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arXiv2026

Particle Monte Carlo Tree Search

Monte Carlo Tree Search (MCTS) is a widely used approach for policy improvement and action selection in Reinforcement Learning. Due to its sequential and deterministic nature, principled runtime-scaling of MCTS with parallel compute remains a major challenge. We introduce Particle MCTS (PMCTS), a parallel MCTS algorithm which is suited for neural network evaluations, designed for GPU-acceleration with batch-parallelization and retains MCTS's principled approximate policy improvement interpretation. Empirically, PMCTS scales well with parallel compute and consistently outperforms or compares well to the popular heuristic-based baselines across a range of popular discrete- and continuous-action benchmark domains, including Chess, 19x19 Go, 9x9 Go, Gardner Chess, Snake, classical control environments from Brax and LLM reasoning in Sokoban.

cs.LG↗
arXiv2026

Mapping the Emergence of Regularization-Driven Dynamics in Grokking

For overparameterized neural networks, many solutions can fit the training data equally well while behaving very differently on unseen samples. Grokking separates training fit from visible generalization, providing a window for studying how this selection develops during training. We sweep short, fixed-duration weight decay (WD) perturbations across the pre-generalization plateau and measure how they shift later generalization time. Across three grokking tasks, these shifts are unordered early in the plateau but later form a stable dose ordering before visible generalization, with stronger WD increases leading to earlier generalization and stronger WD decreases leading to later generalization. Test-loss barriers between perturbed and baseline generalization checkpoints collapse toward zero while the ordered timing effects persist. A similar response reorganization is observed under $\ell_1$ regularization in the grokking setting of Junior et al. (2025). Drawing on Waddington's developmental landscape as an analogy, we call this combination of increasingly constrained solution selection and persistent dose-ordered timing shifts the canalization of grokking solution selection. Together, our response maps and loss-barrier measurements reveal a dynamical reorganization before visible generalization that is consistent with the theoretical picture of regularization-driven motion along a stable slow manifold (Boursier et al., 2025).

cs.LG↗
arXiv2026

Contact Geometry and Covariance Deficits in Volume-Sampled Least Squares

We classify when ordinary fixed-size volume sampling followed by unweighted least squares attains its sharp coefficient-covariance ceiling on a fixed design. For a real whitened design without coloops and a fixed positive-loss residual, the contact space is unchanged at every strict-interior sample size. Its possible nonzero values form a finite orthogonal family: each maximal parallel class of normalized Naimark-complement rows determines a deletion nullspace of dimension one less than the class size. A single residual attains an entire query precisely when the query range lies in one class space. The proof starts from two-sided Loewner comparison of every normalized covariance deficit with an explicit leave-one-out operator, using supported omission moments and reverse deletion. Residual augmentation provides resolvent and second-moment upper bounds, while complement geometry yields query-specific margins, angular concentration, local alignment, and a multi-output energy obstruction. Exact families give closed-form margins and covariances, exhibit support-boundary jumps, and approach the ceiling despite a uniformly positive geometric margin. Finally, the same moment identities give upper and lower bounds on expected fixed-query squared-loss excess. The subset draw is the only randomness; all support and endpoint restrictions are explicit.

cs.LG↗
arXiv2026

The Implications of Linguistic Illegibility for LLM Security

LLMs are trained to generate natural language. However, various strands of evidence indicate that an LLM's externalized linguistic outputs and mechanistically-extracted linguistic features can be an unreliable lens for understanding internal model computation. We introduce the term ``linguistic illegibility'' to broadly refer to scenarios in which an LLM's externalized or mechanistically-probed language artifacts fail to represent how the model actually thinks. We argue that the specter of linguistic illegibility is unavoidable for LLMs whose internal computations are not directly expressed via language, but rather math over activation spaces (with lossy translations between activation spaces and natural language happening at the bookends). If linguistic illegibility is always possible, then security mechanisms that rely on a model's linguistic self-reporting (e.g., chain-of-thought monitoring, constitutional self-critique, activation probing for linguistically-defined feature vectors) can never be completely sound; the model sandbox will always need isolation techniques whose guarantees do not depend on reading a model's linguistic state at all. We argue that observing a model's outputs using taint tracking is a promising approach for an effective sandbox: regardless of how a model linguistically self-reports, a taint tracking policy can define, a priori, various pieces of system state that should never be influenced by model-produced data. We also discuss several additional sandboxing mechanisms (e.g., robust virtualization, third-party auditing of sandboxing configurations) which collectively provide a critical floor beneath linguistic monitoring, and would have mitigated recent sandbox exploits by frontier models.

cs.LG↗
arXiv2026

VoxReason: Auditing Source-Grounded Speech Plans Before Synthesis

Plan accuracy alone cannot show whether a speech-delivery decision follows its source: a fixed prior may match the original label yet fail to respond appropriately when a cue changes. VoxReason provides a 100-case verifier benchmark that holds each utterance fixed, edits one designated source-label cue, and scores cited evidence, eight plan fields, and the permitted response. On a source-key-disjoint test of 24 cases, a source-emotion prior reaches plan-slot accuracy 0.958, but none of the 24 edited neutral targets appears in its training labels; its required-change accuracy is 0.000. This diagnoses the support boundary of this prior, not its performance on supported edits. In a complementary 32-case emotion-disjoint test, the prior has seen all edited neutral targets but neither original test emotion; its plan-slot accuracy is 0.219 and required-change accuracy is 1.000. The partitions reuse and overlap the same 100 cases, so these deterministic diagnostics are not independent cohorts or learned-planner results. The benchmark evaluates derived labels and structured plans, not audio input, generated speech, or listener judgments.

cs.SD↗
arXiv2026

Robust PAC Learning of Concurrent Stochastic Games

We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage. Crucially, we introduce a Nash margin characterisation that enables principled reasoning about equilibrium existence: the framework either returns an $\varepsilon$-approximate NE whose social-welfare value is $\varepsilon$-close to optimal, or provides a sound certificate that no exact NE exists. Under a minimum reachability condition $p_{\mathrm{reach}}>0$ over relevant state-action pairs, the algorithm terminates after a polynomial number of trajectory samples, with sample complexity $\widetilde{O}\left( {R_{\max}^2 H^4 |S|^2 |A| / (p_{\mathrm{reach}} \varepsilon^2)} \right)$. Empirical results on benchmark CSGs demonstrate near-optimal performance, correct handling of equilibrium (non-)existence, and sample complexity consistent with theory.

cs.LG↗
arXiv2026

An Identifiability Theory of Masked Prediction: Mode Blindness and Mask Schedules

Masked prediction learns to infer missing variables from visible context selected by a mask schedule. When does small excess risk guarantee recovery of the true joint distribution? We study this question on finite product spaces under masked-block log loss, with conditionals induced by a single joint distribution. To quantify recovery, we introduce an $\varepsilon$-identifiability modulus measuring the worst-case error among joint distributions with population excess risk at most $\varepsilon$. For data with separated modes pinned down by sufficiently large visible contexts, schedules that always retain such contexts can permit nonvanishing mode-weight errors while incurring exponentially small excess risk. An information decomposition explains why: the loss captures mode-weight mismatch only where the visible context leaves the mode uncertain. We prove two-sided bounds showing that, over a fixed range of mode weights, sensitivity to mode reweighting is governed by residual mode uncertainty averaged over the mask schedule. Assigning schedule mass to low-visibility masks that retain this uncertainty yields recovery bounds within the reweighting family. Beyond this family, positive full-mask probability characterizes uniform control of joint KL divergence by excess risk. Exact calculations and controlled gradient optimization validate these predictions.

cs.LG↗
arXiv2026

RealSWE: A Compositional Evaluation of Coding Agents under Realistic User Requests

Coding agents are now commonly evaluated on the SWE-bench family of benchmarks, whose tasks are built from curated GitHub issues: long, structured, and information-rich. Real user requests, however, are typically far shorter and less structured. To characterize this gap, we define a six-category information taxonomy and four dimensions of linguistic style, and apply them to real user prompts from SWE-chat and problem statements from SWE-bench Verified and Pro. We find that requests carrying only a problem statement, alone or with limited additional context, account for 88% of real prompts but just 7% of benchmark problems. Furthermore, 87% of real prompts are casually written whereas 94% of benchmark problems are formal. Guided by these observations, we introduce RealSWE, 381 multi-variant task families derived from SWE-bench Verified and Pro. Variants within each family share the same underlying task and gold patch while differing only in information composition and linguistic style. Evaluating seven contemporary LLMs with RealSWE, we find that i) realistic inputs reduce resolution rates by 6.4 pp on average and can change model rankings. Controlled analysis further shows that ii) including Desired Behavior and Motivation significantly affects performance, whereas Environment Information and Reproduction Steps merely add tokens without measurable benefit; iii) linguistic style has only small, model-dependent effects. These findings provide actionable guidance for users and agents: explicitly stating the desired behavior and motivation, which most real prompts omit, substantially improves the LLM's software engineering performance.

cs.AI↗
arXiv2026

The PUR-1 Cyber-Physical Digital Twin

Digital twin technologies have the potential to improve operational flexibility and responsiveness capabilities of nuclear systems. To provide decision support, cyber event characterization, state estimation, predictive control, and real-time dynamic processing of operational data, however, an efficient digital twin needs to integrate multiple models (data-driven as well as physics-based) with explainability while at the same time maintain two-way synchronization with the physical facility at a time constant less than its operational cycle. In this work, we present the Purdue University Reactor One Digital Twin (PUR-1 DT), a cyber-physical digital twin with a complete high-fidelity physics-based and AI-driven virtual model stack (neutronics, thermal-hydraulics, point kinetics) which provides closed-loop explainable diagnostics, forecasting, predictive control, and action recommendation back to the reactor via two-way communications and a cyber-physical testbed. We demonstrate real-time synchronized state estimation and short-term forecasting over a full reactor operational cycle and conduct a series of benchmarking experiments to validate accuracy and latency. Our results show good agreement with experimental results and lay the groundwork for further development and experimental demonstration of DT-enabled functionalities in real-world facilities.

cs.CE↗
arXiv2026

"Train classical, deploy quantum" requires rethinking generalization

Generative models have become central across science and industry, from image and text synthesis to the design of molecules and materials. Quantum generative models are considered one of the most promising applications for quantum computers, since a quantum circuit naturally produces samples from the distribution it encodes, and for suitable circuits that distribution is believed to be hard for any classical computer to reproduce. A leading strategy trains these models on a classical computer and reserves the quantum device for generating samples at deployment. This is possible when the training loss can be evaluated on a classical computer. A prime example is the maximum mean discrepancy (MMD$^2$), a moment-matching loss that compares the model and the data through their Pauli-$Z$ correlations. Research so far has asked whether such models can be trained and whether their sampling is hard; whether minimizing such an objective yields a model that \emph{generalizes}, rather than one that merely reproduces the training statistics, remains poorly understood. We benchmark thirteen quantum and classical generative models by direct sampling on two application-inspired datasets: first a cardinality-constrained dataset at up to $30$ qubits and second a dataset of genomic single-nucleotide variants, whose valid set is the observed data. Models that converge the loss to the same value differ widely in how much of the unseen valid set they cover. These results indicate that a converged moment-matching loss is not a reliable measure of generalization, and that a train-classical, deploy-quantum workflow has to measure generalization by sampling the trained model, a step that at the sizes of interest is believed to require the quantum device.

quant-ph↗
arXiv2026

Capability-Gated Language Models: Security Composes, Utility Does Not

Deployed language model safeguards (safety fine-tuning, filtering, unlearning) vary by principal only outside the model weights: filters are reconfigured, tiers are multiplied, and artefacts are reissued; inside one set of weights every request meets the same model configuration. This motivates us to define capability-gated deployment: per-principal access control inside one set of weights, whose configurations form a lattice - meets accumulate a principal's restrictions and joins pool a coalition's reach. We instantiate it by sparse rank gating over an existing nested-factorisation mechanism, guide profile search with one-pass attribution, and read every result once from a pre-registered held-out split. Security approximately composes: provably exactly at meets under a monotone-elicitation assumption we falsify pointwise. In two lineages the median held-out meet deepens suppression; the one effect surviving correction strengthens it. Utility does not: individually harmless profiles can compose to retention and fluency damage, and no compositional bound exists.

cs.CR↗
arXiv2026

Physics-Informed Deep Learning for False Ventricular Tachycardia Alarm Reduction in the ICU

False ventricular tachycardia (VT) alarms are a leading contributor to alarm fatigue in intensive care units. We propose a deep learning framework combining a 1D SE-ResNet with ICU-realistic data augmentations and a physics-informed auxiliary reconstruction task based on the three-element Windkessel hemodynamic model, implemented as a differentiable forward simulation. By requiring the network's latent representation to produce physiologically plausible arterial pressure waveforms, artifact-driven ECG patterns are penalized while true VT remains coherent across modalities. Evaluated on the VTaC benchmark under a strict real-time protocol (10-second pre-alarm window), our method achieves a 5-point Challenge Score improvement over prior state-of-the-art. Ablation studies confirm that the physics-informed objective is the primary performance driver, providing gains in accuracy, 2x label efficiency, and more localized and clinically meaningful ECG segments.

cs.LG↗
arXiv2026

Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning

Chain-of-thought reasoning provides a structured computation between a model's input and final answer. Yet it is often evaluated through endpoint accuracy, which ignores the path taken to reach that answer. An emerging line of work addresses this limitation using entropy profiles, which track how uncertainty evolves over the reasoning process but do not reveal which competing hypotheses account for that uncertainty. We introduce answer-distribution trajectories, a stochastic-dynamics-inspired representation that tracks the model's full predictive distribution over answers as reasoning unfolds. As a strictly finer representation than endpoint and entropy summaries, answer-distribution trajectories enable us to characterize a trace through a dynamical reasoning profile spanning exploration, revision, motion, and commitment, and to distinguish different dynamical mechanisms of reasoning success and failure. Across sixteen open-weight language models and four reasoning benchmarks, we show that traces with the same endpoint and similar entropy profiles can exhibit substantially different reasoning dynamics. We further find substantial variation in these dynamics both within and across models and tasks, with different objectives favoring different dynamical profiles. Additionally, we show that training and inference choices systematically reshape these profiles. Our results suggest that answer-distribution trajectories provide a rich framework for analysing and evaluating the dynamics of LLM reasoning.

cs.AI↗
arXiv2026

DynaTokens: Controlling Token Dynamics for Continual Video-Language Understanding

Continual VideoQA with multimodal LLMs remains challenging because sequential adaptation induces task interference, while storing task-specific prompts becomes impractical as task sequences grow. We introduce DynaTokens, a transformer-based token generator that dynamically produces fine-tuning tokens on demand, enabling task-adaptive prompt updates through shared generation weights. To mitigate forgetting, we introduce meta-learning-inspired regularisers that look ahead to avoid task-specific sharp update directions while anchoring the evolving generator to prior-task behaviours. We theoretically connect this objective to sharpness-aware optimisation, showing how it favours flatter cross-task minima and improves retention. DynaTokens combines gradient-free routing based on robust pretrained token and visual embeddings with lightweight auxiliary multimodal supervision, reducing router drift during continual adaptation. Across standard continual VideoQA benchmarks, DynaTokens achieves higher average accuracy and substantially lower forgetting than strong baselines. It also improves zero-shot generalisation and remains effective in longer domain-incremental sequences with extended task shifts. Finally, we introduce a challenging ImageQA->VideoQA protocol and show that DynaTokens enables robust cross-modal continual transfer.

cs.CV↗
arXiv2026

Can LLMs Discover Scientific Laws in Real and Parallel Worlds?

Scientific law discovery has long been central to scientific progress, proceeding through iterative cycles of generating hypotheses, testing them against empirical evidence, and refining them under scientific constraints. As large language models (LLMs) become increasingly involved in scientific research, whether they can discover scientific laws and how to evaluate this ability remain open questions. A central evaluation challenge is to move beyond familiar published equations while keeping discovery tasks grounded in scientific data and constraints. We introduce SciLaws-Bench, a curated collection of scientific task packages grounded in the source literature, each linking a scientific problem, supporting data, published reference equations, and scientific-validity rubrics. Through agent-assisted curation and human verification, we assemble 118 problems spanning six disciplines, drawing on 381 papers, 291 candidate laws, and roughly 8M data points. Each problem supports two complementary evaluation settings. SciLaws-Real uses fixed scientific data to evaluate proposed laws for held-out predictive fit and scientific validity. SciLaws-Parallel evaluates recovery of a newly synthesized structural variant of a published equation through active queries to a simulator calibrated to the source data. Our evaluation reveals three limitations: good predictive fit need not imply scientific validity, recovering a published formula does not establish recovery of its new structural terms, and candidate selection remains a bottleneck in scientific law discovery. Project page: https://yiyihum.github.io/SciLaws-Bench

cs.AI↗
arXiv2026

From Fixed Keys to Readable Schemas: Small Language Models for Vehicle Agent Function Calls

In-vehicle assistants must translate natural-language requests into accurate vehicle function calls under strict memory and latency constraints, making small language models (SLMs) attractive for on-device deployment. For such models, a key design choice is how the available function surface is presented. Two approaches are to represent each function with a dedicated Functional Token (FT) or provide function schemas directly in the prompt. FTs enable compact inference but are restricted to functions learned during training, whereas Schema-in-Prompt (SIP) can generalize to unseen functions at the cost of longer prompts and higher inference overhead. We introduce a benchmark of 9,822 single-turn examples spanning 79 vehicle functions derived from Android Automotive, including held-out functions and requests requiring refusal. We compare both approaches under matched fine-tuning across four SLMs from 270M to 1.7B parameters. On functions seen during training, scaling provides limited benefit: the 270M model can match the 1.7B model, and the highest Seen accuracy in our main grid occurs at 0.6B. On held-out functions, FT achieves zero accuracy by construction, whereas SIP generalizes and improves substantially with scale. On out-of-scope requests, FT can invoke an unavailable function it was trained to emit, while SIP more reliably refuses based on the functions offered. This flexibility comes with a higher inference cost, chiefly the latency of processing the schema prompt. Our theoretical analysis formalizes why only SIP can predict functions withheld as training targets and why longer schema contexts increase inference cost. Overall, function-surface representation, rather than model scale alone, determines the capabilities and failure modes of SLM-based vehicle function calling.

cs.LG↗
arXiv2026

Mixed Data Clustering Survey and Challenges

The advent of the big data paradigm has transformed how industries manage and analyze information, ushering in an era of unprecedented data volume, velocity, and variety. Within this landscape, mixed-data clustering has become a critical challenge, requiring innovative methods that can effectively exploit heterogeneous data types, including numerical and categorical variables. Traditional clustering techniques, typically designed for homogeneous datasets, often struggle to capture the additional complexity introduced by mixed data, underscoring the need for approaches specifically tailored to this setting. Hierarchical and explainable algorithms are particularly valuable in this context, as they provide structured, interpretable clustering results that support informed decision-making. This paper introduces a clustering method grounded in pretopological spaces. In addition, benchmarking against classical numerical clustering algorithms and existing pretopological approaches yields insights into the performance and effectiveness of the proposed method within the big data paradigm.

cs.LG↗
arXiv2026

Truncated Kernel Stochastic Gradient Descent with General Losses and Spherical Radial Basis Functions

In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an adaptive regularization strategy. By leveraging the infinite series expansion of spherical radial basis functions, this strategy projects the stochastic gradient onto a finite-dimensional hypothesis space, which is adaptively scaled according to the bias-variance trade-off, thereby enhancing generalization performance. To handle the gradient nonlinearity arising from general losses, we develop a new generalization framework combining an inequality-based characterization of the kernel-induced covariance operator with optimization techniques. We prove that both the last iterate and the suffix average converge at minimax-optimal rates, and we further establish optimal strong convergence in the reproducing kernel Hilbert space. Our framework accommodates a broad class of classical loss functions, including least-squares, Huber, and logistic losses. Moreover, the proposed algorithm significantly reduces computational complexity and achieves optimal storage complexity by incorporating coordinate-wise updates from linear SGD, thereby avoiding the costly pairwise operations typical of kernel SGD and enabling efficient processing of streaming data. Finally, extensive numerical experiments provide empirical support for the theoretical results and the computational advantages of our algorithm.

cs.LG↗