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01.
arXiv (CS.AI) 2026-06-16

Learn from Your Mistakes: Tree-like Self-Play for Secure Code LLMs

arXiv:2606.03489v2 Announce Type: replace-cross Abstract: While Large Language Models (LLMs) excel in code generation, they remain prone to replicating subtle yet critical vulnerabilities endemic to their training data. Current alignment techniques, such as Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), typically apply coarse-grained optimization at the sequence level. This approach often fails to address the localized nature of security flaws, where a single incorrect token choice can compromise an entire program. To bridge this gap, we introduce Tree-like Self-Play (TSP), a framework that reframes secure code generation as a fine-grained sequential decision process. Unlike standard methods that blindly maximize likelihood, TSP constructs a decision tree where the model explores branching trajectories–generating both secure "golden paths" and vulnerable variants. By treating code generation as a self-play game, the model learns to strictly discriminate against its own localized errors. This provides a dense, on-policy learning signal that forces self-correction precisely at the critical decision nodes where vulnerabilities typically emerge. Our experiments demonstrate that TSP fundamentally enhances model reliability. In Python security benchmarks, TSP boosts CodeLlama-7B's pass rate (SPR@1) to 75.8%, significantly outperforming SFT (57.0%) and unstructured self-play baselines. Crucially, TSP induces robust out-of-distribution generalization: the model not only reduces vulnerabilities in unseen categories (CWEs) by 24.5% but also successfully transfers security principles learned from C/C++ to diverse languages, including Python, Go, and JavaScript. This suggests that TSP does not merely memorize patches, but internalizes abstract, language-agnostic security logic.

02.
arXiv (CS.CV) 2026-06-17

Contactless Respiratory Monitoring on Heterogeneous Mobile Robots: A Multimodal Edge-Computing Framework

Respiratory-rate (RR) monitoring is a critical component of remote triage and victim assessment in emergency response, disaster recovery, and infectious-disease scenarios, where minimizing physical contact can reduce responder risk and improve operational safety. However, field deployment of contactless RR monitoring remains challenging due to variable illumination, posture changes, platform heterogeneity, and the impracticality of wearable sensors in hazardous environments. In this paper, we present a modality-adaptive contactless RR monitoring framework for heterogeneous mobile robots with onboard edge computing. The proposed system combines brightness-adaptive sensor selection across RGB, thermal, near-infrared (NIR), and low-light cameras, keypoint-guided chest ROI extraction for posture-robust monitoring, and a signal-quality-index (SQI)-based filtering mechanism for reliable respiratory estimation. We implement and evaluate the framework on three robotic platforms spanning quadruped and wheeled locomotion and multiple edge-computing architectures. Experiments conducted across diverse lighting conditions, subject poses, and robot-to-subject distances demonstrate that the framework generalizes across platforms without per-platform algorithmic retuning, while revealing modality-specific operational boundaries. RGB provides the broadest coverage up to 8m, NIR remains effective up to 6m, thermal is reliable only at short range, and low-light sensing supports monitoring in complete darkness up to 8m. Overall, the results demonstrate the feasibility of multimodal contactless RR monitoring on mobile robots and support its use as a foundation for autonomous triage and victim assessment in hazardous search-and-rescue settings.

03.
arXiv (math.PR) 2026-06-16

Geometry of critical discrete structures: long-range percolation on the hierarchical lattice and the discrete torus

arXiv:2509.09589v2 Announce Type: replace Abstract: Consider (a) balls $\Lambda_n$ of growing volumes in the $d$-dimensional hierarchical lattice, and (b) the $d$-dimensional discrete torus $\mathbb{T}_n^d$ on $n^d$ vertices. Place edges independently between each pair of vertices $x\neq y\in\Lambda_n$ or $\mathbb{T}_n^d$ with probability $1-\exp(-\beta J(x, y) )$ where $J(x, y) \asymp \| x-y \|^{-\alpha}$ for some $0

04.
arXiv (CS.CV) 2026-06-17

LADBench: A Benchmark for Logical Fault Detection in Images

Large Vision Language Models (VLMs) excel at visual question answering and semantic grounding, but their capacity for autonomous logical reasoning remains underexplored. Existing anomaly benchmarks emphasize visual errors or direct prompting rather than the physical and social common sense needed for open-world deployment. To address this, we introduce LAD-bench, a benchmark of more than 1,000 curated synthetic images with logical anomalies across four domains: Residential, Urban, Collaborative, and Nature. We further propose a Tiered Prompting Protocol based on progressive disclosure, which measures how much explicit assistance a model needs to localize and reason about a logical fault. Evaluating leading foundation models reveals substantial weaknesses: even the best achieves only 70.11% overall accuracy, showing that implicit logical fault detection remains unsolved. Crucially, models often fail to identify anomalies even after receiving explicit hints in deeper tiers. By surfacing these limitations in sequential multimodal reasoning, LAD-Bench offers a rigorous framework for advancing the safety, reliability, and cognitive alignment of autonomous visual systems. Dataset and Code: https://huggingface.co/datasets/SahasraK/LADBench

05.
arXiv (CS.CV) 2026-06-16

Vision-Encoder Behavioral Fingerprints of Image-to-Image Generative Models: A Training-Paradigm-Driven Taxonomy of Six Commercial APIs

作者:

We study six production image-to-image AI systems (gpt-image-1, Gemini 2.5 Flash Image, Flux Kontext, SDXL img2img, SD3 img2img, and Qwen Image Edit) under a content-adaptive sub-JND adversarial perturbation pipeline, scoring all outputs by frozen DINOv2 ViT-B/14 token distances against clean references. Across a 3,588-call corpus spanning COCO photographs, CelebA-HQ portraits, and AI-generated inputs, the six systems partition into two image-invariant behavioral bands on a 2D (patch_mean, ssim_clean) plane: edit-trained models (Flux Kontext, Qwen Edit, Gemini) cluster in a tight band, while T2I-base models adapted at sampling time (SDXL, SD3, gpt-image-1) cluster in a drift band.

07.
arXiv (quant-ph) 2026-06-15

New Identity for Cayley's First Hyperdeterminant with Applications to Symmetric Tensors and Entanglement

作者:

arXiv:2512.03093v3 Announce Type: replace Abstract: In this article, a new formula for computing Cayley's first hyperdeterminant in terms of the Levi-Civita symbol is given. It is then shown that this formula can be used to compute the hyperdeterminant of symmetric tensors in polynomial time with respect to their order (assuming fixed side length). Applications to quantifying the entanglement of states of bosonic quantum systems are then discussed. Additionally, in order to obtain the fast calculation of the hyperdeterminant on symmetric tensors, generalized elimination and duplication matrices are defined and their explicit formulas are derived.

08.
arXiv (CS.AI) 2026-06-19

Beyond Static Endpoints: Tool Programs as an Interface for Flexible Agentic Web Services

arXiv:2606.19992v1 Announce Type: cross Abstract: In the agentic web era, LLM-based agents increasingly invoke web services as tools, yet most interfaces remain static endpoints that poorly express long-horizon workflows with loops, conditionals, joins, and retries. We present ToolPro, which represents an agent's tool intent as an executable tool program that compactly encodes multi-step service interactions with explicit effect types. ToolPro combines constraint-guided program construction, effect-aware replay for exactly-once state-modifying calls, and a profile-driven policy that decides when program execution outperforms stepwise calling. We instantiate ToolPro over MCP-style services with WebAssembly sandboxing and evaluate it on diverse workflows of real-world applications. ToolPro reduces end-to-end latency by up to 53.4\% and client-side traffic by up to 96.1\%, with larger gains under higher network latency and workflow complexity.

09.
arXiv (CS.AI) 2026-06-19

Enhancing Generative Auto-bidding with Offline Reward Evaluation and Policy Search

arXiv:2509.15927v5 Announce Type: replace-cross Abstract: Auto-bidding is a critical tool for advertisers to improve advertising performance. Recent progress has demonstrated that AI-Generated Bidding (AIGB), which learns a conditional generative planner from offline data, achieves superior performance compared to typical offline reinforcement learning (RL)-based auto-bidding methods. However, existing AIGB methods still face a performance bottleneck due to their inherent inability to explore beyond the static dataset with feedback. To address this, we propose AIGB-Pearl (Planning with \textbf{EvaluAtor via RL}), a novel method that integrates generative planning and policy optimization. The core of AIGB-Pearl lies in constructing a trajectory evaluator to assess the quality of generated scores and designing a provably sound KL-Lipschitz-constrained score-maximization scheme to ensure safe and efficient exploration beyond the offline dataset. A practical algorithm that incorporates the synchronous coupling technique is further developed to ensure the model regularity required by the proposed scheme. Extensive experiments on both simulated and real-world advertising systems demonstrate the state-of-the-art performance of our approach.

10.
arXiv (CS.AI) 2026-06-12

From Imitation to Alignment: Human-Preference Flow Policies for Long-Horizon Sidewalk Navigation

arXiv:2606.12603v1 Announce Type: cross Abstract: Autonomous long-horizon sidewalk navigation is essential for micro-mobility applications such as robotic food delivery and assistive electronic wheelchairs. Unlike autonomous driving on the road, long-horizon sidewalk navigation requires precise maneuvering through unpredictable sidewalk terrains and pedestrians, with a lightweight perception stack as minimal as a single monocular RGB camera. While imitation learning (IL) from demonstrations offers a practical solution, the resulting autopilot policy often suffers from compounding errors, a lack of social compliance on sidewalks, and deficiencies in counterfactual reasoning to handle complex situations. To address these challenges, we introduce FlowPilot, a mapless navigation policy that achieves robust and efficient long-horizon navigation performance using only a monocular RGB camera. We first propose to use anchored flow matching as an action representation for policy pre-training on large-scale robot fleet data and to capture the diverse, complex, multimodal distribution of sidewalk navigation behaviors. To bridge the gap between imitation and alignment, we further design a human-in-the-loop preference learning scheme to tune the policy on a small amount of human intervention data. It strengthens the model's counterfactual reasoning and social compliance on sidewalks. We evaluate FlowPilot through extensive simulation and real-world experiments in diverse sidewalk environments. FlowPilot achieves 42% success rate and 66% route completion in simulation, while FlowPilot-HP further improves real-world robustness and social compliance, reducing IR by 40.0% and NIR by 52.1% relative to the base model.

11.
arXiv (CS.AI) 2026-06-16

Nightjar: Dynamic Adaptive Speculative Decoding for Large Language Models Serving

arXiv:2512.22420v5 Announce Type: replace-cross Abstract: Speculative decoding (SD) accelerates LLM inference by verifying draft tokens in parallel. However, this method presents a critical trade-off: it improves throughput in low-load, memory-bound systems but degrades performance in high-load, compute-bound environments due to verification overhead. Existing speculative decoding methods use fixed lengths and cannot adapt to workload changes or decide when to stop speculation. The cost of restarting speculative inference also remains unquantified. Under high load, the benefit of speculation diminishes, while retaining the draft model reduces KV cache capacity, limiting batch size and degrading throughput. To overcome this, we propose Nightjar, a resource-aware adaptive speculative framework. It first adjusts to the request load by dynamically selecting the optimal speculative length for different batch sizes. Crucially, Nightjar proactively disables speculative decoding when the MAB planner determines that speculation is no longer beneficial, and during the disabled phase, offloads the draft model to the CPU only under GPU memory pressure. This reclaims memory for the KV cache, thereby facilitating larger batch sizes and maximizing overall system throughput. Experiments show that Nightjar achieves up to 14.76% higher throughput than standard speculative decoding and up to 20.18% lower latency in the main benchmark suite under dynamic request arrival rates for real-time LLM serving scenarios.

12.
arXiv (CS.CV) 2026-06-16

Multi-Modal Spatio-Temporal Graph Neural Network with Mixture of Experts for Soil Organic Carbon Prediction

Top-soil organic carbon (SOC) prediction is fundamental to agricultural sustainability, land use policy and fertilization planning. Existing approaches face two limitations: they pair hand-crafted covariates with classical ML or single-modal deep models that miss rich spectral and temporal information, and grid-based architectures ignore the irregular spatial structure of field measurements. We introduce SpTGNN, a multi-modal spatio-temporal graph neural network addressing both. SpTGNN represents soil measurements as nodes in a heterogeneous graph with three edge types (spatial proximity, spectral similarity, elevation), and applies relational graph attention to learn separate patterns per relation. A fine-tuned TerraMind encoder extracts node features from Sentinel-2, Sentinel-1 and DEM signals, combined with per-sample environmental covariates and learned positional and temporal embeddings. A sparse Mixture-of-Experts module fuses the four streams via top-$k$ routing. Uncertainty is captured by pairing heteroscedastic regression (aleatoric) with deep ensembles (epistemic), and a Moran's $I$ penalty regularizes spatial autocorrelation. We evaluate on a global SOC corpus split into three regional instances ($\sim$49k samples globally, Africa $\sim$26k, Europe $\sim$14k). Our 5-member deep ensemble reports $R^2=0.762$, RMSE $=3.51\pm0.48$ g/kg and MAPE $=22.9\%$ on the Africa test split, improving over a tabular XGBoost baseline; the best single checkpoint reaches validation $R^2=0.864$. Ablations confirm the heterogeneous graph, MoE fusion and fine-tuned backbone each contribute substantively, and the ensemble UQ stack achieves post-calibration ECE of $0.031$ (hybrid) and $0.026$ ($\beta$-NLL). To our knowledge, this is the first framework to unify foundation-model feature extraction, heterogeneous graph attention and decomposed uncertainty quantification for SOC estimation.

13.
arXiv (quant-ph) 2026-06-19

Proposal of quantum arrival-time measurement with a Bose-Einstein condensate

arXiv:2606.20278v1 Announce Type: new Abstract: This work shows how a Bose-Einstein condensate of ultracold atoms could be used to address a long-standing question in quantum theory: how much time does it take for a particle to reach a detector? To this end, we propose a realistic experimental setup, whose key idea is not to measure arrival times directly, but the arrival flux on the detector as a function of its position. This novel approach not only solves practical issues with having a detector close to the system, but also results in signals that allow to unambiguously distinguish different theoretical predictions. This proposal raises prospects for resolving the decades-old debate on this fundamental issue.

14.
arXiv (CS.AI) 2026-06-16

RoboPIN: Grounded Embodied Reasoning via Pinned Chain-of-Thought

arXiv:2606.15753v1 Announce Type: new Abstract: Embodied reasoning requires models to perceive task-relevant objects and spaces in physical environments and maintain consistent visual grounding throughout multi-step reasoning. However, current vision-language models rely on text-only or coordinate-augmented chain-of-thought, where entity references remain implicit and ambiguous. This may cause the reasoning process to decouple from visual evidence, entity references to drift across steps, and a causal disconnection between the reasoning trajectory and the final answer, with these problems further amplified in multi-view scenarios due to cross-view appearance changes. To address these issues, we propose Pinned Chain-of-Thought (\pincot{}), a structured reasoning paradigm that pins every reasoning step to visual evidence. \pincot{} introduces the concept of \reasoninganchor{}, which binds each task-relevant entity to a structured visual anchor with entity name, unique identity, view index, and spatial grounding, enabling consistent entity tracking across reasoning steps and views. We build a fully automated data generation pipeline to construct \dataset{}, a high-quality \pincot{}-formatted reasoning dataset. We then train \method{} through three-stage post-training that progressively injects embodied knowledge, structured reasoning ability, and process-supervised alignment, with rewards that directly constrain both anchor localization and identity consistency during reasoning. On 14 benchmarks covering embodied spatial reasoning, multi-view reasoning, and pointing, \method{} with only 4B parameters consistently outperforms 7B level open-source embodied models, achieving a 12\% average improvement over the strongest 7B baseline, Mimo-Embodied. Further analysis shows that \pincot{} improves grounding accuracy and cross-step identity consistency, validating the effectiveness of process supervision.

15.
arXiv (quant-ph) 2026-06-12

Beyond the Unruh vacuum: multi-time correlations in black hole collapse and evaporation

arXiv:2606.13383v1 Announce Type: new Abstract: The black hole information paradox originates from the thermal character of Hawking radiation, which appears to erase information about the collapsing matter. However, thermality constrains only observables defined at a single time and leaves the structure of temporal quantum correlations largely unexplored. Here we show that multi-time quantum-field correlations provide a concrete mechanism for the survival of pre-collapse information in black hole evaporation. Using a two-dimensional model of gravitational collapse and evaporation, we demonstrate that late-time multi-time correlations are not fully reproduced by the Unruh vacuum. In particular, they contain a contribution that depends explicitly on parameters characterizing the pre-collapse state, despite the thermal character of the asymptotic radiation. Our results identify measurable multi-time correlations as carriers of information in Hawking radiation and suggest that formulations of the black hole information paradox based solely on single-time observables are incomplete.

16.
arXiv (CS.CL) 2026-06-15

Fodor and Pylyshyn's Systematicity Challenge Still Stands

The recent successes of neural networks producing human-like language have caused significant stir in cognitive science, with many researchers arguing that classical puzzles about human cognition and challenges to artificial intelligence are being solved by neural networks. A notable case is the argument from systematicity due to Jerry Fodor and Zenon Pylyshyn, argues that humans display systematic biconditional dependencies. For example, someone can understand the sentence "John saw Mary" just in case that they understand the sentence "Mary saw John." Symbolic systems explain this systematicity of language and thought, while neural networks offer no immediate explanation. Several recent articles argue that this challenge has now been met by neural networks. In particular, Brenden Lake and Marco Baroni argue that their meta-learning for compositionality protocol matches and perhaps explains human systematicity. We demonstrate that these conclusions are premature. Among other results, we found that their model struggles to learn rules that are even slightly out of distribution compared to their training data. Furthermore, the model behaves unsystematically even on many within-distribution problems. We conclude that Fodor and Pylyshyn's challenge to neural networks remains unmet.

17.
arXiv (CS.AI) 2026-06-16

DOG-DPO:Dynamic Optimization in Geometry for Safety Alignment

arXiv:2606.07678v2 Announce Type: replace-cross Abstract: Safety alignment for large language models relies on preference data, but current pipelines often train on large, redundant datasets. Existing data selection methods typically score each preference pair independently, collapsing directional preference information into scalar quality or diversity scores. This sample-centric view is especially limiting in multi-dataset settings, where shared safety directions coexist with dataset-specific residual risks. We propose DOG-DPO, a training-free data selection framework that treats preference pairs as structured geometric signals. DOG-DPO first represents each preference pair as a direction in model representation space. It then decomposes multi-dataset preference geometry into a global anchor subspace and dataset-specific residual subspaces. Finally, it selects subsets by maximizing diversity-based coverage, encouraging broad, non-redundant coverage of alignment directions before DPO training. Across six safety benchmarks and two model backbones, DOG-DPO achieves a strong utility-robustness trade-off using only 11% of the preference pairs. It recovers most of the safety gains of full-data training while remaining entirely teacher-free, training-free, and substantially faster than representative selection baselines.

18.
arXiv (CS.LG) 2026-06-19

PaAno+: Multiscale Encoding and Cross-Variable Attention for Time Series Anomaly Detection

arXiv:2606.20055v1 Announce Type: new Abstract: Time-series anomaly detection has significant practical value for industrial and medical monitoring, as well as other critical domains. Current Transformer- and large-model-based detection approaches incur excessive computational overhead, while existing lightweight alternatives are constrained by insufficient feature extraction and inadequate modeling of dependencies across multivariate variables. To mitigate the above drawbacks, this study develops a lightweight, efficient anomaly detection model, dubbed PaAno, within the patch-oriented representation learning paradigm. In the encoder module, a multiscale feature-extraction backbone is constructed using convolutional kernels with differentiated receptive fields to capture hierarchical temporal characteristics; subsequent cross-scale adaptive attention aggregation, combined with residual connection optimization, further stabilizes feature representation learning. A cross-variable fusion attention module is embedded to explicitly characterize inter-variable correlations, empowering the model to identify anomalous patterns amid intricate operational conditions. Moreover, a novel pretext task based on temporal patch-window sorting is customized to uncover intrinsic structural properties of time series, and triplet loss is leveraged to optimize the patch embedding space for enhanced feature discrimination. Extensive experiments on the TSB-AD benchmark demonstrate that the proposed PaAno achieves state-of-the-art detection accuracy on both univariate and multivariate tasks, yielding significant performance gains across evaluation metrics, including VUS-PR, relative to the original PaAno. Leveraging a compact network design, the presented model achieves favorable computational efficiency, enabling deployment on resource-limited terminals for real-time anomaly inference.

19.
arXiv (CS.CV) 2026-06-19

Mix-QVLA: Task-Evidence-Aware Mixed-Precision Quantization of Vision-Language-Action Models

We propose Mix-QVLA, a task-evidence-aware mixed-precision PTQ framework for VLA models. Mix-QVLA anchors each quantized variant to the full-precision action-token reference decision and evaluates whether quantization preserves task-relevant evidence across key VLA functional boundaries. It computes normalized gradient-weighted task-evidence maps from boundary activations and compares full-precision and quantized maps using evidence-mass and attribution-distribution distortion, capturing changes in both the strength and allocation of decision-supporting evidence. A soft-bottleneck objective aggregates boundary-level degradation into layer-wise sensitivity scores. Mix-QVLA further models sensitivity throughout task execution, capturing phase-dependent shifts in layer importance rather than assuming a fixed sensitivity profile. The resulting evidence- and time-aware scores guide mixed-precision bit allocation under model-size and BitOps budgets. Extensive evaluations on OpenVLA-style policies show that Mix-QVLA improves the accuracy-efficiency trade-off of low-bit VLA deployment. On LIBERO, Mix-QVLA reduces OpenVLA-OFT memory from 15.4 GB to 4.1 GB, retains 96.3 average success compared with 97.1 for the BF16 model, and achieves a 1.52x inference speedup.

20.
arXiv (CS.CV) 2026-06-16

Timestep Rescheduling in Diffusion Inversion

Diffusion inversion, which maps images back to the Gaussian latent space of a diffusion model, is a critical task for image reconstruction and editing. While DDIM enables fast deterministic inversion, it inherently introduces deviations that accumulate into noticeable inversion errors. Existing methods often address this by solving a fixed-point problem but largely overlook how the selection of the diffusion timestep in the noise scheduler influences inversion fidelity. In this work, we reveal that the deviation scale in diffusion inversion is strongly dependent on the timestep size, and exhibits a parabolic trend, with larger errors concentrated at both small and large timesteps. Based on this finding, we propose a simple yet effective nonuniform timestep scheduler that integrates a global rescaling with a local dynamic programming based rescheduling, enabling a strategic allocation of computational effort that minimizes the overall inversion error and preserves higher inversion accuracy. Our method serves as an off-the-shelf enhancement for existing inversion techniques and requires no extra parameters or computational overhead. Through extensive experiments, we verify that integrating our scheduler consistently boosts the performance of existing inversion methods, achieving superior results in image reconstruction and editing.

22.
arXiv (CS.LG) 2026-06-15

A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery

arXiv:2605.18250v3 Announce Type: replace-cross Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of physical, engineered, and data-driven systems. The objective of this work is to establish a unified perspective on such systems, to identify modeling approaches that balance expressivity, interpretability, computational complexity, and data requirements, and to investigate how highly expressive models can be used to uncover the dominant mechanisms underlying observed dynamics. Starting from the Helmholtz-Hodge decomposition of continuous vector fields, we review the recently proposed Graph Vector Field (GVF) framework and its discrete representation on simplicial complexes. We then introduce a hierarchy of alternative approaches, including parametric conditional models, linear graph dynamical systems, and reduced Hodge representations. Finally, we propose a verification and validation methodology based on benchmark datasets from well-understood physical systems and on systematic model-reduction and ablation studies. The resulting family of structured-flow models within a common framework, ranging from low-dimensional parametric representations to full GVF formulations, supports a diagnostic methodology in which gradient, curl, harmonic, and topological contributions are systematically assessed through ablation studies. This process enables the identification of dominant mechanisms underlying the observed dynamics and guides the construction of simplified models tailored to the available data and operational constraints. By separating structural verification, behavioral verification, and domain-specific validation, the proposed approach provides a foundation for scalable and interpretable analysis of complex dynamical systems across multiple application domains.

23.
arXiv (math.PR) 2026-06-18

Power Partitions and Hayman Functions

arXiv:2602.18575v3 Announce Type: replace Abstract: We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy–Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{\alpha_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(\beta_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $\alpha_k$ and~$\beta_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

24.
arXiv (CS.LG) 2026-06-17

Reward hacking in physical reinforcement learning revealed by turbulent drag reduction

arXiv:2606.06227v2 Announce Type: replace-cross Abstract: A reinforcement-learning agent maximises its reward, which can diverge from the outcome its designer intended. In physical control the reward rarely closes that gap, and drag reduction in wall turbulence makes it concrete. A mass-conservation projection couples agents' outputs and erases the per-agent credit the policy gradient needs; a memoryless policy cannot resolve the slow near-wall cycle it acts on; and a pressure-gradient reward pays for nominal drag reduction by pumping power through the wall. Two degenerate controllers achieve large drag reductions while total dissipation rises, so the reported figure can mask a more wasteful flow. We trace each fault to its cause and fix it: a differentiable projection that restores credit, a recurrent policy with a widened sensing stencil, and a reward scored on the true wall power. The corrected controller acts on the flow within a closed energy budget, earning a conservative $17\%$ under honest accounting.

25.
arXiv (CS.AI) 2026-06-11

Knowing When to Ask: Self-Gated Clarification for Hierarchical Language Agents

arXiv:2606.11349v1 Announce Type: new Abstract: In hierarchical reasoning, failures often originate at intermediate decision points where the agent commits to a wrong branch without recognizing that it lacks critical information. Rather than treating clarification as an external uncertainty trigger, we propose ACTION-RATING, a formulation that places it inside the agent's action space on a shared ordinal scale with navigation, so that asking competes directly with acting at every decision point and help-seeking becomes observable at intermediate states. Two structurally distinct information-seeking modes emerge from the agent's own ratings: mandatory (no viable branch) and opportunistic (residual uncertainty despite a leading candidate). On Harmonized Tariff Schedule classification (30,000-node taxonomy, three benchmarks, 9~LLMs across 4 families), we observe a regime shift from mandatory to opportunistic clarification, with Information-Seeking Effectiveness (ISE), a local diagnostic defined as the fraction of help interactions followed by a correct next navigation step (not a final-task metric), rising from 50% to 74%. Three diagnostic contrasts fail to reproduce this structure. A separability test shows that the information-seeking pattern (mode split, ISE ranking) persists when answer quality is degraded (-18.8% accuracy), supporting an empirical separation between where an agent seeks help and the quality of the help it receives. Under the controlled answer channel, accuracy gains reach +16.2% at 10-digit; we read this as an upper bound on what better localization could unlock, not a deployment estimate.