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arXiv2026

Hierarchical Secure Distributed Linearly Separable Computation with Arbitrary Heterogeneous Data Assignment

This paper studies secure distributed linearly separable computation over a three-layer hierarchical network, where clustered users communicate with a central server through relays. The server aims to recover Kc linear combinations of K intermediate outcomes, where each intermediate outcome is a separable function of one dataset. We consider a more general setting with arbitrary heterogeneous data assignment across users, where ''arbitrary'' means that the data assignment is given in advance (which can be in any form) and ''heterogeneous'' means that the users may hold different numbers of datasets. Under this assignment, each user computes the intermediate outcomes of its assigned datasets and sends masked messages to its associated relay. The relays subsequently process and forward the received messages to the server. We impose two security constraints: (i) security against server, requiring the server to learn only the desired task function without gaining any additional information about users' inputs; and (ii) security against relays, ensuring each relay learns nothing about users' inputs. Moreover, the server or any relay may collude with a subset of users. For Kc=1, the underlying computation reduces to distributed gradient coding. We propose a secure scheme tolerating user dropouts and user collusion, achieving the optimal two-layer communication rates in one regime and order-optimal communication rates within a factor of 2 in the other regime. For Kc>1, we extend the proposed construction to multi-dimensional linearly separable tasks under the no-dropout setting.

cs.DC↗
arXiv2026

The Breakdown of Classical Minicrypt Equivalences in the Quantum-Computation Classical-Communication Model

Classically, it is well-known that several fundamental cryptographic primitives, including one-way functions, pseudorandom number generators, commitments, and signatures, characterize the same cryptographic world, which is known as "Minicrypt". In this paper, we investigate to what extent this picture persists in the quantum-computation classical-communication (QCCC) setting, where parties may perform quantum local computation, but communicate through only classical messages. We demonstrate that the classical Minicrypt landscape breaks down in the QCCC model by oracle separations. We construct two oracle worlds where efficiently verifiable one-way puzzles (EV-OWPuzz) exist. By a known equivalence, QCCC one-time signatures also exist in both worlds. In the first, one-way functions do not exist, even if we allow quantum pseudodeterministic evaluation. In the second, QCCC bit commitments do not exist. Thus, the classical Minicrypt reductions from signatures to one-way functions and bit commitments have no fully black-box counterparts in the QCCC setting. Our proofs develop techniques for analyzing the random phase states, including a concentration theorem and an LOCC decoupling theorem, which may be of independent interest.

quant-ph↗
arXiv2026

Compositional Safety Failures in Harness Evolution: Identification and Runtime Monitoring

Self-evolving agent harnesses continually update persistent components such as memory, prompts, skills, and tools. We call this process harness evolution. However, such evolution could introduce unexpected safety risks. Existing work studies harness misevolution and validates candidate harnesses or attributed individual component updates, leaving safety analysis of cross-component update interactions largely unexamined. To address this gap, we study compositional safety failures in harness evolution, where interactions among individually safe and utility-preserving component updates can produce undesirable or unsafe agent behavior, revealing a safety risk intrinsic to harness evolution. Across three safety-related benchmarks, we identify 43 pairwise and 18 irreducible 3-way compositional safety failures. Conventional solution incurs combinatorial complexity in validating cross-component interactions, leaving the safety checking impractical as the harness evolves. To solve this, we introduced a typed hypergraph that represents component states as nodes and safety-relevant higher-order interactions as hyperedges. When the harness changes, the hypergraph updates only the interaction neighborhood of the changed states rather than reconstructing the global composition space. Building on that, we develop a hypergraph-guided runtime monitoring mechanism. Experiments show that our method effectively mitigates compositional safety risks while preserving task utility and reducing interaction-checking costs, and further reveal an empirical safety-utility-cost trade-off across different safety mechanisms.

cs.AI↗
arXiv2026

Knowing Is Not Choosing: What Explicit Verification Adds Beyond Generative Preference

Generating a correct answer does not mean that a language model will select it. We separate factual recall into three steps: generating a correct candidate, ranking the available candidates, and selecting the final answer. Pre-generation readouts predict factual recall and which questions sampling will cover across three model families, but say little about whether an available correct answer will ultimately be selected. Explicit verification with $P(\mathrm{True})$ improves within-question ranking over mean log-likelihood in Gemma, Qwen3, and Llama, with AUROC gains of $0.08$--$0.12$. In a prospectively defined Gemma cohort, verification raises plurality accuracy by about $5$ points, and still gains about $2$ points over chat-template likelihood, a stronger generative baseline. The advantage is strongest for relations with common-answer priors and depends on access to the entity; masking the entity removes the ranking advantage in larger Qwen models. Finally, the measured benefit depends on how correctness is defined: recall-oriented reference matching can credit option lists favored by likelihood and substantially understate the improvement seen under human semantic judgments. Prior work shows that models can carry latent factual knowledge and judge candidate answers; we show that these capabilities do not collapse into a single notion of ``knowing,'' and trace where information is gained, lost, or mismeasured between availability, ranking, and final choice.

cs.CL↗
arXiv2026

Beyond State-as-Action: Exploiting Command-State Discrepancy for Robot Imitation Learning

Constructing action targets from measured robot motion is an established approach in imitation learning. Under interaction constraints, however, command-state discrepancy may reflect control demands that motion alone does not capture. We investigate when this information matters and how to exploit it. Across three real-robot tasks, task and phase analyses reveal larger supervision gaps under constrained interaction, while selective command retention provides evidence of locally useful command information. Building on these findings, we propose Command-State Discrepancy Weighting (CSDW), which accounts for robot response times and combines subsequent progress, persistent unmet demand, and demand changes into continuous weights for command supervision. The method requires no task-phase annotations or changes to policy architecture or inference. CSDW improves over uniform command supervision on constrained tasks, while methods perform similarly in the less constrained task. Project page: https://seen-e.github.io/CSDW/.

cs.RO↗
arXiv2026

Which Self-Improvements Should We Trust? Reliable Self-Improvement When Agents Reuse Their Benchmarks

As recursive self-improvement (RSI) rapidly advances, reliable evaluation becomes critical for guiding adaptive search. RSI typically relies on finite evaluation resources, such as fixed benchmarks, to determine which modifications are retained and what is proposed next. However, when these finite resources are repeatedly reused, new candidates are proposed based on feedback from the same evaluation set, so the search trajectory can adaptively overfit and empirical improvement may not reflect genuine population improvement on the underlying task distribution. Some existing methods account for multiple comparisons but assume that candidates are chosen independently of the evaluation set, and therefore do not control this adaptive dependence. To address this, we propose REUSE (Risk-controlled Evaluation Under Sequential Evolution), a certified evaluation and promotion framework that allows a fixed evaluation set to support repeated adaptive decisions while providing statistical guarantees. For a user-specified error level $α$, with probability at least $1-α$, every promoted modification is a genuine population improvement on the underlying task distribution. REUSE achieves this by strictly limiting the evaluation feedback returned to the search process and accounting for possible promotion histories within the error budget. We develop detailed statistical theory for RSI evaluation in this setting, including simultaneous error control, valid lower bounds on cumulative improvement, and a characterization of the fundamental limits of adaptive evaluation reuse. In live self-improvement experiments, REUSE commits substantially fewer false promotions than evaluation frameworks from current RSI systems and error-controlled baselines, reducing the proportion of false promotions from up to 20.7% to 0%, while achieving final true population performance comparable to the best baselines.

stat.ML↗
arXiv2026

Teach Yourself Where to Look: On-Policy Attention Self-Distillation for Reasoning

On-policy self-distillation trains reasoning models on their own trajectories using dense token distribution guidance from a privileged teacher with access to a verified solution. This supervision transfers what the teacher predicts without directly transferring where it attends within the preceding context. We introduce On-Policy Attention Self-Distillation (OPASD), which complements token-level supervision with solution-conditioned attention distillation. Because the privileged teacher can attend to verified solution tokens unavailable to the student, OPASD projects teacher attention onto student-visible positions and renormalizes the resulting distribution before alignment. Across three model sizes and four competition-level mathematics benchmarks, OPASD consistently outperforms token-only OPSD, improving average accuracy by 4.98 to 8.40 percentage points. OPASD also avoids the response-length inflation and performance degradation observed with token-only distillation, reducing generated rollout tokens by 73.9% and estimated model compute by 72.6% while training 1.53x faster. These results show that solution-conditioned attention provides a complementary supervision signal that makes on-policy self-distillation more accurate, stable, and compute-efficient.

cs.LG↗
arXiv2026

PARSEE-VAD: Efficient Training-Free Online Video Anomaly Detection via Proposition-Aware Reasoning and Streaming Evidence Escalation

Training-free online video anomaly detection (VAD) with frozen multimodal language models faces two coupled challenges: extracting reliable current-window semantics under causal and computational constraints, and maintaining temporal continuity without repeatedly transmitting high-dimensional history. Encoding history through text can compress visual evidence and introduce semantic bias, whereas retaining visual history expands multimodal context. We introduce PARSEE-VAD, a two-module framework that separates semantic evidence acquisition from score-state evolution. Proposition-Aware Reasoning (PAR) extracts structured propositional evidence from the current causal window and conditionally activates more specific queries when coarse evidence warrants further refinement. By sharing a reusable causal visual prefix across queries, PAR reduces redundant computation through selective execution. Streaming Evidence Escalation (SEE) maps the acquired proposition evidence into a compact score-domain event state through current evidence escalation, then propagates only the resulting bounded state across decisions to support temporal continuity. Experiments on four benchmarks demonstrate strong training-free online performance while selective routing reduces specialist computation and score-state propagation remains sparse. These results support a current-first principle for streaming multimodal inference: resolve present semantics first, then use compact historical state only to repair residual continuity gaps.

cs.CV↗
arXiv2026

GTRL: Grounding Divide-and-Conquer Value Learning with Temporal Differences

In offline goal-conditioned reinforcement learning (GCRL), divide-and-conquer scales to long horizons by joining two shorter segments at a subgoal. However, under stochastic dynamics, the base case of this rule values the luckiest trajectories through the data. The subgoal must also lie on a shared trajectory, so a state-goal pair that no trajectory connects gets no value update at all. To address both, we present Grounded Transitive RL (GTRL), an offline GCRL value learning algorithm that grounds the divide-and-conquer update with a one-step TD target. Over a single step, TD is correct, as its target averages over the successors and needs no subgoal. GTRL adds this target to the composition rather than replacing it, so every pair receives an update, and the composition still carries the long horizon. GTRL also corrects the bias from hindsight relabeling by reweighting each goal against how reachable it was from other successors. We evaluate our algorithm on nineteen OGBench tasks spanning stochastic, deterministic, and stitching environments, where it achieves the highest average success rate. Code will be released soon.

cs.LG↗
arXiv2026

Prime-Detecting Identities from Dirichlet Inversion

For each integer k >= 1, let sigma_k(n) = sum_{d|n} d^k, let sigma_k^{-1} denote its Dirichlet inverse, and let J_k denote the kth Jordan totient function. Using established prime-power values of sigma_k^{-1}, we first obtain the elementary criterion sigma_k^{-1}(n) + J_k(n) + 2 = 0 precisely when n is prime. At k = 1, this involves Euler's totient J_1 = phi and provides a prime-only comparison for the next equation. Our main result classifies the zeros of sigma_k^{-1}(n) + mu(n) + J_k(n) + 3: for k = 1, they are precisely the primes and 18; for k >= 2, they are precisely the primes. The proof separates integers according to their prime-exponent patterns. Sign and divisibility arguments exclude composite zeros outside the cube-free nonsquarefree case, where an additional divisibility condition isolates 18 at k = 1 and precludes composite zeros for higher k. Standard convolution and Lambert-series identities provide the arithmetic framework, while an intermediate-divisor relation explains the exceptional zero. These criteria are structural characterizations rather than efficient primality tests, since direct evaluation of the multiplicative formulas generally presupposes a factorization of n.

math.NT↗
arXiv2026

AquaWAM: A Dynamics-aware World Action Model for Underwater Embodied Agents

World Action Models (WAMs) are becoming increasingly important and useful for embodied intelligence, as they enable robots to anticipate the consequences of candidate actions before interacting with the physical environment. However, underwater robots are usually subject to passive dynamics, such as inertia, buoyancy, hydrodynamic drag, and persistent drift, which can continue to affect the vehicle even after an action is completed. Existing WAMs, which primarily predict action-conditioned visual observations, are not explicitly designed to capture such passive motion dynamics. In this paper, we present AquaWAM, the first World Action Model designed for underwater embodied agents. Instead of predicting future images, AquaWAM models both action-conditioned and passive physical dynamics, including the thruster dead band, the inertial glide that outlasts each command, and ambient currents. Specifically, it senses through the DVL, IMU, pressure sensor and joint encoders, while cameras supply only semantics for understanding goals and target pose. By modeling compact navigation states rather than high-dimensional visual observations, AquaWAM substantially reduces the model size and computational cost compared with conventional WAMs. Experimentally, AquaWAM achieves a 72.6% task success rate across 20 underwater tasks on the USIM benchmark, outperforming existing methods while making action decisions 2.7x faster than U0 on an NVIDIA Jetson AGX Orin. Our model also remains effective when some onboard sensor measurements are unavailable. For example, without DVL velocity measurements, our method still achieves a 61.6% success rate, compared with 39.4% for U0.

cs.RO↗
arXiv2026

PulseQuant: Propagation-Guided Subspace Correction for 4-Bit Video Diffusion Transformers

Quantization errors in video diffusion transformers can be amplified or attenuated by subsequent denoising updates, making local reconstruction error an incomplete predictor of final impact. We introduce PulseQuant, a 4-bit post-training quantization method that combines trajectory sensitivity with activation geometry to guide offline calibration. Isolated block--step interventions estimate propagation risk, which prioritizes sensitive trajectory states during row-radius selection. With these radii fixed, response-subspace correction uses neighboring-code edits to reduce residual components along dominant activation directions. Both stages preserve the original 4-bit weight representation. Controlled interventions show that short-horizon propagated error predicts final latent error more reliably than immediate block-output error, supporting calibration beyond local reconstruction objectives. Evaluations on Wan models, Self Forcing, and MiniMax-H3 demonstrate improvements in key consistency and dense-reference metrics while remaining competitive on other attributes across model scales and generation paradigms.

cs.CV↗
arXiv2026

SciGen-Verifier: A Multimodal Reasoner for Explainable Verification in Scientific Image Generation

In realistic education, a solution is often expressed not only in words but in a drawing--a circuit, a geometric construction, a function plot--and a teacher must grade the drawing as carefully as the text. Recent advances in unified multimodal models have enabled scientific image generation, yet verifying the correctness of these specialized visual outputs remains a critical bottleneck: errors often arise from intricate domain knowledge, structural reasoning, and multi-step instruction rather than surface-level artifacts. Existing verifiers mainly target natural images and compress judgement into scalar scores, leaving scientific coverage and explainable feedback for error correction underexplored. To bridge this gap, we make three main contributions. (1) We construct SciGen-Verify, a benchmark dedicated to explainable verification of scientific image generation, spanning instruction following, multidisciplinary reasoning, and world knowledge domains. It contains a three-tier hierarchical protocol over the binary judgement, supporting explanation, and corrective editing instruction. (2) We develop SciGen-Verifier, a reasoning-driven multimodal verifier trained via cold-start supervised fine-tuning followed by a curriculum-based two-stage reinforcement learning pipeline. The rubric-guided process rewards first strengthen scientific reasoning exploration and outcome rewards subsequently align output with ground-truth annotation. (3) On SciGen-Verify, SciGen-Verifier achieves competitive performance against much larger proprietary models. It further serves as a practical online critic for iterative image rectification.

cs.CV↗
arXiv2026

Evaluating System One Models for Agent Security Decisions: Reliability, Calibration, and Selective Automation

Model-based judges support agent security by detecting prompt injections, assessing interaction risks, and screening harmful requests. System One models select from predefined answers and report probabilities that software can use to allow, block, or review inputs, but the reliability of these automated decisions remains unclear. We evaluate Jev, Laya, Decider, and Bespoke Nimble against specialized classifiers and language-model judges, examining decision accuracy, probability calibration, and selective automation. We draw the following conclusions. (1) Strong overall performance and favorable aggregate calibration can hide failures concentrated in particular attack groups, including attacks classified as safe with high confidence. (2) The evaluated adapted configurations do not consistently improve classification over their base models across tasks. (3) Under the strictest evaluated error limits, the policies allow few inputs automatically, and separate allow and block thresholds increase automation mainly through more blocks. Passing confirmation does not ensure that these limits hold on test. (4) Judges can detect attacks missed by another model, but may also falsely flag more benign inputs and share the other model's high-confidence errors. These findings support evaluating model accuracy, probability calibration, and the resulting allow/block/review decisions together.

cs.CR↗
arXiv2026

Supergaussian pulse distortion in single-mode fibers with arbitrary dispersion

Marcuse theory of pulse distortion in singlemode fibers provides closed-form results for Gaussian pulses launched from sources of arbitrary spectral width. We extend the theory to supergaussian pulses of arbitrary order with linear or edge-concentrated chirp, single or multiline sources and an arbitrary number of dispersion coefficients. The rms output width is obtained exactly from the moments of the Wigner distribution, and all the pulse moments involved reduce to finite sums of Gamma functions. Supergaussian pulses are considerably more sensitive than Gaussian pulses to higher order dispersion and are compressed less efficiently by chirp. Near the zero-dispersion wavelength their rms width is governed by weak spectral side lobes and overestimates the broadening of the pulse energy. For pulse sequences, interference between neighboring pulses leaves all time moments unchanged when the input pulses do not overlap, but it redistributes energy locally with a visibility set by the source spectrum filtered by the pulse spectrum.

physics.optics↗
arXiv2026

TT-VidT: Decoupling the Temporal Axis for Efficient Motion-Centric Video Pretraining

Comparisons in video self-supervised learning often evaluate complete training recipes rather than isolating the method itself: architecture, objective, data exposure, schedule, scale, and decoder capacity can all vary at once. This makes it hard to identify which choices yield motion-prioritized representations, whose gains concentrate on frame-to-frame change while retaining useful appearance. We address this with a matched $4 \times 6 = 24$ architecture-objective study at roughly 170M ~ 190M encoder scale on $\sim$1.7M OpenVid and Moments-in-Time v2 clips for 8 epochs, and propose TT-VidT. TT-VidT combines a DINOv3-initialized ViT-B/16 per-frame spatial path with a compact Temporal Transfer Layer, trained by Diff Compression to reconstruct target frames from a first-frame appearance anchor and frame-specific motion tokens. The sweep shows that TT3D with Diff Compression, not either component alone, enters the strongest motion-sensitive regime, and decoder ablations favor a compact video-pretrained decoder. In final comparison, TT-VidT leads Jester, Something-Something V2, ARID, and Diving48 fine-tuning simultaneously, improving over the strongest non-TT row by 54% ~ 121%, while using 48% fewer encoder FLOPs than DisMo and 55% fewer than VideoMAE or V-JEPA2. HMDB51, IARD, and EPIC-Kitchens bound the claim.

cs.CV↗
arXiv2026

What Shared Prefixes Hide: Trajectory Dropout for On-Policy Distillation

On-policy distillation (OPD) trains a student model on its own trajectories using dense token-level feedback from a stronger teacher model. Since each update is conditioned on the reasoning prefix already generated by the student, the prefix also shapes how effectively teacher feedback is converted into learning. We find that shared prefixes can lead to weak token-level updates, a phenomenon we call Prefix-Induced Supervision Attenuation (PISA). This attenuation arises in two common cases. (i) High student confidence can weaken corrective gradients even when the teacher disagrees. (ii) Tokens that rely on earlier reasoning can receive learning signals as weak as those for simple local continuations. To solve this problem, we propose Trajectory Dropout, a simple training-time intervention that exposes these weakened signals. The student first performs a standard full-context rollout to generate a complete trajectory. During training, we randomly drop a certain proportion of the student's reasoning trajectory, while the teacher continues to observe the complete trajectory for token-level supervision. This intervention strengthens corrections for overconfident predictions and introduces additional supervision at prefix-sensitive positions. Trajectory Dropout consistently improves average performance across teacher--student model pairs of different scales and six mathematical reasoning benchmarks, while also yielding gains on two out-of-domain benchmarks. It can also be flexibly integrated into existing OPD variants with negligible computational overhead, further improving their performance. These results demonstrate that Trajectory Dropout provides a simple mechanism for strengthening token-level supervision across model scales and OPD objectives.

cs.AI↗
arXiv2026

SphMind: Towards Robust, Training-Free VLM-based Spatial Reasoning with a 360 Camera

Omnidirectional or 360 cameras provide embodied AI agents with a holistic, wide field-of-view (FoV) view of their surroundings, motivating the use of Multi-modal Large Language Models (MLLMs) for omnidirectional spatial reasoning. However, most MLLMs are trained on conventional 2D perspective images and struggle with the severe distortions and wrap-around discontinuities induced by spherical geometry. Enabling them to generalize to non-Euclidean 3D spaces without retraining therefore remains challenging. We propose SphMind, a training-free, plug-and-play framework that decouples semantic perception from geometric reasoning. Rather than requiring MLLMs to learn spherical geometry internally, SphMind preserves their semantic capabilities while handling geometry externally. We introduce a Spherical Harmonics-based Spatial Graph (SHSG) that models spatial relationships through equivariant transformations on the sphere, together with Inference-Time Geometric Grounding (IGG), a model-agnostic closed-loop optimization process that aligns MLLM representations with spherical geometric constraints during inference. Experiments on three benchmarks show that SphMind achieves over 21.4% average improvement in directional reasoning on MP3D and Stanford2D-3D, outperforms prompt-engineering baselines by 8.7% on the real-world ODI-Bench, and improves rotational invariance by 5.9% under panorama rotations, without additional training or dataset-specific tuning. In-the-wild evaluations further show that SphMind resolves directional reasoning queries that baseline vision-language models fail to answer correctly.

cs.CV↗