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arXiv2026

Rate-Coding Bundle Memory: A Unified Model of Memory and Control for Symbolic Computation in the Brain

We propose a neurobiologically plausible model of cognition that combines the advantages of connectionist and symbolic systems, and that can explain a wide range of cognitive phenomena. This model, called Rate-Coding Bundle Memory (RCBM), is based on the Symbolic Subsystem Hypothesis, which posits that the brain implements a symbolic subsystem within its fundamentally connectionist nature. RCBM is a hybrid model that uses rate coding to represent symbols in a continuous space, and it uses a bundle memory system to store and retrieve these symbols. The model is capable of solving a wide range of cognitive phenomena, including one-shot learning, pattern separation, and the binding problem. We argue that RCBM provides a promising framework for understanding the nature of cognition, and that it can be used to develop more sophisticated models of cognition in the future.

q-bio.NC↗
arXiv2026

Learning Fast Monomial Orders for Gröbner Basis Computations

The efficiency of Gröbner basis computation, the standard engine for solving systems of polynomial equations, depends on the choice of monomial ordering. Despite a near-continuum of possible monomial orders, most implementations rely on static heuristics such as GrevLex, guided primarily by expert intuition. We address this gap by casting the selection of monomial orderings as a reinforcement learning problem over the space of admissible orderings. Our approach leverages domain-informed reward signals that accurately reflect the computational cost of Gröbner basis computations and admits efficient Monte Carlo estimation. Experiments on benchmark problems from systems biology and computer vision show that the resulting learned policies consistently outperform standard heuristics, yielding substantial reductions in computational cost. Moreover, we find that these policies resist distillation into simple interpretable models, providing empirical evidence that deep reinforcement learning allows the agents to exploit non-linear geometric structure beyond the scope of traditional heuristics.

cs.SC↗
arXiv2026

Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests

Symbolic regression has emerged as a powerful tool for artificial intelligence-driven scientific discovery by learning interpretable analytical expressions that reveal governing relationships directly from data. Existing methods, however, often rely on heuristic search, struggle to balance predictive accuracy with expression complexity in noisy settings, and offer limited characterization of symbolic uncertainty. Probabilistic approaches that address these challenges in a unified manner remain underexplored. We introduce a probabilistic symbolic regression framework that represents mathematical expressions as ensembles of symbolic trees. A regularizing prior over tree topology controls expression complexity, while an Occam's window-based posterior summary captures uncertainty across multiple plausible symbolic models. Given the limited existing theoretical treatment of symbolic regression, we develop posterior concentration guarantees when symbolic expressions approximate the underlying relationship arbitrarily well, with a near-parametric rate when an exact finite formula exists. Additionally, we establish a sharp oracle concentration result under symbolic misspecification. Comparisons of our proposed framework with state-of-the-art competitors demonstrate superior predictive accuracy, optimal symbolic complexity, and stable structural recovery when learning benchmark scientific equations, together with the identification of scientifically interpretable descriptor formulas in a challenging materials discovery application.

stat.ME↗
arXiv2026

Anchored Scenario Coverage for Failure-Aware First-Hit Batch Inverse Design

Early discovery of at least one valid design satisfying a target requirement is a central objective in failure-prone closed-loop inverse design. A natural batch baseline ranks candidates by a product-form marginal valid-hit score, but selecting the highest-ranked candidates independently can produce redundant recommendations under predictive uncertainty and waste the experiment budget. We introduce ARC-SC(Anchored Risk-Constrained Scenario Coverage), a batch acquisition method that preserves strong marginal candidates as anchors and allocates the remaining batch positions by maximizing complementary coverage over predictive target scenarios under a risk-support constraint. In frozen-oracle closed-loop simulations on superconductivity and JARVIS materials-property benchmarks, ARC-SC yields a statistically supported improvement in first-hit discovery and remains competitive with directionally favorable first-hit performance on more challenging design space. These results establish ARC-SC as a POF-anchored, scenario-aware batch strategy for improving early valid-target discovery under structured experimental failure.

math.OC↗
arXiv2026

Where Induction Runs Out: Description-Length Difficulty and the Memorisation Gap in Integer-Sequence Benchmarks

Integer sequences from the On-Line Encyclopedia of Integer Sequences (OEIS) are increasingly used to benchmark mathematical reasoning in language models. We ask what such benchmarks actually measure, using an exactly computable reference learner: two-part minimum description length (MDL) over the class of P-recursive (holonomic) recurrences, evaluated on every prefix of a sequence as terms arrive. Three findings follow. First, MDL difficulty is a parameter count. The discovery point nd, the first prefix length at which a symbolic hypothesis beats verbatim storage, is predicted almost exactly by a combinatorial identifiability bound on the selected operator's order and degree. It is invariant to term magnitude: scaling Fibonacci over twelve orders of magnitude leaves nd unchanged, because a hypothesis must encode its own initial conditions and the magnitude cancels. Second, at scale the learner exhibits a regime our curated corpus could not produce even once: across 20,000 OEIS sequences, 89.98% of those that fit a recurrence on some prefix fit none at full length. We call this the wilderness -- induction acquires a theory, loses it, and never recovers. Third, evaluating three language models on sequences stratified by these MDL regimes refuted our pre-registered hypothesis: models do not confabulate where MDL reports no theory, but hedge appropriately. Confident errors are inverted, concentrating on the easy stratum, where apparent competence tracks recognition of the sequence rather than induction of its rule. OEIS-derived benchmarks therefore substantially measure memorisation, and MDL supplies a cheap, contamination-free difficulty signal they currently lack. Code and data are released.

cs.LG↗
arXiv2026

Spectral and combinatorial methods for efficiently computing the rank of unambiguous finite automata

A zero-one matrix is a matrix with entries from $\{0, 1\}$. We study monoids containing only such matrices. A finite set of zero-one matrices generating such a monoid can be seen as the matrix representation of an unambiguous finite automaton, an important generalisation of deterministic finite automata which shares many of their good properties. Let $\mathcal{A}$ be a finite set of $n \times n$ zero-one matrices generating a monoid of zero-one matrices, and $m$ be the cardinality of $\mathcal{A}$. We study the computational complexity of computing the minimum rank of a matrix in the monoid generated by $\mathcal{A}$. By using linear-algebraic techniques, we show that this problem is in $\textsf{NC}$ and can be solved in $\mathcal{O}(mn^4)$ time and $\mathcal{O}(n^2)$ space. We also provide a combinatorial algorithm finding a matrix of minimum rank in $\mathcal{O}(mn^4)$ time and $\mathcal{O}(n^3)$ space. As a byproduct, we show a very weak version of a generalisation of the Černý conjecture: there always exists a straight line program of size $\mathcal{O}(n^2)$ describing a product resulting in a matrix of minimum rank. For the special case corresponding to total DFAs (that is, for the case where all matrices have exactly one 1 in each row), the minimum rank is the size of the smallest image of the set of all states under the action of a word. Our combinatorial algorithm finds a matrix of minimum rank in time $\mathcal{O}(n^3 + mn^2)$ in this case.

cs.FL↗
arXiv2026

Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems

Neural operators provide fast surrogates for partial differential equation (PDE) solvers, but their reliability can degrade for high-dimensional spatial inputs and inverse or repeated inference. State-only training constrains solution values but not the learned input--output response. We study sensitivity-constrained neural operators (SC-NOs), which augment standard training with sampled solver-derived Jacobian supervision. Selected sensitivities from differentiable solvers or discrete adjoints are matched during training, allowing response information to be amortized across minibatches without imposing the full Jacobian at every update. We evaluate SC-NO on advection--diffusion and RANS--Spalart--Allmaras benchmarks, input-dimensionality scaling tests, long-horizon autoregressive rollout, and a shallow-water Tohoku tsunami source-inversion case. Sensitivity supervision improves forward prediction and yields larger gains in gradient-based inverse reconstruction of distributed fields. Scaling experiments show an improved accuracy--cost tradeoff for high-dimensional gridded inputs, while ablations indicate that state values and Jacobian information provide complementary supervision. In the tsunami case, SC-FNO reconstructs gridded seafloor deformation from sparse early gauge observations and forecasts subsequent wave propagation in a near-real-time proof-of-concept workflow. These results support sampled sensitivity supervision as a practical way to improve neural PDE surrogates when forward accuracy, inverse stability, robustness, and computational cost must be considered together.

cs.LG↗
arXiv2026

Visual Token Coding for Video Multimodal Large Language Models

In this paper, we propose a new token compression paradigm for video Multimodal Large Language Models (MLLMs), termed Visual Token Coding (VTC). Inspired by classical video coding principles, e.g., HEVC, VTC performs structured compression by predicting the I/P frames of a video and measuring their frame-wise residuals to estimate token redundancy. Based on this baseline framework, we also enhance VTC with a set of novel dynamic designs, such as Dynamic Resolution Input (DyRSO), Dynamic Token Allocation (DyTA), and Spatial Coverage Top-K (SC-TopK), and term this new approach $VTC_{Dy}$. To validate VTC, we apply it to three MLLMs and conduct experiments on multiple video understanding benchmarks. The experimental results show that VTC$_{\mathrm{Dy}}$ achieves an average performance retention of 100.1% with a 50% token budget for Qwen3-VL, while still retaining 97.8% of the average performance when the token budget is reduced to 25%. Moreover, as a plug-and-play design, VTC requires no additional tuning of MLLMs for token coding. Our code is available at https://github.com/Msr233/VTC.

cs.CV↗
arXiv2026

Fully Distributed GNE Algorithms for Multi-Robot Placement without Consensus on Multipliers

Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.

cs.LG↗
arXiv2026

VIBE: Video Instruction-aligned Background music gEneration

Current video-to-music (V2M) models lack semantic control and fail to penalize instruction violations, largely due to their reliance on reconstruction objectives and the representational bottleneck of static cross-modal conditioning in Diffusion Autoregressive (DAR) architectures. To resolve this, we introduce VIBE, a novel text-and-video-to-music (T+V2M) generation model that leverages: (1) Conditioning Connection, a depth-wise cross-layer conditioning mechanism that dynamically bridges the planning and diffusion refinement heads and (2) a comprehensive reward modeling taxonomy, optimizing for both hard, verifiable constraints (e.g., tempo, key) and soft, subjective qualities (e.g., musicality, multimodal alignment) with a structured 5-stage training curriculum. Upon evaluation using audio-visual alignment, instruction following, and audio quality metrics, along with a subjective human evaluation study, we observe that VIBE demonstrates enhanced controllability and instruction adherence while performing comparably to most evaluated baselines on generation fidelity and multimodal alignment.

cs.SD↗
arXiv2026

Aligning Agentic World Models via Knowledgeable Experience Learning

Current Large Language Models (LLMs) exhibit a critical modal disconnect: they possess vast semantic knowledge but lack the procedural grounding to respect the immutable laws of the physical world. Consequently, while these agents implicitly function as world models, their simulations often suffer from physical hallucinations-generating plans that are logically sound but physically unexecutable. Existing alignment strategies predominantly rely on resource-intensive training or fine-tuning, which attempt to compress dynamic environmental rules into static model parameters. However, such parametric encapsulation is inherently rigid, struggling to adapt to the open-ended variability of physical dynamics without continuous, costly retraining. To bridge this gap, we introduce WorldMind, a framework that autonomously constructs a symbolic World Knowledge Repository by synthesizing environmental feedback. Specifically, it unifies Process Experience to enforce physical feasibility via prediction errors and Goal Experience to guide task optimality through successful trajectories. Experiments on EB-ALFRED and EB-Habitat demonstrate that WorldMind achieves superior performance compared to baselines with remarkable cross-model and cross-environment transferability.

cs.CL↗
arXiv2026

Transformer-Based Autonomous Driving Models and Deployment-Oriented Compression: A Survey

Transformer-based models are becoming a central paradigm in autonomous driving because they can capture long-range spatial dependencies, multi-agent interactions, and multimodal context across perception, prediction, and planning. At the same time, their deployment in real vehicles remains difficult because high-capacity attention-based architectures impose substantial latency, memory, and energy overhead. This survey reviews representative Transformer-based autonomous driving models and organizes them by task role, sensing configuration, and architectural design. More importantly, it examines these models from a deployment-oriented perspective and analyzes how efficiency constraints reshape model design choices in practice. We further review compression and acceleration strategies relevant to Transformer-based driving systems, including quantization, pruning, knowledge distillation, low-rank approximation, and efficient attention, and discuss their benefits, limitations, and task-dependent applicability. Rather than treating compression as an isolated post-processing step, we highlight it as a system-level design consideration that directly affects deployability, robustness, and safety. Finally, we identify open challenges and future research directions toward standardized, safety-aware, and hardware-conscious evaluation of efficient autonomous driving systems.

cs.LG↗
arXiv2026

SkillSafetyBench: Evaluating Agent Safety under Skill-Facing Attack Surfaces

Reusable skills are becoming a common interface for extending large language model agents, packaging procedural guidance with access to files, tools, memory, and execution environments. However, this modularity introduces attack surfaces that are largely missed by existing safety evaluations: even when the user request is benign, unsafe influence may reside in skill guidance, local artifacts, or execution-environment files that steer the agent toward unsafe actions. We present SkillSafetyBench, a runnable benchmark for evaluating such skill-facing safety failures. SkillSafetyBench includes 155 adversarial cases across 47 tasks, 6 risk domains, and 30 safety categories, each evaluated with a case-specific rule-based verifier. Experiments with multiple CLI agents and model backends show that non-user attacks can consistently induce unsafe behavior, with distinct failure patterns across domains, attack methods, and scaffold-model pairings. Our findings suggest that agent safety depends not only on model-level alignment, but also on how agents interpret skills, trust workflow context, and act through executable environments. The complete benchmark is available at https://github.com/AI45Lab/skill-safety-bench.

cs.CR↗
arXiv2026

DesignAsCode: Bridging Structural Editability and Visual Fidelity in Graphic Design Generation

Graphic design generation demands a delicate balance between high visual fidelity and fine-grained structural editability. However, existing approaches typically bifurcate into either non-editable raster image synthesis or abstract layout generation devoid of visual content. Recent combinations of these two approaches attempt to bridge this gap but often suffer from rigid composition schemas and unresolvable visual dissonances (e.g., text-background conflicts) due to their inexpressive representation and open-loop nature. To address these challenges, we propose DesignAsCode, a novel framework that reimagines graphic design as a programmatic synthesis task using HTML/CSS. Specifically, we introduce a Plan-Implement-Reflect pipeline, incorporating a Semantic Planner to construct dynamic, variable-depth element hierarchies and a Visual-Aware Reflection mechanism that optimizes the code to rectify rendering artifacts. Extensive experiments demonstrate that DesignAsCode significantly outperforms baselines in both structural validity and aesthetic quality. Furthermore, our code-native representation unlocks advanced capabilities, including automatic layout retargeting, complex document generation (e.g., resumes), and CSS-based animation. Our project page is available at https://liuziyuan1109.github.io/design-as-code/.

cs.GR↗
arXiv2026

Language-Guided Tuning: Configuration Optimization for Automated ML Research

Configuration optimization remains a critical bottleneck in machine learning, requiring coordinated tuning across model architecture, training strategy, feature engineering, and hyperparameters. Traditional approaches treat these dimensions independently and lack interpretability, while recent automated methods struggle with dynamic adaptability and semantic reasoning about optimization decisions. We introduce Language-Guided Tuning (LGT), a framework that employs multi-agent Large Language Models to automatically optimize configurations through natural language reasoning. We apply textual feedback signals that complement numerical optimization by providing semantic understanding of training dynamics and configuration interdependencies. LGT coordinates three specialized agents: an Advisor that proposes configuration changes, an Evaluator that assesses progress, and an Optimizer that refines the decision-making process, creating a self-improving feedback loop. Through comprehensive evaluation on seven diverse datasets, LGT demonstrates substantial improvements over traditional optimization methods while maintaining high interpretability.

cs.AI↗
arXiv2026

Implementing Grassroots Logic Programs with Multiagent Transition Systems and AI (Full Version)

Grassroots Logic Programs (GLP) is a concurrent logic programming language in which logic variables are partitioned into paired readers and writers. An assignment is produced at most once via a writer and consumed at most once via its paired reader, and may contain additional readers and/or writers. This enables the concise expression of rich multidirectional communication modalities. The language was introduced together with concurrent (cGLP) and multiagent (maGLP) operational semantics. Here, we derive from these (1) dGLP, a deterministic counterpart of cGLP, and (2) madGLP, a counterpart of maGLP in which deterministic agents communicate solely by asynchronous message passing, and prove them correct against their abstract counterparts. maGLP shared variable pairs spanning agents can be implemented by two local variable pairs joined by a \emph{global link}, with correctness following from disjoint substitution commutativity (a consequence of GLP's single-occurrence invariant). We further prove that madGLP is grassroots. Both dGLP and madGLP serve as formal specifications for an AI-driven implementation discipline (math $\to$ informal spec $\to$ Dart) employed and described here: from dGLP, AI (Claude) developed a workstation-based GLP implementation in Dart, and from madGLP it is developing a smartphone-based multiagent one.

cs.PL↗
arXiv2026

Peer Oversight in Collective Decision Making

This article introduces peer $k$-oversight, a property of sequential collective decision mechanisms requiring at least $k$ agents to be responsible for every harmful outcome. It is shown that whenever $k$-oversight can be achieved by redistributing control over the decisions in a mechanism, it can be achieved using just $k$ agents. A polynomial-time algorithm is also presented that determines whether such a redistribution exists and, when it does, constructs one. These results establish peer oversight as a tractable design principle for multiagent decision-making systems.

cs.GT↗
arXiv2026

Stay Within Your Bounds: Distance-Guided Decoding for Guaranteed Context-Free Grammar Compliance

Grammar-constrained decoding helps large language models produce syntactically valid structured outputs, such as code, JSON, and SQL. For context-free grammars, many practical decoders enforce local prefix feasibility: each token must keep the current prefix extendable to some valid completion. Yet, under tokenizer-grammar mismatch and finite token budgets, feasible prefixes may still fail to reach acceptance. We propose a lookahead-guided decoding framework for context-free grammars based on pushdown automata. Offline, we compute bounded pushdown summaries with reachability labels and upper-bound distances to acceptance. Online, these estimates guide horizon-aware pruning and beam search. The resulting decoder is syntactically sound: every output is accepted by the target grammar. Experiments on JSON, SQL, and Linear Temporal Logic (LTL) show both consistent syntactic validity and improved completion quality over existing baselines.

cs.AI↗