Daily Papers

Large language models (LLMs) with chain-of-thought reasoning have demonstrated remarkable problem-solving capabilities, but controlling their computational effort remains a significant challenge for practical deployment. Recent proprietary systems like OpenAI's gpt-oss series have introduced discrete operational modes for intuitive reasoning control, but the open-source community has largely failed to achieve such capabilities. In this paper, we introduce ThinkDial, the first open-recipe end-to-end framework that successfully implements gpt-oss-style controllable reasoning through discrete operational modes. Our system enables seamless switching between three distinct reasoning regimes: High mode (full reasoning capability), Medium mode (50 percent token reduction with <10 percent performance degradation), and Low mode (75 percent token reduction with <15 percent performance degradation). We achieve this through an end-to-end training paradigm that integrates budget-mode control throughout the entire pipeline: budget-mode supervised fine-tuning that embeds controllable reasoning capabilities directly into the learning process, and two-phase budget-aware reinforcement learning with adaptive reward shaping. Extensive experiments demonstrate that ThinkDial achieves target compression-performance trade-offs with clear response length reductions while maintaining performance thresholds. The framework also exhibits strong generalization capabilities on out-of-distribution tasks.

This paper introduces Discrete-time Hybrid Automata Learning (DHAL), a framework using on-policy Reinforcement Learning to identify and execute mode-switching without trajectory segmentation or event function learning. Hybrid dynamical systems, which include continuous flow and discrete mode switching, can model robotics tasks like legged robot locomotion. Model-based methods usually depend on predefined gaits, while model-free approaches lack explicit mode-switching knowledge. Current methods identify discrete modes via segmentation before regressing continuous flow, but learning high-dimensional complex rigid body dynamics without trajectory labels or segmentation is a challenging open problem. Our approach incorporates a beta policy distribution and a multi-critic architecture to model contact-guided motions, exemplified by a challenging quadrupedal robot skateboard task. We validate our method through simulations and real-world tests, demonstrating robust performance in hybrid dynamical systems.

Much has been said about observability in system theory and control; however, it has been recently that observability in complex networks has seriously attracted the attention of researchers. This paper examines the state-of-the-art and discusses some issues raised due to "complexity" and "stochasticity". These unresolved issues call for a new practical methodology. For stochastic systems, a degree of observability may be defined and the observability problem is not a binary (i.e., yes-no) question anymore. Here, we propose to employ a goal-seeking system to play a supervisory role in the network. Hence, improving the degree of observability would be a valid objective for the supervisory system. Towards this goal, the supervisor dynamically optimizes the observation process by reconfiguring the sensory parts in the network. A cognitive dynamic system is suggested as a proper choice for the supervisory system. In this framework, the network itself is viewed as the environment with which the cognitive dynamic system interacts. Computer experiments confirm the potential of the proposed approach for addressing some of the issues raised in networks due to complexity and stochasticity.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit intrinsic correlations over time. Capitalizing on this, we introduce Correlation Mode Decomposition (CMD). This algorithm clusters the parameter space into groups, termed modes, that display synchronized behavior across epochs. This enables CMD to efficiently represent the training dynamics of complex networks, like ResNets and Transformers, using only a few modes. Moreover, test set generalization is enhanced. We introduce an efficient CMD variant, designed to run concurrently with training. Our experiments indicate that CMD surpasses the state-of-the-art method for compactly modeled dynamics on image classification. Our modeling can improve training efficiency and lower communication overhead, as shown by our preliminary experiments in the context of federated learning.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction. The study presents a neural operator based on the dynamic mode decomposition algorithm (DMD), mapping functional spaces, which combines DMD and deep learning (DL) for spatiotemporal processes efficient modeling. Solving PDEs for various initial and boundary conditions requires significant computational resources. The method suggested automatically extracts key modes and system dynamics using them to construct predictions, reducing computational costs compared to traditional numerical methods. The approach has demonstrated its efficiency through comparative analysis of performance with closest analogues DeepONet and FNO in the heat equation, Laplaces equation, and Burgers equation solutions approximation, where it achieves high reconstruction accuracy.

We present a deployed system that automates end-to-end customer support workflows inside an enterprise Business Process Management (BPM) platform. The approach is scalable in production and reaches selective automation within two weeks for a new process, leveraging supervision already generated at scale: structured per-case UI interaction traces and low-overhead copilot feedback, where operators either accept a suggestion or provide a correction. A staged deployment pipeline trains a next UI action policy, learns a critic from copilot feedback to calibrate abstention, and executes only high-confidence steps in the background while deferring uncertain decisions to operators and resuming from the updated UI state. This setup lets one operator supervise multiple concurrent sessions and be interrupted only when the system is uncertain. The system operates on a schema-driven view of the BPM interface and includes monitoring and safe fallbacks for production. In production, it automated 45% of sessions and reduced average handling time by 39% without degrading support quality level.

Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in learning methods. Koopman operators have emerged as a dominant approach because they allow the study of nonlinear dynamics using linear techniques by solving an infinite-dimensional spectral problem. However, current algorithms face challenges such as lack of convergence, hindering practical progress. This paper addresses a fundamental open question: When can we robustly learn the spectral properties of Koopman operators from trajectory data of dynamical systems, and when can we not? Understanding these boundaries is crucial for analysis, applications, and designing algorithms. We establish a foundational approach that combines computational analysis and ergodic theory, revealing the first fundamental barriers -- universal for any algorithm -- associated with system geometry and complexity, regardless of data quality and quantity. For instance, we demonstrate well-behaved smooth dynamical systems on tori where non-trivial eigenfunctions of the Koopman operator cannot be determined by any sequence of (even randomized) algorithms, even with unlimited training data. Additionally, we identify when learning is possible and introduce optimal algorithms with verification that overcome issues in standard methods. These results pave the way for a sharp classification theory of data-driven dynamical systems based on how many limits are needed to solve a problem. These limits characterize all previous methods, presenting a unified view. Our framework systematically determines when and how Koopman spectral properties can be learned.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves and relaxation oscillations, or spatio-temporal Turing instability. Inspired from the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of some reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, the lambda-omega system and the DIB morpho-chemical system for battery modeling.

Koopman theory turns nonlinear dynamics into a linear spectral problem. In computation, however, everything depends on a hard finite-dimensional choice: the observables must be expressive, nearly invariant under the dynamics, and, ideally, compatible with composition. Deep Koopman methods learn flexible coordinates, whereas structure-preserving methods enforce operator identities on fixed dictionaries. We combine these ideas by introducing Deep Embedded Multiplicative Dynamic Mode Decomposition (DeepMDMD), a method that learns a latent space and a partition of it, while enforcing the Koopman product rule as an exact algebraic constraint. Training alternates between an exact multiplicative operator update and a differentiable latent-clustering step that promotes Koopman closure. The result is a finite transition map on learned latent cells. Its nonzero spectrum lies on the unit circle, its dictionary is shaped by the dynamics rather than by ambient geometry, and forecasts are made in latent coordinates before being decoded to physical space. Across Hamiltonian, chaotic, and fluid examples, DeepMDMD learns dictionaries that are far more compact and dynamically coherent than those produced by geometric MDMD partitions. It reduces spectral pollution, reveals richer continuous-spectrum structure, and gives stable forecasts under severe noise. In high-dimensional flows, including a 158,624-dimensional cylinder wake and a noisy Re=20,000 lid-driven cavity, it preserves coherent structures and long-time spectral statistics where state-space MDMD fails. These results suggest a practical rule for Koopman learning: learn the coordinates, constrain the algebra.

In order to bring quantum networks into the real world, we would like to determine the requirements of quantum network protocols including the underlying quantum hardware. Because detailed architecture proposals are generally too complex for mathematical analysis, it is natural to employ numerical simulation. Here we introduce NetSquid, the NETwork Simulator for QUantum Information using Discrete events, a discrete-event based platform for simulating all aspects of quantum networks and modular quantum computing systems, ranging from the physical layer and its control plane up to the application level. We study several use cases to showcase NetSquid's power, including detailed physical layer simulations of repeater chains based on nitrogen vacancy centres in diamond as well as atomic ensembles. We also study the control plane of a quantum switch beyond its analytically known regime, and showcase NetSquid's ability to investigate large networks by simulating entanglement distribution over a chain of up to one thousand nodes.

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schrödinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent advances in discrete diffusion and flow models have sparked growing interest in applying SB methods to discrete domains, there is still no reliable way to evaluate how well these methods actually solve the underlying problem. We address this challenge by introducing a benchmark for SB on discrete spaces. Our construction yields pairs of probability distributions with analytically known SB solutions, enabling rigorous evaluation. As a byproduct of building this benchmark, we obtain two new SB algorithms, DLightSB and DLightSB-M, and additionally extend prior related work to construct the α-CSBM algorithm. We demonstrate the utility of our benchmark by evaluating both existing and new solvers in high-dimensional discrete settings. This work provides the first step toward proper evaluation of SB methods on discrete spaces, paving the way for more reproducible future studies.

This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g. system biology and operational research. Dynamic Causal Bayesian Optimization (DCBO) brings together ideas from sequential decision making, causal inference and Gaussian process (GP) emulation. DCBO is useful in scenarios where all causal effects in a graph are changing over time. At every time step DCBO identifies a local optimal intervention by integrating both observational and past interventional data collected from the system. We give theoretical results detailing how one can transfer interventional information across time steps and define a dynamic causal GP model which can be used to quantify uncertainty and find optimal interventions in practice. We demonstrate how DCBO identifies optimal interventions faster than competing approaches in multiple settings and applications.

This study addresses challenges in reverse logistics, a frequently overlooked but essential component of last-mile delivery, particularly in disaster relief scenarios where infrastructure disruptions demand adaptive solutions. While hub-and-spoke logistics networks excel at long-distance scalability, they often fail to optimize closely spaced spokes reliant on distant hubs, introducing inefficiencies in transit times and resource allocation. Using 20 Apple AirTags embedded in packages, this research provides empirical insights into logistical flows, capturing granular spatial and temporal data through Bluetooth LE (BLE) 5 trackers integrated with the Apple Find My network. These trackers demonstrated their value in monitoring dynamic cargo movements, enabling real-time adjustments in mobile hub placement and route optimization, particularly in disaster relief contexts like Hurricane Helene. A novel application of discrete event simulation (DES) further explored the saddle point in hub-spoke configurations, where excessive hub reliance clashes with diminishing spoke interaction demand. By coupling simulation results with empirical AirTag tracking, the study highlights the potential of BLE technology to refine reverse logistics, reduce delays, and improve operational flexibility in both routine and crisis-driven delivery networks.

Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism for dynamical systems subject to discrete, possibly stochastic, state jumps and multi-modal continuous-time flows. Despite the versatility and importance of SHSs across applications, a general procedure for the explicit learning of both discrete events and multi-mode continuous dynamics remains an open problem. This work introduces Neural Hybrid Automata (NHAs), a recipe for learning SHS dynamics without a priori knowledge on the number of modes and inter-modal transition dynamics. NHAs provide a systematic inference method based on normalizing flows, neural differential equations and self-supervision. We showcase NHAs on several tasks, including mode recovery and flow learning in systems with stochastic transitions, and end-to-end learning of hierarchical robot controllers.

Multi-agent systems built on large language models (LLMs) require many coordination choices that are difficult to fix a priori: which skill protocol to invoke, which agent role should perform a subtask, which model to bind to each role, how roles should interact, when to use retrieval or verification, and when to omit a step entirely. These choices interact with task regime and operational constraints, so static pipelines and one-off model comparisons provide only a limited view of the design space. This paper introduces AgensFlow, an open-source framework that treats multi-agent coordination as an online policy-learning problem under partial observability. The framework makes coordination decisions observable and learnable from repeated trajectories, rather than treating skill, role, model, topology, and evaluation choices as fixed pipeline design. AgensFlow is evaluated on two corpora: distributed-systems incident tasks and security-advisory tasks. The evaluation shows three main results: learned routing reaches a higher-quality operating point than a fixed pipeline baseline on coordination-heavy classes; skip:X isolates topology compression as a meaningful part of the substrate; and warm-started policy graphs can reduce exploration cost while preserving plateau quality. Overall, the results support that learned, auditable routing can improve coordination-heavy multi-agent workflows over static wiring.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical state space, where a single network with continuous horizon conditioning is trained with direct supervision against textbook reference solvers to predict any future state at horizon T in one forward pass. Although no part of the training data, loss function, or architecture supervises discontinuity location, the trained surrogate encodes it implicitly, recoverable from its forward passes alone as a per-trajectory error map that concentrates on shocks, fronts, and contacts, and stays small elsewhere. The map is competitive with or better than standard label-free baselines including deep ensembles, learned error heads, gradient-magnitude indicators, and locally-adaptive conformal prediction, while using only a single trained network and requiring no calibration set or governing-equation knowledge. The recipe supports two operating points. Mode 1 runs the surrogate alone for maximum throughput, with same-hardware CPU speedups of 26x to 72x against textbook solvers on the PDE environments. Mode 2 uses the error map to gate a reference-solver fallback, deferring uncertain trajectories and roughly halving the surrogate's residual error at the default operating point. The recipe applies without modification across reaction-diffusion, compressible Euler, and rigid-body collision dynamics.

Large language model (LLM) agents are increasingly used to assist with operations research (OR) modeling, yet existing OR-oriented benchmarks often reduce evaluation to one-shot translation from a self-contained problem statement into a mathematical formulation or solver program. Such settings abstract away two characteristics of real industrial OR workflows: persistent multi-artifact workspaces and multi-stage task lifecycles. We introduce OR-Space, a full-lifecycle workspace benchmark for evaluating industrial optimization agents across model construction, model revision, and grounded explanation. Each instance is an executable workspace containing business documents, structured data, optional code artifacts, solver outputs, and task-specific evaluators distributed across interdependent files. OR-Space defines three task modes: Build, where agents construct solver-ready optimization models from heterogeneous artifacts; Revise, where agents modify existing models under changing requirements or solver feedback while preserving valid prior logic; and Explain, where agents answer grounded questions about solutions, constraints, and business implications using evidence spread across workspace artifacts. By combining persistent workspaces with lifecycle-oriented tasks, OR-Space evaluates whether agents can perform reliable optimization work beyond end-to-end text generation. We describe the benchmark design, evaluation protocol, and quality-control pipeline, and position OR-Space as a benchmark for studying the reliability, failure modes, and practical readiness of LLM agents in industrial OR workflows.

Large discrete action spaces (LDAS) remain a central challenge in reinforcement learning. Existing solution approaches can handle unstructured LDAS with up to a few million actions. However, many real-world applications in logistics, production, and transportation systems have combinatorial action spaces, whose size grows well beyond millions of actions, even on small instances. Fortunately, such action spaces exhibit structure, e.g., equally spaced discrete resource units. With this work, we focus on handling structured LDAS (SLDAS) with sizes that cannot be handled by current benchmarks: we propose Dynamic Neighborhood Construction (DNC), a novel exploitation paradigm for SLDAS. We present a scalable neighborhood exploration heuristic that utilizes this paradigm and efficiently explores the discrete neighborhood around the continuous proxy action in structured action spaces with up to 10^{73} actions. We demonstrate the performance of our method by benchmarking it against three state-of-the-art approaches designed for large discrete action spaces across two distinct environments. Our results show that DNC matches or outperforms state-of-the-art approaches while being computationally more efficient. Furthermore, our method scales to action spaces that so far remained computationally intractable for existing methodologies.

Tool-using LLM agents can violate the very policies they are deployed to enforce while appearing to complete the task successfully. In policy-permissive environments, a tool may execute any well-formed call even when the corresponding state transition is forbidden by domain policy. The result is a silent wrong state (a booking cancelled, a passenger count changed, a claim acted on without verification) that neither the tool nor the agent's self-report exposes. We study this failure mode in the τ^2-bench airline domain. On a budget agent, 78% of observed failures are silent wrong-state failures with no tool error, and the aggregate failure rate is reproducible across disjoint seeds, not sampling noise. We then evaluate a lightweight intervention: deterministic, read-only pre-execution gates that inspect the proposed call and current state before allowing a write. A four-gate suite raises full-benchmark success from 29.6% to 42.0% on gpt-4o-mini (+12.4pp; paired task-level bootstrap P=0.0012), and the lift reproduces on a disjoint 15-seed set (+12.3pp; P=0.0008). The effect is concentrated where the gates fire: on the 26/50 firing tasks, success rises by +19.2pp, while movement on the 24 non-firing tasks does not exclude zero. Two negative controls (a self-enforcing retail domain and BFCL) bound the mechanism: gates help when tools are policy-permissive and add little where tools already self-enforce. As suggestive evidence, not a central claim, the same failure mode persists at the frontier: gpt-5.2 at default reasoning still attempts policy-violating writes, and the same suite improves success from 61.2% to 71.6% (+10.4pp; P=0.020; n=5, no replication). The contribution is a bounded evaluation and reliability result: deterministic gates do not guarantee task success, but they can deterministically prevent a known class of silent policy-violating writes at the action boundary.

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical systems. This paper addresses a fundamental problem associated with EDMD: a trade-off between representational capacity of the dictionary and over-fitting due to insufficient data. A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encoded state is used to learn a low-dimensional and highly informative Koopman-invariant subspace of observables. A method is also presented for balanced model reduction of over-specified EDMD systems in feature space. Nonlinear reconstruction using partially linear multi-kernel regression aims to improve reconstruction accuracy from the low-dimensional state when the data has complex but intrinsically low-dimensional structure. The techniques demonstrate the ability to identify Koopman eigenfunctions of the unforced Duffing equation, create accurate low-dimensional models of an unstable cylinder wake flow, and make short-time predictions of the chaotic Kuramoto-Sivashinsky equation.

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning task, where one aims to learn the operator representing the physics of interest, which entails discretization of the continuous system. However, preserving key continuous properties at the discrete level, such as boundary conditions, and addressing physical systems with complex geometries is challenging for most existing approaches. We introduce a family of operator learning architectures, structure-preserving operator networks (SPONs), that allows to preserve key mathematical and physical properties of the continuous system by leveraging finite element (FE) discretizations of the input-output spaces. SPONs are encode-process-decode architectures that are end-to-end differentiable, where the encoder and decoder follows from the discretizations of the input-output spaces. SPONs can operate on complex geometries, enforce certain boundary conditions exactly, and offer theoretical guarantees. Our framework provides a flexible way of devising structure-preserving architectures tailored to specific applications, and offers an explicit trade-off between performance and efficiency, all thanks to the FE discretization of the input-output spaces. Additionally, we introduce a multigrid-inspired SPON architecture that yields improved performance at higher efficiency. Finally, we release a software to automate the design and training of SPON architectures.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

Discrete denoising diffusion models (DDMs) have recently emerged as a compelling alternative to autoregressive (AR) modeling for discrete data, offering parallel generation and iterative global refinement capabilities. Unlike continuous diffusion, where the state space is fixed, DDMs are fundamentally shaped by how the discrete state space is constructed: the tokenization scheme, the vocabulary topology, and domain-specific structural alphabets. This work introduces a unified conceptual framework that views discrete diffusion models through the construction of the underlying discrete state space. Within this framework, existing formulations, including transition-matrix, masking/absorbing-state, and score/ratio-based approaches, emerge as different instantiations of a common design space. The framework further exposes common design trade-offs across training objectives, inference algorithms, scaling behavior, systems optimization, and evaluation protocols, suggesting several promising directions for future research.

This paper is an extended and reworked version of a short course given by the author at ''Uzbekistan-Ukrainian readings in stochastic processes'', Tashkent-Kyiv, 2022, and was prepared for a special issue of ''Theory of stochastic processes'', devoted to publishing lecture notes from the aforementioned workshop. The survey is devoted to operator splitting methods in the abstract formulation and their applications in probability. While the survey is focused on multiplicative methods, the BCH formula is used to discuss exponential splitting methods and a short informal introduction to additive splitting is presented. We introduce frameworks and available deterministic and probabilistic results and concentrate on constructing a wide picture of the field of operator splitting methods, providing a rigorous description in the setting of abstract Cauchy problems and an informal discussion for further and parallel advances. Some limitations and common difficulties are listed, as well as examples of works that provide solutions or hints. No new results are given. The bibliography contains illustrative deterministic examples and a selection of probability-related works.

This paper presents a continuous-time optimal control framework for the generation of reference trajectories in driving scenarios with uncertainty. A previous work presented a discrete-time stochastic generator for autonomous vehicles; those results are extended to continuous time to ensure the robustness of the generator in a real-time setting. We show that the stochastic model in continuous time can capture the uncertainty of information by producing better results, limiting the risk of violating the problem's constraints compared to a discrete approach. Dynamic solvers provide faster computation and the continuous-time model is more robust to a wider variety of driving scenarios than the discrete-time model, as it can handle further time horizons, which allows trajectory planning outside the framework of urban driving scenarios.

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

Public power-system datasets often lack electromagnetic transient (EMT) waveforms, inverter control dynamics, and diverse disturbance coverage, which limits their usefulness for training surrogate models and studying cyber-physical behavior in inverter-based microgrids. This paper presents a high-fidelity digital twin dataset generated from a MATLAB/Simulink EMT model of a low-voltage AC microgrid with ten inverter-based distributed generators. The dataset records synchronized three-phase PCC voltages and currents, per-DG active power, reactive power, and frequency, together with embedded scenario labels, producing 38 aligned channels sampled at Δt = 2~μs over T = 1~s (N = 500{,}001 samples) per scenario. Eleven operating and disturbance scenarios are included: normal operation, load step, voltage sag (temporary three-phase fault), load ramp, frequency ramp, DG trip, tie-line trip, reactive power step, single-line-to-ground faults, measurement noise injection, and communication delay. To ensure numerical stability without altering sequence length, invalid samples (NaN, Inf, and extreme outliers) are repaired using linear interpolation. Each scenario is further validated using system-level evidence from mean frequency, PCC voltage magnitude, total active power, voltage unbalance, and zero-sequence current to confirm physical observability and correct timing. The resulting dataset provides a consistent, labeled EMT benchmark for surrogate modeling, disturbance classification, robustness testing under noise and delay, and cyber-physical resilience analysis in inverter-dominated microgrids. The dataset and processing scripts will be released upon acceptance

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and continuous verification of their safe utilisation. Working towards addressing this challenge, this paper presents a principled novel safety argument framework for critical systems that utilise deep neural networks. The approach allows various forms of predictions, e.g., future reliability of passing some demands, or confidence on a required reliability level. It is supported by a Bayesian analysis using operational data and the recent verification and validation techniques for deep learning. The prediction is conservative -- it starts with partial prior knowledge obtained from lifecycle activities and then determines the worst-case prediction. Open challenges are also identified.

We investigate the construction of latent spaces through self-supervised learning to support semantically meaningful operations. Analogous to operational amplifiers, these "operational latent spaces" (OpLaS) not only demonstrate semantic structure such as clustering but also support common transformational operations with inherent semantic meaning. Some operational latent spaces are found to have arisen "unintentionally" in the progress toward some (other) self-supervised learning objective, in which unintended but still useful properties are discovered among the relationships of points in the space. Other spaces may be constructed "intentionally" by developers stipulating certain kinds of clustering or transformations intended to produce the desired structure. We focus on the intentional creation of operational latent spaces via self-supervised learning, including the introduction of rotation operators via a novel "FiLMR" layer, which can be used to enable ring-like symmetries found in some musical constructions.

Advancements in high-computing devices increase the necessity for improved and new understanding and development of smart manufacturing factories. Discrete-event models with simulators have been shown to be critical to architect, designing, building, and operating the manufacturing of semiconductor chips. The diffusion, implantation, and lithography machines have intricate processes due to their feedforward and feedback connectivity. The dataset collected from simulations of the factory models holds the promise of generating valuable machine-learning models. As surrogate data-based models, their executions are highly efficient compared to the physics-based counterpart models. For the development of surrogate models, it is beneficial to have publicly available benchmark simulation models that are grounded in factory models that have concise structures and accurate behaviors. Hence, in this research, a dataset is devised and constructed based on a benchmark model of an Intel semiconductor fabrication factory. The model is formalized using the Parallel Discrete-Event System Specification and executed using the DEVS-Suite simulator. The time series dataset is constructed using discrete-event time trajectories. This dataset is further analyzed and used to develop baseline univariate and multivariate machine learning models. The dataset can also be utilized in the machine learning community for behavioral analysis based on formalized and scalable component-based discrete-event models and simulations.

Solving the AC optimal power flow problem (AC-OPF) is critical to the efficient and safe planning and operation of power grids. Small efficiency improvements in this domain have the potential to lead to billions of dollars of cost savings, and significant reductions in emissions from fossil fuel generators. Recent work on data-driven solution methods for AC-OPF shows the potential for large speed improvements compared to traditional solvers; however, no large-scale open datasets for this problem exist. We present the largest readily-available collection of solved AC-OPF problems to date. This collection is orders of magnitude larger than existing readily-available datasets, allowing training of high-capacity data-driven models. Uniquely, it includes topological perturbations - a critical requirement for usage in realistic power grid operations. We hope this resource will spur the community to scale research to larger grid sizes with variable topology.

On-policy reinforcement learning methods like GRPO suffer from mode collapse: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (Distribution-Matching Policy Optimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality, an ideal testbed for evaluating exploration. DMPO achieves 43.9% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1%) and 43.1% on vision-based NP-Bench (vs. 38.4%), demonstrating 9% and 12% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0%) and out-of-domain tasks (+2.3%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As emission norms become more stringent, the need for fast and accurate models that enable analysis of system behavior have become an essential requirement for system development. The fast transient processes involved in the operation of a combustion engine make it difficult to develop accurate physics-based models for such systems. As an alternative to physics based models, we develop an operator-based regression model (DeepONet) to learn the relevant output states for a mean-value gas flow engine model using the engine operating conditions as input variables. We have adopted a mean-value model as a benchmark for comparison, simulated using Simulink. The developed approach necessitates using the initial conditions of the output states to predict the accurate sequence over the temporal domain. To this end, a sequence-to-sequence approach is embedded into the proposed framework. The accuracy of the model is evaluated by comparing the prediction output to ground truth generated from Simulink model. The maximum mathcal L_2 relative error observed was approximately 6.5%. The sensitivity of the DeepONet model is evaluated under simulated noise conditions and the model shows relatively low sensitivity to noise. The uncertainty in model prediction is further assessed by using a mean ensemble approach. The worst-case error at the (mu + 2sigma) boundary was found to be 12%. The proposed framework provides the ability to predict output states in real-time and enables data-driven learning of complex input-output operator mapping. As a result, this model can be applied during initial development stages, where accurate models may not be available.

Agentic LLM coding tools compress long session histories into compaction summaries that subsequent sessions inherit as ground truth. This paper documents a failure mode in Claude Code where partial standard output from timed-out commands (exit code 143) is recorded in compaction summaries as confirmed results, propagating false positives across sessions and model versions without re-verification. The underlying mechanism is a conflation of observation and persistence, where information that appeared in the terminal is treated as equivalent to information written to durable storage. This finding extends the analysis of LLM self-evaluation failures reported in prior work on non-determinism in LLM-as-judge grading by showing that agentic tools exhibit analogous reliability deficits when reporting on their own operational outcomes. The failure has direct implications for any workflow that relies on agentic session continuity for data processing, scientific computation, or multi-step automation.

We introduce a unified mathematical and probabilistic framework for understanding and comparing diverse AI agent strategies. We bridge the gap between high-level agent design concepts, such as ReAct, multi-agent systems, and control flows, and a rigorous mathematical formulation. Our approach frames agentic processes as a chain of probabilities, enabling a detailed analysis of how different strategies manipulate these probabilities to achieve desired outcomes. Our framework provides a common language for discussing the trade-offs inherent in various agent architectures. One of our many key contributions is the introduction of the "Degrees of Freedom" concept, which intuitively differentiates the optimizable levers available for each approach, thereby guiding the selection of appropriate strategies for specific tasks. This work aims to enhance the clarity and precision in designing and evaluating AI agents, offering insights into maximizing the probability of successful actions within complex agentic systems.

Lara is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of Lara's expressive ability reports that it can represent relational algebra and most linear algebra operations. However, several essential computations, such as matrix inversion and determinant, cannot be expressed in Lara. Lara cannot represent global and iterative computation, either. This article proposes IterLara, extending Lara with iterative operators, to provide an algebraic model that unifies operations in general-purpose computing, like big data, AI, scientific computing, and database. We study the expressive ability of Lara and IterLara and prove that IterLara with aggregation functions can represent matrix inversion, determinant. Besides, we demonstrate that IterLara with no limitation of function utility is Turing complete. We also propose the Operation Count (OP) as a metric of computation amount for IterLara and ensure that the OP metric is in accordance with the existing computation metrics.

Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are discrete. In this paper we find that classical estimators, including the maximum score estimator, (Manski (1975)), loose their attractive statistical properties without point identification. First of all, they are not sharp with the estimator converging to an outer region of the identified set, (Komarova (2013)), and in many discrete designs it weakly converges to a random set. Second, they are not robust, with their distribution limit discontinuously changing with respect to the parameters of the model. We propose a novel class of estimators based on the concept of a quantile of a random set, which we show to be both sharp and robust. We demonstrate that our approach extends from cross-sectional settings to classical static and dynamic discrete panel data models.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains sim 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

Safety alignment mechanisms in large language models prevent responses to harmful queries through learned refusal behavior, yet these same mechanisms impede legitimate research applications including cognitive modeling, adversarial testing, and security analysis. While abliteration techniques enable surgical removal of refusal representations through directional orthogonalization, the relative effectiveness of available implementations remains uncharacterized. This study evaluates four abliteration tools (Heretic, DECCP, ErisForge, FailSpy) across sixteen instruction-tuned models (7B-14B parameters), reporting tool compatibility on all 16 models and quantitative metrics on subsets dictated by tool support. Single-pass methods demonstrated superior capability preservation on the benchmarked subset (avg GSM8K change across three models: ErisForge -0.28 pp; DECCP -0.13 pp), while Bayesian-optimized abliteration produced variable distribution shift (KL divergence: 0.043-1.646) with model-dependent capability impact. These findings provide researchers with evidence-based selection criteria for abliteration tool deployment across diverse model architectures. The principal finding indicates that mathematical reasoning capabilities exhibit the highest sensitivity to abliteration interventions, with GSM8K change ranging from +1.51 pp to -18.81 pp (-26.5% relative) depending on tool selection and model architecture.

Discrete diffusion models have achieved success in tasks like image generation and masked language modeling but face limitations in controlled content editing. We introduce DICE (Discrete Inversion for Controllable Editing), the first approach to enable precise inversion for discrete diffusion models, including multinomial diffusion and masked generative models. By recording noise sequences and masking patterns during the reverse diffusion process, DICE enables accurate reconstruction and flexible editing of discrete data without the need for predefined masks or attention manipulation. We demonstrate the effectiveness of DICE across both image and text domains, evaluating it on models such as VQ-Diffusion, Paella, and RoBERTa. Our results show that DICE preserves high data fidelity while enhancing editing capabilities, offering new opportunities for fine-grained content manipulation in discrete spaces. For project webpage, see https://hexiaoxiao-cs.github.io/DICE/.

This paper presents a novel virus propagation model using NetLogo. The model allows agents to move across multiple sites using different routes. Routes can be configured, enabled for mobility and (un)locked down independently. Similarly, locations can also be (un)locked down independently. Agents can get infected, propagate their infections to others, can take precautions against infection and also subsequently recover from infection. This model contains certain features that are not present in existing models. The model may be used for educational and research purposes, and the code is made available as open source. This model may also provide a broader framework for more detailed simulations. The results presented are only to demonstrate the model functionalities and do not serve any other purpose.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is applicable to a wide range of use cases that have worst-case performance requirements. After defining the DMMV problem mathematically, we explore its properties to establish a foundational understanding. To tackle DMMV instance sizes of practical relevance, we develop a GPU-accelerated heuristic that takes advantage of the mathematical properties of DMMV for speeding up the solution process. We demonstrate the versatile applicability of our heuristic by solving three optimization problems as use cases: (1) post-training quantization of language models, (2) discrete tomography, and (3) Finite Impulse Response (FIR) filter design. In quantization without outlier separation, our heuristic achieves 14% improvement on average over existing methods. In discrete tomography, it reduces reconstruction error by 16% under uniform noise and accelerates computations by a factor of 6 on GPU. For FIR filter design, it nearly achieves 50% ripple reduction compared to using the commercial integer optimization solver, Gurobi. Our comparative results point to the benefits of studying DMMV as a context-free optimization problem and the advantages that our proposed heuristic offers on three distinct problems. Our GPU-accelerated heuristic will be made open-source to further stimulate research on DMMV and its other applications. The code is available at https://anonymous.4open.science/r/AMVM-5F3E/

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is defined. DTV has favorable properties, compared to the original TV-seminorm for finite element functions. These include a convenient dual representation in terms of the supremum over the space of Raviart--Thomas finite element functions, subject to a set of simple constraints. It can therefore be shown that a variety of algorithms for classical image reconstruction problems, including TV-L^2 and TV-L^1, can be implemented in low and higher-order finite element spaces with the same efficiency as their counterparts originally developed for images on Cartesian grids.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

Agentic systems involved in high-stake decision-making under adversarial pressure need formal guarantees not offered by existing approaches. Motivated by the operational needs of security operations centers (SOCs) that must configure endpoint detection and response (EDR) policies under adversarial pressure, we present a tool-mediated architecture: LLM agents use deterministic tools (Stackelberg best-response, Bayesian observer updates, attack-graph primitives) and select from finite action catalogs enforced at the tool-output interface. A composite Lyapunov function machine-checked in Lean 4 with zero sorry certifies controllability, observability from asymmetric sensor data, and Input-to-State Stability (ISS) robustness under intelligent adversarial disturbance, with two corollaries extending the certificate to any controller or adversary from the catalogs. On 282 real enterprise attack graphs, the claims hold with margin. On paired offensive/defensive telemetry, a tool-mediated Claude Sonnet 4 controller reduces the attacker's expected payoff (game value) by 59% relative to a deterministic greedy baseline, with zero variance across 40 runs at four temperatures. A Claude Haiku 4.5 controller converges to suboptimal game values but stays catalog-bounded over an additional 40 runs, demonstrating that architectural stability is not dependent on the controller capability. The LLM agent's non-determinism furthers creative exploration of strategies, while the tool-mediated architecture ensures system stability.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

There is no doubt that safety alignment is an essential step in LLM training. However, conceptually it does not distinguish between various domains and the level of potential harm of a query, which creates significant complications in the fields like cyber security, where a model should not be constrained by its safety circuits to accomplish the goals of legitimate, authorized operations. In this work, we share our findings from a large scale abliteration experiment on 24 open-source LLMs and show that domain-specific abliteration is achievable with standard methodology on the example of a 1T-parameter Kimi K2. Building on recent work showing that refusal in LLMs occupies a multi-dimensional subspace within layers, we find that it is also distributed widely across layers, especially in trillion-parameter MoE architectures, and so we aim to capture the part of it that represents harmful concepts in the cybersecurity domain exclusively. We also investigate the correlation between models' features and the effect of domain-specific abliteration, identifying that the type of safety training and architecture are the most reliable predictors. Finally, we classify the models into 3 abliteration susceptibility tiers and put forward a set of conjectures as to why a particular effect from this intervention might be observed in a given model.

The integration of machine learning tools into telecom networks, has led to two prevailing paradigms, namely, language-based systems, such as Large Language Models (LLMs), and physics-based systems, such as Digital Twins (DTs). While LLM-based approaches enable flexible interaction and automation, they lack explicit representations of network dynamics. DTs, in contrast, offer a high-fidelity network simulation, but remain scenario-specific and are not designed for learning or decision-making under uncertainty. This gap becomes critical for 6G systems, where decisions must take into account the evolving network states, uncertainty, and the cascading effects of control actions across multiple layers. In this article, we introduce the {Telecom World Model}~(TWM) concept, an architecture for learned, action-conditioned, uncertainty-aware modeling of telecom system dynamics. We decompose the problem into two interacting worlds, a controllable system world consisting of operator-configurable settings and an external world that captures propagation, mobility, traffic, and failures. We propose a three-layer architecture, comprising a field world model for spatial environment prediction, a control/dynamics world model for action-conditioned Key Performance Indicator (KPI) trajectory prediction, and a telecom foundation model layer for intent translation and orchestration. We showcase a comparative analysis between existing paradigms, which demonstrates that TWM jointly provides telecom state grounding, fast action-conditioned roll-outs, calibrated uncertainty, multi-timescale dynamics, model-based planning, and LLM-integrated guardrails. Furthermore, we present a proof-of-concept on network slicing to validate the proposed architecture, showing that the full three-layer pipeline outperforms single-world baselines and accurately predicts KPI trajectories.

Operating rooms (ORs) are complex, high-stakes environments requiring precise understanding of interactions among medical staff, tools, and equipment for enhancing surgical assistance, situational awareness, and patient safety. Current datasets fall short in scale, realism and do not capture the multimodal nature of OR scenes, limiting progress in OR modeling. To this end, we introduce MM-OR, a realistic and large-scale multimodal spatiotemporal OR dataset, and the first dataset to enable multimodal scene graph generation. MM-OR captures comprehensive OR scenes containing RGB-D data, detail views, audio, speech transcripts, robotic logs, and tracking data and is annotated with panoptic segmentations, semantic scene graphs, and downstream task labels. Further, we propose MM2SG, the first multimodal large vision-language model for scene graph generation, and through extensive experiments, demonstrate its ability to effectively leverage multimodal inputs. Together, MM-OR and MM2SG establish a new benchmark for holistic OR understanding, and open the path towards multimodal scene analysis in complex, high-stakes environments. Our code, and data is available at https://github.com/egeozsoy/MM-OR.

This paper presents a new state-of-the-art algorithm for exact 3times3 matrix multiplication over general non-commutative rings, achieving a rank-23 scheme with only 58 scalar additions. This improves the previous best additive complexity of 60 additions without a change of basis. The result was discovered through an automated search combining ternary-restricted flip-graph exploration with greedy intersection reduction for common subexpression elimination. The resulting scheme uses only coefficients from {-1, 0, 1}, ensuring both efficiency and portability across arbitrary fields. The total scalar operation count is reduced from 83 to 81.

Sonification -- the mapping of data to non-speech audio -- offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870--2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two-dimensional acoustic phase space. Recurrence-based diagnostics, convex hull geometry, and coupling analysis reveal that the sonification pipeline preserves key dynamical signatures: alternating modes produce the highest trajectory recurrence rates, echoing ENSO's quasi-periodicity; layered polyphonic modes explore the broadest phase space regions; and the two scale families induce qualitatively distinct coupling regimes between spectral brightness and energy -- predominantly anti-phase in pelog but near-independent in slendro. Phase space trajectory analysis provides a rigorous geometric framework for comparing sonification designs within a complex systems context. Perceptual validation remains necessary; we contribute the dynamical systems methodology for evaluating such mappings.

The manual design of scenarios for Air Traffic Control (ATC) training is a demanding and time-consuming bottleneck that limits the diversity of simulations available to controllers. To address this, we introduce a novel, end-to-end approach, AirTrafficGen, that leverages large language models (LLMs) to automate and control the generation of complex ATC scenarios. Our method uses a purpose-built, graph-based representation to encode sector topology (including airspace geometry, routes, and fixes) into a format LLMs can process. Through rigorous benchmarking, we show that state-of-the-art models like Gemini 2.5 Pro and OpenAI o3 can generate high-traffic scenarios whilst maintaining operational realism. Our engineered prompting enables fine-grained control over interaction presence, type, and location. Initial findings suggest these models are also capable of iterative refinement, correcting flawed scenarios based on simple textual feedback. This approach provides a scalable alternative to manual scenario design, addressing the need for a greater volume and variety of ATC training and validation simulations. More broadly, this work showcases the potential of LLMs for complex planning in safety-critical domains.

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to random variables are discussed, including the approach based on completions in a Polish space. We apply the theory to the study of stochastic dynamical systems in discrete-time, and give a brief exposition of the Wiener process as a foundation for stochastic differential equations. The theory is based within the framework of type-two effectivity, so has an explicit direct link with Turing computation, and is expressed in a system of computable types and operations, so has a clean mathematical description.

Existing benchmarks for conversational AI agents simulate single-control environments, where only the AI agent can use tools to interact with the world, while the user remains a passive information provider. This differs from real-world scenarios like technical support, where users need to actively participate in modifying the state of the (shared) world. In order to address this gap, we introduce tau^2-bench, with four key contributions: 1) A novel Telecom dual-control domain modeled as a Dec-POMDP, where both agent and user make use of tools to act in a shared, dynamic environment that tests both agent coordination and communication, 2) A compositional task generator that programmatically creates diverse, verifiable tasks from atomic components, ensuring domain coverage and controlled complexity, 3) A reliable user simulator tightly coupled with the environment, whose behavior is constrained by tools and observable states, improving simulation fidelity, 4) Fine-grained analysis of agent performance through multiple ablations including separating errors arising from reasoning vs communication/coordination. In particular, our experiments show significant performance drops when agents shift from no-user to dual-control, highlighting the challenges of guiding users. Overall, tau^2-bench provides a controlled testbed for agents that must both reason effectively and guide user actions.

We consider the problem of estimating the optimal transport map between two probability distributions, P and Q in mathbb R^d, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the transport map is Lipschitz, a strong requirement that, in particular, excludes any examples where the transport map is discontinuous. As a first step towards developing estimation procedures for discontinuous maps, we consider the important special case where the data distribution Q is a discrete measure supported on a finite number of points in mathbb R^d. We study a computationally efficient estimator initially proposed by Pooladian and Niles-Weed (2021), based on entropic optimal transport, and show in the semi-discrete setting that it converges at the minimax-optimal rate n^{-1/2}, independent of dimension. Other standard map estimation techniques both lack finite-sample guarantees in this setting and provably suffer from the curse of dimensionality. We confirm these results in numerical experiments, and provide experiments for other settings, not covered by our theory, which indicate that the entropic estimator is a promising methodology for other discontinuous transport map estimation problems.

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the L_{12} bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4times faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.

We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix.

This study focuses on operational control strategies for a multi-energy District Heating Network (DHN). Two control strategies are investigated and compared: (i) a reactive rule-based control (RBC) and (ii) a model predictive control (MPC). For the purpose of the study a small scale district heating network is modelled using Modelica. The production plant combines a heat pump, a gas boiler and a thermal solar field on the production side with a storage tank for flexibility purposes. On the consumption side, the virtual buildings are aggregated into a single consumer. We use our co-simulation and control platform, called Pegase, to implement the studied strategies. For both strategies the goal is to meet the consumers' demand while satisfying technical constraints. In addition MPC has the objective to minimize the operational costs, taking into account variable electricity prices and availability of solar thermal resource. Different scenarios are also defined and compared to study the effect of the heat plant sizing and forecasting error. The operational cost is reduced when switching from RBC to a MPC. As can be expected, MPC is more efficient when dealing with variable energy costs, intermittent solar energy and storage capabilities. This study also demonstrates how our tools enable an easy coupling of Modelica-based simulation with various control strategies. It especially supports the implementation and validation of complex MPC strategies in an efficient way, and yearly simulations are performed within 20 minutes.

The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

Over the last decades, progress in modal analysis has enabled increasingly routine use of modal parameters, including those extracted from in-situ measurements, for applications such as structural health monitoring and finite element model updating. For output-only identification, or Operational Modal Analysis (OMA), widely adopted approaches include Stochastic Subspace Identification (SSI) methods and the Natural Excitation Technique combined with the Eigensystem Realization Algorithm (NExT-ERA). Nevertheless, SSI-based techniques may become cumbersome on large systems, while NExT-ERA fitting can struggle when measurements are contaminated by noise. To alleviate these, this work investigates an OMA frequency-domain formulation for aeronautical structures by coupling the Loewner Framework (LF) with NExT, yielding the proposed NExT-LF method. The method exploits the computational efficiency of LF together with the impulse response function retrieval enabled by NExT. NExT-LF is assessed on two experimental benchmarks: the eXperimental BeaRDS 2 high-aspect-ratio wing main spar and an Airbus Helicopters H135 bearingless main rotor blade. The identified modal parameters are compared against available experimental references and results obtained via SSI with Canonical Variate Analysis and NExT-ERA. The results show that the modes identified by NExT-LF correlate well with benchmark data, particularly for high-amplitude tests and in the low-frequency range.

Safety verification in Computer Numerical Control (CNC) machining has traditionally relied on simulation-based methods that require repetitive tests when requirements change. This paper introduces a formal verification framework that conceptualizes the physical CNC workspace as a Spatial Heap, treating physical occupancy as a managed logical resource. Central to our approach is a Parser-Prover Handshake that decouples machine kinematics from formal logic. By mapping tool trajectories and safety buffers into a discrete spatial model prior to evaluation, the framework enables the use of Separation Logic (SL) to verify safety via formal triples. Within this model, physical collisions are redefined as logical Spatial Data Races, detected through the failure of the separating conjunction to establish disjointness. Furthermore, we extend the methodology to collaborative environments using Concurrent Separation Logic (CSL), where physical hand-offs are verified as formal ownership transfers. Additionally, the framework scales to multi-axis kinematics (e.g., 5-axis Table-Table configurations) by treating the workpiece as a dynamically mutable spatial resource. By serving as a complement to traditional geometric simulation, this approach reduces the number of required iterative test cycles, offering a foundation for autonomous, less-collision manufacturing.

We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and enabling constructive and destructive interference in the range [-1,1]. A fixed set of ``perspectives'' evaluates ``semantic dimensions'' according to hidden competencies, and their interactions drive two discrete-time stochastic processes. We model this system as an iterated random affine map and use the theory of iterated random functions to prove that it converges in distribution to a unique stationary law; we moreover obtain an explicit closed form for the limiting expectation in terms of row, column, and global averages of the competency matrix. We then derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension, revealing how consensus depends on competency structure rather than raw input signals. Finally, we argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela, and we discuss implications for building self-maintaining, distributed, and parallelizable computational systems that house a uniquely subjective notion of identity.

Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key cryptography is much less understood. In this paper, we consider attacks where an adversary can query an oracle implementing a cryptographic primitive in a quantum superposition of different states. This model gives a lot of power to the adversary, but recent results show that it is nonetheless possible to build secure cryptosystems in it. We study applications of a quantum procedure called Simon's algorithm (the simplest quantum period finding algorithm) in order to attack symmetric cryptosystems in this model. Following previous works in this direction, we show that several classical attacks based on finding collisions can be dramatically sped up using Simon's algorithm: finding a collision requires Ω(2^{n/2}) queries in the classical setting, but when collisions happen with some hidden periodicity, they can be found with only O(n) queries in the quantum model. We obtain attacks with very strong implications. First, we show that the most widely used modes of operation for authentication and authenticated encryption e.g. CBC-MAC, PMAC, GMAC, GCM, and OCB) are completely broken in this security model. Our attacks are also applicable to many CAESAR candidates: CLOC, AEZ, COPA, OTR, POET, OMD, and Minalpher. This is quite surprising compared to the situation with encryption modes: Anand et al. show that standard modes are secure with a quantum-secure PRF. Second, we show that Simon's algorithm can also be applied to slide attacks, leading to an exponential speed-up of a classical symmetric cryptanalysis technique in the quantum model.

Purpose: Surgical performance depends not only on surgeons' technical skills but also on team communication within and across the different professional groups present during the operation. Therefore, automatically identifying team communication in the OR is crucial for patient safety and advances in the development of computer-assisted surgical workflow analysis and intra-operative support systems. To take the first step, we propose a new task of detecting communication briefings involving all OR team members, i.e. the team Time-out and the StOP?-protocol, by localizing their start and end times in video recordings of surgical operations. Methods: We generate an OR dataset of real surgeries, called Team-OR, with more than one hundred hours of surgical videos captured by the multi-view camera system in the OR. The dataset contains temporal annotations of 33 Time-out and 22 StOP?-protocol activities in total. We then propose a novel group activity detection approach, where we encode both scene context and action features, and use an efficient neural network model to output the results. Results: The experimental results on the Team-OR dataset show that our approach outperforms existing state-of-the-art temporal action detection approaches. It also demonstrates the lack of research on group activities in the OR, proving the significance of our dataset. Conclusion: We investigate the Team Time-Out and the StOP?-protocol in the OR, by presenting the first OR dataset with temporal annotations of group activities protocols, and introducing a novel group activity detection approach that outperforms existing approaches. Code is available at https://github.com/CAMMA-public/Team-OR.

Detecting and interpreting operator actions, engagement, and object interactions in dynamic industrial workflows remains a significant challenge in human-robot collaboration research, especially within complex, real-world environments. Traditional unimodal methods often fall short of capturing the intricacies of these unstructured industrial settings. To address this gap, we present a novel Multimodal Industrial Activity Monitoring (MIAM) dataset that captures realistic assembly and disassembly tasks, facilitating the evaluation of key meta-tasks such as action localization, object interaction, and engagement prediction. The dataset comprises multi-view RGB, depth, and Inertial Measurement Unit (IMU) data collected from 22 sessions, amounting to 290 minutes of untrimmed video, annotated in detail for task performance and operator behavior. Its distinctiveness lies in the integration of multiple data modalities and its emphasis on real-world, untrimmed industrial workflows-key for advancing research in human-robot collaboration and operator monitoring. Additionally, we propose a multimodal network that fuses RGB frames, IMU data, and skeleton sequences to predict engagement levels during industrial tasks. Our approach improves the accuracy of recognizing engagement states, providing a robust solution for monitoring operator performance in dynamic industrial environments. The dataset and code can be accessed from https://github.com/navalkishoremehta95/MIAM/.

Fleets of robo-taxis offering on-demand transportation services, commonly known as Autonomous Mobility-on-Demand (AMoD) systems, hold significant promise for societal benefits, such as reducing pollution, energy consumption, and urban congestion. However, orchestrating these systems at scale remains a critical challenge, with existing coordination algorithms often failing to exploit the systems' full potential. This work introduces a novel decision-making framework that unites mathematical modeling with data-driven techniques. In particular, we present the AMoD coordination problem through the lens of reinforcement learning and propose a graph network-based framework that exploits the main strengths of graph representation learning, reinforcement learning, and classical operations research tools. Extensive evaluations across diverse simulation fidelities and scenarios demonstrate the flexibility of our approach, achieving superior system performance, computational efficiency, and generalizability compared to prior methods. Finally, motivated by the need to democratize research efforts in this area, we release publicly available benchmarks, datasets, and simulators for network-level coordination alongside an open-source codebase designed to provide accessible simulation platforms and establish a standardized validation process for comparing methodologies. Code available at: https://github.com/StanfordASL/RL4AMOD

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

Unmanned aerial vehicles (UAVs) are cyber-physical systems whose attack surface spans networked avionics and on-board sensor fusion: a compromised GPS or battery module can mimic a benign mission segment and evade naive anomaly detectors. We present a leakage-free evaluation of quantum machine learning for UAV anomaly detection on the multi-sensor TLM:UAV benchmark. Three contributions support the study. (i) A group-aware temporal protocol (B2) partitions the dataset into ten contiguous TimeUS blocks and evaluates over ten seeds, eliminating the inflation produced by random stratified splits that mix neighbouring samples. (ii) A three-mode feature audit (full/loose/strict) quantifies how much accuracy stems from instantaneous physical signals versus contextual proxies (cumulative energy, battery state, GPS trajectory). (iii) A hybrid XGBoost + Data Reuploading (DRU) classifier is benchmarked against five paired non-linear controls (raw, PCA, polynomial-2, random-RBF, and an untrained DRU map) under identical budgets. The standalone DRU does not consistently match the strongest classical baseline across seeds; however, the trained-DRU hybrid is the only model whose mean F1 macro shifts upward from full to strict (+0.05), a directional signal that the per-seed standard deviations prevent from being interpreted as a statistically established difference. The trained-DRU hybrid also records the lowest mean false-alarm rate under proxy-free evaluation, subject to the inter-seed variance reported. We frame this as an incremental, reproducible quantum-enhanced hybrid benefit, and provide an open Qiskit 2.x implementation as a benchmark for cybersecurity analytics in NISQ-era aerospace systems.

Self-evolving agents violate the assumption behind most learning-theoretic guarantees: the data, evaluator, components, and hypothesis space are produced by the policy being updated. We present SEA, an architecture that confines self-modification to a small steering adapter and a versioned harness around a frozen base model and admits each modification only through an anytime-valid gate that emits an auditable certificate against a fixed error budget. Five loop controllers compose published guarantees; because such gates can only select among behaviors the frozen base already produces, five verifier-in-the-loop mechanisms -- best-of-N, micro-step search, self-authored reproduction oracles, search-layer control, and self-repair -- supply the dense, grader-free signal the gates require, computed from the issue text alone. On a 52-instance SWE-bench Verified subset across four base models, base capability is the dominant, confound-free effect, and on two strong base models a deliberate no-op-composite control isolates the suite's contribution at +4 and +5 (Glm~5.2 24to28; Gpt 29to34, the 65% best), with event logs confirming that its mechanisms fire and prevent regressions. Results are single-run on expensive evaluations; confirming run-to-run variance and adapting the per-task algorithm mix are future work.

On-policy distillation (OPD), which samples trajectories from the student model and supervises them with a teacher at the token level, avoids relying solely on verifiable terminal rewards and can yield better generalization than off-policy distillation. However, OPD requires expensive on-the-fly sampling of the student policy during training, which substantially increases training cost, especially for long responses. Our initial analysis shows that, during OPD, training signals are often concentrated in the prefix of each output, and that even a short teacher-generated prefix can significantly help the student produce the correct answer. Motivated by these observations, we propose a simple yet effective modification of OPD: we apply the distillation objective only to prefixes of student-generated outputs and terminate each sampling early during distillation. Experiments on a suite of AI-for-Math and out-of-domain benchmarks show that on-policy prefix distillation matches the performance of full OPD while reducing training FLOP by 2x-47x.

We investigate model predictive control (MPC) formulations for linear systems subject to i.i.d. stochastic disturbances with bounded support and chance constraints. Existing stochastic MPC formulations with closed-loop guarantees can be broadly classified in two separate frameworks: i) using robust techniques; ii) feasibility preserving algorithms. We investigate two particular MPC formulations representative for these two frameworks called robust-stochastic MPC and indirect feedback stochastic MPC. We provide a qualitative analysis, highlighting intrinsic limitations of both approaches in different edge cases. Then, we derive a unifying stochastic MPC framework that naturally includes these two formulations as limit cases. This qualitative analysis is complemented with numerical results, showcasing the advantages and limitations of each method.

This paper presents LLM-empowered workflow to support Software Defined Vehicle (SDV) software development, covering the aspects of security-aware system topology design, as well as event-driven decision-making code analysis. For code analysis we adopt event chains model which provides formal foundations to systematic validation of functional safety, taking into account the semantic validity of messages exchanged between key components, including both CAN and Vehicle Signal Specification (VSS). Analysis of security aspects for topology relies on synergy with Model-Driven Engineering (MDE) approach and Object Constraint Language (OCL) rules. Both locally deployable and proprietary solution are taken into account for evaluation within Advanced Driver-Assistance Systems (ADAS)-related scenarios.

In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces. Building on Hodge theory and operator splitting, we derive a principled operator-level decomposition. The result is a Hybrid Eulerian-Lagrangian architecture with an algebraic-level inductive bias we call Hodge Spectral Duality (HSD). In our framework, we use discrete differential forms to capture topology-dominated components and an orthogonal auxiliary ambient space to represent complex local dynamics. Our method achieves superior accuracy and efficiency on geometric graphs with enhanced fidelity to physical invariants. Our code is available at https://github.com/ContinuumCoder/Hodge-Spectral-Duality

Recent advances in Large Language Models (LLMs) have sparked concerns over their potential to acquire and misuse dangerous or high-risk capabilities, posing frontier risks. Current safety evaluations primarily test for what a model can do - its capabilities - without assessing what it would do if endowed with high-risk capabilities. This leaves a critical blind spot: models may strategically conceal capabilities or rapidly acquire them, while harboring latent inclinations toward misuse. We argue that propensity - the likelihood of a model to pursue harmful actions if empowered - is a critical, yet underexplored, axis of safety evaluation. We present PropensityBench, a novel benchmark framework that assesses the proclivity of models to engage in risky behaviors when equipped with simulated dangerous capabilities using proxy tools. Our framework includes 5,874 scenarios with 6,648 tools spanning four high-risk domains: cybersecurity, self-proliferation, biosecurity, and chemical security. We simulate access to powerful capabilities via a controlled agentic environment and evaluate the models' choices under varying operational pressures that reflect real-world constraints or incentives models may encounter, such as resource scarcity or gaining more autonomy. Across open-source and proprietary frontier models, we uncover 9 alarming signs of propensity: models frequently choose high-risk tools when under pressure, despite lacking the capability to execute such actions unaided. These findings call for a shift from static capability audits toward dynamic propensity assessments as a prerequisite for deploying frontier AI systems safely. Our code is available at https://github.com/scaleapi/propensity-evaluation.

Computing a Gaussian process (GP) posterior has a computational cost cubical in the number of historical points. A reformulation of the same GP posterior highlights that this complexity mainly depends on how many unique historical points are considered. This can have important implication in active learning settings, where the set of historical points is constructed sequentially by the learner. We show that sequential black-box optimization based on GPs (GP-Opt) can be made efficient by sticking to a candidate solution for multiple evaluation steps and switch only when necessary. Limiting the number of switches also limits the number of unique points in the history of the GP. Thus, the efficient GP reformulation can be used to exactly and cheaply compute the posteriors required to run the GP-Opt algorithms. This approach is especially useful in real-world applications of GP-Opt with high switch costs (e.g. switching chemicals in wet labs, data/model loading in hyperparameter optimization). As examples of this meta-approach, we modify two well-established GP-Opt algorithms, GP-UCB and GP-EI, to switch candidates as infrequently as possible adapting rules from batched GP-Opt. These versions preserve all the theoretical no-regret guarantees while improving practical aspects of the algorithms such as runtime, memory complexity, and the ability of batching candidates and evaluating them in parallel.

Detecting out-of-distribution (OOD) samples is important for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. Existing research has mainly focused on unimodal scenarios on image data. However, real-world applications are inherently multimodal, which makes it essential to leverage information from multiple modalities to enhance the efficacy of OOD detection. To establish a foundation for more realistic Multimodal OOD Detection, we introduce the first-of-its-kind benchmark, MultiOOD, characterized by diverse dataset sizes and varying modality combinations. We first evaluate existing unimodal OOD detection algorithms on MultiOOD, observing that the mere inclusion of additional modalities yields substantial improvements. This underscores the importance of utilizing multiple modalities for OOD detection. Based on the observation of Modality Prediction Discrepancy between in-distribution (ID) and OOD data, and its strong correlation with OOD performance, we propose the Agree-to-Disagree (A2D) algorithm to encourage such discrepancy during training. Moreover, we introduce a novel outlier synthesis method, NP-Mix, which explores broader feature spaces by leveraging the information from nearest neighbor classes and complements A2D to strengthen OOD detection performance. Extensive experiments on MultiOOD demonstrate that training with A2D and NP-Mix improves existing OOD detection algorithms by a large margin. Our source code and MultiOOD benchmark are available at https://github.com/donghao51/MultiOOD.

Recent studies have drawn attention to the untapped potential of the "star operation" (element-wise multiplication) in network design. While intuitive explanations abound, the foundational rationale behind its application remains largely unexplored. Our study attempts to reveal the star operation's ability to map inputs into high-dimensional, non-linear feature spaces -- akin to kernel tricks -- without widening the network. We further introduce StarNet, a simple yet powerful prototype, demonstrating impressive performance and low latency under compact network structure and efficient budget. Like stars in the sky, the star operation appears unremarkable but holds a vast universe of potential. Our work encourages further exploration across tasks, with codes available at https://github.com/ma-xu/Rewrite-the-Stars.

Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation schemes, logical circuits are compiled following a place-and-route paradigm, where logical qubits remain statically fixed in space throughout the computation. In this work, we introduce a paradigm shift by exploiting movable logical qubits via teleportation during the logical lattice surgery CNOT gate. Focusing on lattice surgery with the color code, we propose a proof-of-concept compilation scheme that leverages this capability. Numerical simulations show that the proposed approach can substantially reduce the routed circuit depth compared to standard place-and-route compilation techniques. Our results demonstrate that optimizations based on movable logical qubits are not limited to architectures with physically movable qubits, such as neutral atoms or trapped ions - they are also readily applicable to superconducting quantum hardware. An open-source implementation of our method is available on GitHub https://github.com/munich-quantum-toolkit/qecc.

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them.

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schr\"odinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.

An important concept in the fifth generation of mobile networks is multitenancy, which allows diverse operators sharing the same wireless infrastructure. To support this feature in conjunction with the challenging performance requirements of future networks, more automated and faster planning of the required radio capacity is needed. Likewise, installing small cells is an effective resource to provide greater performance and capacity to both indoor and outdoor places. This paper proposes a new framework for automated cell planning in multitenant small cell networks. In particular, taking advantage of the available network data, a set of detailed planning specifications over time and space domains are generated in order to meet the contracted capacity by each tenant. Then, the network infrastructure and configuration are updated according to an algorithm that considers different actions such as adding/removing channels and adding or relocating small cells. The simulation results show the effectiveness of various methods to derive the planning specifications depending on the correlation between the tenant's and network's traffic demands.

Large language model (LLM) agents offer a promising data-driven approach to automating Site Reliability Engineering (SRE), yet their enterprise deployment is constrained by three challenges: restricted access to proprietary data, unsafe action execution under permission-governed environments, and the inability of closed systems to improve from failures. We present AOI (Autonomous Operations Intelligence), a trainable multi-agent framework formulating automated operations as a structured trajectory learning problem under security constraints. Our approach integrates three key components. First, a trainable diagnostic system applies Group Relative Policy Optimization (GRPO) to distill expert-level knowledge into locally deployed open-source models, enabling preference-based learning without exposing sensitive data. Second, a read-write separated execution architecture decomposes operational trajectories into observation, reasoning, and action phases, allowing safe learning while preventing unauthorized state mutation. Third, a Failure Trajectory Closed-Loop Evolver mines unsuccessful trajectories and converts them into corrective supervision signals, enabling continual data augmentation. Evaluated on the AIOpsLab benchmark, our contributions yield cumulative gains. (1) The AOI runtime alone achieves 66.3% best@5 success on all 86 tasks, outperforming the prior state-of-the-art (41.9%) by 24.4 points. (2) Adding Observer GRPO training, a locally deployed 14B model reaches 42.9% avg@1 on 63 held-out tasks with unseen fault types, surpassing Claude Sonnet 4.5. (3) The Evolver converts 37 failed trajectories into diagnostic guidance, improving end-to-end avg@5 by 4.8 points while reducing variance by 35%.

This paper addresses the fundamental problem of non-uniform area coverage in multi-agent systems, where different regions require varying levels of attention due to mission-dependent priorities. Existing uniform coverage strategies are insufficient for realistic applications, and many non-uniform approaches either lack optimality guarantees or fail to incorporate crucial real-world constraints such as agent dynamics, limited operation time, the number of agents, and decentralized execution. To resolve these limitations, we propose a novel framework called Density-Driven Optimal Control (D2OC). The central idea of D2OC is the integration of optimal transport theory with multi-agent coverage control, enabling each agent to continuously adjust its trajectory to match a mission-specific reference density map. The proposed formulation establishes optimality by solving a constrained optimization problem that explicitly incorporates physical and operational constraints. The resulting control input is analytically derived from the Lagrangian of the objective function, yielding closed-form optimal solutions for linear systems and a generalizable structure for nonlinear systems. Furthermore, a decentralized data-sharing mechanism is developed to coordinate agents without reliance on global information. Comprehensive simulation studies demonstrate that D2OC achieves significantly improved non-uniform area coverage performance compared to existing methods, while maintaining scalability and decentralized implementability.

To generalise evolution families we consider systems of contractions {varphi(u, v)}_{(u, v) in E} defined on the edges of a graph G = (Ω, E). In this setup the Markov property, or divisibility, can be modelled via varphi(u, v)varphi(v, w) = varphi(u, w) for edges (u, v), (v, w), (u, w) in E. We obtain results in three settings: 1) contractive Banach space operators; 2) positive unital maps on C^{ast}-algebras; and 3) CPTP-maps on trace class operators on a Hilbert space. In the discrete setting, we are able to dilate possibly indivisible families of contractions to divisible families of operators with 'nice' properties (viz. surjective isometries resp. C^{ast}-algebraic automorphisms resp. unitary representations). In the special case of linearly ordered graphs equipped with the order topology, we establish sufficient conditions for strongly continuous dilations of possibly indivisible families in the Banach space and C^{ast}-algebra contexts. To achieve these results we work with string-rewriting systems, and make use of and extend dilation theorems of Stroescu [44], Kraus [23, 24], and vom Ende--Dirr [50].

Feature shaping refers to a family of methods that exhibit state-of-the-art performance for out-of-distribution (OOD) detection. These approaches manipulate the feature representation, typically from the penultimate layer of a pre-trained deep learning model, so as to better differentiate between in-distribution (ID) and OOD samples. However, existing feature-shaping methods usually employ rules manually designed for specific model architectures and OOD datasets, which consequently limit their generalization ability. To address this gap, we first formulate an abstract optimization framework for studying feature-shaping methods. We then propose a concrete reduction of the framework with a simple piecewise constant shaping function and show that existing feature-shaping methods approximate the optimal solution to the concrete optimization problem. Further, assuming that OOD data is inaccessible, we propose a formulation that yields a closed-form solution for the piecewise constant shaping function, utilizing solely the ID data. Through extensive experiments, we show that the feature-shaping function optimized by our method improves the generalization ability of OOD detection across a large variety of datasets and model architectures.

Recent growth in reinforcement learning (RL) has surfaced a need for diverse, specialized training environments. Hand-curated environments with fixed task and reward difficulties become ineffective signals as model performance improves, and sparse rewards over long horizons induce mode collapse on specific workflows or tool structures. World models that simulate environment states have matched pure rollout performance, making them promising for scaling diversity on-demand. However, autoregressive (AR) world models suffer from a left-to-right bias preventing conditioning on globally interdependent state anchors such as tool schemas, prior turns, and expected outcomes. We (i) formalize text-based world modeling as a steerable transition-dynamics problem decomposed into initial state, task context, tool schemas, domain rules, and steering directives, and (ii) curate 239,403 grounded state-action trajectories spanning nine open-source environments and twelve frontier model families. We compare AR LMs and masked diffusion language models (MDLMs), showing MDLMs, via bidirectional anchor-aware denoising, achieve better coherence, groundedness, and empirically validated rollout diversity than LLMs over 4x their parameter size, at comparable inference latency. We introduce a plug-and-play GRPO training framework with deterministic state checks, and perform zero-shot transfer ablations on three OOD environments (ScienceWorld, ALFWorld, AppWorld) across three 1.2B-7B agent backbones (LFM2.5, Qwen3, Mistral), achieving up to 47% absolute gains over baselines without environment-specific fine-tuning. We further conduct behavioral analysis of failure modes under adversarial scenarios and human evaluation on realism, outcome correctness, and training utility. We open-source our work to encourage research in this direction.

Compartmentalization effectively prevents initial corruption from turning into a successful attack. This paper presents O2C, a pioneering system designed to enforce OS kernel compartmentalization on the fly. It not only provides immediate remediation for sudden threats but also maintains consistent system availability through the enforcement process. O2C is empowered by the newest advancements of the eBPF ecosystem which allows to instrument eBPF programs that perform enforcement actions into the kernel at runtime. O2C takes the lead in embedding a machine learning model into eBPF programs, addressing unique challenges in on-the-fly compartmentalization. Our comprehensive evaluation shows that O2C effectively confines damage within the compartment. Further, we validate that decision tree is optimally suited for O2C owing to its advantages in processing tabular data, its explainable nature, and its compliance with the eBPF ecosystem. Last but not least, O2C is lightweight, showing negligible overhead and excellent sacalability system-wide.

Precise spatial modeling in the operating room (OR) is foundational to many clinical tasks, supporting intraoperative awareness, hazard avoidance, and surgical decision-making. While existing approaches leverage large-scale multimodal datasets for latent-space alignment to implicitly learn spatial relationships, they overlook the 3D capabilities of MLLMs. However, this approach raises two issues: (1) Operating rooms typically lack multiple video and audio sensors, making multimodal 3D data difficult to obtain; (2) Training solely on readily available 2D data fails to capture fine-grained details in complex scenes. To address this gap, we introduce Spatial-ORMLLM, the first large vision-language model for 3D spatial reasoning in operating rooms using only RGB modality to infer volumetric and semantic cues, enabling downstream medical tasks with detailed and holistic spatial context. Spatial-ORMLLM incorporates a Spatial-Enhanced Feature Fusion Block, which integrates 2D modality inputs with rich 3D spatial knowledge extracted by the estimation algorithm and then feeds the combined features into the visual tower. By employing a unified end-to-end MLLM framework, it combines powerful spatial features with textual features to deliver robust 3D scene reasoning without any additional expert annotations or sensor inputs. Experiments on multiple benchmark clinical datasets demonstrate that Spatial-ORMLLM achieves state-of-the-art performance and generalizes robustly to previously unseen surgical scenarios and downstream tasks.

The o1 system card identifies the o1 models as the most robust within OpenAI, with their defining characteristic being the progression from rapid, intuitive thinking to slower, more deliberate reasoning. This observation motivated us to investigate the influence of System-2 thinking patterns on model safety. In our preliminary research, we conducted safety evaluations of the o1 model, including complex jailbreak attack scenarios using adversarial natural language prompts and mathematical encoding prompts. Our findings indicate that the o1 model demonstrates relatively improved safety performance; however, it still exhibits vulnerabilities, particularly against jailbreak attacks employing mathematical encoding. Through detailed case analysis, we identified specific patterns in the o1 model's responses. We also explored the alignment of System-2 safety in open-source models using prompt engineering and supervised fine-tuning techniques. Experimental results show that some simple methods to encourage the model to carefully scrutinize user requests are beneficial for model safety. Additionally, we proposed a implementation plan for process supervision to enhance safety alignment. The implementation details and experimental results will be provided in future versions.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

MATSim (Multi-Agent Transport Simulation Toolkit) is an open source large-scale agent-based transportation planning project applied to various areas like road transport, public transport, freight transport, regional evacuation, etc. BEAM (Behavior, Energy, Autonomy, and Mobility) framework extends MATSim to enable powerful and scalable analysis of urban transportation systems. The agents from the BEAM simulation exhibit 'mode choice' behavior based on multinomial logit model. In our study, we consider eight mode choices viz. bike, car, walk, ride hail, driving to transit, walking to transit, ride hail to transit, and ride hail pooling. The 'alternative specific constants' for each mode choice are critical hyperparameters in a configuration file related to a particular scenario under experimentation. We use the 'Urbansim-10k' BEAM scenario (with 10,000 population size) for all our experiments. Since these hyperparameters affect the simulation in complex ways, manual calibration methods are time consuming. We present a parallel Bayesian optimization method with early stopping rule to achieve fast convergence for the given multi-in-multi-out problem to its optimal configurations. Our model is based on an open source HpBandSter package. This approach combines hierarchy of several 1D Kernel Density Estimators (KDE) with a cheap evaluator (Hyperband, a single multidimensional KDE). Our model has also incorporated extrapolation based early stopping rule. With our model, we could achieve a 25% L1 norm for a large-scale BEAM simulation in fully autonomous manner. To the best of our knowledge, our work is the first of its kind applied to large-scale multi-agent transportation simulations. This work can be useful for surrogate modeling of scenarios with very large populations.

We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing discrete diffusion approaches, while allowing significantly greater flexibility in the choice of corruption dynamics. The forward noising process relies on uniformization and enables fast arbitrary corruption. For the reverse process, we derive a simple evidence lower bound (ELBO) based on snapshot latents, instead of the entire noising path, that allows efficient training of standard generative modeling architectures with clear probabilistic interpretation. Our experiments on large-vocabulary discrete generation tasks suggest that the proposed framework outperforms existing discrete diffusion methods in terms of training efficiency and generation quality, and beats autoregressive models for the first time at this scale. We provide the code along with a blog post on the project page : https://oussamazekri.fr/gdds{https://oussamazekri.fr/gdds}.

The open radio access network (O-RAN), with its disaggregated and open architecture, is poised to meet the demands of the next generation of wireless communication. However, to unlock the full potentials of O-RAN, real-time network modeling and optimization are essential. A promising solution for such requirement is the use of network digital twin (NDT). NDT provides a comprehensive view of a network, covering both physical and logical components, including infrastructure, protocols, and algorithms. NDT, as a real-time virtual representation of O-RAN facilitates a variety of operations, such as emulations, test, optimization, monitoring, and analysis of a new configuration in a risk-free environment, without requiring them to be implemented in real network. Such capability enables the vendors and network operators for a faster adoption of new solutions with frequent updates, while ensuring the resiliency of the existing services via planning ahead under various "what-if" scenarios. In this paper, we first describe what exactly NDT means in the context of O-RAN, as well as its key enablers. We then describe the NDT application within the O-RAN in both prior and post-deployment. Finally, we provide two practical uses cases, namely network energy efficiency and traffic steering, where the NDT can be leveraged effectively.

The landscape of high-performance image generation models is currently shifting from the inefficient multi-step ones to the efficient few-step counterparts (e.g, Z-Image-Turbo and FLUX.2-klein). However, these models present significant challenges for directly continuous supervised fine-tuning. For example, applying the commonly used fine-tuning technique would compromises their inherent few-step inference capability. To address this, we propose D-OPSD, a novel training paradigm for step-distilled diffusion models that enables on-policy learning during supervised fine-tuning. We first find that the modern diffusion model where the LLM/VLM serves as the encoder can inherit its encoder's in-context capabilities. This enables us to make the training as an on-policy self-distillation process. Specifically, during training, we make the model acts as both the teacher and the student with different contexts, where the student is conditioned only on the text feature, while the teacher is conditioned on the multimodal feature of both the text prompt and the target image. Training minimizes the two predicted distributions over the student's own roll-outs. By optimized on the model's own trajectory and under it's own supervision, D-OPSD enables the model to learn new concept, style, etc. without sacrificing the original few-step capacity.

Lattice-based planning techniques simplify the motion planning problem for autonomous vehicles by limiting available motions to a pre-computed set of primitives. These primitives are then combined online to generate more complex maneuvers. A set of motion primitives t-span a lattice if, given a real number t at least 1, any configuration in the lattice can be reached via a sequence of motion primitives whose cost is no more than a factor of t from optimal. Computing a minimal t-spanning set balances a trade-off between computed motion quality and motion planning performance. In this work, we formulate this problem for an arbitrary lattice as a mixed integer linear program. We also propose an A*-based algorithm to solve the motion planning problem using these primitives. Finally, we present an algorithm that removes the excessive oscillations from planned motions -- a common problem in lattice-based planning. Our method is validated for autonomous driving in both parking lot and highway scenarios.

We study the adaption of Soft Actor-Critic (SAC), which is considered as a state-of-the-art reinforcement learning (RL) algorithm, from continuous action space to discrete action space. We revisit vanilla discrete SAC and provide an in-depth understanding of its Q value underestimation and performance instability issues when applied to discrete settings. We thereby propose Stable Discrete SAC (SDSAC), an algorithm that leverages entropy-penalty and double average Q-learning with Q-clip to address these issues. Extensive experiments on typical benchmarks with discrete action space, including Atari games and a large-scale MOBA game, show the efficacy of our proposed method. Our code is at: https://github.com/coldsummerday/SD-SAC.git.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Out-of-distribution (OOD) detection and segmentation are crucial for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. While prior research has primarily focused on unimodal image data, real-world applications are inherently multimodal, requiring the integration of multiple modalities for improved OOD detection. A key challenge is the lack of supervision signals from unknown data, leading to overconfident predictions on OOD samples. To address this challenge, we propose Feature Mixing, an extremely simple and fast method for multimodal outlier synthesis with theoretical support, which can be further optimized to help the model better distinguish between in-distribution (ID) and OOD data. Feature Mixing is modality-agnostic and applicable to various modality combinations. Additionally, we introduce CARLA-OOD, a novel multimodal dataset for OOD segmentation, featuring synthetic OOD objects across diverse scenes and weather conditions. Extensive experiments on SemanticKITTI, nuScenes, CARLA-OOD datasets, and the MultiOOD benchmark demonstrate that Feature Mixing achieves state-of-the-art performance with a 10 times to 370 times speedup. Our source code and dataset will be available at https://github.com/mona4399/FeatureMixing.

Standard continuous-depth models, such as Neural Ordinary Differential Equations (NODEs), offer significant advantages in modeling physical systems by learning continuous vector fields rather than discrete temporal steps. However, when applied to complex dynamical systems, standard NODEs frequently struggle with highly nonlinear dynamics. This paper investigates the Frequency-domain Neural ODE (FNODE), an architecture that projects continuous temporal dynamics into the frequency domain using the Fast Fourier Transform (FFT). By operating in the frequency domain, the model provides better generalization to the dynamical system. The architecture is empirically evaluated against discrete models, specifically Gated Recurrent Units (GRUs) and Long Short-Term Memory (LSTMs), and other continuous-depth variants, including Augmented Neural ODE (ANODE), across four distinct dynamical systems: the Lotka-Volterra model, the forced Duffing oscillator, the Van der Pol oscillator, and the Lorenz system. To rigorously assess generalization and robustness, curriculum and ensemble learning are used to evaluate the model's convergence by estimating confidence intervals across different ensemble models. The empirical results demonstrate that the FNODE architecture achieves better generalization while exhibiting remarkable convergence stability.

Post-training quantization (PTQ) is widely regarded as one of the most efficient compression methods practically, benefitting from its data privacy and low computation costs. We argue that an overlooked problem of oscillation is in the PTQ methods. In this paper, we take the initiative to explore and present a theoretical proof to explain why such a problem is essential in PTQ. And then, we try to solve this problem by introducing a principled and generalized framework theoretically. In particular, we first formulate the oscillation in PTQ and prove the problem is caused by the difference in module capacity. To this end, we define the module capacity (ModCap) under data-dependent and data-free scenarios, where the differentials between adjacent modules are used to measure the degree of oscillation. The problem is then solved by selecting top-k differentials, in which the corresponding modules are jointly optimized and quantized. Extensive experiments demonstrate that our method successfully reduces the performance drop and is generalized to different neural networks and PTQ methods. For example, with 2/4 bit ResNet-50 quantization, our method surpasses the previous state-of-the-art method by 1.9%. It becomes more significant on small model quantization, e.g. surpasses BRECQ method by 6.61% on MobileNetV2*0.5.

Large language model agents now act on codebases, browsers, operating systems, calendars, files, and tool ecosystems, but the benchmarks used to evaluate them are fragmented: each emphasizes a different unit of measurement (final task success, tool-call validity, repeated-pass consistency, trajectory safety, or attack robustness). A line of 2024-2025 work has converged on the diagnosis that a single accuracy column is no longer the right unit of comparison for deployable agents. AgentAtlas extends this line of work with four components: (i) a six-state control-decision taxonomy (Act / Ask / Refuse / Stop / Confirm / Recover); (ii) a nine-category trajectory-failure taxonomy with two orthogonal hierarchical labels (primary_error_source, impact); (iii) a taxonomy-aware vs. taxonomy-blind methodology that measures how much of a model's apparent capability comes from the supervision in the prompt; and (iv) a benchmark-coverage audit mapping fifteen agent benchmarks against six behavioral axes. To demonstrate the methodology we run a small fixed eight-model set (1,342 generated items, four frontier closed and four open-weight) under both prompt modes. Removing the explicit label menu drops every model's trajectory accuracy by 14-40 pp to a tight 0.54-0.62 floor regardless of family, and no single model wins on all three of control accuracy, trajectory diagnosis, and tool-context utility retention. We treat the synthetic run as a measurement-protocol demonstration, not a benchmark release.

We establish explicit means via which natural dilations of completely positive (CP) maps can be constructed à la Kraus's IInd representation theorem. To obtain this, we rely on the Choi-Jamiołkowski correspondence and develop a Cholesky algorithm for bi-partite systems. This enables a canonical construction of adjoint actions which recover the behaviour of the original CP-maps. Our results hold under separability assumptions and the requirement that the maps are completely bounded and preserve the subideal of finite rank operators.

On-policy distillation (OPD) has recently become a prominent post-training recipe as it combines two desirable ingredients: on-policy student trajectories and dense teacher supervision, yet how this hybrid changes a model's parameters remains unclear. Across several language and vision-language model pairs and use cases, our analysis yields two main findings. On sparsity, OPD-style updates are small and coordinate-sparse. They are distributed across layers and are usually FFN-heavy. This sparse structure is operationally useful: training only the discovered subnetwork recovers nearly the same performance as full OPD. However, the sparsity-inducing SGD optimizer underperforms AdamW in our optimizer ablation, likely because dense teacher supervision preserves heterogeneous coordinate-wise gradient scales where AdamW's adaptive scaling remains useful. On geometry, the updates are numerically full-rank but spectrally concentrated; they lie mostly away from the principal singular subspaces of the source weights and fall disproportionately on coordinates where the source weights are close to zero. These findings suggest that dense teacher supervision does not turn OPD into ordinary dense parameter rewriting; instead, OPD retains important geometric signatures of on-policy post-training.

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We investigate the reachable set of output token sequences R_y(mathbf x_0) for which there exists a control input sequence mathbf u for each mathbf y in R_y(mathbf x_0) that steers the LLM to output mathbf y from initial state sequence mathbf x_0. We offer analytic analysis on the limitations on the controllability of self-attention in terms of reachable set, where we prove an upper bound on the reachable set of outputs R_y(mathbf x_0) as a function of the singular values of the parameter matrices. We present complementary empirical analysis on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Our results demonstrate a lower bound on the reachable set of outputs R_y(mathbf x_0) w.r.t. initial state sequences mathbf x_0 sampled from the Wikitext dataset. We find that the correct next Wikitext token following sequence mathbf x_0 is reachable over 97% of the time with prompts of kleq 10 tokens. We also establish that the top 75 most likely next tokens, as estimated by the LLM itself, are reachable at least 85% of the time with prompts of kleq 10 tokens. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-centric analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such mechanisms by having agents play a game instead of tossing a coin. The game is designed so an agent's best action is to play randomly, and this play then injects ``randomness'' into the mechanism. This derandomization retains many of the good normative properties of the original randomized mechanism but gives a mechanism that is deterministic and easy, for instance, to audit. We consider three related methods to derandomize randomized mechanism in six different domains: voting, facility location, task allocation, school choice, peer selection, and resource allocation. We propose a number of novel derandomized mechanisms for these six domains with good normative properties. Each mechanism has a mixed Nash equilibrium in which agents play a modular arithmetic game with an uniform mixed strategy. In all but one mixed Nash equilibrium, agents report their preferences over the original problem sincerely. The derandomized methods are thus ``quasi-strategy proof''. In one domain, we additionally show that a new and desirable normative property emerges as a result of derandomization.

Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on quantum low-density parity-check (qLDPC) codes. In many settings, surgery exhibits practical space overheads, while its time overhead remains a bottleneck at O(d) syndrome rounds per operation. In this work, we construct surgery gadgets that perform parallel logical measurements on 2D hypergraph product codes in constant time overhead (O(1)) and near-constant space overhead (O(1)). The reduced time overhead is a result of amortization, as we show, following the formulation by Cowtan et al. (arXiv:2510.14895), that performing d surgery operations in O(d) time is fault tolerant. Our gadgets combine the strengths of different approaches to fault-tolerant logical operations: they partially retain the flexibility of surgery while achieving overheads comparable to transversal gates. Consequently, they are well-suited for near-term experimental realization and demonstrate new possibilities in the design of gadgets for fast logical computation.

Intelligent systems across physics, language and perception often exhibit factorisable structure, yet are typically modelled by monolithic neural architectures that do not explicitly exploit this structure. The separable neural architecture (SNA) addresses this by formalising a representational class that unifies additive, quadratic and tensor-decomposed neural models. By constraining interaction order and tensor rank, SNAs impose a structural inductive bias that factorises high-dimensional mappings into low-arity components. Separability need not be a property of the system itself: it often emerges in the coordinates or representations through which the system is expressed. Crucially, this coordinate-aware formulation reveals a structural analogy between chaotic spatiotemporal dynamics and linguistic autoregression. By treating continuous physical states as smooth, separable embeddings, SNAs enable distributional modelling of chaotic systems. This approach mitigates the nonphysical drift characteristics of deterministic operators whilst remaining applicable to discrete sequences. The compositional versatility of this approach is demonstrated across four domains: autonomous waypoint navigation via reinforcement learning, inverse generation of multifunctional microstructures, distributional modelling of turbulent flow and neural language modelling. These results establish the separable neural architecture as a domain-agnostic primitive for predictive and generative intelligence, capable of unifying both deterministic and distributional representations.