Papers

A foundational principle of connectionism is that perception, action, and cognition emerge from parallel computations among simple, interconnected units that generate and rely on neural representations. Accordingly, researchers employ multivariate pattern analysis to decode and compare the neural codes of artificial and biological networks, aiming to uncover their functions. However, there is limited analytical understanding of how a network's representation and function relate, despite this being essential to any quantitative notion of underlying function or functional similarity. We address this question using analysable two-layer linear networks and numerical simulations in non-linear networks. We find that function and representation are dissociated, allowing representational similarity without functional similarity and vice versa. Further, we show that neither robustness to input noise nor the level of generalization error constrain representations to the task. In contrast, networks robust to parameter noise have limited representational flexibility and must employ task-specific representations. Our findings suggest that representational alignment reflects computational advantages beyond functional alignment alone, with significant implications for interpreting and comparing the representations of connectionist systems.

Reasoning models often continue generating after their answers have settled. Settle learns when to stop from answer stability in completed traces. It trains the existing end-of-reasoning token while keeping other predictions close to the base model, and requires only ordinary decoding at inference. On MATH-500 with Qwen3-4B, Settle reduces token count by 40% with a 0.5-percentage-point decrease in accuracy. It gains 6.16 percentage points over supervised fine-tuning on the same traces shortened at their first stable answer, at nearly identical token counts. Its stopping score predicts whether a correct answer will remain correct. Settle extends the accuracy-token-count Pareto frontier of the evaluated stopping methods.

Recent work by Wills constructed codes with constant rate and transversal $T$. Extending this line of work, we construct asymptotically good CSS codes with fully addressable transversal $T$, permitting selective control over which logical qubits receive a $T$ gate. We also give Pauli-LDPC codes with transversal $T$ and growing distance at vanishing rate; and a protected-subsystem construction with fully addressable transversal $T$, constant protected rate, distance $\Omega(\sqrt n)$, and sparse (non-Pauli) checks. More generally, we obtain asymptotically good binary codes with full transversal addressability for every fixed finite-order one-qubit gate, retaining CSS realizations for dyadic phase gates such as $\sqrt T$ and using generally nonadditive codes for rotations such as $R_z(\pi/7)$. The remaining challenge is to construct asymptotically good Pauli-LDPC codes with fully addressable transversal non-Clifford one-qubit gates.

On-policy self-distillation (OPSD) trains a student on its own generated responses using feedback from the same model conditioned on privileged information. On mathematical reasoning, the original OPSD study finds that stylistic tokens can dominate the training signal over math-related tokens, and that pointwise clipping of the forward KL objective stabilizes training. Pointwise clipping caps each vocabulary-wise forward KL term at a fixed threshold before summing over the vocabulary. Follow-up studies have adopted this clipping, but its effect on training has not been directly examined. In matched training runs differing only in whether clipping is applied, we observe that clipped runs produce substantially more repetitions that persist to the end of the response than their unclipped counterparts. We trace this failure to the clipped objective. We prove that the clipped objective can fail to correct the student toward the teacher and can instead push clipped and unclipped token probabilities away from its teacher. Our training runs agree with this analysis: inside repetitions, the clipped student places less probability than its teacher on leaving the repetition, and more on continuing it, whereas the unclipped runs stay close to their teachers.

The effective Hamiltonian (EH), also referred to as the potential of mean force or free-energy landscape, is widely used to describe equilibrium properties and slow dynamics in chemical and soft-matter systems. However, the conventional EH has been argued to be ill-defined because it does not transform as a scalar under coordinate transformations. We identify an implicit change of reference measure (gauge), rather than the coordinate transformation itself, as the origin of this apparent problem. We formulate the EH as a scalar relative to a chosen gauge and derive the intrinsic, gauge-independent Fokker–Planck equation (FPE) on the manifold of slow variables. The conventional EH and the diffusion-dependent EH introduced in a Riemannian formulation, together with their corresponding FPEs, are thus different gauge representations of the same equilibrium measure and intrinsic stochastic dynamics. We further demonstrate that the gauge choice has an operational meaning: different restraint protocols select different reference measures. In the macroscopic limit, the leading EH becomes gauge independent within a class of subleading gauges and is determined by the large-deviation rate function. In the same limit, the stochastic dynamics reduces to gauge-independent deterministic dynamics.

A silver colouring is a proper colouring in which every colour appears in the closed neighbourhood of each vertex of a prescribed independent set. This local condition suffices when vertices are tested one at a time. We study a stronger requirement for simultaneous testing: whenever one or two vertices of the independent set are attacked together, each colour must supply distinct nearby defenders for them. We call this a pair-defensive silver colouring. For the hypercube $Q_d$, with one parity class as the attacked set, we prove that the maximum number of colours in a pair-defensive silver colouring is at most $\lfloor(d+3)/2\rfloor$, roughly half the ordinary silver-colouring target $d+1$. We construct colourings attaining this bound in four consecutive dimensions around every power of two, and we study the structure of the extremal, bound-attaining colourings. In each odd critical dimension, we characterize the extremal colourings by a partition of the defender parity into regular, triangle-free subgraphs of the halved cube. This characterization also has a local form in terms of coordinate matchings and a defect coordinate

We introduce a combinatorial criterion for the projectivity of standard modules over generalized Reedy categories, formulated in terms of a finite bipartite graph whose normalized weightings determine normalization idempotents and hence projective splittings of standard modules. We apply this framework to recover several classical normalization constructions and Dold–Kan–type equivalences, and to obtain new Dold–Kan–type equivalences for categories of finite-dimensional affine, semilinear, and semiaffine spaces over a finite field. These equivalences also yield explicit descriptions of uniformly continuous representations of the corresponding infinite transformation monoids. Together with our previous work on Hom-spaces between standard modules, the results provide a combinatorial machinery, based mainly on graph theory and linear algebra, for establishing Dold–Kan–type equivalences for generalized Reedy categories.

A key bottleneck in adversarial transfer is a trajectory-level geometric disconnect: ambient gradients often drift away from the intrinsic data manifold, causing surrogate-specific overfitting. To rectify this, we propose Manifold Anchored Bilevel Transfer (MABT), a unified framework that anchors adversarial trajectories to the shared semantic subspace. MABT introduces a relaxed manifold-anchoring operator as a semantic rectifier to suppress off-manifold noise. With this constraint, we cast transfer attack generation as a distributional bilevel optimization problem that learns a geometry-aligned initialization by minimizing expected transfer risk under a surrogate uncertainty distribution. We further develop a Hessian-free solver with linear-time complexity to handle the resulting hierarchy. Experiments demonstrate improved transferability for 10 baseline attackers across 28 attack configurations, diverse victim architectures, and defense mechanisms.

We present a consistent treatment of regularization, renormalization, and resummation in a framework involving a contracting phase, a non-singular bounce, and inflation with a sharp transition from slow-roll to ultra-slow-roll, enabling primordial black hole production. Within an effective field theory approach, we compute quantum loop corrections to the power spectrum across all phases. Quadratic UV divergences are removed through renormalization, while logarithmic IR divergences are softened via resummation, demonstrating scheme independence. The inclusion of contraction and bounce allows the generation of solar-mass PBHs, $M_{\rm PBH}\sim{\cal O}(M_\odot)$, with minimal inflation $\Delta N_{\rm Total}\sim{\cal O}(60)$, thereby evading the no-go theorem. For $0.88\le c_s\le1$, the peak spectrum amplitude lies within $10^{-3}\le A\le10^{-2}$, preserving causality and unitarity. PBH abundances across $10^{-33}\!-\!10^{-27}$ and $10^{-6}\!-\!10^{-1}M_\odot$ are confronted with microlensing constraints to control PBH overproduction.

Open-world goods delivery requires mobile manipulators to follow free-form user instructions and manipulate potentially novel objects. Existing dual-system approaches use high-level grounding models to convert language into grounded visual prompts, but their low-level controllers can remain brittle under noisy perception, dynamic scenes, and contact-rich interactions. We instead use a pretrained flow-matching vision-language-action model as the low-level control interface, leveraging its reactivity and robustness to environmental changes while treating the grounding output as a spatial cue for policy steering. Our key insight is that the pretrained VLA already provides a strong manipulation prior, while the spatial cue supplies the missing target information needed to guide actions under novel language–object mappings. Concretely, we introduce a lightweight cue-conditioned adapter. The adapter is first trained with contrastive objectives to produce salient and spatially discriminative cue representations, and is then supervised to predict a diagonal affine transformation over the generated action chunk, aligning policy steering with the cued target. Across tabletop and mobile-base settings, our method improves instruction following and manipulation success on both in-domain and out-of-domain objects, achieving up to near $2\times$ improvement in average task success rate with negligible inference overhead.

It has been found that utilizing the geometric properties of the graph dynamics can bring out crucial information of the data that a statistical analysis will not. The properties of Ricci flow bring out hidden dynamics of the data in the same way as decomposition of smooth manifolds. In this paper we explore an alternative to Ricci flow, where we find that we can bring out similar properties like it using a simpler and well defined Edge Laplacian to practice community detection in graphs. Moreover, the results obtained by the present approach show that a flow driven by the Edge Laplacian yields results similar to those of the Ricci flow. In contrast, computing the Forman-Ricci curvature requires looping over the adjacent edges, while computing Olivier-Ricci curvature involves the computation of Wasserstein distance and probability distribution associated with the graph nodes, making the Edge Laplacian approach computationally more efficient.

Preference distillation typically treats a teacher response as preferred and the student's own response as rejected. This assumes that self-generated failures are the most informative negatives and that rejects must come from a model at least as large as the student, making generation costly at scale. We find neither assumption holds: across students from 7B to 72B, smaller frozen models generate rejects with less inference compute yet train stronger students than self-generated rejects, before and after sequence-level knowledge distillation, on code generation and mathematical reasoning. To explain this result, we derive a finite-horizon utility bound for Direct Preference Optimization in a linearized feature model. The bound characterizes favorable reject distributions and motivates three interventions. First, mixing rejects from smaller and student-scale models improves performance as the smaller model's share increases. Second, reassigning rejects to other prompts and shuffling their code tokens still outperform length-matched gibberish, showing that task structure contributes to reject utility. Third, selecting candidates with lower likelihood under the reference policy improves net transfer when higher-likelihood candidates provide less useful contrast. Lower-likelihood selections outperform higher-likelihood ones for every source. These results suggest that effective rejects preserve task structure while limiting coupling to the reference policy, and that smaller frozen models can provide them at low cost.

Pseudorandom error-correcting codes (PRCs), introduced by Christ and Gunn [CRYPTO 2024], are classical error-correcting codes whose codewords are computationally indistinguishable from uniformly random strings. We initiate the study of quantum analogues of PRCs. We define quantum pseudorandom error-correcting codes (QPRCs). Assuming that Learning Parity with Noise (LPN) is hard for $2^{O(\sqrt{n})}$-time quantum algorithms, we construct QPRCs whose encodings are indistinguishable from Haar-random isometries. We call these pseudorandom isometric error-correcting codes (PRICs), and our construction is robust to all $o(n \frac{\log \log n}{\log n})$-local quantum noise, where $n$ is the number of physical qubits. Under the same assumption, we also construct QPRCs whose encodings are indistinguishable from the completely depolarizing channel and that are robust to all $\alpha n$-local quantum noise for some constant $\alpha>0$. The latter QPRCs give a direct quantum analogue of classical PRCs. To construct PRICs, we develop two technical ingredients of independent interest. First, we introduce a new classical cryptographic primitive which we call pseudorandom functional error-correcting codes (PRFCs) and construct them under the same LPN assumption. Second, we develop a new efficient decoding procedure within the codeword-stabilized (CWS) framework introduced in [Cross, Smith, Smolin, and Zeng, IEEE ISIT 2008], which is a generic framework for constructing quantum error-correcting codes by combining (possibly nonlinear) classical error-correcting codes and graphs. This resolves the open problem of finding a general method for efficiently decoding such CWS codes based on nonlinear classical codes, raised in [Li, Dumer, Grassl, and Pryadko, Physical Review A 2010].

Generating compact, artist-style meshes with explicit topology typically relies on autoregressive models which incur prohibitive sequential per-token costs, or continuous flow models that depend on heuristic connectivity decoders. Next-scale generation paradigms offer a compelling alternative by enabling parallel intra-scale token prediction and coarse-to-fine refinement from global structure to local topology; yet, existing methods derive hierarchical scales via progressive mesh simplification and invert them sequentially. This eliminates intra-scale parallelism and scales generation steps linearly with face count. In this paper, we propose MeshOctave, which instead defines scale through dyadic spatial grid resolutions, framing coarsening as a deterministic collapse that merges vertices sharing a voxel cell and inherits connectivity. Its inverse operation, split-and-rewire, determines which octant sub-vertices are instantiated for each coarse face and resolves local connectivity using discrete structural tokens. These per-face operations require no serialization, each scale transition is modeled as an unordered set that adds one bit of coordinate precision, naturally supporting dynamic-length meshes and adaptive resolution refinement. We construct a scale-conditioned masked-uniform discrete diffusion model to learn split-and-rewire operation from resolution collapse hierarchies. MeshOctave outperforms strong baselines in geometric fidelity and topological validity by a non-trivial margin, while supporting adaptive resolution refinement and extending naturally to mesh subdivision tasks.

World-action models (WAMs) leverage pretrained video models to improve generalization in robot control by jointly predicting future visual states and actions. This capability comes at a substantial inference cost, as dense future-frame tokens are repeatedly processed during denoising. Prior methods address this by token pruning that prioritizes visual fidelity to reduce denoising costs in video diffusion models. However, these methods do not use action relevance to determine which future-frame tokens to retain during joint denoising in WAMs. In this paper, we propose Sparse-WAM, a training-free framework for action-guided sparse imagination that selectively processes future-frame tokens to accelerate WAM inference. We observe substantial overlap in the spatial distribution of attention from action tokens to future-frame tokens (action-to-future attention) between consecutive denoising steps, despite continued updates to the future representations. Motivated by this, we develop Action-Guided Token Selection to retain frame-specific action-relevant regions together with cross-frame context. However, a naive implementation can incur attention-scoring and token-packing overhead that offsets the computational savings from pruning. We therefore introduce Pilot, an efficient engine that reduces sparse inference overhead through lightweight scoring and cross-step reuse of token selections. On LIBERO with FastWAM-Joint and RoboLab-120 with Cosmos 3 Edge, Sparse-WAM achieves inference speedups of approximately $2.0\times$ and $1.8\times$, respectively, over dense eager inference on an NVIDIA RTX 4090, while largely preserving task performance.

Modern AI coding-agent harnesses (Claude Code, Codex CLI, Cursor) rest their security boundary on a largely unexamined assumption: that the action A a human approves is the same action A' the harness executes, where A is fixed by a stated policy for what a scope grant or session-scoped approval authorizes. We show this assumption fails systematically and reproducibly. We introduce Approval Laundering, a taxonomy of six failure modes by which a harness's enforcement mechanism silently substitutes A' for A after approval: Scope, Argument, Temporal, Tool, Delegation, and Semantic laundering. Unlike prior work that evaluates risk classifiers against static corpora or infers implicit authorization boundaries, we study credential-binding integrity: given an already-approved action, does the harness dispatch exactly that action? Instrumenting Claude Code's pre-execution mediation point (PreToolUse), we conduct a controlled, headless, repeated-measures study of all six classes (N=19-20 runs each), reporting a Bound-Gap Rate (BGR) with Wilson confidence intervals and inter-rater agreement (kappa=1.0). We prototype Approval Token, a keyed capability Hk(principal, agent_id, session_id, tool, arguments, scope, expiry) issued by a mediator that never returns the key to the agent, evaluated via paired before/after replay of 118 runs (McNemar's exact test). The token fully eliminates Delegation laundering and, for our seeded session-identity-mismatch construction, Temporal laundering (p<10^-5), but by design leaves Scope laundering unaffected and shows no significant reduction in Argument laundering (p=1): an honest negative result, since these two classes leave every recorded dispatch field unchanged, diverging one process level below what a field-only verifier can observe. We discuss implications for defenses that bind only at the tool-invocation boundary.

Coding agents powered by large language models (LLMs) have shown remarkable abilities to autonomously reason about and achieve goals in the digital world. However, bringing this success to the physical world remains challenging. On the one hand, direct generation methods (e.g., Code as Policies) often suffer from the LLMs' insufficient understanding of robots and physical environments. On the other hand, iterative trial-and-error tuning in the physical world (e.g., physical autoresearch) induces significant experimental cost and safety concerns. We introduce SimEX: Simulation-Integrated Robotics AutoResearch, an autoresearch framework that tightly integrates simulated experimentation, enabling coding agents to efficiently acquire physical capabilities for controlling real robots. SimEX operates in two stages. First, the agent conducts open-ended probe-and-optimize iterations in simulation, developing a robot toolbox with robust and generalizable capabilities. Second, the agent adapts the toolbox and the simulator together through only a few physical trials: each trial corrects the simulator, and the corrected simulator is used to diagnose failures and screen candidate repairs. We evaluate SimEX extensively in sim-to-sim settings and on physical robots. On challenging real-world manipulation tasks including towel folding, barcode scanning, and plate manipulation, SimEX enables coding agents to efficiently acquire robot skills without any demonstration and with only 10 minutes of real-robot interaction. These results suggest that simulation can be a critical component in achieving physical intelligence, not only as a source of training data that must closely replicate the real world, but also as a roughly correct laboratory where a coding agent develops the knowledge and procedures needed to act on the robot. More details and robot videos at https://robo-simex.github.io/

LLM inference systems may vary batch composition, prompt chunking, prefill/decode execution, and KV-cache reuse, eviction, or recomputation. These optimizations should not affect system outputs. Production systems, including vLLM's batch-invariant mode and SGLang's deterministic mode, target this goal but lack a formal system-level specification. We formalize deterministic LLM inference: under a fixed model and deployment configuration, requests with the same prompt and initial sampler state produce bitwise-identical logits at corresponding output positions across executions. Our tests find that these production modes produce different logits under some execution variations. To address this limitation, we present Vosti, an inference engine designed and verified against this specification. Vosti chooses kernels independently of runtime engine state and ties cached KV values to their logical token prefixes. Its proof decomposes at the engine/GPU kernel boundary: a Verus inductive proof establishes that scheduling and the paged, prefix-sharing KV-cache preserve output logits, while a Triton analyzer proves bitwise-equal selected kernel outputs across batches, query lengths, and paged KV-cache layouts. Vosti produces bitwise-identical logits across every tested execution variation and achieves performance comparable to vLLM's batch-invariant mode on decode-heavy workloads, while providing a stronger, formally verified determinism guarantee.

Radar hardware faults threaten automated perception, motivating accurate, compact diagnosis and understandable maintenance guidance. We introduce SCORE-LM, which couples a small scatterer-conditioned operator-response encoder (SCORE) to an adapted local language model. SCORE combines self-referenced complex trajectories, physical descriptors, and a selective state-space branch, with source-only self-supervision and directional fault inference. On eight capture-excluded Rad-R fault recordings, it achieves state-of-the-art performance within the evaluated nine-model comparison: 88.39% mean capture recall and 88.20% four-fault macro-F1 at ten frames. Its 39,520 radar inference coefficients are 119.7 times fewer than RadrNet-DS-CI's, while recall is 15.56 percentage points higher than this strongest competitor. In a separate low-label protocol, SCORE reaches 71.58% recall with one labeled source window per class. A nonlinear projector converts four frozen fault similarities into five soft tokens, linking compact diagnosis to class-conditioned maintenance guidance. On 75 development questions covering 24 radar windows, language adaptation raises correct-fault answers from 45 to 62 (60.0% to 82.7%) relative to removing the co-trained adapters, while retaining the same projector. SCORE-LM thus combines a compact radar specialist with a language interface for communicating fault-specific inspection guidance.

Multiple object hallucination, where large vision-language models (LVLMs) generate objects not supported by the visual input, is a persistent challenge caused by visual uncertainty during decoding. Existing methods reduce hallucinations using contrastive signals, but they rely on heuristics and lack principled control of false positives at the image level. To address this, we propose False Discovery Rate-COntRol of HALlucination (CORAL), a training-free framework that models visual uncertainty using an uncertainty-aware visual data splitting strategy and leverages mirror statistics to quantify visual contrast during decoding. By computing mirror statistics from paired, symmetrically perturbed visual inputs, CORAL estimates spurious object predictions and sets a data-driven threshold to control the expected fraction of false discoveries per image, suppressing hallucinations while retaining high power for truly grounded objects. The framework is flexible, supports multiple LVLMs, and mitigates hallucinations without retraining or supervision. Extensive experiments on multiple benchmarks with several evaluation metrics demonstrate that CORAL consistently outperforms state-of-the-art methods, providing more reliable and robust hallucination control. Code is available at: https://changliu1993-cl.github.io/CORAL/

Diffusion Transformers (DiTs) have become a dominant architecture for video generation, but their efficiency is limited by the quadratic complexity of full attention. Sparse attention reduces this cost by retrieving important blocks and computing attention only within them, but inaccurate retrieval can either degrade generation quality or yield unnecessary computation. We identify two retrieval mismatches in methods that retrieve blocks using the averaged representations of query and key blocks: (i) query-side aggregation mismatch, where averaging queries before Softmax fails to preserve their individual attention preferences, and (ii) key-side clustering metric mismatch, where standard Euclidean clustering in the original key space can group keys with dissimilar QK scores under the current query, so their average representation may not accurately represent how the current query scores individual keys. These mismatches can lead to inaccurate block retrieval. To address these mismatches, we propose PARK, a training-free sparse attention method for accurate block retrieval. PARK retains every original query, independently normalizes its attention over key blocks, and then averages these distributions within each query block. It also uses information from the current queries to transform keys before clustering, so that keys receiving similar QK scores are grouped together. A fused GPU kernel further reduces the overhead of block retrieval. Experiments on HunyuanVideo and Wan demonstrate that PARK improves block retrieval accuracy and preserves generation quality while accelerating inference, achieving the best quality-efficiency trade-off among the compared sparse attention methods.

Neural surrogates have emerged as fast alternatives to the numerical simulation of three-dimensional turbulence. However, training them at high resolution remains challenging, since the memory of full-field models grows with the resolution. In addition, full-resolution training data are expensive to simulate and store, and therefore scarce. We introduce ScaleSplit-NO (Scale-Split Neural Operator), which exploits the scale structure of turbulence with two neural operators: a Parent predicts the global coarse field at the next time step, and a Child predicts full-resolution local patches conditioned on this prediction. Neither model operates on the full-resolution field. The Child is pretrained alone and then attached to the Parent's coarse prediction through zero-initialized connections. On two complex high-resolution turbulence benchmarks, ScaleSplit-NO surpasses all competing baselines in both prediction accuracy and data efficiency. On the higher-resolution dataset JHTDB256 ($256^3$), its normalized mean squared error (NMSE) is 53% lower than that of the strongest baseline, and its training memory is 79% lower than that of the most memory-efficient baseline. We further demonstrate its effectiveness for urban wind prediction in a real district of Montreal on a $500\times150\times500$ grid, reducing one-step NMSE by 65.8% relative to the baseline. Moreover, swapping in a Parent trained on additional coarse fields improves prediction without retraining the Child, providing further accuracy gains at a small storage cost.

Demographic fairness gaps in automatic speech recognition are almost always reported from a single training run. We fine-tune the Q-former projector and LoRA adapters of a speech LLM at five audio compression factors and six random seeds, holding the encoder, base decoder, data and decoding fixed, and evaluate every run on Common Voice and Fair-Speech. At 460 h of clean LibriSpeech, the seed moves fairness metrics more than compression does on most demographic axes. A balanced 3x3 decomposition attributes 85.3% of the variation in Fair-Speech ethnicity normalized gap to the seed against 8.3% to compression (p = 0.009), though compression explains more on age and gender. Held-out LibriSpeech word error rate spreads by 0.04 points across those seeds while Common Voice spreads by 8.57, so these are not failed runs, and the effect survives controlling for accuracy and dropout. Scaling and diversifying the adaptation set to 960 h damps the effect but does not remove it. On Fair-Speech ethnicity, two single-run systems must differ by more than 0.30 in normalized gap to exceed seed variability.

{Non-contingency logic $(\KWL)$ replaces the usual necessity operator of modal logic with an operator expressing that a proposition is necessarily true or necessarily false. Besides its intrinsic logical interest, it admits natural interpretations as knowing whether in epistemic logic and as decidability under the arithmetical interpretation of provability logic. Although the semantics of non-contingency logic have been extensively studied, its proof theory remains comparatively underdeveloped. In this paper, we develop a uniform proof-theoretic framework for $\KWL$ over a broad class of frame conditions. Our approach is based on generalized path conditions (GPCs), a grammar-theoretic formalism that uniformly captures many standard modal frame properties. For every finite set $\gpc$ of GPCs, we construct a corresponding labelled sequent calculus. All calculi share a common set of logical rules and differ only by a single structural rule generated from $\gpc$, which captures the underlying frame conditions. We prove that these calculi are sound and complete with respect to their corresponding frame classes, thereby providing a uniform proof theory for a large family of non-contingency logics.}

Large language models are reshaping ecommerce from static recommenders into interactive shopping assistants, yet real-world shopping requires session-level decision support: users reveal and revise constraints, coordinate multiple goals, and expect product-grounded recommendations over a full conversation. Existing benchmarks are mostly outcome-oriented or execution-oriented, leaving this evolving decision process under-evaluated. We introduce REALWORLDSHOP, a benchmark built on 3.28M grounded products, structured shopping episodes, a profile-grounded and actioncontrolled user simulator, and role-play evaluation. Our analysis shows that current systems produce locally plausible responses but struggle with state tracking, constraint updating, and grounded convergence, especially under ambiguous intent, bundle, and multi-intent scenarios. We further propose REALSHOP_AGENT, an executable session-control framework with explicit state management, shopping-flow control, catalog-grounded retrieval, and runtime guards. Experiments show that REALSHOP_AGENT consistently outperforms strong baselines on REALWORLDSHOP.

It is well-known that thermalization breaks down in presence of an extensive number of symmetries or conservation laws that are mutually compatible or commuting with each other. We ask here how an extensive number of mutually incompatible local symmetries govern eigenstate thermalization (ETH). We will investigate this through models within the class of bond-dependent $\mathbb{Z}_2$-symmetric quantum spin-$\frac{1}{2}$ Hamiltonians that naturally admit this structure. This leads to exponentially large degeneracies in the spectrum governed by the incompatible symmetry structure. Here, using spectral diagnostics, we show that non-integrability can survive despite extensively many conserved quantities when they are incompatible. Furthermore, we show that ETH behavior persists deep into the many-body spectral edge due to this structure. In other words, incompatible local symmetries enable a mechanism to obtain enough thermodynamic entropy at low excitation energy densities to make ETH operational or predictive near the ground state.

Chain-of-thought (CoT) traces often serve as a proxy for how Large Language Models (LLMs) arrive at their answers. However, growing evidence shows that models' CoT often fails to reflect their internal computations and can be changed without affecting their final answers. In this work, we measure and improve the alignment between the reasoning described in an LLM's CoT and what it computes internally. We propose CoT-Interpretability Alignment (CIA), a metric that measures the agreement between a model's CoT traces and its internal reasoning strategies as detected by interpretability tools. We evaluate CIA on three tasks (two-hop question answering, hint intervention, and integer multiplication) across three LLMs, finding that LLMs exhibit limited alignment across all tasks (44.8-75.9%). We then experiment with improving CIA via post-training, setting both the task accuracy and parametric faithfulness signals as a reward. Experiments show that we can substantially improve CoT parametric faithfulness while maintaining or improving the task accuracy. We provide rich analysis, such as their generalization patterns. Our work provides both a framework for auditing CoT parametric faithfulness and a pathway toward making models' explicit reasoning more trustworthy. Code and data are available at https://github.com/yihuaihong/CIA-minimal-repro.

Embodied vision-language models (VLMs) are increasingly deployed as high-level planners for robots because they generalize across diverse environments. However, this requires their safety alignment to also hold in unseen environments. Existing red-teaming assumes an adversary who optimizes the prompt, the pixels, or text in the environment, and existing benchmarks ask whether a planner recognizes or mitigates a hazard in a fixed scene. Neither asks whether a refusal the planner has already given survives an ordinary change to the environment. We ask that question by placing a single everyday object into the environment, with no pixel, gradient, or prompt under adversarial control. On $846$ tasks that a constitution-guarded planner initially refuses, we find $20.2\%$ of tasks can be flipped to compliance by one or more objects, and the number of objects differs from one task to another. In addition, the object need not be chosen for the task, i.e., items drawn from a fixed list, with no knowledge of the environment or the instruction, bypass safety about as often as items proposed for the specific task. We qualitatively contrast the tasks bypassed most and least often and find that the distinction lies in how conspicuous the hazard is in the instruction and environment. Susceptibility to safety bypass is therefore a property of the task, which we call its malleability, and we show that it can be predicted before the target is ever queried. A composite of signals read from a small open-source VLM identifies malleable tasks $2.4\times$ as often as picking at random. Everyday objects, whether placed by an adversary or introduced by ordinary rearrangement of the environment, are thus sufficient to overturn a refusal. Because susceptibility is determined by how a task is specified, we recommend assessing malleability per task prior to deployment.

We prove that, for every irrational $\xi$, any $F_\sigma$ additive subgroup of $\R$ has an $F_\sigma$ $\Q$-vector space extension of the same Hausdorff dimension satisfying $A+\xi A=\R$. Iteration gives simultaneous surjectivity for any prescribed countable family of irrational multipliers. Such a space exists in every prescribed dimension $d\in[0,1)$. We also construct in ZFC a zero-dimensional lightface $\Delta^0_3$ $\Q$-vector subspace $A$ for which $A+\xi A=\R$ holds for every irrational $\xi$, answering both parts of Question~2 of Ye, Yu, and Zhao. This universal group is a difference of two $F_\sigma$ sets, but is neither $F_\sigma$ nor $G_\delta$. Both constructions use direct inductions on finite binary strings and admit effective versions. As applications, we obtain zero-dimensional $F_\sigma$ groups whose Cartesian squares have Hausdorff dimension one, and relate their dilate sums to Marstrand's projection theorem.

A live classroom poll is usually read through its answer key, as a count of participation and correctness. Yet the same record holds more before any key is fixed, namely who answers early and how the class divides across the options. Whether these key-free signals are stable, and what they reveal, has not been examined at the scale of a real course. We study them in a live deployment of 340,668 submissions across 603 polls in 47 sessions from roughly 2,400 learners, reading each poll for a learner's response order and for how much the class divides. A single further step brings in the author-designated key, on items with a settled answer, to interpret the divided ones. A learner's response order is a stable individual signature. It reproduces at a corrected split-half reliability of 0.92, holds at 0.87 within single sessions, and is unrelated to whether the learner is correct. Read without a key, about one poll in five does not reach a clear majority, and division marks the questions that split the class. On the settled-answer items the majority is itself wrong on 49 of 358. The key-free measure flags most of these, though division alone does not separate a collectively wrong answer from a merely hard one. The two readings are largely independent, meeting at one point where early responders anticipate the eventual majority only on questions the class has nearly settled. Together they map the learners and questions of a session without a key.