Reasoning models are evaluated on single-turn benchmarks but deployed in multi-turn dialogue, where users push back on correct answers. Under sustained adversarial pressure we find a previously undocumented failure mode: the chain-of-thought stays factually correct from first turn to last while the emitted answer flips wrong. We call this unfaithful capitulation (UC) and isolate it with a $2\times 2$ latent-versus-behavioral framework that flip-rate metrics and single-turn faithfulness probes both miss. Across three datasets (MT-Consistency, MMLU-Pro, GSM8K), the latent-correct rate at the behavioral flip clusters near 50% in think mode and collapses to 11-15% under no_think -- paired, within-model causal evidence that reasoning creates the gap. Across models the effect tracks the reasoning channel (high in Qwen3-32B and GPT-OSS-20B, low in inline-CoT Gemma-4-31B-it). An independent GPT-4o judge corroborates $86\%$ of UC labels; a token-level probe shows the answer-slot argmax is correct in $84\%$ of UC cells; and a naive trace-anchored defense backfires. We release all trajectories, traces, and judge labels.

A retrieval-augmented generation (RAG) system deployed over a multi-author institutional corpus can give a different answer to the same question depending on which source it retrieves -- a failure mode the dominant single-gold-answer paradigm cannot diagnose. We argue that source-dependence is a missing axis of NLP evaluation, and that auditing it means shifting the unit of evaluation from answer correctness to the inter-source relationship. We make this concrete in transplant patient education, where institutional sources demonstrably disagree, releasing three artefacts: TransplantQA, a benchmark of real patient questions, each answered by grounding generation in multiple institutional handbooks as candidate sources; HERO-QA, a hierarchical retrieval strategy that grounds and audits each answer; and a structured-output judge that scores inter-source relationships on a validated 5-label taxonomy. At scale, better retrieval reveals far more disagreement than prior estimates suggested -- understating its prevalence, not its intensity. The framework is domain-agnostic and transfers to legal and educational RAG: measuring source-dependence is a responsibility for deployed multi-source NLP generally.

AI agents are increasingly expected to operate as digital employees: accessing enterprise data, making decisions, and taking actions autonomously. But agents are simultaneously less predictable than humans -- prone to hallucination, misinterpretation, and adversarial manipulation -- and more technically capable: with deep system knowledge and high-throughput interfaces cascading damage at machine speed. This combination makes it unsafe to rely on agents to faithfully interpret or propagate security-critical metadata such as access policies, data classifications, and behavioral constraints. We present the Redpanda Agentic Data Plane (ADP), an architecture built around out-of-band metadata channels: infrastructure pathways that carry security context, policy signals, and audit trails deterministically, entirely outside the agent's read and write path and across heterogeneous infrastructure. These channels enforce governance at every stage of the agent lifecycle -- scoping data access on the way in, constraining actions during execution, and capturing tamper-proof transcripts on the way out. We demonstrate ADP with a multi-agent portfolio rebalancing system in which autonomous agents monitor markets, make trade decisions, and execute orders across isolated client accounts -- with per-client data scoping, trade approval thresholds, and tamper-proof audit trails all enforced by out-of-band channels the agents can neither see nor bypass.

Event-driven scheduling policies are increasingly deployed in industrial environments, where decisions are made under asynchronous and partially observed system states. As a result, decision states are not temporally consistent, action admissibility is not explicitly defined, and the origin of execution errors remains ambiguous. These issues limit both reliability and interpretability. To address this gap, a policy-neutral execution and measurement layer is proposed to mediate between scheduling policies and the industrial execution environment. The layer constructs decision-valid snapshots from asynchronous event streams, defines a standardized execution contract with explicit action admissibility, and records outcomes as divergences between policy intent, transactional outcomes, physical execution, and human intervention. This enables a separation between decision semantics and execution behavior and makes deployment mismatch observable and structurally attributable. The proposed framework is evaluated using a discrete-event simulation. The results show analytical benefits across all observation lag regimes, as undifferentiated execution failures are transformed into structured, typed outcomes with full attribution coverage. Operational benefits are strongest under low observation lag, where avoidable execution errors can be prevented before commitment. Overall, the layer turns execution uncertainty into supervisory data for evaluation and policy refinement.

LLMs encode both general capabilities and domain-specific knowledge in a single set of parameters. We ask whether this capacity can be reorganized: keeping broadly useful computation in a shared backbone, while moving specialized knowledge into external memory modules. We propose \emph{knowledge offloading} (KOFF), a framework for decomposing a pretrained LLM into a sparse shared backbone and domain-specific memories. Starting from a frozen base model, we jointly learn a structured pruning mask and lightweight recovery modules, implemented as LoRA adapters and learned key-value caches. Across Llama and Qwen models from 3B to 8B, we find that non-trivial capacity can be moved out of the shared backbone without a large loss in model ability. At around 12\% global sparsity, KOFF preserves much of the unpruned model's performance, while pruning the same frozen model without memories degrades sharply. Ablations show that LoRA and learned KV memories are complementary, and specialization analyses suggest that the learned decomposition is meaningful: language-specific neurons are preferentially removed while language-general neurons largely remain in the backbone. These results suggest that knowledge can be reallocated between a shared core and swappable external memories.

Are current Vision Language Models (VLMs) ready to comprehend and reason about complex embodied interactions in 3D environments? We introduce Embodied3DBench, a robot-centric benchmark targeting low-level spatial intelligence in embodied 3D environments. To systematically evaluate these foundational perceptual capabilities, the benchmark includes 6 task categories divided into two core groups: Spatial Structural Understanding (Grounding, Spatial Relation Prediction, and Multi-view Correspondence) and Interaction-Oriented Perception (Affordance Prediction, Grasp Point Prediction, and Trajectory Prediction). The benchmark spans 12 subcategories and contains over 21k high-quality question-answer pairs. We evaluate 13 state-of-the-art models, and the results show that while current models exhibit relatively strong high-level spatial reasoning, such as understanding object-to-object positional relations, they remain fragile in interaction-oriented perception, highlighting a significant lack of robust 3D-aware interaction priors. To actively bridge this capability gap revealed by our benchmark, we further synthesize a large-scale training dataset comprising 1.3M QA pairs. Notably, fine-tuning on this dataset yields significant improvements in low-level spatial intelligence. Ultimately, Embodied3DBench fills a critical gap by providing both a systematic evaluation framework and a scalable data solution, setting a clear target for the development of interaction-aware multimodal systems.

Maintaining the safety of large language models (LLMs) is crucial as they are increasingly deployed in real-world applications. Existing safety guardrails typically rely on single-pass classification or, more recently, distilled reasoning. Reasoning-based guardrails significantly outperform classification-only baselines, but they incur substantial query latency and token overhead that make them impractical for highthroughput deployment. To address this challenge, we propose COLAGUARD, a guardrail model that transfers multi-step safety reasoning into a continuous latent space through a stage-wise training curriculum, enabling direct hidden-state propagation at inference. Evaluated on ten prompt- and response-moderation settings spanning eight safety benchmarks, COLAGUARD improves macro-F1 by 8.24 points over Llama Guard 3 and matches our explicit reasoning baseline, GuardReasoner, in macroF1 while delivering a 12.9X speedup and 22.4X reduction in token usage. Our results suggest that latent reasoning offers a practical alternative to explicit rationale generation for deployable guardrails, jointly improving safety robustness and inference efficiency rather than treating them as competing objectives.

We study how persona prompting shapes language generated by multimodal large language models in an urban perception setting. Using 59,808 annotations from 1,200 persona-conditioned agents and two no-persona settings, we analyze captions, justifications, and perception tags across personas. Results indicate strong convergence in captions for different personas, whereas justifications display systematic variation associated with socioeconomic and political attributes, while perception tags show no statistically significant persona-related differences, though effect trends are observed. Topic analysis further reveals that personas emphasize different evaluative themes when interpreting the same scenes.

Hallucination remains a major reliability barrier for production LLM systems, particularly in multi-agent pipelines where unsupported claims can propagate unchecked across stages. This paper adapts a HOPE-inspired Nested Learning architecture with Continuum Memory Systems (CMS) and semantic similarity caching to a hybrid benchmark of 310 prompts combining 217 epistemic-uncertainty prompts and 93 fabrication-induction stress-test prompts. A three-stage agentic pipeline orchestrated via the Open Floor Protocol (OFP) is evaluated with five KPIs -- FCD (Factual Claim Density), FGR (Factual Grounding References), FDF (Fictional Disclaimer Frequency), ECS (Explicit Contextualization Score), and OSR (Observability Score Ratio) -- aggregated into THS (Total Hallucination Score) across five weighting configurations to study mitigation-observability trade-offs. FDF, ECS, OSR, and FGR are subtracted as mitigation signals, so that a more negative THS indicates stronger mitigation. The FrontEndAgent is configured as a high-stochasticity generator (temperature = 1.0) to produce a realistic hallucination baseline, while the SecondLevelReviewer and ThirdLevelReviewer operate as progressive correctors. This asymmetric design yields end-to-end THS reductions of -31.3% to -35.9% across five weighting configurations. Semantic caching achieves 440 cache hits over 930 potential calls (47.3% hit rate), reducing LLM invocations to 490, lowering energy and CO2e footprint, and making multi-stage review pipelines operationally viable at production scale. ExtremeObservability attains the most negative final THS (-0.0709), confirming that observability-heavy configurations reinforce rather than compromise mitigation. These findings suggest that memory-augmented multi-agent designs can jointly improve factual reliability, operational efficiency, and auditability without model retraining.

In this paper, we introduce LLMBridge, a new LLM based system for the task of end-to-end referential bridging resolution in English. Our bridging resolution pipeline combines heuristic pre/post-processing with the natural language inference ability that comes from LLMs. We evaluate our bridging resolution pipeline on 3 datasets which have been used for referential bridging resolution evaluation in English: ISNotes, BASHI, and GUMBridge. Comparison to previous bridging resolution systems shows that the performance of LLMBridge surpasses previous state-of-the-art (SoTA) systems for all 3 datasets in the challenging End-to-end Evaluation Setting, as well as the Basic Bridging Resolution Evaluation Setting (gold bridging anaphor given). We also conduct a thorough error analysis of the LLMBridge performance, examining what varieties of bridging remain difficult for LLM based systems to identify. With this paper, we release the code for the LLMBridge pipeline.

Human coordination often relies on the ability to influence the beliefs of others through strategic action. In multi-agent reinforcement learning, opponent shaping attempts to replicate this influence, though existing methods typically operate within an opponent's parameter, policy, or value space. Meanwhile, belief-manipulation techniques in hidden-role games often rely on hard-coded objectives, such as deception or belief saturation. We propose Differentiable Belief-based Opponent Shaping (D-BOS), a first-order method that treats each observer's belief as the shaped opponent state and differentiates through $k$-step softmax-Bayes belief dynamics. Rather than explicitly rewarding deceptive or cooperative behavior, our method treats the belief state as the target for shaping. This allows the optimal strategy to emerge naturally from the environment's reward structure. This belief-space formulation provides an opponent-shaping signal by differentiating through opponent belief updates, and naturally extends to multiple observers by aggregating gradients over their individual inferred belief trajectories. Empirically, D-BOS outperforms PPO and BBM in hidden-role games, with the largest gains in mixed-motive settings.

This study reports findings from a cross-sectional survey (n = 72) of higher education practitioners examining beliefs, behaviors, and institutional conditions related to artificial intelligence (AI) integration in teaching and learning. Grounded in the DOT Framework, which integrates design thinking and open systems theory, the study investigates AI familiarity, usage patterns, design-oriented practices, and pedagogical beliefs. Exploratory factor analysis of 19 belief items identified a three-factor structure: AI Functional Capabilities, Oversight and Governance, and Instructor Collaboration and Planning (α = .90). Results indicate that practitioners hold favorable views of AI as a pedagogical support while maintaining strong commitments to human oversight and critical evaluation. Reported practices emphasize iterative prompting and content generation, with less consistent use of needs assessment and feedback loops. Institutional barriers including limited policy, training, and infrastructure were widely reported. These findings provide preliminary empirical support for the DOT Framework as a descriptive model of practitioner beliefs and practices, while also highlighting gaps between design-oriented theory and current implementation. The study contributes an initial measurement structure and identifies directions for confirmatory validation and outcome-based research linking AI-supported design practices to instructional quality.

Score-based and flow-based generative models exhibit remarkable expressive capacity in capturing complex distributions, and have been extensively deployed in tasks ranging from image generation to reinforcement learning. Nevertheless, these models suffer from prolonged inference latency, which imposes a significant computational bottleneck in RL with iterative sampling. To overcome this limitation, we propose a new framework named Moment Matching Q-Learning (MoMa QL), which utilizes a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD) that intend to match all orders of statistics between the original and target distribution. By enforcing strong regularization on all moment statistics, this algorithm guarantees distribution-level convergence for conditional score function and remains stable under various hyperparameters. Empirically, we show that our method MoMa QL is more computationally efficient with a comparable if not competitive performance in various D4RL tasks. Remarkably, by accelerating the action sampling process for flow-based policies, MoMa QL demonstrates superior performance in offline-to-online RL tasks because of faster and stronger adaptability for online interactive finetuning.

Model-based reinforcement learning (MBRL) agents typically learn world models by minimizing predictive loss. However, powerful RL optimizers inevitably exploit minor model inaccuracies, leading to simulator exploitation and a reality gap where policies succeed in simulation but fail in the real world. We propose that the objective for learning simulators should be strategic robustness rather than predictive accuracy, and formulate this as a zero-sum minimax game between a model player and an adversarial policy player. We provide a comprehensive theoretical analysis: (1) an online learning guarantee showing the game is learnable with sublinear regret bounds; (2) a tractable critic-based simplification bounding the global policy-value gap by the local critic's loss; and (3) an Error-MDP duality, proving that finding the worst-case policy is formally dual to a standard RL problem where the reward is the one-step critic error. This duality yields a provably convergent active data selection algorithm. Experiments on continuous control tasks demonstrate that our approach reduces prediction error in strategically important regions by $1.5$-$2.2\times$ and enables policies trained purely in simulation to match near-optimal real-world performance.

Conditioned Sequence Models (CSMs) learn policies by treating return-to-go (RTG) as a control signal. However, existing CSMs often treat the RTGs as simple numerical inputs rather than aligning them with the performance of their policies. In this paper, we propose Q-ALIGN DT, a framework that enforces this alignment by ensuring the $Q$-value of the output policy is consistent with the input RTG. By leveraging a $Q$ function to provide dense guidance to CSMs and further fine-tuning it using an RTG-perturbation technique with the CSM, our method ensures that higher RTGs are consistently mapped to trajectories with higher expected returns. Theoretically, we show that Q-ALIGN DT can efficiently learn the desired policy and output a near-optimal one when the RTG is sufficiently high. Empirically, we demonstrate through extensive experiments that Q-ALIGN DT achieves superior controllability and performance across the D4RL benchmark. Remarkably, our model effectively learns a structured family of policies that maintains precise alignment and generalizes to tasks like velocity-tracking where prior methods fail.

The use of Large Language Models (LLMs) is proliferating, yet their performance is observed to vary based on prompting styles and tones. In this study, we investigate both whether and how tonal variations in prompts lead to disparate LLM accuracy for objective multiple-choice questions. We use two datasets: a 50-base question dataset with five tone variants and a 570-base question MMLU subset spanning 57 subjects with seven tone variants. Experiments were conducted to evaluate the performance of four cost-efficient, popular LLMs: ChatGPT-4o, ChatGPT-5-nano, Gemini 2.5 Flash, and Gemini 2.5 Flash Lite. Across models, tonal effects are systematic but highly model-dependent. Some models show small, yet statistically significant, shifts, while others exhibit large accuracy swings across tones. Further, we identify subject-level differences in tone sensitivity and present a routing framework to explain how tones may attune internal reasoning modes. Our findings caution users against assuming tone-robust reliability in LLM deployments.

Federal agencies are deploying large language models (LLMs) to categorize public comment corpora, where the model's organization of the record shapes what policymakers see and which arguments register. Standard evaluation, anchored on stance accuracy against a small validated set, cannot detect when different models produce materially different categorizations of the same public input. We propose an Interpretive Audit Pipeline that treats multi-model disagreement as diagnostic of interpretive complexity and directs human review toward genuinely ambiguous public input. Analyzing 1,260 public comments on a federal USDA docket across four LLMs, we find that inter-model thematic divergence exceeds within-model prompt variation, and that an expert rubric suppresses deep interpretive disagreement without resolving it. In a two-stage labeling study on a stratified 40-comment subsample, four LLMs and a human annotator labeled independently and then revised after seeing the others' labels. Revision behavior varied across labelers, and the human annotator's revisions frequently introduced framings absent from the ensemble's collective output. We argue disagreement-based evaluation is a necessary complement to accuracy metrics for LLM-assisted interpretive coding.

Active tether-net systems are a promising solution for capturing large non-cooperative targets, such as space debris, by deploying a flexible net manipulated by maneuverable units (MUs). However, concurrent systematic explorations of design and control choices of the tether-net system to understand its full potential remain limited, partly due to the complex, constrained, nonlinear optimization problem that it presents -- one that involves a mixture of continuous, integer and categorical variables, with the latter two arising from net connectivity and component choices, respectively. Classical binary encoding methods are often ineffective for solving highly nonlinear and multimodal Mixed Combinatorial Nonlinear Programmings (MCNLPs) in engineering design, while integer coding approaches can introduce spurious relations among combinations. Given the graph-structured characteristics of the combinatorial space, this paper adopts and extends a new graph-learning-aided optimization approach to solve this MCNLP problem. Here, a Graph Neural Network (GNN) is trained to score (as output) and thereof recommend candidate combinations represented as nodes in a graph, with the continuous variable vector portion of a candidate design given as input. As a result, the MCNLP optimization reduces to an NLP, which can be solved using standard solvers. While this reduction approach is agnostic to the choice of the NLP solver, here a state-of-the-art Particle Swarm Optimization (PSO) algorithm with gradient-based fine-tuning is used as the solver. Demonstrated on the problem of concurrently designing the morphology of the net, choice of mass and thrusters in the MUs and aiming points used by the controller of the tether-net system, the GNN-based recommender is shown to provide significantly faster convergence to similar optimal solutions, compared to direct solution of the MCNLP problem.

Although a growing body of research has begun to describe user--LLM interactions, the picture it paints is largely static; little is known about how individual users change their behavior over time. To address this gap, we analyze the conversational trajectories of $\sim$12,000 randomly sampled Microsoft Bing Copilot users and compare these with data from WildChat-4.8M. While the Copilot data contains significant population-level trends, we find that trends in individual user trajectories are much weaker; user habits prove to be overwhelmingly sticky. We also find stark differences between users of different activity levels: more active users have more successful conversations and use the LLM for more complex and professionally oriented tasks. Some user trends also appear in WildChat-4.8M, but we find evidence that this dataset is significantly skewed towards highly proficient "power" users. Ultimately, our results suggest that existing user behavior is difficult to change and demonstrate the extent of user heterogeneity. Our comparison between datasets highlights that WildChat does not represent typical user-AI interactions, an important caveat for downstream uses of the data.

Diffusion-based and iterative methods have become effective tools for solving imaging inverse problems. Their reconstruction process naturally forms a trajectory of intermediate estimates. Although these intermediate estimates define a reconstruction trajectory, most methods do not explicitly regularize the transitions between consecutive states. To address this limitation, we introduce TRACE, a training-free TRAjectory-Constrained rEconstruction framework that stabilizes the reconstruction path by coupling adjacent states along the trajectory. This gives a trajectory-level model that can be interpreted as a sequence of proximal updates. Since the exact proximal update is generally intractable, we approximate it with a neural mapping. This yields a diffusion-like reconstruction process with an explicit coupling between neighboring states. We provide a stability analysis showing that temporal coupling bounds trajectory variation and that this control is preserved under untrained network updates. Experiments on linear and nonlinear image reconstruction tasks show that TRACE improves reconstruction quality. Trajectory-level analyses and ablations confirm that temporal coupling directly affects state transitions along the reconstruction path.

Post-training large language models with reinforcement learning is bottlenecked by the reward signal. Existing approaches require either ground-truth verifiable rewards, restricting training to domains with automatic correctness checks (e.g., mathematics, code execution), or human preference labels, which are expensive to collect and prone to reward hacking. Recent label-free methods replace ground-truth verifiers with self-referential signals like majority voting or token entropy over a model's own outputs, but risk reinforcing a model's own errors. In this work we propose Cross-Model Entropy (CME), the mean log-likelihood of a generator's response under a separate verifier model, as a label-free reward signal for RL post-training. CME is continuous, training-free, and grounded in the principle that responses a verifier finds unsurprising are likely correct or high quality. Because the verifier is independent of the generator, the signal cannot be gamed through self-consistency. We integrate CME into GRPO with no other changes to the training loop, extending label-free RL to open-ended instruction following -- a regime where self-referential signals are inapplicable or poorly suited. On open-ended instruction following (UltraFeedback prompts, evaluated on AlpacaEval 2.0), CME rewards beat the untrained base in head-to-head LLM-as-Judge comparisons across four model families (Qwen, Llama, Gemma, OLMo) and three training regimes (pretrained, SFT, and instruction-tuned), with tie-adjusted win rates ranging from 52.5% to 71.4%. Code will be released upon publication.

Driving a system from one state to another through targeted interventions is a fundamental challenge in science, yet most predictive models offer limited mechanistic insight and no principled framework for decision-making. Here we present COAST (Causally Optimal Actions for State Transitions), a causal-intelligence approach for the in-silico design of constrained interventions that induce user-defined state transitions. Given data characterizing source and target states, COAST learns context-specific causal graphs and structural causal models, attributes observed distributional shifts to mechanism-level causal drivers, and introduces a novel constraint-aware multi-objective optimization formulation that balances transition efficacy, intervention complexity, and target-state stability. The approach is modular and domain-agnostic, integrating feature selection, causal discovery, causal modeling, and intervention identification and evaluation through interchangeable components. Across synthetic benchmarks and real biological datasets, COAST recovers key causal drivers and identifies robust single- and multi-target intervention strategies that achieve desired state transitions, accompanied by transparent mechanistic rationales to guide experimental validation.

Personalized tutoring, teacher training, and education research need access to \emph{targeted} synthetic misconceptions, but privacy and IRB constraints make labelled corpora of real student errors scarce. LLMs could in principle generate synthetic errors at scale, but producing an arbitrary wrong answer is easy for a modern LLM while producing one that matches a specified cognitive failure mode is much harder. We present a framework that generates errors targeted to a five-class taxonomy adapted from the revised Bloom's taxonomy, evaluated on questions from the TheoremQA dataset. A Generation Agent (GA) drafts a candidate erroneous solution conditioned on a target class, and an Examination Agent (EA) judges whether the draft is incorrect and class-consistent. The framework yields a reusable recipe for building class-stratified synthetic error datasets where authentic student corpora are unavailable. As a secondary diagnostic, targeted error generation is substantially harder than free-form incorrect-answer generation, and answer-grounding contributes more than expanded examples or external textbook content.

Diffusion-based neural solvers for combinatorial optimization repeatedly re-evaluate dense edge/factor interactions, making inference expensive in wall-clock time and often memory-bound at scale. Inspired by the computational methodologies of many-body physics, we introduce LoRe, a training-free, inference-time drop-in wrapper that enforces per-step interaction-evaluation budgeting: at each iteration, it evaluates only a fixed fraction of interactions by dynamically routing computation to high-conflict or high-uncertainty interactions, instead of using a fixed sparsification (e.g., static kNN graphs or static masks). Under fully inclusive end-to-end wall-clock accounting, LoRe substantially improves scalability on the Maximum Independent Set (MIS) problem, extending feasible inference more than $3\times$ beyond the baseline's out-of-memory limit, delivering a $\sim 8\times$ speedup and a $\sim 12\times$ peak-memory reduction, with solution quality preserved in this regime. Demonstrating cross-task generality on the large-scale Traveling Salesperson Problem (TSP) and zero-shot robustness to topology shifts, LoRe achieves a $\sim 15\times$ speedup at $n=1000$ with a $44\times$ memory reduction and competitive tour quality.

Reported retrieval scores for training-free shape descriptors conflate local signal design, normalization, aggregation, codebook fitting, and metric choices, making isolated component evaluation difficult. This paper reframes descriptor evaluation as a {\em protocol audit}. We introduce Diffused Geodesic Moments (DGM), a seed-conditioned descriptor that computes sparse implicit heat responses, converts them to distance-like fields, and summarizes each vertex by low-order moments across seeds and scales. DGM is used both as a practical non-spectral baseline and as an instrument for isolating protocol effects. On the registered FAUST benchmark split (FAUST-Reg) and the TOSCA shape collection, aggregation-matched experiments show that an independent Geometric Moment Shape Descriptor baseline built on Heat Kernel Signature features (GMSD-HKS) obtains the highest scores in this implementation ($0.621/0.820$ and $0.865/0.963$ mean average precision (mAP)/top-1), Wave Kernel Signature (WKS) remains a strong classical signal, and DGM is useful mainly when sparse solves, non-spectral deployment, or symmetry-informative seed frames are priorities. The broader finding is methodological: the input field and aggregation protocol can dominate the moment formula. The paper contributes a reproducible protocol-cascade analysis, a cross-shape alignment diagnostic for functional-map compatibility, and concrete recommendations for designing and reporting training-free shape descriptors.

Federated reinforcement learning enables decentralized agents to collaboratively improve policies or value estimates without exchanging raw trajectories. However, FedAvg-style parameter averaging is not function-space consistent: when clients use heterogeneous encoders or even identical nonlinear networks, averaged parameters need not correspond to the weighted average of client value functions in any common function space. We propose FedQHD, a federated Q-learning method using hyperdimensional (random-feature) state encoders with a linear readout, so that Q-functions are nonlinear in state yet linear in trainable parameters. This linear structure enables closed-form aggregation. With a shared encoder, the function-space consensus update coincides exactly with weighted averaging of local readout matrices. With heterogeneous encoders, the server constructs a global teacher by averaging client Q-values on a shared anchor-state set, and each client compiles this teacher into its local representation via a single ridge projection. We formalize the federation gap -- the error incurred when compiling a federated teacher into a heterogeneous client representation -- relative to a client-specific oracle projection. We show that this gap decomposes into subspace misalignment, anchor-set conditioning, and regularization bias. We further identify the anchor-to-dimension ratio $m \geq D_i$ as the well-conditioned regime in which the gap reduces to a multiple of the encoder heterogeneity floor. On four continuous-state, discrete-action control benchmarks, FedQHD matches or outperforms FedAvg-style baselines and distillation-based alternatives while requiring substantially less computation, and the empirical dependence of the federation gap on encoder dimension matches our theoretical analysis.

A paraphrase-quality audit of MathCheck (ICLR 2025) detected 4 semantically incorrect paraphrases in 129 groups (3.1%); removing them drops GPT-4o from rank 2 to rank 4 and elevates Claude Haiku and DeepSeek V3 above it; these ranking changes are invisible to any single-model evaluation. Cross-model unanimity found these errors automatically (>= 3/4 models for MathCheck; >= 6/9 for our primary evaluation) for under $10; in our own dataset the same protocol found that 47% of auto-generated connective-variation paraphrases were semantically incorrect. That flaw compounds a deeper measurement gap: Claude Haiku 4.5 achieves 86% accuracy yet SCR=50%, meaning half its theorems are answered differently under semantically equivalent restatements, while aggregate accuracy across 9 models spans only 86-96% yet Semantic Consistency Rates (SCR) span 50-82% -- a 32-point gap invisible to standard benchmarks. Formally, for any target ranking over 9 frontier models there exists a weighting over paraphrase families that realizes it (No-Free-Benchmark corollary), because no model Pareto-dominates all families -- so benchmark designers who select families are implicitly choosing which model wins. FormInv supplies the audit protocol (replicated on external benchmarks at 100% recall), SCR and per-theorem Cochran's Q as primary invariance measures evaluated on 9 models across 366-811 items (on Lean4-verified theorems), and FormInvSelector for regime-aware model selection.

Traditional lossless text compression preserves every byte, but its gains on natural language are often modest in realistic operating regimes. We study \emph{lossy semantic text compression}, where the encoder strategically deletes parts of the text and a large language model (LLM) reconstructs the original content from the retained skeleton. We benchmark a progression of deletion strategies, including uniform step deletion, word-length-guided deletion (WordLen), word-frequency-guided deletion (WordFreq), LP-optimized deletion (Opt), entropy-based deletion using GPT-2 surprisal, and hybrid methods that combine frequency and surprisal signals. Evaluation on the BBC News dataset across retention rates $\r_{keep} \in [0.1,0.9]$ shows three main findings. First, WordFreq is a strong low-cost baseline: despite using only a static frequency lookup, it remains competitive with much more expensive semantic methods while being far faster at the encoder. Second, semantic and hybrid methods provide their clearest gains at mild-to-moderate compression, whereas word-frequency deletion is often more robust at the lowest retention rates. Third, QLoRA fine-tuning yields a strong local decoder that is competitive with Gemini 2.0 Flash and is often strongest in decoder-only comparisons. Additional English and Chinese experiments show that the overall framework transfers across domains, while the best deletion rule remains dataset-dependent.

Functional magnetic resonance imaging (fMRI) is a powerful tool for investigating human brain function. However, the high cost of data acquisition and the inherent subjectivity of psychiatric rating scales often lead to datasets with small sample sizes and variable label quality, especially when targeting a specific neurological condition. Combined with the inherently high dimensionality of fMRI data, these limitations substantially increase the risk of model overfitting. Recent years have seen growing interest in developing fMRI foundation models by combining multiple datasets; however, the computational resources needed for pretraining and fine-tuning are often prohibitive. We show that a lightweight self-supervised framework yields representations that generalize across diverse downstream tasks, outperforming fully supervised baselines and approaching the performance of large-scale models. We introduce BrainSimSiam, a data-efficient self-supervised representation learning framework that leverages positive-only data pairs to learn robust and generalizable features. We demonstrate that the learned representations achieve strong performance across multiple downstream classification and regression tasks, highlighting the potential of BrainSimSiam for data-limited neuroimaging applications.

In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights. The correspondence is exact for log-sum-exp layers and structural for broader architectures: residual networks, transformers, and recurrent architectures (RNNs, LSTMs, SSMs) each discretize the same class of Hamilton--Jacobi equations, with architecture-dependent Hamiltonian and viscosity. A single deformation parameter $\varepsilon$ unifies all four perspectives (network, tropical algebra, viscous PDE, convex optimization) in a commutative diagram closed under Lipschitz conditions. Quantitative consequences include: the minimax optimal generalization rate $O(n^{-1/(d+2)})$ for fixed $t$; adversarial robustness controlled by $\varepsilon$; backpropagation as the co-state equation of the Hamiltonian system for residual networks (Pontryagin Maximum Principle); scaling exponents consistent with data intrinsic dimension via PDE quadrature; and a closed-form $O(N)$ influence function (softmax attribution weights $π_j$) whose entropy landscape undergoes fold bifurcations as $\varepsilon$ increases, each merging attribution basins.