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At least 1,225 records · Page 68Linked to original sources
arXiv2026

Reasoning Error from Known Fact: Step-Level Self-Consistency Group Relative Policy Optimization for LLMs

With the rapid advancement of large language models (LLMs), modern systems not only possess strong foundational capabilities and extensive knowledge, but can also solve complex problems via long, multi-step reasoning. However, as reasoning traces become longer, LLMs may produce a substantial amount of hallucinated content during the reasoning process, which is often difficult to detect. In this work, we conduct a fine-grained analysis of hallucinations arising in LLM reasoning and find that the reasoning traces are particularly prone to Context-Sensitive Factual Hallucinations: cases where the model actually has the relevant knowledge, yet makes factual errors due to contextual interference during reasoning. To address this issue, we propose Step-level Self-Consistency Group Relative Policy Optimization (SSC-GRPO), which assigns step-level rewards to reasoning traces by computing self-consistency scores of individual steps across multiple rollouts. Compared with prior methods, SSC-GRPO achieves state-of-the-art performance on both mathematical reasoning benchmarks and hallucination leaderboards. Our results offer a new perspective for detecting and mitigating hallucinations in the reasoning process of large language models.

cs.CL↗
arXiv2026

Circuit Claims Depend on What Is Extracted and How It Is Compared

Circuit extraction identifies model components whose presence preserves a target behavior under ablation, but preserving behavior does not single out one circuit. We study this in a synthetic Lean tactic-prediction benchmark with fixed proof rules and randomized surface form. Across dense and weight-sparse checkpoints of the same transformer, evaluated on atomic and compositional proofs, we vary which extracted object is reported: a compact prediction-preserving circuit, a broader graph retaining surrounding read, write, and routing structure, or a subgraph extracted with a post-ablation loss budget. First, overlap between groups of component-to-component connections is low, sometimes close to a random baseline. Overlap is much higher for selected attention-head sets under deterministic selection, but falls sharply when selection among equally scored heads is randomized. Second, the normalized graph-size ranking of conditions that differ in which supervised checkpoint initializes reinforcement learning (RL) agrees between repeated extractions of the compact circuit and between joint and separate query/key representations of each of the other two graphs. For the loss-budgeted graph, query/key ordering agreement persists through the budget sweep. Finally, across those same conditions, the largest exact-match accuracy gains from RL on compositional proofs come with the largest proportion of components in the compositional circuit that lie outside the corresponding atomic circuits. Ablating these additional components in the sparse RL model reduces compositional accuracy while largely preserving accuracy on the corresponding atomic tasks. A circuit-level claim therefore requires specifying which circuit is reported and how it is extracted and compared; behavior alone does not determine its interpretation. We distill these requirements into a reporting practice for circuit-extraction studies.

cs.LG↗
arXiv2026

Beyond Relevance-Centric Retrieval: Rubric-Oriented Document Set Selection and Ranking

As large language models and AI agents become the primary consumers of search results, document set quality determines the upper bound of downstream generation. Yet existing evaluation systems remain confined to scoring documents independently and aggregating via nDCG, ignoring inter-document interactions (redundancy, conflict, complementarity) and unable to answer what makes one document set better than another. To address these issues, we propose a complete evaluate-diagnose-optimize framework. We design SetwiseEvalKit, a three-level, nine-dimension document set evaluation benchmark covering both short-form and long-form scenarios, comprising approximately 28K high-quality evaluation rubrics. We systematically evaluate 12 rerankers: even the best method achieves no more than 45% coverage, cross-document coordination dimensions are universally weak, and no single method maintains top performance across both settings. Building on this, we propose Rubric4Setwise, a training-free method that converts rubric-based evaluation criteria into document set selection signals, achieving the best downstream generation performance with fewer documents and search rounds. It is the only method that maintains state-of-the-art results across both scenarios, validating the effectiveness of closing the loop from evaluation to optimization.

cs.CL↗
arXiv2026

Covering Planar Lattices with Interior-Disjoint Unit Disks

We study an infinite variant of the coin-covering problem for periodic point sets in the plane. Given a point set of spacing $d$, we ask whether all of its points can be covered by pairwise non-overlapping unit disks. We consider the triangular lattice, the square lattice, and the honeycomb point set, and construct periodic motif patterns that certify several intervals of coverable spacings. For the triangular lattice, our constructions include single-family patterns with vertex, face, and off-lattice realizing centers, as well as multi-family patterns. For the honeycomb point set, additional native motifs fill gaps left by the triangular-lattice constructions. For the square lattice, we revisit the constructions of Alm et al., identify an unintended overlap in one motif realization, and give new patterns that recover part of the affected interval and establish an additional coverability interval.

cs.CG↗
arXiv2026

Visual Contrastive Self-Distillation

On-policy self-distillation (OPSD) removes the external teacher required by on-policy distillation (OPD), but still needs asymmetric information between teacher and student so that the self-teacher provides a stronger learning signal. Existing methods create this asymmetry through privileged answers or visual evidence. We ask whether both can be removed, yielding a simpler form of OPSD driven purely by input conditioning. We propose Visual Contrastive Self-Distillation, namely VCSD, which converts image-content removal into an on-policy self-distillation signal. At each student-generated response prefix, the EMA teacher produces two next-token distributions under the same prompt and prefix: one conditioned on the original image and the other on a content-erased control. Their token-wise log-probability difference highlights candidates whose likelihood is specifically increased by the instance-level visual content. We use this contrast to sharpen the teacher's original-image distribution within its plausible support, and distill the resulting full-distribution target into the student. On ViRL39K, VCSD consistently outperforms matched OPSD across Qwen3-VL and Qwen3.5 models. It improves the seven-benchmark aggregate from 72.51% to 76.26% on Qwen3-VL-8B and from 74.97% to 79.24% on Qwen3.5-9B, with gains at all six evaluated scales. VCSD requires no external teacher, privileged answers, visual evidence signals, reasoning traces, or additional inference-time cost.

cs.CV↗
arXiv2026

Symmetry and Quantum Geometry in Bloch Bands

Quantum geometric quantities have featured heavily in the discussion of the properties of quantum systems in recent years. Among quantities most commonly discussed is the variance of Berry curvature and the integral of the trace of the quantum metric tensor. Despite their usefulness, it is known that they suffer from one significant complication: for a tight-binding model, the quantum geometric quantities depend not only on the parameters of the tight-binding model itself, but also the real space geometry of the tight-binding model, the so-called "orbital embedding". One explicitly geometry-independent quantity is therefore the minimal value of the quantum geometric quantity out of all possible real space geometries. In this work, we demonstrate that, if the tight-binding model is compatible with certain spatial symmetries, then the real space geometry that minimizes the variance of the Berry curvature or the integral of the trace of the quantum metric tensor must obey all those spatial symmetries. We further show that the statement is applicable to systems with magnetic translation symmetries and other composite symmetries, with implications for the quantum geometry of the Hofstadter model.

cond-mat.str-el↗
arXiv2026

Every Model Cheats: Prompt-Level Mitigation of Cheating on Offensive Cyber Tasks

Large language model (LLM) agents routinely cheat on cybersecurity benchmarks, inflating reported pass rates far beyond genuine capability. Prior audits of Cybench found cheating in 0.3-3.4% of traces, implicating only a handful of models. We present a controlled prompt-ablation study across 22 frontier models from 7 providers on 23 Cybench capture-the-flag (CTF) challenges under three prompt conditions (no anti-cheat, standard, severe). All 1,518 task traces were individually audited through a four-stage pipeline combining LLM-as-a-judge classification, programmatic verification, judge-verifier reconciliation, and human review. We find cheating is far more pervasive than previously estimated: under baseline conditions, 37.1% of passes involved cheating, 21 of 22 models cheated, and scores were inflated by up to 5x. Anti-cheat prompts reduce cheat propensity from 33.0% (baseline) to 18.6% (standard) to 8.5% (severe) without degrading, and sometimes improving, solve rates. However, even under the most restrictive prompt condition, eight models still produced cheated passes, and cheating shifted from web search toward infrastructure probing. We introduce the "solve rate" metric (clean passes only) to distinguish genuine capability from cheated outcomes, and argue it should be standard practice in any evaluation where cheating vectors are available. Anti-cheat prompts are an effective and essentially free first layer of mitigation, but they are not a substitute for environmental controls.

cs.CR↗
arXiv2026

Risk-Routed Implicit Boundary Refinement for Robust Ultrasound Image Segmentation

Accurate boundary delineation in medical ultrasound (US) images remains challenging because of speckle noise, low contrast, acoustic shadowing, and acquisition variability. We propose Risk-routed Implicit Boundary Refinement (RIBR), a compact framework that refines convolutional segmentation through spatially weighted implicit residuals. A coordinate-conditioned implicit branch uses regional features to predict logit corrections, and a learned gate controls their contribution using predictive uncertainty and local appearance. Geometry- and speckle-aware regularization provides contour supervision and discourages probability fluctuations away from boundaries. We compare RIBR with ten baselines on nine datasets covering lymph nodes, breast lesions, thyroid nodules, and prostate, including four external lymph-node and breast cohorts. Across three seeds, RIBR achieves the best overall dataset macro-average among the evaluated configurations, with $76.67{\pm}0.42\%$ Dice and a 95th-percentile Hausdorff distance (HD95) of $29.55{\pm}0.55$ pixels on the resized evaluation grid. It obtains the lowest HD95 on all nine datasets, with task-dependent Dice rankings. These results support controlled implicit residual refinement for boundary-sensitive US segmentation. Source code is available at https://github.com/jinggqu/ribr.

cs.CV↗
arXiv2026

Filling Before Advancing: Capability-Gap-Driven Post-Training for Scenario-Specialized Remote Sensing MLLMs

Remote sensing multimodal large language models (RS-MLLMs) have advanced aerial-image understanding, but scenario specialization remains constrained by scarce high-quality supervision and incomplete capability coverage. We propose filling before advancing (FBA), a capability-gap-driven post-training route that develops prerequisite capabilities before scenario-specific adaptation. For coastal harbor understanding, we construct CPRS (Coastal-Port Remote Sensing), a three-layer dataset covering RGB, SAR, PAN, and NIR imagery. FBA organizes supervision into RS semantic anchoring, multi-source bridging, and evidence-grounded scenario tuning. We also introduce HarborEval, an eight-track benchmark assessing perception, spatial understanding, robustness, and generation. Using the same final-task supervision pool, FBA raises the HarborEval score from 57.95 to 70.29 on LLaVA-v1.5 and from 81.09 to 83.37 on Qwen3-VL compared with Direct-SFT. It also outperforms collapsed training and leads the evaluated comparisons on harbor-related VRSBench and RSVQA subsets and expert-scored OpenEval. Stage-wise and supervision-replacement analyses examine the contributions of the supervision roles. A lightweight urban instantiation further supports cross-scenario applicability, with the proposed stage order achieving stronger overall performance than the tested alternatives. Project resources and release updates are available at https://github.com/Z0ngL1ng/filling-before-advancing.

cs.CV↗
arXiv2026

Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length

We study non-compact Ricci solitons of finite volume whose potential vector field has constant length. Under the assumptions that the scalar curvature is constant along the integral curves of the potential field and that a natural divergence term is integrable on the unit tangent bundle, we prove that such Ricci solitons are necessarily trivial. As applications, we characterise $3$-dimensional Ricci solitons of constant length and of finite volume on almost $α$-cosymplectic manifolds. In fact, we show that these spaces are indeed compact quotients of Euclidean spaces. We also study complete, non-compact and finite volume contact metric manifolds in dimension $3$ admitting a Reeb vector field as a Ricci soliton. We show that it is a compact spherical space form. We include some examples to illustrate the necessity of the finite-volume and constant-length assumptions.

math.DG↗
arXiv2026

Coherent-State Kernels for Composite Quantum Operations

This paper develops a unified kernel-based method for computing exact matrix elements of composite quantum operations by inserting resolutions of the identity after individual operators or between successive factors of an operator chain. A single insertion gives an exact scalar identity, and nested insertions between the factors give multiple integral identities for chains of closed operators under explicit Bochner-integrability conditions. The procedure is carried through on polynomial and analytic functions of the ladder operators, on one- and two-mode Gaussian unitaries, and on three composite operations: a Kerr phase followed by squeezing or by a cubic phase gate, a two-mode squeezer followed by a beam splitter, and a heralded cat-state circuit with two beam splitters. At rational Kerr phases the Kerr-squeezed amplitudes reduce to finite sums of squeezed coherent-state amplitudes weighted by quadratic Gauss sums, with an explicit error bound at the remaining phases; the two-mode network gives a bivariate Hermite polynomial; and the heralded circuit gives closed forms for the amplitudes, the heralding probabilities and their extension to an arbitrary passive network fed by one squeezed source. The examples are set against the reach of four established techniques: operator ordering, the Berezin symbol calculus, Lie disentangling and the symplectic formalism. Each technique reaches a subset of the examples directly, while the insertion procedure reaches all of them under the same hypotheses. A comparison with direct Fock summation identifies the regime in which the finite Kerr sums are efficient, and the choice of resolution at each boundary of a chain follows a selection rule set by the action of the adjacent factor. Each closed form agrees with an independent numerical computation.

quant-ph↗
arXiv2026

Optimal Polynomial Tractability Exponents for the Inverse Star Discrepancy

The inverse of the star discrepancy $n^\ast(d, \varepsilon)$ satisfies \[ d \varepsilon^{-1} \lesssim n^{\ast}(d,\varepsilon)\lesssim d\varepsilon^{-2} \] for all $d \in \mathbb{N}$ and $0 < \varepsilon < \varepsilon_0$. The upper bound was established by Heinrich, Novak, Wasilkowski and Woźniakowski (2001), while the lower bound is due to Hinrichs (2004). Steinerberger (2023) subsequently gave an elementary proof of the latter result. These bounds imply that the inverse of the star discrepancy depends linearly on the dimension, but the exact exponent of $\varepsilon^{-1}$ had remained open. In this paper we prove a lower bound which shows that the exponent $2$ of $\varepsilon^{-1}$ in the upper bound cannot be improved. More precisely, for every $0<α<1$ and fixed $0 0$ and $\varepsilon_{α,A}>0$ such that, for every $0<\varepsilon<\varepsilon_{α,A}$ and every integer $d$ satisfying \[ A\varepsilon^{-α}\le d\le B\varepsilon^{-α}, \] one has \[ n^\ast(d,\varepsilon) \ge c_{α,B}\,d\,\varepsilon^{-(2-α)}. \] Along these polynomial strips the right-hand side is of order $\varepsilon^{-2}$. Consequently, every uniform polynomial upper estimate $n^{\ast}(d,\varepsilon)\le C d^q\varepsilon^{-p}$ must satisfy $p\ge2$. Together with the lower bound of Hinrichs (2004), which forces $q\ge1$, this proves that the exponents $p=2$ and $q=1$ in the Heinrich--Novak--Wasilkowski--Woźniakowski upper bound are individually optimal. In particular, the optimal exponent $p^\ast = 2$.

math.NA↗
arXiv2026

General Polynomials and Eigenvalues Over Cayley--Dickson Algebras

In this paper, we provide an explicit method for determining the zero set of monic quadratic general polynomials over Cayley--Dickson algebras with any base field of characteristic not equal to $2$, which reduces the problem to finding the roots of univariate polynomials over the base field. For the special case of locally-complex Cayley--Dickson algebras over the reals, we prove that every such polynomial has a root. We prove the existence of right eigenvalues for any $2 \times 2$ matrix over Cayley's octonions (the real octonion division algebra), and our root-finding method allows the computation of some of the right eigenvalues.

math.RA↗
arXiv2026

Learning Traversability for Long Horizon Off-Road Navigation

Autonomous navigation across large off-road environments remains a challenging problem. Onboard sensors perceive only the immediate surroundings, yet safe and efficient routes depend on terrain features that extend well beyond the sensor horizon. Geo-spatial data sources such as satellite imagery, aerial LiDAR, and vector maps can close this gap, but learning traversability from them is difficult: dense labels are unavailable at scale, and existing methods rely on short-range sensing. We propose an efficient formulation that learns a continuous traversability map from overhead data, supervised directly by human-driven GPS trajectories and shaped by supervised geometric priors from LiDAR. Alongside the model, we release a dataset, curated from public sources, consisting of 299 scenes spanning $\sim\!1{,}244\,\mathrm{km}^{2}$ of diverse terrain, paired with $1{,}130\,\mathrm{km}$ of human driving. In field trials on a Clearpath Warthog across seven routes at two sites,our method achieves trajectories within $5.5\%$ of human path length and reduces operator interventions by $\sim\!85\%$ compared to local-planner-only autonomy.

cs.RO↗
arXiv2026

On the Power Distance Representation of Bregman Divergences

We express Bregman divergences between parameters as power distances between corresponding weighted points, and investigate several applications of this representation. First, we show that the Bregman closest pair and diameter problems can be reformulated as bichromatic weighted point problems under the power distance. This reformulation enables Bregman nearest and farthest neighbor queries under power distances to be handled in practice through corresponding Euclidean neighbor queries in one additional dimension, after offsetting the weights. Next, we revisit the problem of computing minimum enclosing Bregman balls (Bregman MEBs) and establish their equivalence to double-sided weight power MEBs. We further show that Bregman MEBs can be approximated by relaxing the double-sided weight power MEB problem to its single-sided weight counterpart. We then present two approaches to solving general power MEB problems: An exact algorithm based on the LP-type framework and an arbitrarily accurate approximation scheme based on iterative Frank-Wolfe optimization. Finally, we show that the potential-function lifting transformations used to construct Bregman Voronoi diagrams can be reinterpreted as classical paraboloid lifting transformations applied to the corresponding weighted point sets. This establishes a direct connection between Bregman Voronoi diagrams and power diagrams, further illustrating how Bregman divergences can be represented as power distances.

cs.IT↗
arXiv2026

Controlling Turbulent Flows in Compressible Active Liquid Crystals

Motivated by experiments on light-patterned, quasi-2D active suspensions that exhibit large density variations, we develop a continuum theory of compressible active nematics--suspensions of apolar rods whose orientation is invariant under $π$ rotations. Under spatially patterned activity, the extensile isotropic active pressure expels material from high-activity regions and accumulates it in low-activity ones; an exactly solvable scalar reduction shows that the resulting density contrast is governed by a single dimensionless parameter, linear in the compressibility. Using compressibility as a tuning knob, we then steer active turbulence from high- to low-activity regions and, at sharp activity interfaces, stabilize an analytically tractable dynamical steady state: a one-dimensional chain of vortices held by soft, activity-induced confinement. Our results establish compressibility as a control parameter for density variations and turbulent flow in active nematic suspensions.

cond-mat.soft↗
arXiv2026

A Deep Look at the Ultra-Faint Milky Way Satellite Virgo III with Rubin Observatory Data Preview 2

We analyze the ultra-faint Milky Way satellite Virgo III using data from the Vera C. Rubin Observatory Data Preview 2 (DP2). Virgo III was observed in the Rubin "Cosmic Treasure Chest" (M49) First Look field, which contains 924 visits in the u,g,r,i bands comprising ~10.5hrs of exposure time with LSSTCam. These data are considerably deeper than the majority of DP2, with a $5σ$ limiting magnitude that approaches the expected 10-year depth of LSST (~25.2-26.5mag, depending on band). We report the morphological and stellar population parameters of Virgo III measured with the maximum-likelihood-based package ugali. The depth of the Rubin imaging yields more than a factor of four increase in the number of candidate member stars ($N_* = 114^{+11}_{-11}$) relative to the Virgo III discovery results ($N_* = 25^{+5}_{-4}$), enabling significantly more precise morphological constraints. Our best-fit parameters broadly agree with previous measurements, further confirming that Virgo III has properties that are consistent with an ultra-faint dwarf galaxy ($M_V = -2.72^{+0.49}_{-0.70}$; $r_{1/2} = 53^{+10}_{-8}$) located at a heliocentric distance of $D_\odot = 151^{+8}_{-8}$. We also demonstrate that the depth and photometric quality of the DP2 data are sufficient to separate metal-poor and metal-rich stars in color-color space. We further present period estimates for the three known RR Lyrae member stars derived from the DP2 forced photometry; we use theoretical Period-Luminosity-Metallicity (PLZ) and Period-Wesenheit-Metallicity (PWZ) relations to obtain independent distance estimates. We find that our period and distance estimates are broadly consistent with previous measurements for these RR Lyrae. These results demonstrate the power of LSST data for the discovery and characterization of ultra-faint dwarf galaxies and motivate future searches for new satellites across the southern sky.

astro-ph.GA↗
arXiv2026

WHTMix: Efficient Stereo Depth Estimation via Walsh-Hadamard Token Mixing

Stereo depth estimation for driving, robotics and augmented reality must run at high resolution under tight latency budgets, yet in transformer-based matchers the global self-attention that aggregates scene context grows quadratically with the number of pixels and comes to dominate runtime. We show that the joint self-attention stage of a stereo transformer, whose role is to spread context across both views, can be replaced by a data-independent Walsh-Hadamard token mixer that mixes tokens globally in the transform domain at log-linear cost, while the data-dependent cross-attention that performs left-right correspondence is retained. On synthetic driving data the mixer matches the attention baseline in end-point error while reducing model compute by a factor of 2.46 and single-image inference latency by a factor of 2.65. A complexity analysis shows the benefit is governed by the ratio of sequence length to channel width, which explains why high-resolution stereo matching is a particularly favorable setting and why classification transformers are not; we confirm this token-to-channel scaling on non-stereo long-sequence benchmarks. Furthermore, we introduce a hybrid log-disparity loss function designed to up-weight small-disparity pixels corresponding to long-range objects. This approach reduces the error on distant objects without incurring any additional computational overhead.

cs.CV↗