA in transferability assessment.

Accurate and reliable energy time series prediction is of great significance for power generation planning and allocation. At present, deep learning time series prediction has become the mainstream method. However, the multi-scale time dynamics and the irregularity of real data lead to the limitations of the existing methods. Therefore, we propose EnergyPatchTST, which is an extension of the Patch Time Series Transformer specially designed for energy forecasting. The main innovations of our method are as follows: (1) multi-scale feature extraction mechanism to capture patterns with different time resolutions; (2) probability prediction framework to estimate uncertainty through Monte Carlo elimination; (3) integration path of future known variables (such as temperature and wind conditions); And (4) Pre-training and Fine-tuning examples to enhance the performance of limited energy data sets. A series of experiments on common energy data sets show that EnergyPatchTST is superior to other commonly used methods, the prediction error is reduced by 7-12%, and reliable uncertainty estimation is provided, which provides an important reference for time series prediction in the energy field.

Battery Electric Vehicles (BEVs) are increasingly significant in modern cities due to their potential to reduce air pollution. Precise and real-time estimation of energy consumption for them is imperative for effective itinerary planning and optimizing vehicle systems, which can reduce driving range anxiety and decrease energy costs. As public awareness of data privacy increases, adopting approaches that safeguard data privacy in the context of BEV energy consumption modeling is crucial. Federated Learning (FL) is a promising solution mitigating the risk of exposing sensitive information to third parties by allowing local data to remain on devices and only sharing model updates with a central server. Our work investigates the potential of using FL methods, such as FedAvg, and FedPer, to improve BEV energy consumption prediction while maintaining user privacy. We conducted experiments using data from 10 BEVs under simulated real-world driving conditions. Our results demonstrate that the FedAvg-LSTM model achieved a reduction of up to 67.84\% in the MAE value of the prediction results. Furthermore, we explored various real-world scenarios and discussed how FL methods can be employed in those cases. Our findings show that FL methods can effectively improve the performance of BEV energy consumption prediction while maintaining user privacy.

Neural posterior estimation (NPE), a type of amortized variational inference, is a computationally efficient means of constructing probabilistic catalogs of light sources from astronomical images. To date, NPE has not been used to perform inference in models with spatially varying covariates. However, ground-based astronomical images have spatially varying sky backgrounds and point spread functions (PSFs), and accounting for this variation is essential for constructing accurate catalogs of imaged light sources. In this work, we introduce a method of performing NPE with spatially varying backgrounds and PSFs. In this method, we generate synthetic catalogs and semi-synthetic images for these catalogs using randomly sampled PSF and background estimates from existing surveys. Using this data, we train a neural network, which takes an astronomical image and representations of its background and PSF as input, to output a probabilistic catalog. Our experiments with Sloan Digital Sky Survey data demonstrate the effectiveness of NPE in the presence of spatially varying backgrounds and PSFs for light source detection, star/galaxy separation, and flux measurement.

Denoising and score estimation have long been known to be linked via the classical Tweedie's formula. In this work, we first extend the latter to a wider range of distributions often called "energy models" and denoted elliptical distributions in this work. Next, we examine an alternative view: we consider the denoising posterior P(X|Y) as the optimizer of the energy score (a scoring rule) and derive a fundamental identity that connects the (path-) derivative of a (possibly) non-Euclidean energy score to the score of the noisy marginal. This identity can be seen as an analog of Tweedie's identity for the energy score, and allows for several interesting applications; for example, score estimation, noise distribution parameter estimation, as well as using energy score models in the context of "traditional" diffusion model samplers with a wider array of noising distributions.

Reliable uncertainty estimation is critical for medical image segmentation, where automated contours feed downstream quantification and clinical decision support. Many strong uncertainty methods require repeated inference, while efficient single-forward-pass alternatives often provide weaker failure ranking or rely on restrictive feature-space assumptions. We present SegWithU, a post-hoc framework that augments a frozen pretrained segmentation backbone with a lightweight uncertainty head. SegWithU taps intermediate backbone features and models uncertainty as perturbation energy in a compact probe space using rank-1 posterior probes. It produces two voxel-wise uncertainty maps: a calibration-oriented map for probability tempering and a ranking-oriented map for error detection and selective prediction. Across ACDC, BraTS2024, and LiTS, SegWithU is the strongest and most consistent single-forward-pass baseline, achieving AUROC/AURC of 0.9838/2.4885, 0.9946/0.2660, and 0.9925/0.8193, respectively, while preserving segmentation quality. These results suggest that perturbation-based uncertainty modeling is an effective and practical route to reliability-aware medical segmentation. Source code is available at https://github.com/ProjectNeura/SegWithU.

In multi-person pose estimation actors can be heavily occluded, even become fully invisible behind another person. While temporal methods can still predict a reasonable estimation for a temporarily disappeared pose using past and future frames, they exhibit large errors nevertheless. We present an energy minimization approach to generate smooth, valid trajectories in time, bridging gaps in visibility. We show that it is better than other interpolation based approaches and achieves state of the art results. In addition, we present the synthetic MuCo-Temp dataset, a temporal extension of the MuCo-3DHP dataset. Our code is made publicly available.

Prior works on event-based optical flow estimation have investigated several gradient-based learning methods to train neural networks for predicting optical flow. However, they do not utilize the fast data rate of event data streams and rely on a spatio-temporal representation constructed from a collection of events over a fixed period of time (often between two grayscale frames). As a result, optical flow is only evaluated at a frequency much lower than the rate data is produced by an event-based camera, leading to a temporally sparse optical flow estimation. To predict temporally dense optical flow, we cast the problem as a sequential learning task and propose a training methodology to train sequential networks for continuous prediction on an event stream. We propose two types of networks: one focused on performance and another focused on compute efficiency. We first train long-short term memory networks (LSTMs) on the DSEC dataset and demonstrated 10x temporally dense optical flow estimation over existing flow estimation approaches. The additional benefit of having a memory to draw long temporal correlations back in time results in a 19.7% improvement in flow prediction accuracy of LSTMs over similar networks with no memory elements. We subsequently show that the inherent recurrence of spiking neural networks (SNNs) enables them to learn and estimate temporally dense optical flow with 31.8% lesser parameters than LSTM, but with a slightly increased error. This demonstrates potential for energy-efficient implementation of fast optical flow prediction using SNNs.

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated based on sub-sampling of the same training data. The accuracy of the uncertainty prediction can be benchmarked by maximum likelihood estimation, which can also be used to correct for correlations between resampled models, and to improve the performance of the uncertainty estimation by a cross-validation procedure. In the case of sparse Gaussian Process Regression models, this resampled estimator can be evaluated at negligible cost. We demonstrate the reliability of these estimates for the prediction of molecular energetics, and for the estimation of nuclear chemical shieldings in molecular crystals. Extension to estimate the uncertainty in energy differences, forces, or other correlated predictions is straightforward. This method can be easily applied to other machine learning schemes, and will be beneficial to make data-driven predictions more reliable, and to facilitate training-set optimization and active-learning strategies.

Out-of-distribution (OOD) detection is a critical requirement for the deployment of deep neural networks. This paper introduces the HEAT model, a new post-hoc OOD detection method estimating the density of in-distribution (ID) samples using hybrid energy-based models (EBM) in the feature space of a pre-trained backbone. HEAT complements prior density estimators of the ID density, e.g. parametric models like the Gaussian Mixture Model (GMM), to provide an accurate yet robust density estimation. A second contribution is to leverage the EBM framework to provide a unified density estimation and to compose several energy terms. Extensive experiments demonstrate the significance of the two contributions. HEAT sets new state-of-the-art OOD detection results on the CIFAR-10 / CIFAR-100 benchmark as well as on the large-scale Imagenet benchmark. The code is available at: https://github.com/MarcLafon/heatood.

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by optimizing EBFlow with score-matching objectives, the computation of Jacobian determinants for linear transformations can be entirely bypassed. This feature enables the use of arbitrary linear layers in the construction of flow-based models without increasing the computational time complexity of each training iteration from O(D^2L) to O(D^3L) for an L-layered model that accepts D-dimensional inputs. This makes the training of EBFlow more efficient than the commonly-adopted maximum likelihood training method. In addition to the reduction in runtime, we enhance the training stability and empirical performance of EBFlow through a number of techniques developed based on our analysis of the score-matching methods. The experimental results demonstrate that our approach achieves a significant speedup compared to maximum likelihood estimation while outperforming prior methods with a noticeable margin in terms of negative log-likelihood (NLL).

Because of the diversity in lighting environments, existing illumination estimation techniques have been designed explicitly on indoor or outdoor environments. Methods have focused specifically on capturing accurate energy (e.g., through parametric lighting models), which emphasizes shading and strong cast shadows; or producing plausible texture (e.g., with GANs), which prioritizes plausible reflections. Approaches which provide editable lighting capabilities have been proposed, but these tend to be with simplified lighting models, offering limited realism. In this work, we propose to bridge the gap between these recent trends in the literature, and propose a method which combines a parametric light model with 360{\deg} panoramas, ready to use as HDRI in rendering engines. We leverage recent advances in GAN-based LDR panorama extrapolation from a regular image, which we extend to HDR using parametric spherical gaussians. To achieve this, we introduce a novel lighting co-modulation method that injects lighting-related features throughout the generator, tightly coupling the original or edited scene illumination within the panorama generation process. In our representation, users can easily edit light direction, intensity, number, etc. to impact shading while providing rich, complex reflections while seamlessly blending with the edits. Furthermore, our method encompasses indoor and outdoor environments, demonstrating state-of-the-art results even when compared to domain-specific methods.

Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity multiplication L-Mul algorithm that approximates floating point number multiplication with integer addition operations. The new algorithm costs significantly less computation resource than 8-bit floating point multiplication but achieves higher precision. Compared to 8-bit floating point multiplications, the proposed method achieves higher precision but consumes significantly less bit-level computation. Since multiplying floating point numbers requires substantially higher energy compared to integer addition operations, applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by element-wise floating point tensor multiplications and 80% energy cost of dot products. We calculated the theoretical error expectation of L-Mul, and evaluated the algorithm on a wide range of textual, visual, and symbolic tasks, including natural language understanding, structural reasoning, mathematics, and commonsense question answering. Our numerical analysis experiments agree with the theoretical error estimation, which indicates that L-Mul with 4-bit mantissa achieves comparable precision as float8_e4m3 multiplications, and L-Mul with 3-bit mantissa outperforms float8_e5m2. Evaluation results on popular benchmarks show that directly applying L-Mul to the attention mechanism is almost lossless. We further show that replacing all floating point multiplications with 3-bit mantissa L-Mul in a transformer model achieves equivalent precision as using float8_e4m3 as accumulation precision in both fine-tuning and inference.

In this work we propose an analytical model that reproduces the core-bounds phase of gravitational waves (GW) of Rapidly Rotating (RR) from Core Collapse Supernovae (CCSNe), as a function of three parameters, the arrival time tau, the ratio of the kinetic and potential energy beta and a phenomenological parameter alpha related to rotation and equation of state (EOS). To validate the model we use 126 waveforms from the Richers catalog Richers_2017 selected with the criteria of exploring a range of rotation profiles, and involving EOS. To quantify the degree of accuracy of the proposed model, with a particular focus on the rotation parameter beta, we show that the average Fitting Factor (FF) between the simulated waveforms with the templates is 94.4\%. In order to estimate the parameters we propose a frequentist matched filtering approach in real interferometric noise which does not require assigning any priors. We use the Matched Filter (MF) technique, where we inject a bank of templates considering simulated colored Gaussian noise and the real noise of O3L1. For example for A300w6.00\_BHBLP at 10Kpc we obtain a standar deviation of sigma = 3.34times 10^{-3} for simulated colored Gaussian noise and sigma= 1.46times 10^{-2} for real noise. On the other hand, from the asymptotic expansion of the variance we obtain the theoretical minimum error for beta at 10 kpc and optimal orientation. The estimation error in this case is from 10^{-2} to 10^{-3} as beta increases. We show that the results of the estimation error of beta for the 3-parameter space (3D) is consistent with the single-parameter space (1D), which allows us to conclude that beta is decoupled from the others two parameters.

Direction of Arrival (DoA) estimation techniques face a critical trade-off, as classical methods often lack accuracy in challenging, low signal-to-noise ratio (SNR) conditions, while modern deep learning approaches are too energy-intensive and opaque for resource-constrained, safety-critical systems. We introduce HYPERDOA, a novel estimator leveraging Hyperdimensional Computing (HDC). The framework introduces two distinct feature extraction strategies -- Mean Spatial-Lag Autocorrelation and Spatial Smoothing -- for its HDC pipeline, and then reframes DoA estimation as a pattern recognition problem. This approach leverages HDC's inherent robustness to noise and its transparent algebraic operations to bypass the expensive matrix decompositions and "black-box" nature of classical and deep learning methods, respectively. Our evaluation demonstrates that HYPERDOA achieves ~35.39% higher accuracy than state-of-the-art methods in low-SNR, coherent-source scenarios. Crucially, it also consumes ~93% less energy than competing neural baselines on an embedded NVIDIA Jetson Xavier NX platform. This dual advantage in accuracy and efficiency establishes HYPERDOA as a robust and viable solution for mission-critical applications on edge devices.

Since batch algorithms suffer from lack of proficiency in confronting model mismatches and disturbances, this contribution proposes an adaptive scheme based on continuous Lyapunov function for online robot dynamic identification. This paper suggests stable updating rules to drive neural networks inspiring from model reference adaptive paradigm. Network structure consists of three parallel self-driving neural networks which aim to estimate robot dynamic terms individually. Lyapunov candidate is selected to construct energy surface for a convex optimization framework. Learning rules are driven directly from Lyapunov functions to make the derivative negative. Finally, experimental results on 3-DOF Phantom Omni Haptic device demonstrate efficiency of the proposed method.

Generative Adversarial Networks (GANs) have shown compelling results in various tasks and applications in recent years. However, mode collapse remains a critical problem in GANs. In this paper, we propose a novel training pipeline to address the mode collapse issue of GANs. Different from existing methods, we propose to generalize the discriminator as feature embedding and maximize the entropy of distributions in the embedding space learned by the discriminator. Specifically, two regularization terms, i.e., Deep Local Linear Embedding (DLLE) and Deep Isometric feature Mapping (DIsoMap), are designed to encourage the discriminator to learn the structural information embedded in the data, such that the embedding space learned by the discriminator can be well-formed. Based on the well-learned embedding space supported by the discriminator, a non-parametric entropy estimator is designed to efficiently maximize the entropy of embedding vectors, playing as an approximation of maximizing the entropy of the generated distribution. By improving the discriminator and maximizing the distance of the most similar samples in the embedding space, our pipeline effectively reduces the mode collapse without sacrificing the quality of generated samples. Extensive experimental results show the effectiveness of our method, which outperforms the GAN baseline, MaF-GAN on CelebA (9.13 vs. 12.43 in FID) and surpasses the recent state-of-the-art energy-based model on the ANIME-FACE dataset (2.80 vs. 2.26 in Inception score). The code is available at https://github.com/HaozheLiu-ST/MEE

Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on the tractability of the normalizing constant, thus are more flexible to parameterize and can model a more expressive family of probability distributions. However, the unknown normalizing constant of EBMs makes training particularly difficult. Our goal is to provide a friendly introduction to modern approaches for EBM training. We start by explaining maximum likelihood training with Markov chain Monte Carlo (MCMC), and proceed to elaborate on MCMC-free approaches, including Score Matching (SM) and Noise Constrastive Estimation (NCE). We highlight theoretical connections among these three approaches, and end with a brief survey on alternative training methods, which are still under active research. Our tutorial is targeted at an audience with basic understanding of generative models who want to apply EBMs or start a research project in this direction.

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3times sampling speedup over existing diffusion models.

State of health (SOH) is a crucial indicator for assessing the degradation level of batteries that cannot be measured directly but requires estimation. Accurate SOH estimation enhances detection, control, and feedback for Li-ion batteries, allowing for safe and efficient energy management and guiding the development of new-generation batteries. Despite the significant progress in data-driven SOH estimation, the time and resource-consuming degradation experiments for generating lifelong training data pose a challenge in establishing one large model capable of handling diverse types of Li-ion batteries, e.g., cross-chemistry, cross-manufacturer, and cross-capacity. Hence, this paper utilizes the strong generalization capability of large language model (LLM) to proposes a novel framework for adaptable SOH estimation across diverse batteries. To match the real scenario where unlabeled data sequentially arrives in use with distribution shifts, the proposed model is modified by a test-time training technique to ensure estimation accuracy even at the battery's end of life. The validation results demonstrate that the proposed framework achieves state-of-the-art accuracy on four widely recognized datasets collected from 62 batteries. Furthermore, we analyze the theoretical challenges of cross-battery estimation and provide a quantitative explanation of the effectiveness of our method.

Monocular depth estimation (MDE) plays a crucial role in enabling spatially-aware applications in Ultra-low-power (ULP) Internet-of-Things (IoT) platforms. However, the limited number of parameters of Deep Neural Networks for the MDE task, designed for IoT nodes, results in severe accuracy drops when the sensor data observed in the field shifts significantly from the training dataset. To address this domain shift problem, we present a multi-modal On-Device Learning (ODL) technique, deployed on an IoT device integrating a Greenwaves GAP9 MicroController Unit (MCU), a 80 mW monocular camera and a 8 x 8 pixel depth sensor, consuming approx300mW. In its normal operation, this setup feeds a tiny 107 k-parameter μPyD-Net model with monocular images for inference. The depth sensor, usually deactivated to minimize energy consumption, is only activated alongside the camera to collect pseudo-labels when the system is placed in a new environment. Then, the fine-tuning task is performed entirely on the MCU, using the new data. To optimize our backpropagation-based on-device training, we introduce a novel memory-driven sparse update scheme, which minimizes the fine-tuning memory to 1.2 MB, 2.2x less than a full update, while preserving accuracy (i.e., only 2% and 1.5% drops on the KITTI and NYUv2 datasets). Our in-field tests demonstrate, for the first time, that ODL for MDE can be performed in 17.8 minutes on the IoT node, reducing the root mean squared error from 4.9 to 0.6m with only 3 k self-labeled samples, collected in a real-life deployment scenario.

Monocular Depth Estimation (MDE) has emerged as a pivotal task in computer vision, supporting numerous real-world applications. However, deploying accurate depth estimation models on resource-limited edge devices, especially Application-Specific Integrated Circuits (ASICs), is challenging due to the high computational and memory demands. Recent advancements in foundational depth estimation deliver impressive results but further amplify the difficulty of deployment on ASICs. To address this, we propose QuartDepth which adopts post-training quantization to quantize MDE models with hardware accelerations for ASICs. Our approach involves quantizing both weights and activations to 4-bit precision, reducing the model size and computation cost. To mitigate the performance degradation, we introduce activation polishing and compensation algorithm applied before and after activation quantization, as well as a weight reconstruction method for minimizing errors in weight quantization. Furthermore, we design a flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, enhancing throughput and efficiency. Experimental results demonstrate that our framework achieves competitive accuracy while enabling fast inference and higher energy efficiency on ASICs, bridging the gap between high-performance depth estimation and practical edge-device applicability. Code: https://github.com/shawnricecake/quart-depth

Text generation is ubiquitous in many NLP tasks, from summarization, to dialogue and machine translation. The dominant parametric approach is based on locally normalized models which predict one word at a time. While these work remarkably well, they are plagued by exposure bias due to the greedy nature of the generation process. In this work, we investigate un-normalized energy-based models (EBMs) which operate not at the token but at the sequence level. In order to make training tractable, we first work in the residual of a pretrained locally normalized language model and second we train using noise contrastive estimation. Furthermore, since the EBM works at the sequence level, we can leverage pretrained bi-directional contextual representations, such as BERT and RoBERTa. Our experiments on two large language modeling datasets show that residual EBMs yield lower perplexity compared to locally normalized baselines. Moreover, generation via importance sampling is very efficient and of higher quality than the baseline models according to human evaluation.

In diffraction-based crystal structure analysis, thermal ellipsoids, quantified via Anisotropic Displacement Parameters (ADPs), are critical yet challenging to determine. ADPs capture atomic vibrations, reflecting thermal and structural properties, but traditional computation is often expensive. This paper introduces CartNet, a novel graph neural network (GNN) for efficiently predicting crystal properties by encoding atomic geometry into Cartesian coordinates alongside the crystal temperature. CartNet integrates a neighbour equalization technique to emphasize covalent and contact interactions, and a Cholesky-based head to ensure valid ADP predictions. We also propose a rotational SO(3) data augmentation strategy during training to handle unseen orientations. An ADP dataset with over 200,000 experimental crystal structures from the Cambridge Structural Database (CSD) was curated to validate the approach. CartNet significantly reduces computational costs and outperforms existing methods in ADP prediction by 10.87%, while delivering a 34.77% improvement over theoretical approaches. We further evaluated CartNet on other datasets covering formation energy, band gap, total energy, energy above the convex hull, bulk moduli, and shear moduli, achieving 7.71% better results on the Jarvis Dataset and 13.16% on the Materials Project Dataset. These gains establish CartNet as a state-of-the-art solution for diverse crystal property predictions. Project website and online demo: https://www.ee.ub.edu/cartnet

Sub-10cm diameter nano-drones are gaining momentum thanks to their applicability in scenarios prevented to bigger flying drones, such as in narrow environments and close to humans. However, their tiny form factor also brings their major drawback: ultra-constrained memory and processors for the onboard execution of their perception pipelines. Therefore, lightweight deep learning-based approaches are becoming increasingly popular, stressing how computational efficiency and energy-saving are paramount as they can make the difference between a fully working closed-loop system and a failing one. In this work, to maximize the exploitation of the ultra-limited resources aboard nano-drones, we present a novel adaptive deep learning-based mechanism for the efficient execution of a vision-based human pose estimation task. We leverage two State-of-the-Art (SoA) convolutional neural networks (CNNs) with different regression performance vs. computational costs trade-offs. By combining these CNNs with three novel adaptation strategies based on the output's temporal consistency and on auxiliary tasks to swap the CNN being executed proactively, we present six different systems. On a real-world dataset and the actual nano-drone hardware, our best-performing system, compared to executing only the bigger and most accurate SoA model, shows 28% latency reduction while keeping the same mean absolute error (MAE), 3% MAE reduction while being iso-latency, and the absolute peak performance, i.e., 6% better than SoA model.

This paper presents a nonlinear location estimation to infer the position of a user holding a smartphone. We consider a large location with M number of grid points, each grid point is labeled with a unique fingerprint consisting of the received signal strength (RSS) values measured from N number of Bluetooth Low Energy (BLE) beacons. Given the fingerprint observed by the smartphone, the user's current location can be estimated by finding the top-k similar fingerprints from the list of fingerprints registered in the database. Besides the environmental factors, the dynamicity in holding the smartphone is another source to the variation in fingerprint measurements, yet there are not many studies addressing the fingerprint variability due to dynamic smartphone positions held by human hands during online detection. To this end, we propose a nonlinear location estimation using the kernel method. Specifically, our proposed method comprises of two steps: 1) a beacon selection strategy to select a subset of beacons that is insensitive to the subtle change of holding positions, and 2) a kernel method to compute the similarity between this subset of observed signals and all the fingerprints registered in the database. The experimental results based on large-scale data collected in a complex building indicate a substantial performance gain of our proposed approach in comparison to state-of-the-art methods. The dataset consisting of the signal information collected from the beacons is available online.

Massive multiple-input multiple-output (MIMO) communication systems have a huge potential both in terms of data rate and energy efficiency, although channel estimation becomes challenging for a large number of antennas. Using a physical model allows to ease the problem by injecting a priori information based on the physics of propagation. However, such a model rests on simplifying assumptions and requires to know precisely the configuration of the system, which is unrealistic in practice.In this paper we present mpNet, an unfolded neural network specifically designed for massive MIMO channel estimation. It is trained online in an unsupervised way. Moreover, mpNet is computationally efficient and automatically adapts its depth to the signal-to-noise ratio (SNR). The method we propose adds flexibility to physical channel models by allowing a base station (BS) to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase.It is applied to realistic millimeter wave channels and shows great performance, achieving a channel estimation error almost as low as one would get with a perfectly calibrated system. It also allows incident detection and automatic correction, making the BS resilient and able to automatically adapt to changes in its environment.

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.

Iterative generative policies, such as diffusion models and flow matching, offer superior expressivity for continuous control but complicate Maximum Entropy Reinforcement Learning because their action log-densities are not directly accessible. To address this, we propose Field Least-Energy Actor-Critic (FLAC), a likelihood-free framework that regulates policy stochasticity by penalizing the kinetic energy of the velocity field. Our key insight is to formulate policy optimization as a Generalized Schrödinger Bridge (GSB) problem relative to a high-entropy reference process (e.g., uniform). Under this view, the maximum-entropy principle emerges naturally as staying close to a high-entropy reference while optimizing return, without requiring explicit action densities. In this framework, kinetic energy serves as a physically grounded proxy for divergence from the reference: minimizing path-space energy bounds the deviation of the induced terminal action distribution. Building on this view, we derive an energy-regularized policy iteration scheme and a practical off-policy algorithm that automatically tunes the kinetic energy via a Lagrangian dual mechanism. Empirically, FLAC achieves superior or comparable performance on high-dimensional benchmarks relative to strong baselines, while avoiding explicit density estimation.

The term GreenAI refers to a novel approach to Deep Learning, that is more aware of the ecological impact and the computational efficiency of its methods. The promoters of GreenAI suggested the use of Floating Point Operations (FLOPs) as a measure of the computational cost of Neural Networks; however, that measure does not correlate well with the energy consumption of hardware equipped with massively parallel processing units like GPUs or TPUs. In this article, we propose a simple refinement of the formula used to compute floating point operations for convolutional layers, called {\alpha}-FLOPs, explaining and correcting the traditional discrepancy with respect to different layers, and closer to reality. The notion of {\alpha}-FLOPs relies on the crucial insight that, in case of inputs with multiple dimensions, there is no reason to believe that the speedup offered by parallelism will be uniform along all different axes.

Establishing the relationship between 3D structures and the energy states of molecular systems has proven to be a promising approach for learning 3D molecular representations. However, existing methods are limited to modeling the molecular energy states from classical mechanics. This limitation results in a significant oversight of quantum mechanical effects, such as quantized (discrete) energy level structures, which offer a more accurate estimation of molecular energy and can be experimentally measured through energy spectra. In this paper, we propose to utilize the energy spectra to enhance the pre-training of 3D molecular representations (MolSpectra), thereby infusing the knowledge of quantum mechanics into the molecular representations. Specifically, we propose SpecFormer, a multi-spectrum encoder for encoding molecular spectra via masked patch reconstruction. By further aligning outputs from the 3D encoder and spectrum encoder using a contrastive objective, we enhance the 3D encoder's understanding of molecules. Evaluations on public benchmarks reveal that our pre-trained representations surpass existing methods in predicting molecular properties and modeling dynamics.

Visual motion processing is essential for humans to perceive and interact with dynamic environments. Despite extensive research in cognitive neuroscience, image-computable models that can extract informative motion flow from natural scenes in a manner consistent with human visual processing have yet to be established. Meanwhile, recent advancements in computer vision (CV), propelled by deep learning, have led to significant progress in optical flow estimation, a task closely related to motion perception. Here we propose an image-computable model of human motion perception by bridging the gap between biological and CV models. Specifically, we introduce a novel two-stages approach that combines trainable motion energy sensing with a recurrent self-attention network for adaptive motion integration and segregation. This model architecture aims to capture the computations in V1-MT, the core structure for motion perception in the biological visual system, while providing the ability to derive informative motion flow for a wide range of stimuli, including complex natural scenes. In silico neurophysiology reveals that our model's unit responses are similar to mammalian neural recordings regarding motion pooling and speed tuning. The proposed model can also replicate human responses to a range of stimuli examined in past psychophysical studies. The experimental results on the Sintel benchmark demonstrate that our model predicts human responses better than the ground truth, whereas the state-of-the-art CV models show the opposite. Our study provides a computational architecture consistent with human visual motion processing, although the physiological correspondence may not be exact.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

In this paper we introduce the concept of what we call "NUDAR" (NeUtrino Direction and Ranging), making the point that measurements of the observed energy and direction vectors can be employed to passively deduce the exact three-dimensional location and thermal power of geophysical and anthropogenic neutrino sources from even a single detector. We present the most precise background estimates to date, all handled in full three dimensions, as functions of depth and geographical location. For the present calculations, we consider a hypothetical 138 kiloton detector which can be transported to an ocean site and deployed to an operational depth. We present a Bayesian estimation framework to incorporate any a priori knowledge of the reactor that we are trying to detect, as well as the estimated uncertainty in the background and the oscillation parameters. Most importantly, we fully employ the knowledge of the reactor spectrum and the distance-dependent effects of neutrino oscillations on such spectra. The latter, in particular, makes possible determination of range from one location, given adequate signal statistics. Further, we explore the rich potential of improving detection with even modest improvements in individual neutrino direction determination. We conclude that a 300 MWth reactor can indeed be geolocated, and its operating power estimated with one or two detectors in the hundred kiloton class at ranges out to a few hundred kilometers. We note that such detectors would have natural and non-interfering utility for scientific studies of geo-neutrinos, neutrino oscillations, and astrophysical neutrinos. This motivates the development of cost effective methods of constructing and deploying such next generation detectors.

We present Monte Carlo (MC) simulation results from a study of a compact plastic-scintillator detector suitable for imaging fast neutrons in the 1 -- 10 MeV energy range: the miniTimeCube (mTC). Originally designed for antineutrino detection, the mTC consists of 24 MultiChannel Plate (MCP) photodetectors surrounding a 13 cm cube of boron-doped plastic scintillator. Our simulation results show that waveform digitization of 1536 optically sensitive channels surrounding the scintillator should allow for spatiotemporal determination of individual neutron-proton scatters in the detector volume to thicksim100 picoseconds and thicksim5 mm. A Bayesian estimation framework is presented for multiple-scatter reconstruction, and is used to estimate the incoming direction and energy of simulated individual neutrons. Finally, we show how populations of reconstructed neutrons can be used to estimate the direction and energy spectrum of nearby simulated neutron sources.

Block-sparse attention is promising for accelerating long-context LLM pre-filling, yet identifying relevant blocks efficiently remains a bottleneck. Existing methods typically employ coarse-grained attention as a proxy for block importance estimation, but often resort to expensive token-level searching or scoring, resulting in significant selection overhead. In this work, we trace the inaccuracy of standard coarse-grained attention via mean pooling to a theoretical root cause: the interaction between mean pooling and Rotary Positional Embeddings (RoPE). We prove that mean pooling acts as a low-pass filter that induces destructive interference in high-frequency dimensions, effectively creating a "blind spot" for local positional information (e.g., slash patterns). To address this, we introduce Prism, a training-free spectral-aware approach that decomposes block selection into high-frequency and low-frequency branches. By applying energy-based temperature calibration, Prism restores the attenuated positional signals directly from pooled representations, enabling block importance estimation using purely block-level operations, thereby improving efficiency. Extensive evaluations confirm that Prism maintains accuracy parity with full attention while delivering up to 5.1times speedup.

Prior research on out-of-distribution detection (OoDD) has primarily focused on single-modality models. Recently, with the advent of large-scale pretrained vision-language models such as CLIP, OoDD methods utilizing such multi-modal representations through zero-shot and prompt learning strategies have emerged. However, these methods typically involve either freezing the pretrained weights or only partially tuning them, which can be suboptimal for downstream datasets. In this paper, we highlight that multi-modal fine-tuning (MMFT) can achieve notable OoDD performance. Despite some recent works demonstrating the impact of fine-tuning methods for OoDD, there remains significant potential for performance improvement. We investigate the limitation of na\"ive fine-tuning methods, examining why they fail to fully leverage the pretrained knowledge. Our empirical analysis suggests that this issue could stem from the modality gap within in-distribution (ID) embeddings. To address this, we propose a training objective that enhances cross-modal alignment by regularizing the distances between image and text embeddings of ID data. This adjustment helps in better utilizing pretrained textual information by aligning similar semantics from different modalities (i.e., text and image) more closely in the hyperspherical representation space. We theoretically demonstrate that the proposed regularization corresponds to the maximum likelihood estimation of an energy-based model on a hypersphere. Utilizing ImageNet-1k OoD benchmark datasets, we show that our method, combined with post-hoc OoDD approaches leveraging pretrained knowledge (e.g., NegLabel), significantly outperforms existing methods, achieving state-of-the-art OoDD performance and leading ID accuracy.

We propose the first learning-based approach for fast moving objects detection. Such objects are highly blurred and move over large distances within one video frame. Fast moving objects are associated with a deblurring and matting problem, also called deblatting. We show that the separation of deblatting into consecutive matting and deblurring allows achieving real-time performance, i.e. an order of magnitude speed-up, and thus enabling new classes of application. The proposed method detects fast moving objects as a truncated distance function to the trajectory by learning from synthetic data. For the sharp appearance estimation and accurate trajectory estimation, we propose a matting and fitting network that estimates the blurred appearance without background, followed by an energy minimization based deblurring. The state-of-the-art methods are outperformed in terms of recall, precision, trajectory estimation, and sharp appearance reconstruction. Compared to other methods, such as deblatting, the inference is of several orders of magnitude faster and allows applications such as real-time fast moving object detection and retrieval in large video collections.

In the last few years, the Internet throughput, usage and reliability have increased almost exponentially. The introduction of broadband wireless mobile ad hoc networks (MANETs) and cellular networks together with increased computational power have opened the door for a new breed of applications to be created, namely real-time multimedia applications. Delivering real-time multimedia traffic over a complex network like the Internet is a particularly challenging task since these applications have strict quality-of-service (QoS) requirements on bandwidth, delay, and delay jitter. Traditional Internet protocol (IP)-based best effort service is not able to meet these stringent requirements. The time-varying nature of wireless channels and resource constrained wireless devices make the problem even more difficult. To improve perceived media quality by end users over wireless Internet, QoS supports can be addressed in different layers, including application layer, transport layer and link layer. Cross layer design is a well-known approach to achieve this adaptation. In cross-layer design, the challenges from the physical wireless medium and the QoS-demands from the applications are taken into account so that the rate, power, and coding at the physical (PHY) layer can adapted to meet the requirements of the applications given the current channel and network conditions. A number of propositions for cross-layer designs exist in the literature. In this chapter, an extensive review has been made on these cross-layer architectures that combine the application-layer, transport layer and the link layer controls. Particularly, the issues like channel estimation techniques, adaptive controls at the application and link layers for energy efficiency, priority based scheduling, transmission rate control at the transport layer, and adaptive automatic repeat request (ARQ) are discussed in detail.

The paradigm of large language model (LLM) reasoning is shifting from parameter scaling to test-time compute scaling, yet many existing approaches still rely on uniform brute-force sampling (for example, fixed best-of-N or self-consistency) that is costly, hard to attribute, and can trigger overthinking with diminishing returns. We propose ODAR-Expert, an adaptive routing framework that optimizes the accuracy-efficiency trade-off via principled resource allocation. ODAR uses a difficulty estimator grounded in amortized active inference to dynamically route queries between a heuristic Fast Agent and a deliberative Slow Agent. We further introduce a free-energy-principled, risk-sensitive fusion mechanism that selects answers by minimizing a variational free energy objective, balancing log-likelihood with epistemic uncertainty (varentropy) as a principled alternative to ad hoc voting over heterogeneous candidates. Extensive evaluation across 23 benchmarks shows strong and consistent gains, including 98.2% accuracy on MATH and 54.8% on Humanity's Last Exam (HLE), while improving the compute-accuracy frontier under compute-matched settings. We also validate reproducibility on a fully open-source stack (Llama 4 + DeepSeek), where ODAR surpasses homogeneous sampling strategies while reducing computational costs by 82%. Overall, our results suggest that thinking-optimal scaling requires adaptive resource allocation with free-energy-based decision-making rather than simply increasing test-time compute.

scqubits is an open-source Python package for simulating and analyzing superconducting circuits. It provides convenient routines to obtain energy spectra of common superconducting qubits, such as the transmon, fluxonium, flux, cos(2ϕ) and the 0-π qubit. scqubits also features a number of options for visualizing the computed spectral data, including plots of energy levels as a function of external parameters, display of matrix elements of various operators as well as means to easily plot qubit wavefunctions. Many of these tools are not limited to single qubits, but extend to composite Hilbert spaces consisting of coupled superconducting qubits and harmonic (or weakly anharmonic) modes. The library provides an extensive suite of methods for estimating qubit coherence times due to a variety of commonly considered noise channels. While all functionality of scqubits can be accessed programatically, the package also implements GUI-like widgets that, with a few clicks can help users both create relevant Python objects, as well as explore their properties through various plots. When applicable, the library harnesses the computing power of multiple cores via multiprocessing. scqubits further exposes a direct interface to the Quantum Toolbox in Python (QuTiP) package, allowing the user to efficiently leverage QuTiP's proven capabilities for simulating time evolution.

In recent years, researchers have focused on reducing the model size and number of computations (measured as "multiply-accumulate" or MAC operations) of DNNs. The energy consumption of a DNN depends on both the number of MAC operations and the energy efficiency of each MAC operation. The former can be estimated at design time; however, the latter depends on the intricate data reuse patterns and underlying hardware architecture. Hence, estimating it at design time is challenging. This work shows that the conventional approach to estimate the data reuse, viz. arithmetic intensity, does not always correctly estimate the degree of data reuse in DNNs since it gives equal importance to all the data types. We propose a novel model, termed "data type aware weighted arithmetic intensity" (DI), which accounts for the unequal importance of different data types in DNNs. We evaluate our model on 25 state-of-the-art DNNs on two GPUs. We show that our model accurately models data-reuse for all possible data reuse patterns for different types of convolution and different types of layers. We show that our model is a better indicator of the energy efficiency of DNNs. We also show its generality using the central limit theorem.

Energy is now a critical ML computing resource. While measuring energy consumption and observing trends is a valuable first step, accurately understanding and diagnosing why those differences occur is crucial for optimization. To that end, we begin by presenting a large-scale measurement study of inference time and energy across the generative AI landscape with 46 models, 7 tasks, and 1,858 different configurations on NVIDIA H100 and B200 GPUs. Our empirical findings span order-of-magnitude variations: LLM task type can lead to 25times energy differences, video generation sometimes consumes more than 100times the energy of images, and GPU utilization differences can result in 3--5times energy differences. Based on our observations, we present a framework for reasoning about the underlying mechanisms that govern time and energy consumption. The essence is that time and energy are determined by latent metrics like memory and utilization, which are in turn affected by various factors across the algorithm, software, and hardware layers. Our framework also extends directly to throughput per watt, a critical metric for power-constrained datacenters.

Determining whether inputs are out-of-distribution (OOD) is an essential building block for safely deploying machine learning models in the open world. However, previous methods relying on the softmax confidence score suffer from overconfident posterior distributions for OOD data. We propose a unified framework for OOD detection that uses an energy score. We show that energy scores better distinguish in- and out-of-distribution samples than the traditional approach using the softmax scores. Unlike softmax confidence scores, energy scores are theoretically aligned with the probability density of the inputs and are less susceptible to the overconfidence issue. Within this framework, energy can be flexibly used as a scoring function for any pre-trained neural classifier as well as a trainable cost function to shape the energy surface explicitly for OOD detection. On a CIFAR-10 pre-trained WideResNet, using the energy score reduces the average FPR (at TPR 95%) by 18.03% compared to the softmax confidence score. With energy-based training, our method outperforms the state-of-the-art on common benchmarks.

We reinterpret the final Large Language Model (LLM) softmax classifier as an Energy-Based Model (EBM), decomposing the sequence-to-sequence probability chain into multiple interacting EBMs at inference. This principled approach allows us to track "energy spills" during decoding, which we empirically show correlate with factual errors, biases, and failures. Similar to Orgad et al. (2025), our method localizes the exact answer token and subsequently tests for hallucinations. Crucially, however, we achieve this without requiring trained probe classifiers or activation ablations. Instead, we introduce two completely training-free metrics derived directly from output logits: spilled energy, which captures the discrepancy between energy values across consecutive generation steps that should theoretically match, and marginalized energy, which is measurable at a single step. Evaluated on nine benchmarks across state-of-the-art LLMs (including LLaMA, Mistral, and Gemma) and on synthetic algebraic operations (Qwen3), our approach demonstrates robust, competitive hallucination detection and cross-task generalization. Notably, these results hold for both pretrained and instruction-tuned variants without introducing any training overhead. Code available at: github.com/OmnAI-Lab/spilled-energy

As the adoption of Generative AI in real-world services grow explosively, energy has emerged as a critical bottleneck resource. However, energy remains a metric that is often overlooked, under-explored, or poorly understood in the context of building ML systems. We present the ML.ENERGY Benchmark, a benchmark suite and tool for measuring inference energy consumption under realistic service environments, and the corresponding ML.ENERGY Leaderboard, which have served as a valuable resource for those hoping to understand and optimize the energy consumption of their generative AI services. In this paper, we explain four key design principles for benchmarking ML energy we have acquired over time, and then describe how they are implemented in the ML.ENERGY Benchmark. We then highlight results from the latest iteration of the benchmark, including energy measurements of 40 widely used model architectures across 6 different tasks, case studies of how ML design choices impact energy consumption, and how automated optimization recommendations can lead to significant (sometimes more than 40%) energy savings without changing what is being computed by the model. The ML.ENERGY Benchmark is open-source and can be easily extended to various customized models and application scenarios.

The computation demand for machine learning (ML) has grown rapidly recently, which comes with a number of costs. Estimating the energy cost helps measure its environmental impact and finding greener strategies, yet it is challenging without detailed information. We calculate the energy use and carbon footprint of several recent large models-T5, Meena, GShard, Switch Transformer, and GPT-3-and refine earlier estimates for the neural architecture search that found Evolved Transformer. We highlight the following opportunities to improve energy efficiency and CO2 equivalent emissions (CO2e): Large but sparsely activated DNNs can consume <1/10th the energy of large, dense DNNs without sacrificing accuracy despite using as many or even more parameters. Geographic location matters for ML workload scheduling since the fraction of carbon-free energy and resulting CO2e vary ~5X-10X, even within the same country and the same organization. We are now optimizing where and when large models are trained. Specific datacenter infrastructure matters, as Cloud datacenters can be ~1.4-2X more energy efficient than typical datacenters, and the ML-oriented accelerators inside them can be ~2-5X more effective than off-the-shelf systems. Remarkably, the choice of DNN, datacenter, and processor can reduce the carbon footprint up to ~100-1000X. These large factors also make retroactive estimates of energy cost difficult. To avoid miscalculations, we believe ML papers requiring large computational resources should make energy consumption and CO2e explicit when practical. We are working to be more transparent about energy use and CO2e in our future research. To help reduce the carbon footprint of ML, we believe energy usage and CO2e should be a key metric in evaluating models, and we are collaborating with MLPerf developers to include energy usage during training and inference in this industry standard benchmark.

Generative Pre-trained Transformer (GPT) architectures are the most popular design for language modeling. Energy-based modeling is a different paradigm that views inference as a dynamical process operating on an energy landscape. We propose a minimal modification of the GPT setting to unify it with the EBM framework. The inference step of our model, which we call eNeRgy-GPT (NRGPT), is conceptualized as an exploration of the tokens on the energy landscape. We prove, and verify empirically, that under certain circumstances this exploration becomes gradient descent, although they don't necessarily lead to the best performing models. We demonstrate that our model performs well for simple language (Shakespeare dataset), algebraic ListOPS tasks, and richer settings such as OpenWebText language modeling. We also observe that our models may be more resistant to overfitting, doing so only during very long training.

In the rapidly evolving realm of artificial intelligence, deploying large language models (LLMs) poses increasingly pressing computational and environmental challenges. This paper introduces MELODI - Monitoring Energy Levels and Optimization for Data-driven Inference - a multifaceted framework crafted to monitor and analyze the energy consumed during LLM inference processes. MELODI enables detailed observations of power consumption dynamics and facilitates the creation of a comprehensive dataset reflective of energy efficiency across varied deployment scenarios. The dataset, generated using MELODI, encompasses a broad spectrum of LLM deployment frameworks, multiple language models, and extensive prompt datasets, enabling a comparative analysis of energy use. Using the dataset, we investigate how prompt attributes, including length and complexity, correlate with energy expenditure. Our findings indicate substantial disparities in energy efficiency, suggesting ample scope for optimization and adoption of sustainable measures in LLM deployment. Our contribution lies not only in the MELODI framework but also in the novel dataset, a resource that can be expanded by other researchers. Thus, MELODI is a foundational tool and dataset for advancing research into energy-conscious LLM deployment, steering the field toward a more sustainable future.

Millions of smart meters have been deployed worldwide, collecting the total power consumed by individual households. Based on these data, electricity suppliers offer their clients energy monitoring solutions to provide feedback on the consumption of their individual appliances. Historically, such estimates have relied on statistical methods that use coarse-grained total monthly consumption and static customer data, such as appliance ownership. Non-Intrusive Load Monitoring (NILM) is the problem of disaggregating a household's collected total power consumption to retrieve the consumed power for individual appliances. Current state-of-the-art (SotA) solutions for NILM are based on deep-learning (DL) and operate on subsequences of an entire household consumption reading. However, the non-stationary nature of real-world smart meter data leads to a drift in the data distribution within each segmented window, which significantly affects model performance. This paper introduces NILMFormer, a Transformer-based architecture that incorporates a new subsequence stationarization/de-stationarization scheme to mitigate the distribution drift and that uses a novel positional encoding that relies only on the subsequence's timestamp information. Experiments with 4 real-world datasets show that NILMFormer significantly outperforms the SotA approaches. Our solution has been deployed as the backbone algorithm for EDF's (Electricit\'e De France) consumption monitoring service, delivering detailed insights to millions of customers about their individual appliances' power consumption. This paper appeared in KDD 2025.

Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling problem by means of energy potentials (unnormalized likelihood functions). In contrast, the realm of Optimal Transport (OT) and, in particular, neural OT solvers is much less explored and limited by few recent works (excluding WGAN-based approaches which utilize OT as a loss function and do not model OT maps themselves). In our work, we bridge the gap between EBMs and Entropy-regularized OT. We present a novel methodology which allows utilizing the recent developments and technical improvements of the former in order to enrich the latter. From the theoretical perspective, we prove generalization bounds for our technique. In practice, we validate its applicability in toy 2D and image domains. To showcase the scalability, we empower our method with a pre-trained StyleGAN and apply it to high-res AFHQ 512times 512 unpaired I2I translation. For simplicity, we choose simple short- and long-run EBMs as a backbone of our Energy-guided Entropic OT approach, leaving the application of more sophisticated EBMs for future research. Our code is available at: https://github.com/PetrMokrov/Energy-guided-Entropic-OT

Despite advances in the programmable logic capabilities of modern trigger systems, a significant bottleneck remains in the amount of data to be transported from the detector to off-detector logic where trigger decisions are made. We demonstrate that a neural network autoencoder model can be implemented in a radiation tolerant ASIC to perform lossy data compression alleviating the data transmission problem while preserving critical information of the detector energy profile. For our application, we consider the high-granularity calorimeter from the CMS experiment at the CERN Large Hadron Collider. The advantage of the machine learning approach is in the flexibility and configurability of the algorithm. By changing the neural network weights, a unique data compression algorithm can be deployed for each sensor in different detector regions, and changing detector or collider conditions. To meet area, performance, and power constraints, we perform a quantization-aware training to create an optimized neural network hardware implementation. The design is achieved through the use of high-level synthesis tools and the hls4ml framework, and was processed through synthesis and physical layout flows based on a LP CMOS 65 nm technology node. The flow anticipates 200 Mrad of ionizing radiation to select gates, and reports a total area of 3.6 mm^2 and consumes 95 mW of power. The simulated energy consumption per inference is 2.4 nJ. This is the first radiation tolerant on-detector ASIC implementation of a neural network that has been designed for particle physics applications.

We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, in contrast with previous approaches. The new estimator makes covariance estimation tractable in applications where simulation or data collection is expensive; to that end, we develop an optimal sample allocation scheme that minimizes the mean-squared error of the estimator given a fixed budget. Guaranteed definiteness is crucial to metric learning, data assimilation, and other downstream tasks. Evaluations of our approach using data from physical applications (heat conduction, fluid dynamics) demonstrate more accurate metric learning and speedups of more than one order of magnitude compared to benchmarks.

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.

The conventional evaluation protocols on machine learning models rely heavily on a labeled, i.i.d-assumed testing dataset, which is not often present in real world applications. The Automated Model Evaluation (AutoEval) shows an alternative to this traditional workflow, by forming a proximal prediction pipeline of the testing performance without the presence of ground-truth labels. Despite its recent successes, the AutoEval frameworks still suffer from an overconfidence issue, substantial storage and computational cost. In that regard, we propose a novel measure -- Meta-Distribution Energy (MDE) -- that allows the AutoEval framework to be both more efficient and effective. The core of the MDE is to establish a meta-distribution statistic, on the information (energy) associated with individual samples, then offer a smoother representation enabled by energy-based learning. We further provide our theoretical insights by connecting the MDE with the classification loss. We provide extensive experiments across modalities, datasets and different architectural backbones to validate MDE's validity, together with its superiority compared with prior approaches. We also prove MDE's versatility by showing its seamless integration with large-scale models, and easy adaption to learning scenarios with noisy- or imbalanced- labels. Code and data are available: https://github.com/pengr/Energy_AutoEval

LLMs have transformed NLP, yet deploying them on edge devices poses great carbon challenges. Prior estimators remain incomplete, neglecting peripheral energy use, distinct prefill/decode behaviors, and SoC design complexity. This paper presents CO2-Meter, a unified framework for estimating operational and embodied carbon in LLM edge inference. Contributions include: (1) equation-based peripheral energy models and datasets; (2) a GNN-based predictor with phase-specific LLM energy data; (3) a unit-level embodied carbon model for SoC bottleneck analysis; and (4) validation showing superior accuracy over prior methods. Case studies show CO2-Meter's effectiveness in identifying carbon hotspots and guiding sustainable LLM design on edge platforms. Source code: https://github.com/fuzhenxiao/CO2-Meter

Recent years have seen a surge in the popularity of commercial AI products based on generative, multi-purpose AI systems promising a unified approach to building machine learning (ML) models into technology. However, this ambition of "generality" comes at a steep cost to the environment, given the amount of energy these systems require and the amount of carbon that they emit. In this work, we propose the first systematic comparison of the ongoing inference cost of various categories of ML systems, covering both task-specific (i.e. finetuned models that carry out a single task) and `general-purpose' models, (i.e. those trained for multiple tasks). We measure deployment cost as the amount of energy and carbon required to perform 1,000 inferences on representative benchmark dataset using these models. We find that multi-purpose, generative architectures are orders of magnitude more expensive than task-specific systems for a variety of tasks, even when controlling for the number of model parameters. We conclude with a discussion around the current trend of deploying multi-purpose generative ML systems, and caution that their utility should be more intentionally weighed against increased costs in terms of energy and emissions. All the data from our study can be accessed via an interactive demo to carry out further exploration and analysis.

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy function into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.

This paper studies generative flow networks (GFlowNets) to sample objects from the Boltzmann energy distribution via a sequence of actions. In particular, we focus on improving GFlowNet with partial inference: training flow functions with the evaluation of the intermediate states or transitions. To this end, the recently developed forward-looking GFlowNet reparameterizes the flow functions based on evaluating the energy of intermediate states. However, such an evaluation of intermediate energies may (i) be too expensive or impossible to evaluate and (ii) even provide misleading training signals under large energy fluctuations along the sequence of actions. To resolve this issue, we propose learning energy decompositions for GFlowNets (LED-GFN). Our main idea is to (i) decompose the energy of an object into learnable potential functions defined on state transitions and (ii) reparameterize the flow functions using the potential functions. In particular, to produce informative local credits, we propose to regularize the potential to change smoothly over the sequence of actions. It is also noteworthy that training GFlowNet with our learned potential can preserve the optimal policy. We empirically verify the superiority of LED-GFN in five problems including the generation of unstructured and maximum independent sets, molecular graphs, and RNA sequences.

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

We propose to reinterpret a standard discriminative classifier of p(y|x) as an energy based model for the joint distribution p(x,y). In this setting, the standard class probabilities can be easily computed as well as unnormalized values of p(x) and p(x|y). Within this framework, standard discriminative architectures may beused and the model can also be trained on unlabeled data. We demonstrate that energy based training of the joint distribution improves calibration, robustness, andout-of-distribution detection while also enabling our models to generate samplesrivaling the quality of recent GAN approaches. We improve upon recently proposed techniques for scaling up the training of energy based models and presentan approach which adds little overhead compared to standard classification training. Our approach is the first to achieve performance rivaling the state-of-the-artin both generative and discriminative learning within one hybrid model.

The computing demand of AI is growing at an unprecedented rate, but energy supply is not keeping pace. As a result, energy has become an expensive, contended resource that requires explicit management and optimization. Although recent works have made significant progress in large model training optimization, they focus only on a single aspect of energy consumption: dynamic or static energy. We find that fine-grained kernel scheduling and frequency scaling jointly and interdependently impact both dynamic and static energy consumption. Based on this finding, we design Kareus, a training system that pushes the time--energy tradeoff frontier by optimizing both aspects. Kareus decomposes the intractable joint optimization problem into local, partition-based subproblems. It then uses a multi-pass multi-objective optimization algorithm to find execution schedules that push the time--energy tradeoff frontier. Compared to the state of the art, Kareus reduces training energy by up to 28.3% at the same training time, or reduces training time by up to 27.5% at the same energy consumption.

Large Language Models (LLMs) are becoming integral to daily life, showcasing their vast potential across various Natural Language Processing (NLP) tasks. Beyond NLP, LLMs are increasingly used in software development tasks, such as code completion, modification, bug fixing, and code translation. Software engineers widely use tools like GitHub Copilot and Amazon Q, streamlining workflows and automating tasks with high accuracy. While the resource and energy intensity of LLM training is often highlighted, inference can be even more resource-intensive over time, as it's a continuous process with a high number of invocations. Therefore, developing resource-efficient alternatives for LLM inference is crucial for sustainability. This work proposes GREEN-CODE, a framework for energy-aware code generation in LLMs. GREEN-CODE performs dynamic early exit during LLM inference. We train a Reinforcement Learning (RL) agent that learns to balance the trade-offs between accuracy, latency, and energy consumption. Our approach is evaluated on two open-source LLMs, Llama 3.2 3B and OPT 2.7B, using the JavaCorpus and PY150 datasets. Results show that our method reduces the energy consumption between 23-50 % on average for code generation tasks without significantly affecting accuracy.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

Energy-Based Models (EBMs) have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a comprehensive understanding of EBMs, delineating their connection to other generative models such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and Normalizing Flows. We explore the sampling techniques crucial for EBMs, including Markov Chain Monte Carlo (MCMC) methods, and draw parallels between EBM concepts and statistical mechanics, highlighting the significance of energy functions and partition functions. Furthermore, we delve into state-of-the-art training methodologies for EBMs, covering recent advancements and their implications for enhanced model performance and efficiency. This review is designed to clarify the often complex interconnections between these models, which can be challenging due to the diverse communities working on the topic.

The scaling-law era has transformed artificial intelligence (AI) from research into a global industry, but its rapid growth also raises concerns over energy usage, carbon emissions, and environmental sustainability. Unlike traditional sectors, the AI industry still lacks systematic carbon accounting methods that support large-scale estimates without reproducing the original training process. This leaves open questions about how large the problem is today and how large it might be in the near future. Given its central role in hosting open-source AI models, the Hugging Face (HF) platform provides a large-scale and publicly accessible corpus for carbon accounting. We estimate aggregate training emissions of HF open-source models using available emissions, energy, compute, and model metadata. To address uneven disclosure quality, we introduce a tiered approach to handle incomplete metadata, supported by empirical regressions that assess estimation reliability. We further introduce AI training carbon intensity (ATCI, emissions per compute), a metric to assess the sustainability efficiency of model training. Our results show that training the most popular open-source models (with over 5,000 downloads) has already resulted in approximately 6.0times10^4 metric tons of carbon emissions. Overall, this paper provides a scalable, empirically grounded framework for estimating training emissions from incomplete disclosures and informing future carbon reporting standards in the AI industry. Data and code are available at https://github.com/insait-institute/HuggingCarbon.

Diffusion models may be formulated as a time-indexed sequence of energy-based models, where the score corresponds to the negative gradient of an energy function. As opposed to learning the score directly, an energy parameterization is attractive as the energy itself can be used to control generation via Monte Carlo samplers. Architectural constraints and training instability in energy parameterized models have so far yielded inferior performance compared to directly approximating the score or denoiser. We address these deficiencies by introducing a novel training regime for the energy function through distillation of pre-trained diffusion models, resembling a Helmholtz decomposition of the score vector field. We further showcase the synergies between energy and score by casting the diffusion sampling procedure as a Feynman Kac model where sampling is controlled using potentials from the learnt energy functions. The Feynman Kac model formalism enables composition and low temperature sampling through sequential Monte Carlo.

Scalable and cost-effective solutions to renewable energy storage are essential to addressing the world's rising energy needs while reducing climate change. As we increase our reliance on renewable energy sources such as wind and solar, which produce intermittent power, storage is needed to transfer power from times of peak generation to peak demand. This may require the storage of power for hours, days, or months. One solution that offers the potential of scaling to nation-sized grids is the conversion of renewable energy to other fuels, such as hydrogen or methane. To be widely adopted, this process requires cost-effective solutions to running electrochemical reactions. An open challenge is finding low-cost electrocatalysts to drive these reactions at high rates. Through the use of quantum mechanical simulations (density functional theory), new catalyst structures can be tested and evaluated. Unfortunately, the high computational cost of these simulations limits the number of structures that may be tested. The use of machine learning may provide a method to efficiently approximate these calculations, leading to new approaches in finding effective electrocatalysts. In this paper, we provide an introduction to the challenges in finding suitable electrocatalysts, how machine learning may be applied to the problem, and the use of the Open Catalyst Project OC20 dataset for model training.

Industrial Non-Intrusive Load Monitoring (NILM) is limited by the scarcity of high-quality datasets and the complex variability of industrial energy consumption patterns. To address data scarcity and privacy issues, we introduce the Synthetic Industrial Dataset for Energy Disaggregation (SIDED), an open-source dataset generated using Digital Twin simulations. SIDED includes three types of industrial facilities across three different geographic locations, capturing diverse appliance behaviors, weather conditions, and load profiles. We also propose the Appliance-Modulated Data Augmentation (AMDA) method, a computationally efficient technique that enhances NILM model generalization by intelligently scaling appliance power contributions based on their relative impact. We show in experiments that NILM models trained with AMDA-augmented data significantly improve the disaggregation of energy consumption of complex industrial appliances like combined heat and power systems. Specifically, in our out-of-sample scenarios, models trained with AMDA achieved a Normalized Disaggregation Error of 0.093, outperforming models trained without data augmentation (0.451) and those trained with random data augmentation (0.290). Data distribution analyses confirm that AMDA effectively aligns training and test data distributions, enhancing model generalization.

Calorie and nutrition research has attained increased interest in recent years. But, due to the complexity of the problem, literature in this area focuses on a limited subset of ingredients or dish types and simple convolutional neural networks or traditional machine learning. Simultaneously, estimation of ingredient portions can help improve calorie estimation and meal re-production from a given image. In this paper, given a single cooking image, a pipeline for calorie estimation and meal re-production for different servings of the meal is proposed. The pipeline contains two stages. In the first stage, a set of ingredients associated with the meal in the given image are predicted. In the second stage, given image features and ingredients, portions of the ingredients and finally the total meal calorie are simultaneously estimated using a deep transformer-based model. Portion estimation introduced in the model helps improve calorie estimation and is also beneficial for meal re-production in different serving sizes. To demonstrate the benefits of the pipeline, the model can be used for meal kits generation. To evaluate the pipeline, the large scale dataset Recipe1M is used. Prior to experiments, the Recipe1M dataset is parsed and explicitly annotated with portions of ingredients. Experiments show that using ingredients and their portions significantly improves calorie estimation. Also, a visual interface is created in which a user can interact with the pipeline to reach accurate calorie estimations and generate a meal kit for cooking purposes.

LLM inference is still evaluated mainly as a model or software problem: accuracy, latency, throughput, and hardware utilization. This is incomplete. At deployment scale, the relevant output is a quality-conditioned token produced under joint constraints from effective compute, delivered data-center power, cooling capacity, PUE, and utilization. We argue that the ML community should treat inference as energy-to-token production. We formalize this view with a dimensionally consistent Token Production Function in which token rate is bounded by both compute-per-token and energy-per-token ceilings. Listed API prices vary by over an order of magnitude across providers, but we use price dispersion only as directional motivation, not as causal evidence of marginal cost. The core physical question is instead: under fixed quality and service targets, when does the binding constraint move from theoretical peak compute toward delivered power, cooling, and operational efficiency? Under this framing, system optimizations -- latent KV-cache compression, sparse or heavily compressed attention, quantization, routing, and difficulty-adaptive reasoning -- are not merely local engineering tricks. They are energy-to-token levers because they reduce FLOPs/token, joules/token, memory traffic, or utilization losses under fixed (q^{*},s^{*}). We therefore call for inference papers and benchmarks to report Joules/token, active binding constraint, PUE-adjusted delivered power, and utilization-adjusted token output alongside accuracy and latency.

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution -- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and pathfinding in larger graphs. Key to our method's success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios. Code and visualizations at https://energy-based-model.github.io/ired/

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power system dynamics, primarily because of limitations in encoding the grid topology and sparse measurements. This paper proposes a physics-informed graphical learning state estimation method to address these limitations by leveraging both domain physical knowledge and a graph neural network (GNN). We employ a GNN architecture that can handle the graph-structured data of power systems more effectively than traditional data-driven methods. The physics-based knowledge is constructed from the branch current formulation, making the approach adaptable to both transmission and distribution systems. The validation results of three IEEE test systems show that the proposed method can achieve lower mean square error more than 20% than the conventional methods.

By reinterpreting a robust discriminative classifier as Energy-based Model (EBM), we offer a new take on the dynamics of adversarial training (AT). Our analysis of the energy landscape during AT reveals that untargeted attacks generate adversarial images much more in-distribution (lower energy) than the original data from the point of view of the model. Conversely, we observe the opposite for targeted attacks. On the ground of our thorough analysis, we present new theoretical and practical results that show how interpreting AT energy dynamics unlocks a better understanding: (1) AT dynamic is governed by three phases and robust overfitting occurs in the third phase with a drastic divergence between natural and adversarial energies (2) by rewriting the loss of TRadeoff-inspired Adversarial DEfense via Surrogate-loss minimization (TRADES) in terms of energies, we show that TRADES implicitly alleviates overfitting by means of aligning the natural energy with the adversarial one (3) we empirically show that all recent state-of-the-art robust classifiers are smoothing the energy landscape and we reconcile a variety of studies about understanding AT and weighting the loss function under the umbrella of EBMs. Motivated by rigorous evidence, we propose Weighted Energy Adversarial Training (WEAT), a novel sample weighting scheme that yields robust accuracy matching the state-of-the-art on multiple benchmarks such as CIFAR-10 and SVHN and going beyond in CIFAR-100 and Tiny-ImageNet. We further show that robust classifiers vary in the intensity and quality of their generative capabilities, and offer a simple method to push this capability, reaching a remarkable Inception Score (IS) and FID using a robust classifier without training for generative modeling. The code to reproduce our results is available at http://github.com/OmnAI-Lab/Robust-Classifiers-under-the-lens-of-EBM/ .

Inference-time computation techniques, analogous to human System 2 Thinking, have recently become popular for improving model performances. However, most existing approaches suffer from several limitations: they are modality-specific (e.g., working only in text), problem-specific (e.g., verifiable domains like math and coding), or require additional supervision/training on top of unsupervised pretraining (e.g., verifiers or verifiable rewards). In this paper, we ask the question "Is it possible to generalize these System 2 Thinking approaches, and develop models that learn to think solely from unsupervised learning?" Interestingly, we find the answer is yes, by learning to explicitly verify the compatibility between inputs and candidate-predictions, and then re-framing prediction problems as optimization with respect to this verifier. Specifically, we train Energy-Based Transformers (EBTs) -- a new class of Energy-Based Models (EBMs) -- to assign an energy value to every input and candidate-prediction pair, enabling predictions through gradient descent-based energy minimization until convergence. Across both discrete (text) and continuous (visual) modalities, we find EBTs scale faster than the dominant Transformer++ approach during training, achieving an up to 35% higher scaling rate with respect to data, batch size, parameters, FLOPs, and depth. During inference, EBTs improve performance with System 2 Thinking by 29% more than the Transformer++ on language tasks, and EBTs outperform Diffusion Transformers on image denoising while using fewer forward passes. Further, we find that EBTs achieve better results than existing models on most downstream tasks given the same or worse pretraining performance, suggesting that EBTs generalize better than existing approaches. Consequently, EBTs are a promising new paradigm for scaling both the learning and thinking capabilities of models.

Energy efficiency of Convolutional Neural Networks (CNNs) has become an important area of research, with various strategies being developed to minimize the power consumption of these models. Previous efforts, including techniques like model pruning, quantization, and hardware optimization, have made significant strides in this direction. However, there remains a need for more effective on device AI solutions that balance energy efficiency with model performance. In this paper, we propose a novel approach to reduce the energy requirements of inference of CNNs. Our methodology employs two small Complementary CNNs that collaborate with each other by covering each other's "weaknesses" in predictions. If the confidence for a prediction of the first CNN is considered low, the second CNN is invoked with the aim of producing a higher confidence prediction. This dual-CNN setup significantly reduces energy consumption compared to using a single large deep CNN. Additionally, we propose a memory component that retains previous classifications for identical inputs, bypassing the need to re-invoke the CNNs for the same input, further saving energy. Our experiments on a Jetson Nano computer demonstrate an energy reduction of up to 85.8% achieved on modified datasets where each sample was duplicated once. These findings indicate that leveraging a complementary CNN pair along with a memory component effectively reduces inference energy while maintaining high accuracy.

Aligning large language models with human feedback at inference time has received increasing attention due to its flexibility. Existing methods rely on generating multiple responses from the base policy for search using a reward model, which can be considered as searching in a discrete response space. However, these methods struggle to explore informative candidates when the base policy is weak or the candidate set is small, resulting in limited effectiveness. In this paper, to address this problem, we propose Simple Energy Adaptation (SEA), a simple yet effective algorithm for inference-time alignment. In contrast to expensive search over the discrete space, SEA directly adapts original responses from the base policy toward the optimal one via gradient-based sampling in continuous latent space. Specifically, SEA formulates inference as an iterative optimization procedure on an energy function over actions in the continuous space defined by the optimal policy, enabling simple and effective alignment. For instance, despite its simplicity, SEA outperforms the second-best baseline with a relative improvement of up to 77.51% on AdvBench and 16.36% on MATH. Our code is publicly available at https://github.com/yuanyige/sea

This paper presents a machine-learning study for solar inverter power regulation in a remote microgrid. Machine learning models for active and reactive power control are respectively trained using an ensemble learning method. Then, unlike conventional schemes that make inferences on a central server in the far-end control center, the proposed scheme deploys the trained models on an embedded edge-computing device near the inverter to reduce the communication delay. Experiments on a real embedded device achieve matched results as on the desktop PC, with about 0.1ms time cost for each inference input.

The transformative power of AI is undeniable - but as user adoption accelerates, so does the need to understand and mitigate the environmental impact of AI serving. However, no studies have measured AI serving environmental metrics in a production environment. This paper addresses this gap by proposing and executing a comprehensive methodology for measuring the energy usage, carbon emissions, and water consumption of AI inference workloads in a large-scale, AI production environment. Our approach accounts for the full stack of AI serving infrastructure - including active AI accelerator power, host system energy, idle machine capacity, and data center energy overhead. Through detailed instrumentation of Google's AI infrastructure for serving the Gemini AI assistant, we find the median Gemini Apps text prompt consumes 0.24 Wh of energy - a figure substantially lower than many public estimates. We also show that Google's software efficiency efforts and clean energy procurement have driven a 33x reduction in energy consumption and a 44x reduction in carbon footprint for the median Gemini Apps text prompt over one year. We identify that the median Gemini Apps text prompt uses less energy than watching nine seconds of television (0.24 Wh) and consumes the equivalent of five drops of water (0.26 mL). While these impacts are low compared to other daily activities, reducing the environmental impact of AI serving continues to warrant important attention. Towards this objective, we propose that a comprehensive measurement of AI serving environmental metrics is critical for accurately comparing models, and to properly incentivize efficiency gains across the full AI serving stack.

Accurate battery capacity estimation is key to alleviating consumer concerns about battery performance and reliability of electric vehicles (EVs). However, practical data limitations imposed by stringent privacy regulations and labeled data shortages hamper the development of generalizable capacity estimation models that remain robust to real-world data distribution shifts. While self-supervised learning can leverage unlabeled data, existing techniques are not particularly designed to learn effectively from challenging field data -- let alone from privacy-friendly data, which are often less feature-rich and noisier. In this work, we propose a first-of-its-kind capacity estimation model based on self-supervised pre-training, developed on a large-scale dataset of privacy-friendly charging data snippets from real-world EV operations. Our pre-training framework, snippet similarity-weighted masked input reconstruction, is designed to learn rich, generalizable representations even from less feature-rich and fragmented privacy-friendly data. Our key innovation lies in harnessing contrastive learning to first capture high-level similarities among fragmented snippets that otherwise lack meaningful context. With our snippet-wise contrastive learning and subsequent similarity-weighted masked reconstruction, we are able to learn rich representations of both granular charging patterns within individual snippets and high-level associative relationships across different snippets. Bolstered by this rich representation learning, our model consistently outperforms state-of-the-art baselines, achieving 31.9% lower test error than the best-performing benchmark, even under challenging domain-shifted settings affected by both manufacturer and age-induced distribution shifts. Source code is available at https://github.com/en-research/GenEVBattery.

Non-Intrusive Load Monitoring (NILM) offers a cost-effective method to obtain fine-grained appliance-level energy consumption in smart homes and building applications. However, the increasing adoption of behind-the-meter (BTM) energy sources such as solar panels and battery storage poses new challenges for conventional NILM methods that rely solely on at-the-meter data. The energy injected from the BTM sources can obscure the power signatures of individual appliances, leading to a significant decrease in NILM performance. To address this challenge, we present DualNILM, a deep multi-task learning framework designed for the dual tasks of appliance state recognition and injected energy identification. Using a Transformer-based architecture that integrates sequence-to-point and sequence-to-sequence strategies, DualNILM effectively captures multiscale temporal dependencies in the aggregate power consumption patterns, allowing for accurate appliance state recognition and energy injection identification. Extensive evaluation on self-collected and synthesized datasets demonstrates that DualNILM maintains an excellent performance for dual tasks in NILM, much outperforming conventional methods. Our work underscores the framework's potential for robust energy disaggregation in modern energy systems with renewable penetration. Synthetic photovoltaic augmented datasets with realistic injection simulation methodology are open-sourced at https://github.com/MathAdventurer/PV-Augmented-NILM-Datasets.

The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point arithmetic. However, conventional floating-point implementations can be power hungry. This paper proposes a method to improve the energy efficiency of the matrix engines used in machine learning algorithm acceleration. Our approach leverages approximate normalization within the floating-point multiply-add units as a means to reduce their hardware complexity, without sacrificing overall machine-learning model accuracy. Hardware synthesis results show that this technique reduces area and power consumption roughly by 16% and 13% on average for Bfloat16 format. Also, the error introduced in transformer model accuracy is 1% on average, for the most efficient configuration of the proposed approach.

As Software Engineering enters its new era (SE 3.0), AI coding agents increasingly automate software development workflows. However, it remains unclear how exactly these agents recognize and address software energy concerns-an issue growing in importance due to large-scale data centers, energy-hungry language models, and battery-constrained devices. In this paper, we examined the energy awareness of agent-authored pull requests (PRs) using a publicly available dataset. We identified 216 energy-explicit PRs and conducted a thematic analysis, deriving a taxonomy of energy-aware work. Our further analysis of the applied optimization techniques shows that most align with established research recommendations. Although building and running these agents is highly energy intensive, encouragingly, the results indicate that they exhibit energy awareness when generating software artifacts. However, optimization-related PRs are accepted less frequently than others, largely due to their negative impact on maintainability.

Training large AI models on numerous GPUs consumes a massive amount of energy. We observe that not all energy consumed during training directly contributes to end-to-end training throughput, and a significant portion can be removed without slowing down training, which we call energy bloat. In this work, we identify two independent sources of energy bloat in large model training, intrinsic and extrinsic, and propose Perseus, a unified optimization framework that mitigates both. Perseus obtains the "iteration time-energy" Pareto frontier of any large model training job using an efficient iterative graph cut-based algorithm and schedules energy consumption of its forward and backward computations across time to remove intrinsic and extrinsic energy bloat. Evaluation on large models like GPT-3 and Bloom shows that Perseus reduces energy consumption of large model training by up to 30%, enabling savings otherwise unobtainable before.

Urban Building Energy Modeling plays a critical role in achieving the United Nations' Sustainable Development Goals 7 and 11. Although existing studies based on satellite imagery and deep learning have achieved remarkable progress, many challenges exist: most existing studies are inherently predictive, failing to reflect the generative nature of urban planning; although generative AI and diffusion models have seen explosive growth in satellite imagery, they lack the urban functional generation (e.g., energy layer); third, aligned high-quality high-resolution building energy data with satellite imagery is limited and scarce. Here we propose SENSE (Satellite-based ENergy Synthesis for Sustainable Environment), a unified generative UBEM framework that jointly synthesizes realistic urban satellite imagery and aligned high-quality building energy consumption and height maps. By conditioning on road networks and urban density metrics, SENSE, based on a controllable diffusion model, leverages the knowledge learned by large vision models to generate urban building energy consumption and height information (annotations) in the latent space. Experiments across four cities (New York City, Boston, Lyon, Busan) demonstrate that SENSE achieves high visual fidelity and strong physical consistency, satisfying the ASHRAE standard metric. Experiments demonstrate that SENSE can generate enough annotated synthetic data using less than 20% labeled energy data, boosting downstream prediction performance by 10% IoU. Compared to SOTA urban energy prediction methods, SENSE significantly reduced prediction error (reduced 3%-11% NMBE and 1%-9% CVRMSE). This study offers an energy-efficiency urban planning and physical generation solution for urban science, energy science and building science. The dataset and code: https://huggingface.co/datasets/skl24/MUSE and https://github.com/kailaisun/GenAI4Urban-Energy/.

Achieving stable and energy-efficient locomotion is essential for humanoid robots to operate continuously in real-world applications. Existing MPC and RL approaches often rely on energy-related metrics embedded within a multi-objective optimization framework, which require extensive hyperparameter tuning and often result in suboptimal policies. To address these challenges, we propose ECO (Energy-Constrained Optimization), a constrained RL framework that separates energy-related metrics from rewards, reformulating them as explicit inequality constraints. This method provides a clear and interpretable physical representation of energy costs, enabling more efficient and intuitive hyperparameter tuning for improved energy efficiency. ECO introduces dedicated constraints for energy consumption and reference motion, enforced by the Lagrangian method, to achieve stable, symmetric, and energy-efficient walking for humanoid robots. We evaluated ECO against MPC, standard RL with reward shaping, and four state-of-the-art constrained RL methods. Experiments, including sim-to-sim and sim-to-real transfers on the kid-sized humanoid robot BRUCE, demonstrate that ECO significantly reduces energy consumption compared to baselines while maintaining robust walking performance. These results highlight a substantial advancement in energy-efficient humanoid locomotion. All experimental demonstrations can be found on the project website: https://sites.google.com/view/eco-humanoid.

We present a technique for translating a black-box machine-learned classifier operating on a high-dimensional input space into a small set of human-interpretable observables that can be combined to make the same classification decisions. We iteratively select these observables from a large space of high-level discriminants by finding those with the highest decision similarity relative to the black box, quantified via a metric we introduce that evaluates the relative ordering of pairs of inputs. Successive iterations focus only on the subset of input pairs that are misordered by the current set of observables. This method enables simplification of the machine-learning strategy, interpretation of the results in terms of well-understood physical concepts, validation of the physical model, and the potential for new insights into the nature of the problem itself. As a demonstration, we apply our approach to the benchmark task of jet classification in collider physics, where a convolutional neural network acting on calorimeter jet images outperforms a set of six well-known jet substructure observables. Our method maps the convolutional neural network into a set of observables called energy flow polynomials, and it closes the performance gap by identifying a class of observables with an interesting physical interpretation that has been previously overlooked in the jet substructure literature.

The evaluation of large language models is a complex task, in which several approaches have been proposed. The most common is the use of automated benchmarks in which LLMs have to answer multiple-choice questions of different topics. However, this method has certain limitations, being the most concerning, the poor correlation with the humans. An alternative approach, is to have humans evaluate the LLMs. This poses scalability issues as there is a large and growing number of models to evaluate making it impractical (and costly) to run traditional studies based on recruiting a number of evaluators and having them rank the responses of the models. An alternative approach is the use of public arenas, such as the popular LM arena, on which any user can freely evaluate models on any question and rank the responses of two models. The results are then elaborated into a model ranking. An increasingly important aspect of LLMs is their energy consumption and, therefore, evaluating how energy awareness influences the decisions of humans in selecting a model is of interest. In this paper, we present GEA, the Generative Energy Arena, an arena that incorporates information on the energy consumption of the model in the evaluation process. Preliminary results obtained with GEA are also presented, showing that for most questions, when users are aware of the energy consumption, they favor smaller and more energy efficient models. This suggests that for most user interactions, the extra cost and energy incurred by the more complex and top-performing models do not provide an increase in the perceived quality of the responses that justifies their use.

Energy-based models (EBMs) implement inference as gradient descent on a learned Lyapunov function, yielding interpretable, structure-preserving alternatives to black-box neural ODEs and aligning naturally with physical AI. Yet their use in system identification remains limited, and existing architectures lack formal stability guarantees that globally preclude unstable modes. We address this gap by introducing an EBM framework for system identification with stable, dissipative, absorbing invariant dynamics. Unlike classical global Lyapunov stability, absorbing invariance expands the class of stability-preserving architectures, enabling more flexible and expressive EBMs. We extend EBM theory to nonsmooth activations by establishing negative energy dissipation via Clarke derivatives and deriving new conditions for radial unboundedness, exposing a stability-expressivity tradeoff in standard EBMs. To overcome this, we introduce a hybrid architecture with a dynamical visible layer and static hidden layers, prove absorbing invariance under mild assumptions, and show that these guarantees extend to port-Hamiltonian EBMs. Experiments on metric-deformed multi-well and ring systems validate the approach, showcasing how our hybrid EBM architecture combines expressivity with sound and provable safety guarantees by design.

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross-validation over more than seven thousand small organic molecules yields a mean absolute error of ~10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

Machine learning inference occurs at a massive scale, yet its environmental impact remains poorly quantified, especially on low-resource hardware. We present ML-EcoLyzer, a cross-framework tool for measuring the carbon, energy, thermal, and water costs of inference across CPUs, consumer GPUs, and datacenter accelerators. The tool supports both classical and modern models, applying adaptive monitoring and hardware-aware evaluation. We introduce the Environmental Sustainability Score (ESS), which quantifies the number of effective parameters served per gram of CO_2 emitted. Our evaluation covers over 1,900 inference configurations, spanning diverse model architectures, task modalities (text, vision, audio, tabular), hardware types, and precision levels. These rigorous and reliable measurements demonstrate that quantization enhances ESS, huge accelerators can be inefficient for lightweight applications, and even small models may incur significant costs when implemented suboptimally. ML-EcoLyzer sets a standard for sustainability-conscious model selection and offers an extensive empirical evaluation of environmental costs during inference.

Energy disaggregation estimates appliance-by-appliance electricity consumption from a single meter that measures the whole home's electricity demand. Recently, deep neural networks have driven remarkable improvements in classification performance in neighbouring machine learning fields such as image classification and automatic speech recognition. In this paper, we adapt three deep neural network architectures to energy disaggregation: 1) a form of recurrent neural network called `long short-term memory' (LSTM); 2) denoising autoencoders; and 3) a network which regresses the start time, end time and average power demand of each appliance activation. We use seven metrics to test the performance of these algorithms on real aggregate power data from five appliances. Tests are performed against a house not seen during training and against houses seen during training. We find that all three neural nets achieve better F1 scores (averaged over all five appliances) than either combinatorial optimisation or factorial hidden Markov models and that our neural net algorithms generalise well to an unseen house.

We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as the Hessian-Riemannian and natural gradient descent methods. More specifically, we incorporate these preconditioned gradient descent algorithms in the recently introduced Adaptive Energy Gradient Descent (AEGD) framework. In particular, we discuss theoretical results on the unconditional energy-stability and convergence rates across three classes of objective functions. Furthermore, our numerical results demonstrate excellent performance of the proposed method on several test bed optimization problems.

Machine learning potentials (MLPs) have become essential for large-scale atomistic simulations, enabling ab initio-level accuracy with computational efficiency. However, current MLPs struggle with uncertainty quantification, limiting their reliability for active learning, calibration, and out-of-distribution (OOD) detection. We address these challenges by developing Bayesian E(3) equivariant MLPs with iterative restratification of many-body message passing. Our approach introduces the joint energy-force negative log-likelihood (NLL_JEF) loss function, which explicitly models uncertainty in both energies and interatomic forces, yielding superior accuracy compared to conventional NLL losses. We systematically benchmark multiple Bayesian approaches, including deep ensembles with mean-variance estimation, stochastic weight averaging Gaussian, improved variational online Newton, and laplace approximation by evaluating their performance on uncertainty prediction, OOD detection, calibration, and active learning tasks. We further demonstrate that NLL_JEF facilitates efficient active learning by quantifying energy and force uncertainties. Using Bayesian active learning by disagreement (BALD), our framework outperforms random sampling and energy-uncertainty-based sampling. Our results demonstrate that Bayesian MLPs achieve competitive accuracy with state-of-the-art models while enabling uncertainty-guided active learning, OOD detection, and energy/forces calibration. This work establishes Bayesian equivariant neural networks as a powerful framework for developing uncertainty-aware MLPs for atomistic simulations at scale.

We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The approach builds on the fundamental feature that every observable property of a quantum system must evolve according to the same harmonic components: we can reveal them by post-processing classical shadows of time-evolved quantum states to extract a large number of time-periodic signals N_opropto 10^8, whose frequencies correspond to Hamiltonian energy differences with Heisenberg-limited precision. We provide strong analytical guarantees that (a) quantum resources scale as O(log N_o), while the classical computational complexity is linear O(N_o), (b) the signal-to-noise ratio increases with the number of processed signals as propto N_o, and (c) spectral peak positions are immune to reasonable levels of noise. We demonstrate our approach on model spin systems and the excited state conical intersection of molecular CH_2 and verify that our method is indeed intuitively easy to use in practice, robust against gate noise, amiable to a new type of algorithmic-error mitigation technique, and uses orders of magnitude fewer number of shots than typical near-term quantum algorithms -- as low as 10 shots per timestep is sufficient. Finally, we measured a high-quality, experimental shadow spectrum of a spin chain on readily-available IBM quantum computers, achieving the same precision as in noise-free simulations without using any advanced error mitigation, and verified scalability in tensor-network simulations of up to 100-qubit systems.

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of magnitude while preserving the accuracy of the underlying theory, with the gain depending on oracle cost, search distance, and the availability of analytical forces. We present a unified Bayesian optimization view of minimization, single-point saddle searches, and double-ended path searches: all three share one six-step surrogate loop and differ only in the inner optimization target and the acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning, and we develop optional extensions for production use, including farthest-point sampling with the Earth Mover's Distance, MAP regularization, an adaptive trust radius, and random Fourier features for scaling. Accompanying pedagogical Rust code demonstrates that all three applications use the same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.

Recent progress in hardware and methodology for training neural networks has ushered in a new generation of large networks trained on abundant data. These models have obtained notable gains in accuracy across many NLP tasks. However, these accuracy improvements depend on the availability of exceptionally large computational resources that necessitate similarly substantial energy consumption. As a result these models are costly to train and develop, both financially, due to the cost of hardware and electricity or cloud compute time, and environmentally, due to the carbon footprint required to fuel modern tensor processing hardware. In this paper we bring this issue to the attention of NLP researchers by quantifying the approximate financial and environmental costs of training a variety of recently successful neural network models for NLP. Based on these findings, we propose actionable recommendations to reduce costs and improve equity in NLP research and practice.

Progress in machine learning (ML) comes with a cost to the environment, given that training ML models requires significant computational resources, energy and materials. In the present article, we aim to quantify the carbon footprint of BLOOM, a 176-billion parameter language model, across its life cycle. We estimate that BLOOM's final training emitted approximately 24.7 tonnes of~\carboneq~if we consider only the dynamic power consumption, and 50.5 tonnes if we account for all processes ranging from equipment manufacturing to energy-based operational consumption. We also study the energy requirements and carbon emissions of its deployment for inference via an API endpoint receiving user queries in real-time. We conclude with a discussion regarding the difficulty of precisely estimating the carbon footprint of ML models and future research directions that can contribute towards improving carbon emissions reporting.

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any non-negative integer D for the total number of nestings. Standard Monte Carlo methods typically cost at least O(varepsilon^{-(2+D)}) and sometimes O(varepsilon^{-2(1+D)}) to obtain an estimator up to varepsilon-error. More advanced methods, such as multilevel Monte Carlo, currently only exist for D = 1. In this paper, we propose a novel Monte Carlo estimator called READ, which stands for "Recursive Estimator for Arbitrary Depth.'' Our estimator has an optimal computational cost of O(varepsilon^{-2}) for every fixed D under suitable assumptions, and a nearly optimal computational cost of O(varepsilon^{-2(1 + delta)}) for any 0 < delta < frac12 under much more general assumptions. Our estimator is also unbiased, which makes it easy to parallelize. The key ingredients in our construction are an observation of the problem's recursive structure and the recursive use of the randomized multilevel Monte Carlo method.

The introduction of fifth-generation (5G) radio technology has revolutionized communications, bringing unprecedented automation, capacity, connectivity, and ultra-fast, reliable communications. However, this technological leap comes with a substantial increase in energy consumption, presenting a significant challenge. To improve the energy efficiency of 5G networks, it is imperative to develop sophisticated models that accurately reflect the influence of base station (BS) attributes and operational conditions on energy usage.Importantly, addressing the complexity and interdependencies of these diverse features is particularly challenging, both in terms of data processing and model architecture design. This paper proposes a novel 5G base stations energy consumption modelling method by learning from a real-world dataset used in the ITU 5G Base Station Energy Consumption Modelling Challenge in which our model ranked second. Unlike existing methods that omit the Base Station Identifier (BSID) information and thus fail to capture the unique energy fingerprint in different base stations, we incorporate the BSID into the input features and encoding it with an embedding layer for precise representation. Additionally, we introduce a novel masked training method alongside an attention mechanism to further boost the model's generalization capabilities and accuracy. After evaluation, our method demonstrates significant improvements over existing models, reducing Mean Absolute Percentage Error (MAPE) from 12.75% to 4.98%, leading to a performance gain of more than 60%.

One of the predominant methods for training world models is autoregressive prediction in the output space of the next element of a sequence. In Natural Language Processing (NLP), this takes the form of Large Language Models (LLMs) predicting the next token; in Computer Vision (CV), this takes the form of autoregressive models predicting the next frame/token/pixel. However, this approach differs from human cognition in several respects. First, human predictions about the future actively influence internal cognitive processes. Second, humans naturally evaluate the plausibility of predictions regarding future states. Based on this capability, and third, by assessing when predictions are sufficient, humans allocate a dynamic amount of time to make a prediction. This adaptive process is analogous to System 2 thinking in psychology. All these capabilities are fundamental to the success of humans at high-level reasoning and planning. Therefore, to address the limitations of traditional autoregressive models lacking these human-like capabilities, we introduce Energy-Based World Models (EBWM). EBWM involves training an Energy-Based Model (EBM) to predict the compatibility of a given context and a predicted future state. In doing so, EBWM enables models to achieve all three facets of human cognition described. Moreover, we developed a variant of the traditional autoregressive transformer tailored for Energy-Based models, termed the Energy-Based Transformer (EBT). Our results demonstrate that EBWM scales better with data and GPU Hours than traditional autoregressive transformers in CV, and that EBWM offers promising early scaling in NLP. Consequently, this approach offers an exciting path toward training future models capable of System 2 thinking and intelligently searching across state spaces.

We motivate Energy-Based Models (EBMs) as a promising model class for continual learning problems. Instead of tackling continual learning via the use of external memory, growing models, or regularization, EBMs change the underlying training objective to cause less interference with previously learned information. Our proposed version of EBMs for continual learning is simple, efficient, and outperforms baseline methods by a large margin on several benchmarks. Moreover, our proposed contrastive divergence-based training objective can be combined with other continual learning methods, resulting in substantial boosts in their performance. We further show that EBMs are adaptable to a more general continual learning setting where the data distribution changes without the notion of explicitly delineated tasks. These observations point towards EBMs as a useful building block for future continual learning methods.

This paper considers an aggregator of Electric Vehicles (EVs) who aims to learn the aggregate power of his/her fleet while also participating in the electricity market. The proposed approach is based on a data-driven inverse optimization (IO) method, which is highly nonlinear. To overcome such a caveat, we use a two-step estimation procedure which requires solving two convex programs. Both programs depend on penalty parameters that can be adjusted by using grid search. In addition, we propose the use of kernel regression to account for the nonlinear relationship between the behaviour of the pool of EVs and the explanatory variables, i.e., the past electricity prices and EV fleet's driving patterns. Unlike any other forecasting method, the proposed IO framework also allows the aggregator to derive a bid/offer curve, i.e. the tuple of price-quantity to be submitted to the electricity market, according to the market rules. We show the benefits of the proposed method against the machine-learning techniques that are reported to exhibit the best forecasting performance for this application in the technical literature.

Recently, machine learning Hamiltonian (MLH) models have gained traction as fast approximations of electronic structures such as orbitals and electron densities, while also enabling direct evaluation of energies and forces from their predictions. However, despite their physical grounding, existing Hamiltonian models are evaluated mainly by reconstruction metrics, leaving it unclear how well they perform as energy-force predictors. We address this gap with a benchmark that computes energies and forces directly from predicted Hamiltonians. Within this framework, we propose QHFlow2, a state-of-the-art Hamiltonian model with an SO(2)-equivariant backbone and a two-stage edge update. QHFlow2 achieves 40% lower Hamiltonian error than the previous best model with fewer parameters. Under direct evaluation on MD17/rMD17, it is the first Hamiltonian model to reach NequIP-level force accuracy while achieving up to 20times lower energy MAE. On QH9, QHFlow2 reduces energy error by up to 20times compared to MACE. Finally, we demonstrate that QHFlow2 exhibits consistent scaling behavior with respect to model capacity and data, and that improvements in Hamiltonian accuracy effectively translate into more accurate energy and force computations.

Internet of Things (IoT) applications have opened up numerous possibilities to improve our lives. Most of the remote devices, part of the IoT network, such as smartphones, data loggers and wireless sensors are battery powered. It is vital to collect battery measurement data (Voltage or State-of-Charge (SOC)) from these remote devices. Presence of noise in these measurements restricts effective utilization of this dataset. This paper presents the application of Unscented Kalman Filter (UKF) to mitigate measurement noise in smartphone dataset. The simplicity of this technique makes it a constructive approach for noise removal. The datasets obtained after noise removal could be used to improve data-driven time series forecasting models which aid to accurately estimate critical battery parameters such as SOC. UKF was tested on noisy charge and discharge dataset of a smartphone. An overall Mean Squared Error (MSE) of 0.0017 and 0.0010 was obtained for Voltage charge and discharge measurements. MSE for SOC charge and discharge data measurements were 0.0018 and 0.0010 respectively.

Accelerating material discovery holds the potential to greatly help mitigate the climate crisis. Discovering new solid-state materials such as electrocatalysts, super-ionic conductors or photovoltaic materials can have a crucial impact, for instance, in improving the efficiency of renewable energy production and storage. In this paper, we introduce Crystal-GFN, a generative model of crystal structures that sequentially samples structural properties of crystalline materials, namely the space group, composition and lattice parameters. This domain-inspired approach enables the flexible incorporation of physical and structural hard constraints, as well as the use of any available predictive model of a desired physicochemical property as an objective function. To design stable materials, one must target the candidates with the lowest formation energy. Here, we use as objective the formation energy per atom of a crystal structure predicted by a new proxy machine learning model trained on MatBench. The results demonstrate that Crystal-GFN is able to sample highly diverse crystals with low (median -3.1 eV/atom) predicted formation energy.

Large language model (LLM) queries are predominantly processed by frontier models in centralized cloud infrastructure. Rapidly growing demand strains this paradigm, and cloud providers struggle to scale infrastructure at pace. Two advances enable us to rethink this paradigm: small LMs (<=20B active parameters) now achieve competitive performance to frontier models on many tasks, and local accelerators (e.g., Apple M4 Max) run these models at interactive latencies. This raises the question: can local inference viably redistribute demand from centralized infrastructure? Answering this requires measuring whether local LMs can accurately answer real-world queries and whether they can do so efficiently enough to be practical on power-constrained devices (i.e., laptops). We propose intelligence per watt (IPW), task accuracy divided by unit of power, as a metric for assessing capability and efficiency of local inference across model-accelerator pairs. We conduct a large-scale empirical study across 20+ state-of-the-art local LMs, 8 accelerators, and a representative subset of LLM traffic: 1M real-world single-turn chat and reasoning queries. For each query, we measure accuracy, energy, latency, and power. Our analysis reveals 3 findings. First, local LMs can accurately answer 88.7% of single-turn chat and reasoning queries with accuracy varying by domain. Second, from 2023-2025, IPW improved 5.3x and local query coverage rose from 23.2% to 71.3%. Third, local accelerators achieve at least 1.4x lower IPW than cloud accelerators running identical models, revealing significant headroom for optimization. These findings demonstrate that local inference can meaningfully redistribute demand from centralized infrastructure, with IPW serving as the critical metric for tracking this transition. We release our IPW profiling harness for systematic intelligence-per-watt benchmarking.

With the ubiquitous use of modern large language models (LLMs) across industries, the inference serving for these models is ever expanding. Given the high compute and memory requirements of modern LLMs, more and more top-of-the-line GPUs are being deployed to serve these models. Energy availability has come to the forefront as the biggest challenge for data center expansion to serve these models. In this paper, we present the trade-offs brought up by making energy efficiency the primary goal of LLM serving under performance SLOs. We show that depending on the inputs, the model, and the service-level agreements, there are several knobs available to the LLM inference provider to use for being energy efficient. We characterize the impact of these knobs on the latency, throughput, as well as the energy. By exploring these trade-offs, we offer valuable insights into optimizing energy usage without compromising on performance, thereby paving the way for sustainable and cost-effective LLM deployment in data center environments.