Computation and Language
Papers
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All of arXiv
Wednesday 30 September
On-policy self-distillation (OPSD) has attracted growing interest as a promising approach to improve the reasoning ability of language models. Without external rewards nor a separate stronger teacher, the self-teacher with privileged information could provide dense signals on student's trajectories. However, its behavior in language reasoning remains unclear, with reported outcomes ranging from modest gains to behavioral collapse. In this work, we diagnose OPSD for mathematical reasoning across models spanning 0.6B–8B parameters. We conduct controlled experiments and token-level analyses to fully delve into OPSD. We point out that teacher's signal is shaped by reasoning-mode alignment and the complete teacher prefix, rather than by privileged semantics alone. OPSD improves reasoning only in narrow compatibility regimes. Otherwise, it produces ineffective length growth, stable degradation, or behavioral collapse. Token-level analysis shows that teacher's signal is not stable and does not predict downstream performance. Based on these results, we argue that OPSD is a sensitive algorithm rather than a generally reliable reasoning-improvement post-training method.
Cryptography and Security
SteerProbe: Learning to Bypass Safety Steering in Vision-Language Models
Activation steering offers an inference-time defense for vision–language models (VLMs) by modifying intermediate representations without updating backbone parameters. However, protection on benchmark inputs may not persist across alternative expressions of the same harmful request. We investigate this gap using fixed textual, visual, and joint reformulations designed to preserve the underlying intent, and find that these changes can bypass representative steering defenses. A complementary local analysis provides a sufficient condition under which a reformulation can cross a surrogate safety margin despite any admissible change in the local steering correction. We then introduce SteerProbe, an output-only black-box attack that learns to select effective reformulations for unseen requests from a shared calibration budget. Across three VLM backbones, two benchmarks, and three steering defenses, SteerProbe increases Harmful Rate in all defended settings using 500 total calibration queries per endpoint and benchmark, raising the average from 7.43% to 18.36%. These findings highlight that robustness on original benchmark inputs is insufficient to characterize the safety of steering defenses and motivate reformulation robustness as an important evaluation dimension. They further motivate steering mechanisms that preserve safety across intent-preserving multimodal variations while maintaining benign utility.
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Computer Vision
GRC-Pose: Generation-Reconstruction Correspondence for Prior-Free 6D Object Pose Tracking
Prior-free 6D object pose tracking seeks to recover the trajectory of an unseen object from a single RGB video without object-specific CAD models, posed reference images, or pose annotations. Geometric foundation models provide complementary object-centric and scene-centric cues, yet SAM3D CAD is indexed by an arbitrary object-local surface parameterization, whereas reconstructed evidence is expressed in a sequence-specific world frame with partial surface coverage. To exploit this complementarity, we formulate tracking as generation-reconstruction correspondence and introduce GRC-Pose, a correspondence-based framework that combines learned correspondence prediction with robust pose estimation. Concretely, GeoCorr-Matcher estimates weighted object-scene correspondences and per-match uncertainty for each pose candidate. FGH-Solver integrates these matches through multiple robust geometric estimators and sequence-level posterior inference, while a posterior-gated memory retains only inlier-supported observations through occlusion and viewpoint change. Extensive evaluation shows that with SAM3D CAD, GRC-Pose achieves state-of-the-art Average Recall and motion retention on HOT3D, improving the latter by 58% over prior art. On classical benchmarks including YCBInEOAT and LINEMOD, it remains highly competitive.
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Computer Vision
Beyond Local Linearity: Scale-Resolved Geometry of Learned Image Encoders
Understanding how learned representations respond to finite input changes is important for characterizing their sensitivity, invariances, and robustness. Yet existing geometric analyses are predominantly local and describe only infinitesimal perturbations. We introduce a scale-resolved statistic that compares an encoder's measured feature displacement with its local linear prediction as the perturbation magnitude increases. Across diverse image encoders, we discover a characteristic plateau-rise-peak-decay profile, which we call the bump. The bump is absent at initialization, emerges early during standard training, and does not form under randomized labels or random-noise inputs. Its shape also varies with the training distribution and robustness objective. These results establish departures from local geometry as a signature of how encoder representations are shaped by learning.
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Machine Learning
The Row Normalization Puzzle in Muon
This paper examines how row-wise renormalization affects Muon, focusing on the gap between NorMuon's worst-case guarantees and its practical performance (Li et al.). Despite its growing adoption and promising performance in large language model (LLM) pretraining, NorMuon's worst-case guarantees remain poorly understood. One fundamental question is: Does row normalization yield provable convergence gains, potentially through its interaction with approximate polar computation and exponential moving-average momentum? Our results show that row normalization introduces a dimension-dependent factor in the worst-case iteration complexity under the operator-norm geometry, which persists even with exact polar computation and any fixed momentum parameters. Indeed, we establish an algorithm-dependent lower bound and a matching upper bound in deterministic settings, and extend our upper bound analysis to stochastic settings. Both upper-bound analyses allow approximate polar computation. Experiments show that NorMuon is slower than Muon on synthetic problems inspired by our worst-case construction, yet outperforms Muon in LLM pretraining. These findings sharpen the puzzle of why row normalization helps in practice and complement the recent findings of Dewulf et al.
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Quantum Physics
Optimal testing of fermionic and bosonic Gaussian states
We study the problem of property testing quantum states: given a pure state $|\psi\rangle$ that either (A) belongs to some class $C$ of pure states, or (B) is $\varepsilon$-far in trace distance from all states in $C$, determine which is the case with high probability. It is known that there exists classes $C$ for which the sample complexity of property testing necessarily scales with the size of the system. In this work, we identify classes for which testing only requires a size-independent number of samples. We prove a tight sample complexity of $\Theta(1/\varepsilon^2)$ for the property testing of five important classes of Gaussian quantum states: 1) Fermionic Gaussian states, 2) Slater determinants, 3) bosonic Gaussian states, 4) zero-mean bosonic Gaussian states, and 5) bosonic coherent states. While property testers for some of these classes have been studied previously, those analyses only gave upper bounds scaling polynomially in the number of modes. In each case, our tester is the projection onto the “top” irrep of two or three copies. We get to constant sample complexity by lower bounding how quickly the rejection probability increases with distance from the class; the main technical component involves bounding the spectral gap of symmetric extension of the test projector. We then establish optimality by proving matching lower bounds based on binary state discrimination for each class. Our testers and optimality claims also extend to the tolerant setting, wherein $\psi$ may be $O(\varepsilon)$-close to $C$ in case (A), rather than lying exactly inside.
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Computer Vision
CamAgent: An LLM-Agent Framework for Multi-Species Camera-Trap Workflows
Camera traps accumulated vast, multidimensional data for wildlife monitoring, yet translating raw media archives into meaningful ecological insights remains highly fragmented. Current research workflows require laboriously stitching together disparate analysis tools and scripts, creating steep programming hurdles and complicating end-to-end spatiotemporal analyses. To overcome this fragmentation, we present CamAgent, an autonomous Large Language Model (LLM) agent framework that integrates camera-trap analytical workflows into a unified intelligent ecosystem. CamAgent interprets natural-language ecological intent, schedules computational routing, and executes specialized tools spanning computer-vision perception (e.g., SpeciesNet), CamtrapDP-compatible data management, detection-corrected occupancy modeling, temporal activity analysis, and species co-occurrence networks. The framework automates multi-stage analytical pipelines while maintaining essential data-quality controls and analytical conventions. Consequently, CamAgent significantly reduces manual programming overhead for conservationists, establishing a transparent, scalable, and fully integrated paradigm for camera-trap ecology. Our project is available at https://anonymous.4open.science/r/artifact72c6f4.
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Computation and Language
Bongard: Training Machine Intuition
Human intelligence relies heavily on learned intuition: recognising patterns and judging situations without explicitly unfolding every intermediate step. We introduce Bongard, an open-weight System One model that treats machine intuition as an independent capability to design and train. A T5Gemma 2 4B-4B encoder-decoder separates reading the evidence from making judgments. The encoder reads the state bidirectionally together with the question instructions, and separate decoder branches share this encoding, so many judgments about the same situation require only one reading of the state. A trained head returns probabilities over the supplied candidates without generating text. Training proceeds in three stages, from supervised judgments to semantic relationships to action outcomes, and each stage updates all 7.09 billion trainable parameters on one Blackwell GPU. Joint-embedding post-training raises accuracy on held-out rephrasings from 75.7% to 85.9%. A sandbox stage then learns outcome distributions from action rollouts and exact oracles, raising accuracy on a frozen sandbox panel from 50.6% to 64.8%. On DecisionBench, the final model reaches 78.05% accuracy over 23,900 decisions and ranks fourth of 61 systems in the public comparison. On one RTX PRO 6000, its median latency is 36 ms for short requests, and 32 questions about one state take 221 ms. Bongard demonstrates that machine intuition can be systematically trained via representation learning and outcome feedback, providing an open, efficient alternative for high-throughput decision workloads.
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General Relativity and Quantum Cosmology
Second-order multipole response of two nearby incoherent sources in wave-optical imaging of a Schwarzschild black hole
We study wave-optical imaging of two nearby, mutually incoherent point sources by a Schwarzschild black hole. Using the spherical-harmonic addition theorem, we construct partial-wave fields for arbitrary source directions and form images through a finite-aperture Fourier transform. To isolate the binary structure, we compare the binary image with that of a single source of equal total brightness placed at the brightness centroid. Expanding about the centroid removes the first-order term exactly, so the leading structural correction is controlled by the second central moment, $\mu_2=4a^2q/(1+q)^2$. Numerical calculations confirm the expected dependence of the residual on source half-separation and brightness ratio. We then study its wavelength dependence. At long wavelengths, the imaging kernel varies little across the source separation, making the binary nearly indistinguishable from the centroid reference. As the wavelength decreases, finer fringes enhance the residual, which grows by about a factor of three over $3\leq M\omega\leq12$ ($2.09\geq\lambda/M\geq0.52$), even though the pair remains unresolved in the Rayleigh sense. Meanwhile, the second-order approximation gradually breaks down: its relative error first reaches unity for $17<M\omega<18$ ($0.349<\lambda/M<0.370$), indicating the need for higher-order source moments. These results demonstrate that the distinguishability of a nearby binary is intrinsically chromatic and identify the wavelength range in which the binary is both detectable through its residual and accurately described at second order.
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Machine Learning
T-Router: Learning Thalamic Routing for Reasoning with Parameter-Efficient Reinforcement Learning
Parameter-efficient reinforcement learning aims to improve reasoning with a compact trainable interface to a pretrained model. We introduce the Thalamic Router (T-Router), which concentrates adaptation on the reuse of completed computations. A compressed, addressable bank preserves block changes; a depth-recurrent controller conditions their selection and relative-scale writeback. This coupling gives thalamic context-dependent routing a concrete computational form: learn which earlier contributions a receiving layer uses, and with what influence. Correctness rewards train the interface while preserving backbone parameters and layer order. On an 8.95B-parameter backbone, T-Router allocates 41.73M parameters (0.466% of the backbone) and achieves 83.64 +/- 1.16 MathAvg after GSM8K RL, compared with 73.79 +/- 1.83 for full-parameter GRPO across three evaluation rounds. At a comparable parameter budget and with matched retries, it exceeds LoRA's 77.28 +/- 1.95 MathAvg, improving all three task families and raising mean AIME accuracy from 48.33 to 60.56. Capacity-controlled comparisons favor addressable block changes and recurrent context; separate search training extends the interface to tool-mediated reasoning. These results establish controlled computation reuse as an effective route to parameter-efficient reasoning reinforcement learning.
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Materials Science
Nature of the 175-180 cm$^{-1}$ Raman Feature in Altermagnetic $\alpha$-MnTe
The 175 cm$^{-1}$ Raman mode in $\alpha$-MnTe has long been assigned to the material's only symmetry-allowed phonon ($E_{2g}$), yet first-principles calculations consistently place this mode below 100 cm$^{-1}$. Recent works have offered three competing explanations for the discrepancy: a weak symmetry-lowering ($D_{6h}\rightarrow D_{3h}$) phonon, an electronic plasmon arising from intrinsic hole self-doping, or an extrinsic MnTe$_2$ impurity signature. Here we resolve this controversy using stoichiometry-controlled molecular beam epitaxy (MBE). We deliberately vary the fraction of pyrite-type MnTe$_2$ secondary phase relative to the $\alpha$-MnTe matrix. Across this series, the 175 cm$^{-1}$ mode tracks the presence of MnTe$_2$ essentially one-to-one – present wherever MnTe$_2$ is detectable, absent in stoichiometric, single-phase $\alpha$-MnTe at nominal LASER powers. When LASER power is ramped up, an additional mode emerges in MnTe as well positioned close to $\approx$ 175 cm$^{-1}$; our detailed temperatures dependendent Raman analysis identifies the LASER power scorched region close to a distorted MnTe phase, confirmed via transmission electron microscopy. This direct, growth-controlled correlation identifies the mode as an extrinsic MnTe$_2$ impurity signature or as a distorted MnTe feature, rather than an intrinsic phonon or plasmon feature, providing a practical diagnostic for phase purity in MBE-grown $\alpha$-MnTe and clarifying which Raman features can be reliably attributed to the intrinsic altermagnetic phase.
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Artificial Intelligence
MASCRDM: Multi-Agent System for Compliance Risk Detection and Mitigation in Training Process of Large Language Models
Large Language Models (LLMs) have been applied in various fields. However, ensuring compliance and safety of LLMs, such as avoiding discrimination and bias, still remains a challenge. Current efforts mainly focus on detecting and filtering inputs and outputs of the trained models, rather than studying the intrinsic architecture of the models in real-time. To tackle this challenge, we analyze the LLMs training process and discover two critical issues: 1) Most of the existing methods are predominantly static in their approach to detection and filtering, achieving only localized optimizations without systematically enhancing the compliance of LLMs. 2) Another issue with existing approaches is the lack of real-time risk detection and mitigation across the full training process, which leads to limited flexibility. Motivated by these, we propose MASCRDM (Multi-Agent System for Compliance Risk Detection and Mitigation) during the LLM training process. Firstly, we develop a set of compliance rules based on existing Artificial Intelligence (AI) laws and a compliance-specific LLM with the instruction of compliance law experts. Then, we deconstruct LLMs into several components and identify key nodes based on the compliance knowledge graph. During LLMs training, we implement our multiple agents in the whole process, giving compliance risk alerts and suggestions for LLM developers. Experiments on discrimination and bias benchmark demonstrate that our multi-agent system can effectively improve the compliance while maintaining reasonable semantic performance. The results indicate that our method provides an executable path for mitigating compliance risk from within the LLMs systematically.
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Artificial Intelligence
Reserve-Aware Contrast Certificates for Conservative Bandits with Uncertain Baselines
Conservative bandits must improve an incumbent policy without exhausting a prescribed performance budget. When the incumbent is uncertain, separately bounding candidate and baseline rewards can charge twice for shared estimation error. We develop Reserve-C4B around the baseline-relative contrast itself. A shared confidence set yields an exact expression for this avoidable penalty and a tighter admissibility test at every fixed history. A reserve ledger separates statistical evidence from permitted performance deficit; a prefix-refresh extension recertifies accumulated decisions under the current confidence set without discarding previously certified credit. For linear rewards, self-normalized confidence sets provide simultaneous validity over time and adaptively generated candidates, and the resulting policy satisfies a conditional-mean performance constraint with high probability. Reproducible experiments isolate certificate coupling, prefix refresh, and historical information, showing large reductions in baseline fallback while exposing the limitations of frozen certificates.
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Robotics
Occlusion-Aware, Quasi-Static, Stability-Oriented Trajectory Planning on Uneven Terrain
Autonomous navigation in unstructured off-road environments requires reasoning about both vehicle–terrain interaction and environmental unknowns. We propose a model-based framework for generating quasi-static, stability-oriented reference trajectories for rigid, non-articulated four-wheeled vehicles on highly uneven terrain. Our work makes three primary contributions. First, we model blind spots caused by terrain occlusion as coverage-induced epistemic uncertainty in a fixed-feature Fourier terrain representation, quantified through a regularized inverse-Hessian estimate. Second, we propagate this uncertainty through the Nonlinear Least-Squares (NLS) pose/contact model using implicit differentiation and incorporate the resulting pose, contact-point, and per-wheel surface-normal uncertainty terms into trajectory optimization based on the Cross-Entropy Method (CEM). Third, we introduce a Flow Matching model that warm-starts terrain fitting, and we evaluate its fitting-accuracy–latency trade-off while retaining model-based refinement. Across six synthetic terrains with 30 matched start–goal pairs per terrain, the complete framework produced an observed failure rate of 18.9%, compared with 46.1% and 41.7% for two representative baselines and 34.4% for an ablation that removed the propagated-uncertainty scoring. Hardware evaluations span six distinct outdoor environments, with two representative executions presented in the paper and four additional executions included in the supplementary video. The evaluation also reports the accuracy–latency trade-off for the Flow Matching warm start.
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Algebraic Geometry
Quasi-Projectivity of Weighted Right-Angled Artin Groups
Weighted right-angled Artin groups generalize right-angled Artin groups by adding weights to the edges of the defining graphs. We classify the weighted right-angled Artin groups that occur as fundamental groups of smooth complex quasi-projective varieties. They are precisely the finite direct products of finitely generated free groups and groups of the form $\langle a,b\mid [a,b]^m=1\rangle$.
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Combinatorics
On Eternal Connected Vertex Cover
For a connected graph $G$ with at least one edge, the eternal connected vertex cover number $ecvc(G)$ is the minimum number of guards that can maintain a connected vertex cover after every response to an arbitrary sequence of edge attacks. Denote the minimum size of a connected vertex cover by $cvc(G)$. It is known that $cvc(G)\leq ecvc(G)\leq cvc(G)+1$. A necessary condition for $ecvc(G)=cvc(G)$ is that every vertex belongs to some minimum connected vertex cover. We show that this condition is not sufficient: there exists a $32$-vertex graph $G$ that has $cvc(G)=19$ and $ecvc(G)=20$, although every vertex of $G$ belongs to some minimum connected vertex cover. For connected graphs with minimum degree at least two, we establish the sharp bound $cvc(G)\geq 2|V(G)|-|E(G)|-1$ and $\mathcal F$ denotes the class attaining equality. We prove that $G\in\mathcal F$ if and only if the vertices of degree at least three induce a forest. Within $\mathcal F$, the conditions $ecvc(G)=cvc(G)$, membership of every vertex in some minimum connected vertex cover, and the presence of at least two degree-two vertices on every cycle are equivalent. As applications, we obtain $ecvc(G)=cvc(G)$ for full subdivisions of connected graphs of minimum degree at least two and for minimally $2$-connected graphs. In both the families, every minimum connected vertex cover is an eternally winning configuration. This is not true in general for graphs outside $\mathcal{F}$, we show one example of such a graph.
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Computation and Language
False Frontiers: Diagnosing and Mitigating Co-Cheating in Self-Evolving Search Agents
Self-evolving search agents build their own training curricula by jointly optimizing a proposer that generates questions and a solver that answers them. This closed loop introduces a failure mode we call co-cheating: the proposer and solver increasingly agree on shared errors, so internal reward improves without a matching gain in external correctness. A post-hoc audit against source evidence shows co-cheating growing more severe over successive rounds of self-evolution, with pseudo-label correctness stagnating or declining even as the in-loop training signal improves. The most direct mitigation is to verify proposals before training: we introduce multi-sample verification (MSV), which queries the same model three times with the source and three times without it to decide task admission and replace unreliable pseudo-labels. MSV partially reduces false agreement but leaves substantial residual co-cheating and costs six extra labeler generations per candidate. These limitations motivate CrossFit, our main method: it partitions the proposer's source documents into groups A and B; questions generated from A are scored by an auxiliary solver trained only on B, and vice versa. The cross-fitted agreement determines proposer reward, so a same-source pseudo-label cannot be reproduced through the feedback solver, while the original solver's update rule is unchanged. Rerunning the loop with Qwen3.5-4B and Qwen3.5-9B, MSV reduces false-agreement mass from 6.1% to 5.7% and from 8.8% to 7.2%, whereas CrossFit reduces it to 3.0% and 3.7%. Replaying identical proposals with source-excluded feedback further reduces false agreement to 0.4% and 0.1%, isolating feedback ancestry from curriculum changes. Across seven downstream search benchmarks, CrossFit improves average performance over standard coupled self-evolution by 8.8 and 8.4 points and over Search-R1 by 8.7 and 7.8 points at 4B and 9B.
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Artificial Intelligence
Beyond Prediction: Steering VLM Agents with Retrospective World Modeling
Equipping VLM agents with world modeling capabilities has shown strong potential for complex reasoning and long-horizon planning, while reducing the dependence of policy learning on costly real-world interactions. Existing methods mainly rely on prospective simulation to predict the consequences of candidate actions. However, this forward-only paradigm focuses on what will happen next and provides limited constraints for verifying whether an action is causally consistent with the observed state transition, which can lead to plausible-looking but physically incoherent behaviors. In this paper, we challenge the view of world modeling as only prospective prediction and introduce Retrospective World Modeling, a new agent learning paradigm that enables agents to reason backward by estimating the retrospective attribution distribution $P(\hat{a}{t}|s_t, s{t+1})$ for the action that most likely caused a given transition. Based on this capability, we formulate the Self-Consistency Reward (SCR), an intrinsic signal that measures the probabilistic consistency between the policy action and the retrospective explanation. Integrating SCR into reinforcement learning provides dense transition-level feedback and steers agents toward behaviors that are both task-effective and physically grounded. Extensive experiments across diverse agentic tasks show that our method substantially improves policy robustness and generalization over prospective-only world modeling baselines.
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Instrumentation and Methods for Astrophysics
The Simons Observatory: Design and Initial Performance of the Detector Readout System for the Large-Aperture Telescope
We present the design, implementation, and initial performance of a highly multiplexed cryogenic superconducting detector readout system in the context of its deployment to the Simons Observatory large-aperture telescope (LAT). The Simons Observatory is a cosmic microwave background experiment located at 5,200 m in Chile's Atacama Desert. In addition to its 6 m LAT, whose broad range of science goals spans probing large-scale structure to searching for new Solar System objects, the observatory also currently includes three 0.42 m small-aperture telescopes, which search for signatures of primordial gravitational waves. Nearly 100,000 optically-coupled transition-edge sensor bolometers have been deployed across the observatory's four telescopes to enable these science goals. The readout systems for these telescopes use microwave frequency multiplexing to simultaneously read out 860 optically-coupled bolometers per transmission line. This is enabled by the large-scale fabrication of multiplexing chips which house radio-frequency superconducting quantum interference devices for each detector, and the development of room-temperature electronics to read out these bolometers. This has enabled the largest deployment of superconducting sensors for astronomical observations to date. This paper focuses on the design and implementation of the readout system for the 63,000 detectors in the LAT's cryogenic receiver. We present performance results from an early phase in the telescope's operation. We show that the readout system's performance enables the instrument to meet key benchmarks, including successful readout of 81.4% of its optically-coupled bolometers, which exceeds projections, and readout noise-equivalent current consistent with pre-deployment specifications.
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Machine Learning
A Generalisation Signal Need Not Be a Model-Selection Signal
Model selection in computational biology often relies on validation data drawn from the training regime, even when deployment lies outside it. When validation no longer preserves which model is best, a natural alternative is to rank candidates using properties of the trained network itself. We test this idea using a novel, forward-only proxy motivated by the norm of the Hessian, alongside common Hessian measures, across molecular property, protein fitness, and drug-response tasks. Contrary to our hypothesis, geometry does not become more useful as validation Spearman correlation deteriorates: augmenting validation helps some shifts but significantly harms others. More surprisingly, the proxy still correlates with generalisation gap on most tasks even when Hessian trace and top-eigenvalue relationships are weak or reversed, yet this signal does not reliably identify the deployment-best model. A curvature bound need not preserve cross-model rankings, and low geometric scores can even favour collapsed predictors. Thus, a generalisation signal need not be a model-selection signal.
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Robotics
DiFF: Doppler-informed Flow Matching for Human Motion Flow
Perceiving human motion via privacy-preserving 4D millimeter-wave (mmWave) radar is critical for next-generation human-robot interaction (HRI), where point cloud scene flow serves as a foundational motion representation. Yet the extreme sparsity and noise of 4D radar point clouds make non-rigid motion flow estimation severely ill-posed–a challenge that existing rigid-centric methods and prior works fail to adequately address, largely because they neglect the rich Doppler velocity cues inherent in 4D radar. We propose DiFF, a generative framework that marries Doppler-informed motion priors with a Kolmogorov-Arnold Network (KAN)-based conditional flow matching model. At its core, a KAN-attention mechanism enables expressive feature extraction, while a prior-guided generative process harnesses Doppler cues to regularize the ill-posed solution space. Extensive experiments show that DiFF achieves state-of-the-art (SOTA) performance across diverse real-world datasets, reducing 3D endpoint error to the millimeter scale on the mmBody benchmark.
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Game Theory
Mechanism Design for Bridge Location with Optional Preferences
We study the bridge location problem with optional preferences, where two separated regions each contain one prelocated facility. Each agent has a private location and a private preference specifying a nonempty subset of the two facilities in which she is interested. Her individual cost is measured by one of three natural variants: the maximum, the sum, or the minimum of her distances to the facilities in which she is interested. The social planner must design deterministic strategyproof mechanisms that elicit truthful reports, choose the location of a connecting bridge, and approximately minimize either the social cost or the maximum cost. Our main results are as follows. For the social cost objective, we design optimal mechanisms for the max-variant and sum-variant costs, and provide a 3-approximation mechanism for the min-variant cost, and establish a lower bound of 2 for the min-variant. For the maximum cost objective, we give 5/3-approximation mechanisms for the max-variant and sum-variant costs, and a 3-approximation mechanism for the min-variant cost; we also prove a common lower bound of 5/3 that applies to all three cost variants under the maximum cost objective.
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Computer Vision
DeCoPrune: Efficient KV-Cache Pruning for Autoregressive Video Diffusion via Denoising Consistency
Autoregressive video diffusion supports streaming generation and interactive control, but its KV cache grows continuously with the generated history. Existing compression strategies either discard history using fixed windows or select tokens through local attention and similarity signals, which do not directly measure whether the current chunk contributes information beyond the retained context. We introduce DeCoPrune, a training-free method that treats cache compression as a denoising-consistency problem. We find empirically that denoising difficulty provides a useful proxy for a token's value in long-term retention: tokens with larger step-to-final discrepancies tend to carry visual evidence that is less predictable from the retained context. DeCoPrune measures each current-chunk token's denoising difficulty using the discrepancy between its intermediate clean prediction and final denoised value, retaining high-discrepancy tokens in the long-term cache while pruning those with low discrepancy. To evaluate information retention, we introduce CMBench, comprising 58 approximately one-minute generated or real-world context episodes and 116 Reappear or Revisit continuation tasks that require recalling specific previously observed objects or scenes. Experiments with LingBot World v2 show that DeCoPrune preserves near-FullKV long-range recall while pruning over 85% of historical KV tokens and accelerating continuation generation by over $4\times$, substantially outperforming the evaluated compression baselines at comparable budgets. These results indicate that denoising consistency can serve as a model-intrinsic signal for retaining long-range information while reducing autoregressive inference cost. Our project homepage is https://decoprune.github.io. The code is available at https://github.com/DeCoPrune/CMBench, and the benchmark at https://huggingface.co/datasets/Aoraku/CMBench.
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Representation Theory
Unequal-parameter Kostka–Foulkes polynomials of type $C_n$ at fundamental weights
We establish an explicit formula for the Kostka–Foulkes polynomial of type $C_n$ with unequal parameters at fundamental weights. As an application, we deduce an explicit Lusztig–Kato formula for the Hecke algebra of the special (but not hyperspecial) maximal compact subgroup of a quasi-split but non-split special orthogonal group over a $p$-adic field.
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Materials Science
Three-Dimensional Topology from Stacking-Controlled Umklapp Scattering in Large-Angle Twisted Graphite
Large-angle twisted graphene lies beyond the local-stacking description of conventional moiré systems: inequivalent rotation centers define distinct commensurate interfaces whose low-energy interlayer hybridization is governed by intervalley Umklapp tunneling. For three-dimensional twisted graphite assembled from interfaces with different crystalline symmetries, a symmetry-constrained effective model reveals that competition between nonchiral and chiral tunneling produces one-ring and two-ring nodal-line phases and a $C_3$-protected higher-order topological insulator in the presence of sublattice (chiral) symmetry. The nodal rings carry integer winding numbers, allowing oppositely wound rings to annihilate into the gapped phase. We further examine how sublattice-symmetry breaking modifies these phases. Density functional theory (DFT) and atomistic calculations for $21.8^\circ$ twisted graphite identify the equilibrium structure as a higher-order topological insulator, while compression drives it into a topological Weyl semimetal phase. These findings establish the stacking sequence of symmetry-inequivalent interfaces as a means of engineering band topology in three-dimensional twisted structures.
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Machine Learning
Learning Infinite-Horizon Average-Reward CMDPs via State Augmentation
We study infinite-horizon average-reward constrained Markov decision processes (CMDPs) under the weakly communicating assumption. Existing high-probability guarantees for this setting either require computationally inefficient algorithms or have suboptimal dependence on the number of interactions $T$. We propose, to the best of our knowledge, the first computationally efficient algorithm that achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret and cumulative constraint violation with high probability in the tabular setting. The $\sqrt{T}$ dependence is optimal up to logarithmic factors. Our approach incorporates cumulative constraint violation into the state and defines a reshaped reward through differences of a Huber potential. The added state determines the penalty on further violations while the reward function remains fixed on the augmented state space. Since the added state has known deterministic dynamics, only the original transition kernel needs to be estimated. The bounded slope of the Huber potential keeps the per-step reward bounded, and the potential differences telescope to relate the reshaped return to the original cumulative reward and the terminal potential. These properties allow us to apply finite-horizon approximation and optimistic value iteration with clipping, as used in unconstrained average-reward MDPs, without worsening the regret rate in $T$.
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Quantum Physics
Quantum circuit compilation with constant overhead
Compiling a continuous gate set to a discrete universal gate set generally incurs an overhead. A circuit composed of $G$ arbitrary one- and two-qubit gates can be $\epsilon$-approximated by a sequence of gates from $\{H,T,\mathrm{CNOT}\}$ by replacing each original gate by a sequence of $O(\log(G/\epsilon))$ elementary gates. We show that this overhead can be avoided using adaptivity for polynomial-sized circuits with inverse-polynomial target error, which is optimal.
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Machine Learning (Statistics)
Steepest Guidance: A Practical and Principled Approach to Inference-Time Alignment of Flow and Diffusion-based Models
Inference-time alignment of flow and diffusion-based models is critical for achieving flexible generative modeling. Theoretically, Doob's $h$-transform provides an elegant solution to this problem, and most existing methods are based on this principle. However, in practice, estimating the optimal guidance derived from Doob's $h$-transform at inference time is challenging. To deal with this issue, we regard inference-time alignment as a sequential optimization problem in the space of probability measures and propose a novel framework called *Steepest Guidance*, based on the principle of maximizing local improvement in the objective. We provide a theoretical analysis of the proposed method and demonstrate its effectiveness through extensive experiments.
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Chemical Physics
A strategic roadmap for an atomistic machine-learning ecosystem
Data-driven machine learning (ML) techniques have become an essential tool in many domains of science. Their application to atomistic simulations of matter is particularly widespread and impactful. This success is due largely to the existence of a well-developed and established physics-based modeling framework, ranging from first-principles electronic-structure calculations to molecular dynamics and statistical sampling, into which ML was integrated naturally to reshape long-standing trade-offs between accuracy, efficiency, and scale. Nevertheless, this integration raises both conceptual and practical challenges, from choosing between data-centric and physics-based modeling approaches to adapting established software stacks to modern hardware accelerators and ML libraries. As the field evolves rapidly, fueled in part by widespread enthusiasm but also by tangible impact, it seems appropriate to take a moment to consider the current state of the art and open challenges, and reflect on what can be done to better coordinate efforts across the community. With this goal in mind, several members of this community met in Lausanne in January 2026 at CECAM to discuss algorithms, models, software and hardware infrastructure, and the most promising scientific applications that have become possible thanks to the use of artificial intelligence in atomic-scale simulations. This strategic roadmap paper summarizes the outcomes of these discussions, suggesting some long-term goals, and some concrete actions, to establish a healthy, sustainable and impactful atomistic ML ecosystem.
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Computer Vision
UGOD: Uncertainty-Guided Opacity and Dropout for Sparse-View 3D Gaussian Splatting
Sparse-view 3D Gaussian Splatting is prone to overfitting because limited observations leave many Gaussian primitives weakly constrained, yet their contributions are still accumulated through alpha blending. Without uncertainty estimation, the renderer cannot distinguish unreliable primitives from well-constrained ones, allowing their erroneous contributions to corrupt novel-view synthesis. We introduce UGOD, an uncertainty-guided framework that estimates a view-dependent uncertainty score for each Gaussian and uses it to regulate its rendering contribution. A lightweight uncertainty head conditioned on Gaussian attributes and viewing direction predicts this score, which then drives a differentiable opacity-modulation mechanism that attenuates high-uncertainty primitives before compositing. During training, a detached soft-dropout branch applies an uncertainty-controlled continuous keep mask to discourage the model from relying on poorly constrained Gaussians and thereby reduce overfitting. Crucially, detaching the uncertainty score prevents gradients from this stochastic regulariser from biasing or collapsing the uncertainty prediction. Experiments on Mip-NeRF~360 and LLFF show that UGOD improves sparse-view novel-view synthesis while producing more compact Gaussian representations than the compared methods. These results demonstrate that Gaussian uncertainty provides an effective rendering-time control for sparse-view reconstruction.