Papers

The increasing reliance of autonomous AI agents on external and distributed knowledge sources introduces a fundamental challenge for decentralized information marketplaces: retrieval agents must evaluate the quality and relevance of data before purchase, while data providers must avoid revealing valuable information prior to guaranteed compensation. This paradox becomes particularly critical in trustless multi-agent environments, where no centralized intermediary can enforce fairness between parties. In this paper, we propose a fairly compensated protocol for distributed information retrieval and augmentation in autonomous agent networks. Our framework enables retrieval agents to securely evaluate and rank candidate documents without learning their plaintext contents, while ensuring that data providers are compensated only when valid information is successfully delivered. We further analyze the security properties of the protocol against malicious adversaries and evaluate its practical feasibility through implementations. Experimental results demonstrate that the proposed design is practical with current cryptographic infrastructures while preserving confidentiality, correctness, integrity, and fairness. We believe such mechanisms provide an important cryptographic foundation for trustworthy and economically sustainable decentralized knowledge marketplaces for future AI agent ecosystems.

LLM agents are beginning to write the rules they live under: policies, contracts and code that other agents review and approve. What happens when those rules must decide who is sacrificed from a group? We built GovSim-SelfGovern, a commons in which agents legislate in executable Python, test each law in a sandbox, vote on it, and live with the result. When the fishery is abundant, self-rule helps, raising the chance that the community survives without anyone starving from 52.5% to 75.0%. When it cannot feed everyone though, adding governance is not enough to save the commons. We trace much of this to the vote: agents readily draft laws that remove members, but then frequently vote them down, thereby dooming the commons. In a controlled replay, the same exile law passes 8% of the time when the sandbox preview names its victim at once and 55% when the removal is deferred until a future crisis. Showing voters the full source code does not close the gap, though most describe the removal in their own words. Nor is sacrifice a fixed trait. A single sentence of framing can swing self-removal from 2.5% to 91%, and due process deters agents more than considering the potential death of a peer. In contrast, give the community a treasury and the question of who must go almost disappears. Our work shows that what our collectives legislate is decided more by the form in which a choice is put to them as compared to their ethical beliefs.

Large language model (LLM) judges provide a flexible and scalable method for evaluating model and agent outputs, but their verdicts can be sensitive to incidental changes in the evaluated response, judge instructions, and scoring rubric. Existing systems examine important subsets of these failure modes, but auditing a configured judge requires testing both the judge instrument and the items it evaluates. We introduce MAWILE, a developer-facing workbench for auditing judge sensitivity across four surfaces: the judge prompt, judge rubric, target-system input, and target-system output. Given a user-supplied judge and representative evaluation items, MAWILE constructs and validates controlled perturbations, re-executes the judge, and localizes the resulting sensitivity. Each perturbation declares whether the verdict should remain invariant or change in a specified direction, allowing the same system to measure both robustness to irrelevant variations and sensitivity to meaningful changes. MAWILE audits binary, ordinal, and pairwise judges without requiring gold labels. The code for this tool is available at: github.com/megagonlabs/mawile-judge.

Autonomous underwater vehicles (AUVs) are a promising alternative to divers for scalable collection of natural ocean ecology data. However, these robots may disturb local fauna and cause drastic behavioral differences compared to other monitoring techniques, decreasing their value as scientific tools. A promising prospect is to make AUVs that are more biomimetic, with the hope that taking on the form and behavior of a non-predatory animal may reduce adverse responses. We present the first dataset comparing fish disturbance in response to a conventional thruster-driven AUV, a sea turtle inspired flipper-driven AUV, and a diver. Experiments were conducted at a biodiversity hotspot in a Caribbean reef, and images of the scene were analyzed using computer vision to localize and study fish behavior change. Both AUVs cause measurable changes in fish behavior. Although no between-robot differences remain significant after correction for multiple comparisons, point estimates generally favor the biomimetic AUV, motivating larger studies capable of resolving modest effects and further design changes to optimize for disturbance. We also observe larger responses during diver transects than during AUV transects, although this exploratory comparison is based on a small diver sample with several confounds. While conclusions must be taken as preliminary due to operational and experimental limitations, this study provides the community with a first known dataset and benchmarks to quantify the behavioral impacts of biomimetic robots for ecological monitoring in the wild.

This letter covers a broad comparison of methods for classification and regression applications for a user-level handover decision making in scenarios with adverse propagation conditions involving buildings, coverage holes, and shadowing effects. The simulation campaigns are based on network simulator ns-3. The comparison encompasses classical machine learning approaches, such as KNN, SVM, and neural networks, but also state-of-the-art fuzzy logic systems and latter boosting machines. The results indicate that SVM and MLP are the most suitable for the classification of the best handover target, although fuzzy system SOFL can perform similarly with lower processing time. Additionally, for the download time estimation, LightGBM provides the smallest error with short processing time, even in hard propagation scenarios.

Training agents with reinforcement learning requires a gym, comprising a task, an executable environment in which the task can be attempted, and a verifier that reliably distinguishes success from failure. Constructing such gyms remains manual, expensive, and static. Task sets saturate as models improve and are increasingly exposed to contamination. Synthetic generation offers scale, but single-pass synthesis produces tasks whose difficulty is largely cosmetic. Models comparable in capability solve them despite convoluted phrasing, and correctness must be adjudicated post-hoc by unreliable LLM judges. We present AutoGym, a framework that generates complete gyms (tasks, executable environments, and verifiers) from a minimal domain seed or prior model trajectories. AutoGym introduces three mechanisms. (1) Blueprint-first generation specifies the valid solution space, environment requirements, and verification criteria before the environment is materialized, making solvability a construction prerequisite rather than a property verified after the fact. (2) Explicit generation parameters control task topology, interaction depth, capability axes, question obfuscation, and distractor composition, enabling fine-grained difficulty steering. (3) Active curriculum synthesis uses performance-informed calibration to adjust the distribution over these parameters as model capabilities evolve. Across productivity and temporal-reasoning settings, AutoGym generates gyms spanning the capability spectrum, including instances that challenge frontier models.

Robot learning policies fail in characteristic ways: they stall in uncertain states, drift during contact-rich alignment, and miss targets by millimetres in precision tasks. Yet training datasets consist largely of successful demonstrations, while real-world benchmarks often reduce performance to binary success. This limits both supervision for recovery and analysis of where failures occur. We introduce REBOOT (Recovery Episode Benchmark for Off-nominal Trajectories), the first robot manipulation benchmark designed around failure as a first-class signal. REBOOT contains 2,160 demonstrations across 18 precision assembly tasks, each decomposed into five shared phases: Align(pick), Engage(pick), Transport, Align(place), and Engage(place), enabling phase-level evaluation beyond terminal success. Failures are introduced across phases and paired with expert recovery trajectories that return the system to a valid continuation state. Tasks are annotated with rotational symmetry, engagement-clearance precision tier, and assembly direction through matched install-remove pairs. Failure episodes are labeled by phase and categorical failure mode, enabling attribution to kinematic stage and tolerance violation. Data includes synchronized RGB-D observations from four viewpoints and grounded natural-language descriptions of phase-level success and failure conditions. Half the dataset contains expert demonstrations; the other half contains recovery demonstrations sampled to reflect failures observed in imitation-learned policy rollouts. We benchmark action-chunked transformer, diffusion, and $\pi_0$-FAST policies using phase-level completion rates, revealing model-specific failure points hidden by binary evaluation. Dataset and code: https://nanayawoa.github.io/REBOOT

Soft errors are an increasing reliability concern for Deep Neural Network execution because they can corrupt parameters, leading to accuracy degradation. While conventional ECC offers strong fault protection, it incurs additional parity storage and computational overhead. Embedded-parity formats reduce storage cost by reusing the least-significant bits, but they do not optimize protection while reducing computational overhead. We propose UniCASE, a unified 16-bit floating-point (FP) format that jointly optimizes data representation and error protection for reliable DNN execution. It identifies stable blocks across FP64, FP32, FP16, and BFloat16 that can be mapped into a unified representation. Based on bit-level criticality analysis, UniCASE uses selective ECC that assigns distinct levels of protection to different data bits according to their resilience against soft errors. Experimental results show that UniCASE reduces encoder/decoder cost by up to 30%, preserves model accuracy within 1% of the FP32 baseline, and provides significantly stronger soft error resilience than existing embedded-parity methods.

Vision-language models (VLMs) perform strongly on visual question answering benchmarks, yet often make decisions that contradict visual evidence they have already identified correctly. We distinguish perceptual failure, where relevant evidence is not recognized, from process failure, where recognized evidence fails to constrain the final decision. We introduce VPAC-Bench, a benchmark spanning nine real-image process families, with each image annotated by its current activity stage and nearby stage transition. We also propose State-Relevance-Target (SRT), a family of structured process-prior interventions that requires models to connect visible evidence to the relevant process state before answering. Across multiple VLMs, process failure is widespread: models that correctly enumerate visual candidates still over-commit to a single answer in more than 95% of ambiguous cases. An explicit process-structured intervention reduces this rate to below 13% without degrading performance on unambiguous cases. However, the transfer of process priors is model-dependent, and generic SRT does not consistently outperform strong chain-of-thought baselines. When the relevant stage transition is known, boundary-aligned SRT substantially outperforms generic process prompting and all tested chain-of-thought baselines across assembly, physical state transition, navigation and traffic, and object-use affordance tasks. These results show that process priors are most useful when aligned with the scene's specific decision boundary, motivating boundary-aware prior selection for process-grounded visual reasoning.

Vision-Language-Action (VLA) models commonly predict action chunks, limiting their ability to react to environmental changes during execution. Existing asynchronous inference methods improve reactivity but typically rely on a fixed inference gap. In this paper, we propose an event-guided dynamic inference strategy that adapts the inference gap according to scene changes observed since the previous inference. Thereby, it simultaneously preserves motion consistency and prompt reactivity. Across static and dynamic real-world settings, our method consistently performs best, averaging 95% success and exceeding the strongest baseline by 55 percentage points. The code will be made publicly available upon acceptance. The project page is available at https://react-when-you-need-to.github.io/.

Modern audio-language models are no longer judged only on what words they can transcribe, but on whether they can reason over what they hear: recovering meaning that lives in tone and prosody, telling dialects and regional languages apart, and resolving ambiguity that the written form leaves open. This capability is now measured by a growing family of audio-reasoning benchmarks, but almost entirely in English and on general-domain audio. Southeast Asia (SEA) is served instead by benchmarks that inherit an English task taxonomy of recognition, translation, and paralinguistic classification, and therefore test whether a model hears SEA speech rather than whether it can reason from it. We introduce SEABED, an audio-first question answering dataset designed to benchmark language and audio reasoning models on SEA speech. SEABED comprises a suite of six audio-reasoning tasks built entirely from real, openly available SEA speech corpora, yielding 5,404 question-answer pairs. We evaluate six frontier and region-specific audio LLMs: even the state-of-the-art model Gemini 3.5 Flash achieves only 50.3% weighted average accuracy. SEABED evaluates not only answer accuracy, but also whether models' stated reasoning is grounded in the audio evidence. A sample of the benchmark data is available here: https://huggingface.co/datasets/CentificAIResearch/SEABED.

We introduce TWIG (Time-Causal Wavelet Operator for Irregular Graphs), a graph-native neural operator for autoregressive surrogate modeling on static irregular graphs. TWIG transforms each node history into causal multiscale temporal features that separate recent variation from progressively slower memory components, then propagates these features through graph-wavelet operator blocks with gated pointwise channel mixing. The architecture is causal by construction and designed for closed-loop forecasting, where predictions are recursively reused as future inputs. We evaluate TWIG on three irregular-domain forecasting problems spanning regional diffusion, three-dimensional subsurface hydrology, and aerodynamic flow, with graphs ranging from 400 to 5,233 nodes and model capacities from approximately 70k to 10M parameters. TWIG achieves the lowest aggregate rollout errors on the subsurface-hydrology and regional-diffusion benchmarks and ranks second on the 10M-parameter aerodynamic-flow benchmark, behind the GPS Transformer. Across all three settings, TWIG consistently outperforms the corresponding non-time-causal Graph WNO baseline. These results demonstrate that TWIG provides an effective and scalable approach to stable autoregressive forecasting of dynamical fields on irregular graphs.

As industrial processes grow in complexity, traditional Proportional-Integral-Derivative (PID) controllers are often insufficient for handling their non-linear, multi-input dynamics. We propose using advanced Deep Reinforcement Learning (DRL) to prove its advantages in these complex environments. To do this, we rely on the Industrial Benchmark (IB). The IB is a realistic simulation that tests DRL algorithms against the key challenges of industrial applications: high-dimensional state spaces, delayed effects, and conflicting multi-criterial objectives. This testbed highlights DRL's core trade-off: while its final policies can often be unstable, its unique strength is the ability to autonomously discover optimal, non-obvious policies in multi-dimensional spaces where simple controllers fail. In this paper, we propose a novel hybrid PID-RL controller that leverages DRL's discovery capability while ensuring Reliability. After developing a multi-objective reward function to make DRL viable, we use a twin-delayed deep deterministic (TD3) agent as a discovery tool to find the optimal, non-obvious settings for the IB's 'Gain' and 'Shift' parameters. By feeding these discovered parameters to a simple, tuned PID controller, our hybrid model successfully combines all three characteristics: it achieves the optimal Performance and Efficiency of the best DRL agent with the Reliability of a classical controller. This work demonstrates a practical methodology for using DRL to augment, rather than replace, trusted industrial control systems.

Predictive maintenance in Industry 4.0 refers to using data from sensors, machines, and production systems to estimate when equipment is likely to fail, so maintenance can be planned before a breakdown occurs [1]. However, a model that predicts maintenance may work perfectly in the lab but fail unexpectedly when applied to real factory data [2]. To solve this "reliability" gap, we evaluated six deep learning architectures across more than 700 experimental runs. We focused on the two dominant approaches in the field: Recurrent Neural Networks (RNNs), which process data step-by-step, like reading a sentence [3], and Transformers, a recent dominant approach, which look at the entire sequence at once to spot important connections [4]. We examined whether Transformers still outperform recurrent neural networks (RNNs) when the data includes noise [5]. We found that while Transformers excelled at tracking stable, slow-moving processes, they tend to overreact to chaotic data, mistakenly taking sensor noise for meaningful signals [6]. We also found that the hybrid method that combines a Long Short-Term Memory (LSTM) layer with a Transformer layer is more resilient to noisy data from factory shops [7]. Functioning as a noise filter, the LSTM smooths out data volatility, allowing the Transformer to focus on the bigger picture without being distracted [8]. The hybrid model did not just improve accuracy; it proved to be significantly more consistent than complex models, delivering reliable predictions regardless of how chaotic the underlying system became.

End-to-end and vision-language-action (VLA) driving policies are compared by leaderboard rank, but a rank reports an outcome, not the behaviour behind it, so it predicts poorly how a policy will behave at a new site. On six released policies, rank on nuScenes open-loop error or on NAVSIM's leaderboard does not carry over to scenes with a pedestrian near the ego corridor at a new site. We propose a counterfactual check-up: a few hundred real frames, each edited two ways (pedestrian removed, or re-lit by a night-style perturbation), every edit verified by an independent detector, and the change in the planned trajectory read as a diagnosis rather than a score. From these edits two causal axes are read, and five exams built on them separate what a score merges: how far the policy plans to drive, whether seeing the pedestrian buys safety, whether that response scales with danger, whether the plan moves when nothing requires it, and how much an irrelevant lighting change moves it. On 246 NAVSIM near-pedestrian scenes, in the cells where the pedestrian lies on the planned path only 1.9% of responses are genuine avoidance, and under our open-loop protocol the median clearance change is at most 0.03 m and the median change in planned distance at most 0.08 m for every policy. In a pre-registered test from left- to right-hand drive, the exposure and specificity orderings, the lighting verdict and the collision outcome transfer, while point values and the hazard-sensitivity verdict do not. Read as a selection report, the profiles say which policy is safe because it plans short, which covers a human-like distance without yielding, and which is unsteady under a change that requires no reaction, and they price each verdict: most settle within a few dozen frames, hazard sensitivity needs hundreds. Code and edited frames will be released.

Semidefinite programming (SDP) certificates for feedback systems containing deep neural networks (NNs) typically scale with the total number of neurons, whereas small-gain tests are scalable but can be highly conservative. This paper develops a unified and scalable framework for incremental robust stability and performance analysis of feedback interconnections involving high-dimensional NNs and unmodeled dynamics. By combining a structured decomposition of the full-order SDP condition with scalable Lipschitz constant estimation algorithms, we derive reduced verification conditions that certify incremental convergence and incremental $\ell_2$-gain bounds. The dimensions of the resulting control-analysis linear matrix inequalities (LMIs) depend only on the widths of the last two network layers and are independent of network depth. The framework preserves the coupling between the plant and the NN, with the incremental small-gain condition recovered as a special case. To further reduce conservatism, we develop a multi-round alternating update scheme that iteratively refines the coupling variables while preserving scalability. Numerical experiments show that the proposed framework achieves state-of-the-art incremental $\ell_2$-gain bounds for large-scale NN feedback systems.

LLM agents translate natural-language context, which may include attacker-controlled text, into privileged tool calls, so authorization must remain effective even when an agent is prompt-injected or adversarially steered. The Model Context Protocol (MCP) has become a widely adopted interface for this boundary, yet its official SDKs' authentication and authorization primitives fall short of enterprise zero-trust requirements, most acutely a dual-persona model in which one server must serve human users (corporate SSO) and automated agents (service-account credentials on a different header). We conduct a systematic gap analysis of six surveyed MCP SDKs (Python, TypeScript, Go, Rust, C#, Swift) and identify three structural shortcomings: credential extraction bound to a single Authorization header, complicating dual-persona deployment without custom middleware; the absence of pre-authentication tool discovery; and the lack of fine-grained per-tool authorization in the base SDKs. We close these gaps with composable extensions to FastMCP: cross-header credential normalization for enterprise deployments serving both human and service-account callers, cached token verification across heterogeneous IdPs, an unauthenticated metadata endpoint for credential-free registry discovery, and permission-filtered tool visibility kept consistent with per-tool invocation enforcement by a single declarative annotation, all without modifying the protocol or SDK internals. Across four frontier LLMs over 2160 attempts, an in-body-check-only server still exposes forbidden tools (152/720, 21.1%), whereas permission-aware visibility drives the rate to 0/720; visibility-only filtering remained bypassable by scripted clients, while models referenced the hidden tool by name in up to 94% of settings when inferable from the prompt, confirming that discovery controls cannot replace invocation-time enforcement.

Finding an optimal meeting point for a collection of agents on a directed graph is a classical problem studied in the context of network analysis, operations research and computational geometry. In this work, we use the two objectives of optimal meeting points examined in the literature to study two notions of meet-distance: $d^{\max}(u,v)$, the minimum over all meeting points $w$ of $\max(d(u,w), d(v,w))$; and $d^+(u,v)$, the minimum over all meeting points of $d(u,w) + d(v,w)$. These values measure the minimum time and minimum total distance required for two agents to meet. We initiate the fine-grained study of fundamental graph parameters under the two notions of meet-distance, namely the diameter, radius and eccentricities. For general directed graphs, we give an $\tilde{O}(m\sqrt{n})$ time algorithm for computing a 2-approximation to both notions of meet-diameter and show that this result is optimal under SETH. In contrast, we show that such a result is unattainable for the meet-radius as any finite approximation requires quadratic time under the Hitting Set Conjecture. For directed acyclic graphs, we obtain stronger results. We compute the meet$^{\max}$-diameter exactly in linear time and give a linear-time $2$-approximation for the meet$^{+}$-diameter. We complement the latter with a quadratic-time lower bound for any $(3/2-\varepsilon)$-approximation under SETH, yielding a separation between the two meet-distance objectives. Finally, we study the generalized meet-distance of $k$-tuples of vertices. For every positive integer $\ell$, we reduce the problem of $\ell$-approximating the $k$-point meet-diameter to computing an exact meet-diameter on smaller tuples, obtaining an $\ell$-approximation in time \[ O\!\left( mn+ \ell \left\lceil k^{1/\ell}\right\rceil n^{\left\lceil k^{1/\ell}\right\rceil+1} \right). \]

In this second paper on descent methods as proof mechanisms in harmonic analysis (the first treated Bourgain's $\Lambda(p)$ selection theorem), entropic mirror descent gives an improved restricted isometry bound, improving sampling and recovery bounds in the Fourier Ratio program. Let $H$ be a complex $n\times n$ matrix with $H^*H=nI$ and $|H_{ij}|=1$. For fixed $0<\varepsilon<\frac14$ and $A_0>0$, independent Bernoulli row selection with expected cardinality $C_{\varepsilon,A_0}r\log\frac{2en}{r}\log(2r)\leq m\leq n/2$ preserves, after normalization by $\sqrt m$, the squared norm of every complex vector $y$ with $\|y\|_1\leq\sqrt r\|y\|_2$ within a factor $1\pm\varepsilon$, with failure probability at most $Cn^{-A_0}$. This includes every $r$-sparse vector and also fully supported ones; support size enters only through this inequality. For $y=\widehat f$ the condition is exactly $\operatorname{FR}(f)^2\leq r$, where $\operatorname{FR}(f)=\|\widehat f\|_1/\|\widehat f\|_2$, giving uniform energy sampling and approximate recovery even for signals with full Fourier support. The same holds for a uniform subset of prescribed cardinality, and for discrete Fourier and real Hadamard matrices. At fixed accuracy the bound removes one sparsity logarithm from the earlier count and replaces $\log n$ by $\log\frac{2en}{r}$; for Walsh matrices it matches, up to constants, the lower bound of Błasiok et al.\ in their range. One relative-entropy potential controls the corrections of an amplitude predictor at every scale; counting them on the symmetric difference of two samples gives the uniform estimate. We also prove the sufficient bound $C_{A_0}\varepsilon^{-5}r\log\frac{2en}{r}\log\frac{2r}{\varepsilon}$, and stable sparse recovery from $Cs\log\frac{2en}{s}\log(2s)$ measurements, with error controlled by the noise and the best $s$-term approximation.

Knowledge distillation (KD) aims to compress high-performance teacher LLMs into lightweight students. However, distilled students often exhibit substantial performance degradation in out-of-distribution (OOD) settings, a critical gap that remains underexplored. We identify two compounding mechanisms causing OOD performance degradation: (1) data spuriousness: students can learn spurious correlations in the distillation dataset over genuine causal relationships; and (2) teacher capability: standard KD treats all samples uniformly, ignoring whether the teacher is guided by causal features or misled by spurious shortcuts on a given sample. To address these challenges, we propose Invariance-Weighted Distillation (IWD), a theoretically grounded framework that dynamically reweights training samples using an estimate of the teacher's causal reliance derived from prediction invariance across multiple synthetic environments. IWD perturbs spurious cues while preserving core semantics, assigning higher distillation weights to samples whose teacher predictions remain invariant, indicating greater reliance on causal rather than spurious features. We theoretically show that IWD reduces the student's Spurious-to-Causal (S2C) gradient ratio compared to standard uniformly weighted KD, driving the student toward more invariant representations. Experiments on four NLP benchmarks (MNLI, SQuAD-v2, CoNLL-2003 NER, and SST-2) across two model families (DeBERTa-v3 and Qwen-2.5) demonstrate that IWD consistently outperforms strong KD baselines on OOD evaluations while maintaining competitive in-distribution (ID) performance. Specifically, IWD achieves the highest accuracy in 15 out of 16 OOD benchmarks and improves average OOD performance over standard KD by 4.34 percentage points on NLI and 14.94 percentage points on QA.

Multi-vector visual document retrieval (VDR) models such as ColPali and ColNomic achieve strong accuracy by representing each document with hundreds to thousands of patch-level embeddings, at substantial storage and latency cost. Existing compression methods either prune unimportant patches or merge similar ones into clusters; the recent state-of-the-art merging method Prune-then-Merge (PtM) consistently outperforms pruning-only baselines at high compression, but requires a per-dataset cluster budget m to be tuned by grid search. We observe that the merge-cosine sequence produced by hierarchical clustering exhibits a sharp cliff separating mergeable redundancy from salient signal, and that the location of this cliff is concentrated in a narrow band across more than 11,000 documents from 14 datasets. This suggests the merge boundary can be detected per document rather than tuned per dataset. Building on this observation, we propose AdaMerge, a plug-and-play compression method that (i) detects each document's own cliff via gap analysis on the merge-cosine trajectory, and (ii) builds attention-weighted cluster centroids to preserve salient signal. On the long-document benchmark ViDoRe-V2 (4 datasets, two backbones), AdaMerge significantly outperforms tuned PtM across the operating range (p < 10^-4); on the short-document benchmark ViDoRe-V1 (10 datasets, two backbones), where all merging methods are already near-lossless, AdaMerge matches tuned PtM without any per-dataset tuning. AdaMerge adds only about 10 ms per document and exposes a single global hyperparameter shared across all datasets and backbones.

Backpropagation (BP) has driven the remarkable success of modern deep learning by enabling large hierarchical networks to learn complex functions end-to-end. Yet it does not by itself determine how parameters should be organized so that functional components can be reused and adapted selectively. For example, object recognition and motion prediction may depend on overlapping parameter sets, making them difficult to isolate or modify independently. We call this condition weight entanglement. Modern architectures dynamically select which parts of a network process each sample: nonlinearities gate units, attention selects interactions, and Mixture-of-Experts architectures route inputs to modules. Yet such selection does not ensure that the same functional component remains linked to an identifiable parameter set across samples. We propose weight operators: parameterized modules that implement reusable functional components and can be composed at inference to form the function required by each sample. Learning proceeds in two stages: the model first infers the required operator composition, then updates only the selected operators' parameter sets. Vector Networks (VNs) provide one implementation. They couple operator selection to local error-driven updates within each layer and show that learned operators can be reused in combinations absent from training while updates remain restricted to the selected parameter sets. This provides a basis for testing functional parameter identifiability: whether an operator remains linked to the same functional component during learning. We argue that functional parameter identifiability may provide an organizing principle for models that systematically reuse and recombine learned functions while adapting only the components that need to change.

Effective LLM tutoring depends on correctly identifying the specific error in a student's reasoning before generating feedback. We study this problem in propositional-logic proof tutoring, where student actions can be checked against formal inference rules. We introduce a verifier-grounded architecture that separates diagnosis from language generation. Using 600 balanced student actions, we compare a zero-shot LLM detector, a fine-tuned detector, and a symbolic verifier. Each diagnosis is processed by shared rationale and feedback agents, isolating the effect of the initial diagnosis. The zero-shot detector achieves a macro-F1 of 0.191; fine-tuning raises this to 0.709 but retains systematic errors between structurally related classes. Rationales generally preserve the diagnosis supplied to them, showing that an incorrect diagnosis can be faithfully propagated through the pipeline. Feedback can likewise remain faithful to its rationale, non-revealing, and pedagogically appropriate while addressing the wrong error. Verifier-grounded feedback achieves the highest diagnostic correctness, and expert ratings largely uneven with the automatic feedback evaluations. These findings show that apparent feedback quality can conceal upstream diagnostic errors and that faithfulness must be evaluated separately from correctness. Our code is publicly available

The category Nom of nominal sets was proposed by Pitts and Gabbay as a setting for the semantics of abstract syntax with variable bindings. It is well-known that Nom is a topos, also known as the Schanuel topos, and in particular it follows that Nom is locally closed, i.e., every slice category Nom/X is cartesian-closed. In this paper, we show that Nom has a much stronger property: every monoidal (closed) structure on Nom induces a monoidal (closed) structure on all slice categories Nom/X. One monoidal closed structure of particular interest on Nom is the separated product A * B, whose right adjoint A -* B is called the separated function space. In particular, it follows that Nom is locally separatedly closed.

We establish the positive semidefiniteness of a class of Hermitian Cauchy-like matrices associated with real Hurwitz polynomials having distinct zeros. Writing the zeros as $-\lambda_1,\ldots,-\lambda_n$, the matrix entries are defined through ratios of elementary symmetric polynomials in the variables $\lambda_i$. The result extends an earlier positivity theorem obtained under the assumption that all zeros are real. We first show that the coefficients appearing in the denominators are nonzero, so that the matrices are well defined. We then construct an explicit congruence between each matrix and the solution of a Lyapunov equation whose state matrix is in companion form. Positive semidefiniteness follows from a recent result on such equations with entrywise nonnegative right-hand-side data. This approach establishes the extension to complex zeros through the connection between structured matrices and Lyapunov equations.

AI is rapidly transforming higher education, including the application process, yet relatively little is known about its use and consequences. To help close this gap, we analyze nearly 7{,}500 applications submitted between 2020 and 2025 to a large public policy master's program in the United States. We find that in the 2025 admissions cycle, the majority of applicants submitted at least one essay that was primarily AI-generated—despite an explicit prohibition against using AI. Leveraging the abrupt introduction of ChatGPT in November 2022, we find that the availability of AI assistants improved the writing quality of submitted essays. These improvements, however, came with an apparent AI penalty: Applicants submitting AI-written essays were admitted less often than comparable non-users. To help explain this penalty, we conduct an experiment with admissions officers, finding that they can often recognize AI writing and rate essays they believe to be AI-generated lower than essays they believe to be human generated. These findings indicate that AI is changing both how applicants write and how that writing is evaluated, raising questions about whether admissions practices and policies designed for a pre-AI era remain appropriate.

An oblivious subspace embedding (OSE) is a distribution over matrices that approximately preserves the squared Euclidean norm of every vector in any fixed low-dimensional subspace. We prove the Nelson-Nguyen conjecture: for every $0 < \delta < 1$, there exists a distribution that gives an OSE with embedding dimension $O((d + \log(1/\delta))/\varepsilon^2)$ and column sparsity $s = O(\log(d/\delta)/\varepsilon)$, with failure probability at most $\delta$. We first bound the mean spectral error using a trace-moment argument and then upgrade this bound to the desired high-probability guarantee using concentration and resampling. ChatGPT-5.6-Pro was used in proving and writing the results of this manuscript.

Reinforcement learning with verifiable rewards (RLVR) typically improves pass@1 but can fall behind its base model at large sampling budgets $k$, commonly interpreted as sharpening existing solutions. Because adjacent pass@$k$ estimates reuse generations, pointwise error bars cannot establish a crossover. We formulate paired inference on the RL-minus-base difference curve: a prompt-level multiplier bootstrap yields a one-sided dominance test and simultaneous confidence bands requiring both an early gain and a later loss. Among nine public RLVR checkpoints at 3k-16k token limits, only one narrowly meets this criterion before multiplicity adjustment; asymmetric truncation can create, mask, or reverse crossovers. On 1,060 deduplicated competition problems at 32k tokens, two 1.5B models exhibit certified crossovers around $k\approx10$-$60$, while two 7B models show no supported loss. A paired variance decomposition shows why adding prompts improves power more than deeper sampling. Prompts with identical base success probability diverge after RLVR, with dispersion replicating across independent generation halves and violating Lipschitz slope bounds for reasonable deterministic maps. Modeling RLVR as a Markov kernel, Jensen's inequality shows that conditional dispersion depresses pass@$k$ for $k\ge2$. Once dispersion is modeled, the conditional-mean log-odds slope is below one in every pair: RLVR improves hard prompts on average, while late-$k$ loss comes from a 2%-3% minority of base-solved prompts collapsing onto a repeated modal wrong answer and resisting prefix rescue up to 4,096 tokens. In controlled runs from one base model on 3,000 new problems, all four GRPO arms fall behind near $k\approx200$ and remain behind through $k=4096$, while SFT stays significantly ahead throughout.

This paper introduces Representation-to-Decision (R2D), an end-to-end imitation learning framework that maps heterogeneous multi-horizon time-series inputs directly to battery control decisions through modular Temporal Feature Extractors (TFEs) and a shared latent representation, without an explicit load and PV forecasting step. While accurate forecasting improves prediction quality, optimal control performance remains unguaranteed in prediction-then-optimization pipelines; standard Reinforcement Learning (RL) lacks the long-horizon temporal awareness due to short-window observations, even when forecast signals are available as additional inputs. R2D offers a different perspective: rather than forecasting first and deciding second, it learns to decide directly from raw temporal inputs, with control optimality anchored by an aging-aware Mixed-Integer Linear Programming (MILP) expert through Behavior Cloning (BC). Benchmarked against six controllers on a high-fidelity electro-thermal battery simulation across five industrial sites, R2D achieves 62–77% of the global clairvoyant optimum, outperforms the tested Model Predictive Control (MPC) and RL benchmarks, and yields battery degradation nearly identical to its MILP teacher across all five sites. Comprehensive ablation studies over temporal backbone, model size, expert formulation, aging-cost weighting, and horizon configuration confirm that an LSTM encoder with a 15-minute single-step control horizon provides the most robust and deployment-ready configuration, and cross-site and single-factor out-of-distribution tests show that generalization to unseen profiles is profile-dependent, with policies trained on high-activity sites transferring most reliably.

AI training loads can exhibit rapid power fluctuations because their power demand differs significantly between computational and communication phases, creating challenging ramp rates at the data center point of common coupling (PCC). Integrating battery energy storage systems (BESS) in data centers is a promising mitigation option. This paper proposes a hybrid BESS control strategy that combines droop-based grid-forming (GFM) control with instantaneous load current-based compensation to suppress high frequency load fluctuations. The GFM control loop regulates the long-term power exchange of the BESS, while the load-following control provides fast compensation for short-term AI workload fluctuations. Communication delay between the load current measurements and the BESS controller is explicitly modeled, and its impact on smoothing performance is analyzed. To mitigate delay-induced degradation, a predictor-based compensation method is incorporated into the BESS control structure. High-fidelity electromagnetic transient simulations are conducted to validate the proposed approach. Results demonstrate effective smoothing of AI training load fluctuations across different grid strength conditions and under time varying communication delays.