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01.
arXiv (quant-ph) 2026-06-11

Handbook of Error-Correcting Codes

arXiv:2606.11484v1 Announce Type: new Abstract: Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Error Correction Zoo, a curated reference of methods for protecting classical or quantum information from errors during storage and transmission. The handbook includes descriptions of these error-correcting codes and a classification according to the symbols they use. It also catalogues relations among codes and related objects such as sphere packings, lattices, designs, groups, and classical and quantum phases of matter. The collection is intended both as a rigorous reference and as a practical aid for tracing the web of code relationships and uncovering new connections.

02.
arXiv (CS.LG) 2026-06-12

Scalable anomaly detection via a univariate Christoffel function

arXiv:2606.12483v1 Announce Type: new Abstract: Anomaly detection plays a critical role in identifying unusual patterns across domains such as fraud detection, network intrusion, and system fault diagnosis. Recently, Christoffel function-based methods, rooted in polynomial optimization, have emerged as promising alternatives to deep learning due to their strong mathematical foundations and computational frugality. However, their practical applicability is hindered by the need to invert a matrix whose size grows exponentially with the data dimension, rendering the method intractable even for moderate-dimensional datasets. This paper addresses the dimensionality limitations of Christoffel function-based anomaly detection while preserving its key theoretical properties, i.e., the on-off support dichotomy behavior and the accurate support shape capture. We introduce UCF, a univariate Christoffel function which is based on the squared distance between the query point and the support points. Extensive experiments on the ADBench benchmark demonstrate that UCF consistently outperforms 14 state-of-the-art baselines in terms of Average Precision. By resolving the scalability bottleneck of the Christoffel Function, this work expands the toolkit of anomaly detection methods with a robust, theoretically grounded, and universally applicable approach.

03.
arXiv (CS.LG) 2026-06-16

ShipNet: A Geometric Deep Learning Surrogate for Real-Time Ship Hydrodynamics

arXiv:2606.15356v1 Announce Type: cross Abstract: Accurate prediction of hydrodynamic performance is central to ship design, yet high-fidelity computational fluid dynamics remains prohibitively expensive for large-scale parametric exploration. This motivates the development of data-driven surrogate models that provide rapid approximations to hydrodynamic predictions at substantially reduced cost. We present ShipNet, a geometric deep-learning surrogate that predicts both hull-surface pressure distributions and far-field free-surface wave patterns directly from hull geometry and speed. The network employs a regularized dynamic graph convolutional backbone on hull point clouds, with a multi-head decoder for simultaneous near-body pressure and free-surface elevation outputs. Training data consist of 420 inviscid free-surface simulations generated using a potential-flow panel method for two parent yacht hulls, each parameterized into 70 variants and evaluated at three speeds. ShipNet predicts per-point pressure coefficient and two-dimensional wave elevation map using a composite loss that combines point-wise regression and image-structure terms. On a geometry-held-out test set, ShipNet achieves R^2=0.98 for hull pressure and R^2=0.91 for wave fields. Inference requires approximately 0.15s per case, yielding over a 550x speedup relative to the potential-flow solver on conventional hardware. Limitations include the restricted geometry and speed ranges and the inviscid training data, while future work will extend the model to high-fidelity viscous simulations with physics-informed regularization.

04.
arXiv (CS.AI) 2026-06-16

The Distributed Detectability Band Against Marginal-Preserving Attacks

arXiv:2606.10456v2 Announce Type: replace-cross Abstract: AI-control monitors score individual agent actions to detect misbehavior, but real harm can be distributed across many benign-looking steps, each individually below any per-step alarm. We construct a marginal-preserving, correlation-encoded distributed-sabotage attack using a Gaussian-copula AR(1) construction: the per-step monitor-score marginal is held exactly equal to benign, so mean, max, top-k tail, and threshold monitors (Monitor A) are defeated by construction, while harm is encoded in the temporal correlation structure. We sequence the paper around three reviewer-mandated gates. (1) Realizability gate: the stealthy attack achieves KS-distance to benign of 0.013 (effectively zero) at all tested harm levels up to 3.0, confirming that harm is fully decoupled from the per-step marginal and realizability is not harm-limited. (2) Monitor-A-vs-B reconciliation: we show formally that the attack, built against Monitor A's score marginal, remains marginal-preserving under a different-score Monitor B (the correlation/sequence family: CUSUM, SPRT, HMM-LR, runs test, autocorrelation, windowed logistic), and scope worst-case claims to score functions that admit a temporal signature. (3) Non-empty detectability band: Monitor A achieves AUC 0.52 (chance); Monitor B spans AUC 0.79-0.97 at the same 1% FPR target, and as harm is amortized over more steps Monitor A collapses to chance while Monitor B holds at AUC ~0.95. These results demonstrate a non-empty detectability band and characterize the sub-threshold sabotage frontier: distribution-shape monitors fail by construction; temporal-correlation monitors can detect but are not trivially optimal.

05.
bioRxiv (Bioinfo) 2026-06-16

scIsoAgent enables autonomous isoform-resolved characterization and sequence-informed interpretation of long-read single-cell transcriptomes

Alternative isoform usage can alter gene function independently of total gene expression, creating a need to resolve transcript isoforms at single-cell resolution. Long-read single-cell RNA sequencing meets this need by linking cellular identity to transcript isoforms and sequence-level features. Realizing its full biological value requires reproducible workflows that connect specialized long-read analysis with biological interpretation. Existing large language model (LLM)-based biomedical agents support general omics analysis, but are not designed for isoform-resolved long-read single-cell workflows. Here, we present scIsoAgent, an autonomous LLM-powered scientific agent for long-read single-cell RNA-seq analysis. scIsoAgent turns heterogeneous long-read single-cell inputs into traceable isoform-resolved workflows, using stage-aware planning and persistent computational context to support both execution and interpretation. Across complementary evaluations, this design improved the continuity from analysis planning to executable, interactive workflows compared with general-purpose LLM baselines. In real-data reanalysis, scIsoAgent recovered major findings from published long-read single-cell resources and extended a representative differential transcript usage event into a sequence-informed functional hypothesis. By linking full-length isoform sequences with model-inferred transcript properties, scIsoAgent connects observed isoform usage with potential sequence-level functional consequences. These results demonstrate that autonomous scientific agents can transform fragmented long-read single-cell analysis into coherent, reproducible workflows for isoform-resolved discovery and biological interpretation.

06.
arXiv (math.PR) 2026-06-15

Trivariate Hypergeometric Series Formulas for Pure Partition Functions of Multiple $3$-SLE$_\kappa$

作者:

arXiv:2606.14038v1 Announce Type: new Abstract: Pure partition functions of multiple SLE are characterized by null-state partial differential equations, Möbius covariance, and boundary asymptotics. After quotienting by Möbius covariance, the case of three curves is the first genuinely multivariable one: the moduli space has three independent variables, naturally represented by the three unoriented cross-ratios of the three pairs of links. We solve this Möbius-normalized three-variable problem for the two basic link-pattern types of multiple \(3\)-SLE\(_\kappa\), namely the rainbow and neighbor patterns. Writing \(\beta=4/\kappa\), we construct explicit trivariate hypergeometric-series normal forms and identify them with the corresponding pure partition functions for all \(\beta>1/2\) in the rainbow case and all \(\beta\ge2/3\) in the neighbor case. Equivalently, these ranges are \(\kappa\in(0,8)\) and \(\kappa\in(0,6]\), respectively. The proof is analytic. The null-state PDEs and Möbius covariance yield recursion relations for the trivariate coefficient arrays. In the rainbow case, coefficient estimates give convergence and boundary regularity on the closed cube. In the neighbor case, Pfaff systems continue the local power series to a neighborhood of \([0,1)^3\), while side-face equations, regular normal estimates, and corner propagation give continuity on \([0,1]^3\) for \(\beta\ge2/3\). The endpoint \(\beta=2/3\), corresponding to \(\kappa=6\), requires a logarithmic normal term. The two-dimensional boundary degenerations are classical Appell \(F_1\) and Horn \(G_2\) functions. The probabilistic identification uses SLE martingale arguments and Itô calculus, together with positivity and boundary regularity. We also discuss boundary degenerations, including heuristic connections with boundary Green's functions.

07.
arXiv (CS.LG) 2026-06-18

On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials

arXiv:2602.14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been associated with favorable features. While prior work often relies on linearization to determine stability, it remains unclear whether linearized dynamics faithfully capture the full nonlinear behavior. Recent work has shown that GD may stably oscillate near a linearly unstable minimum and still converge once the step size decays, indicating that linear analysis can be misleading. In this work, we explicitly study the effect of nonlinear terms. Specifically, we derive an exact criterion for stable oscillations of GD near minima in the multivariate setting. Our condition depends on high-order derivatives, generalizing existing results. Extending the analysis to stochastic gradient descent (SGD), we show that nonlinear dynamics can diverge in expectation even if a single batch is unstable. This implies that stability can be dictated by a single batch that oscillates unstably, rather than an average effect, as linear analysis suggests. Finally, we prove that if all batches are linearly stable, the nonlinear dynamics of SGD are stable in expectation.

08.
arXiv (CS.CV) 2026-06-12

Where, What, Why, and Importance: Structured Defect Grounding for Text-to-Image Feedback

Despite generating increasingly photorealistic images, text-to-image (T2I) models still exhibit localized, subtle, and structurally complex failures. Diagnosing these failures requires instance-level feedback that answers where a defect occurs, what type it is, why it is defective, and its importance to overall image quality. While recent dense-feedback methods move beyond scalar supervision, their heatmap-centric representations still formulate diagnosis as pixel-field regression, making it difficult to localize variable-cardinality defects and bind semantic reasons to individual failures. To address this representation bottleneck, we propose Structured Defect Grounding (SDG), which casts T2I diagnosis as structured set prediction by modeling each defect as a (location, type, reason, importance) tuple. To make this formulation trainable and measurable, we introduce SDG-30K, a 30K-image dataset with box-grounded annotations across four modern T2I generators, together with a dedicated evaluation protocol, SDG-Eval. Building on this structured representation, we further present a diagnosis-to-alignment framework in which a Vision-Language Model (VLM) serves as the SDG detector, and BoxFlow-GRPO converts predicted defect sets into box-derived, importance-weighted spatial rewards for diffusion model alignment. Extensive experiments show that our SDG detector outperforms leading proprietary VLMs on structured defect grounding, while SDG-guided rewards consistently improve T2I alignment and support localized image refinement. These results establish SDG as a unified, instance-level interface for diagnosing, evaluating, and enhancing modern generative models.

09.
bioRxiv (Bioinfo) 2026-06-18

Robust Conditional Diffusion with Noisy Templates for Antibody Sequence-Structure Design

Antibodies specifically recognize antigens and play a central role in therapeutic discovery. Designing antibodies for a given antigen remains challenging because antigen-antibody complex data are limited, whereas the sequence and conformational spaces of complementarity-determining regions (CDRs) are large. Retrieved CDR templates from databases or candidate libraries can narrow the design space and improve controllability, but retrieval for novel antigens is often sparse and imperfect; treating retrieved templates as hard conditions can bias the denoising process and cause negative transfer. To address this problem, we propose Robust Conditional Diffusion with Noisy Templates for antibody sequence-structure design (NT-ABDiff), a joint diffusion framework that treats candidate CDR-only templates as optional and potentially unreliable conditions. NT-ABDiff uses reliability-aware template modulation to estimate the context-conditioned usefulness of each candidate and to adaptively reweight and fuse multiple templates during conditioning. We further train the model with mixed-quality and corrupted templates as conditional perturbation regularization, encouraging the denoiser to exploit informative templates while remaining stable when templates are uninformative. Experiments under controlled template shifts and a train-set retrieval evaluation show that NT-ABDiff improves CDR-H3 sequence recovery and structural accuracy over strong baselines, while retaining robustness to missing, mismatched, and corrupted templates. Under a stringent random-template CDR-H3 evaluation, NT-ABDiff improves amino-acid recovery (AAR) from 30.03% to 39.47% and reduces RMSD from 3.160 to 2.915A; with train-set retrieval candidates, it achieves 39.50% AAR and 2.76 {ring} A RMSD. Code, processed splits, {ring} configuration files, and evaluation scripts are available at https://github.com/ShiDeng7rz/NT-ABDiff.

10.
arXiv (CS.CL) 2026-06-15

WorkBench Revisited: Workplace Agents Two Years On

作者:

The best agent on WorkBench in March 2024, GPT-4, completed 43% of tasks and took an unintended harmful action, such as emailing the wrong person, on 26% of them. We re-visit the benchmark in June 2026 and find that the best agent to date, Claude Opus 4.8, completes 89% and takes an unintended harmful action on 2.5%. Aside from this considerable progress in frontier agent performance, three things stand out. First, capability and safety go together on WorkBench rather than trade off, so the models that finish the most tasks also do the least unintended damage. Second, while several classes of error have been totally eliminated, frontier models still make some basic mistakes that occasionally result in irreversible harm, such as sending an email to the wrong person. Third, the rise of open-weight models has drastically lowered costs for a performance level that was previously only accessible to proprietary models, while frontier costs have stayed relatively stable. We release an updated version of the benchmark with data and code quality improvements, new model scores, and analysis of agent progress on WorkBench since 2024.

11.
medRxiv (Medicine) 2026-06-12

Home-based binocular serious games in virtual reality to treat visual acuity and stereovision in residual amblyopia: AMBER study

Objectives: Amblyopia is a pediatric visual disorder traditionally treated by patching the fellow eye, though many patients retain residual amblyopia post-treatment. Increasing evidence suggests that visual plasticity allows treat-ment beyond the classical therapeutic window. AMBER evaluated the efficacy of binocular serious games in virtual reality (VR) in residual amblyopia. Methods and Analysis: The monocentric, prospective, randomized, crossover trial (reported as case series) includ-ed 14 anisometropic, strabismic, or mixed residual amblyopia patients (6-35 years; 5 children, 9 adults). Participants underwent two 2-month intervention phases: optical correction (standard care) and standard care plus VR games (2.5 h/week), each with a 2-month follow-up. Best-corrected visual acuity (BCVA), stereoacuity, and reading speed were assessed (5 timepoints) using the Sloan and Landolt charts, the Titmus, TNO, Lang II, Asteroid, and Mnread tests. Compliance and adverse events (AE) were recorded. Results: VR training improved BCVA in 10 amblyopic eyes (Landolt and Sloan), with more pronounced effects in anisometropic patients. Six patients showed improved stereoacuity (Titmus; 4x mixed, 1x anisometropic, 1x stra-bismic amblyopia), persistent only in children (1x strabismic, 1x mixed amblyopia). Four improvements were ob-served with TNO (1x), Lang II (1x), Asteroid (0x), and MNread (1x). Despite positive trends, when comparing re-sults of individual patients, between both eyes, and with standard treatment, consistency of improvements cannot be conclusively demonstrated. One non-severe AE (dizziness) was reported. Conclusions: Following individual cases, VR training improved BCVA and stereoacuity, particularly in children and patients with high compliance. However, considering the cohort as a whole, consistency of effects has to be confirmed in larger groups. Thus, the methodologically sophisticated AMBER study revealed differences in VR treatment efficacy between amblyopia types, children/adults, endpoints and tests, offering precious data for the design of meaningful future studies. It shows that neurovisual plasticity gauged by VR-games offers safe, engaging treatment options for residual amblyopia.

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

Reasoning as Pattern Matching: Shared Mechanisms in Human and LLM Everyday Reasoning

arXiv:2606.13607v1 Announce Type: new Abstract: When large language models (LLMs) fail to generalize or make haphazard errors in reasoning, it is often taken as evidence that LLMs are not truly reasoning, but rather performing a kind of pattern matching. The implication is that people's behavior does not exhibit the same types of failures because human reasoning uses principled and abstract world models. We evaluate human participants and 25 LLMs on their ability to engage in common-sense reasoning about a variety of everyday situations and observe similar patterns of errors in both people and models. We then identify the set of attention heads driving LLM responses and find that these heads implement a form of pattern-matching. These attention heads allow us to predict seemingly inexplicable reasoning errors in people caused by ostensibly irrelevant prompt details. Taken together, our results suggest that everyday causal reasoning in people and LLMs is more consistent with a form of pattern-matching than with abstract world models.

13.
medRxiv (Medicine) 2026-06-15

Sociodemographic Disparities in Tafamidis Initiation and Clinical Outcomes in ATTR-CM Across the United States

BACKGROUND Transthyretin amyloid cardiomyopathy (ATTR-CM) is a progressive, life-threatening disease. Sociodemographic factors may influence time to treatment initiation and resulting clinical outcomes, yet these relationships are poorly characterized. OBJECTIVE Assess the effects of sex and race on tafamidis initiation and subsequent outcomes and their interaction with factors such as ATTR-CM type and social deprivation measures. METHODS A retrospective cohort analysis was conducted using the US Komodo Healthcare Map (01/2016-06/2024) among patients with amyloidosis, identified by ICD-10-CM diagnosis codes. Cumulative incidence of treatment initiation and survival probabilities for cardiovascular-related hospitalization (CVH) or death were estimated by Kaplan-Meier, stratified by sex and race. Cox proportional hazards models were fitted for both endpoints to estimate hazard ratios, adjusting for demographics and clinical characteristics. RESULTS Of 11,311 patients identified, White and Black patients (n=9,223) were included in subsequent analyses. Within 12 months of diagnosis, White women had the lowest cumulative incidence of tafamidis initiation (11.4%), followed by Black women (22.0%), Black men (26.7%), and White men (31.0%). Event-free survival at 12 months was lowest in Black women (42.9%), followed by Black men (46.8%), White women (48.6%), and White men (54.4%). Median (95% CI) time to CVH or death was shortest for Black women (8.0 months [6.8-10.0]) followed by Black men (9.9 months [8.8-12.0]), White women (11.0 months [9.6-13.0]), and White men (15.0 months [14.0-16.0]). CONCLUSIONS In this large, real-world cohort of US patients with ATTR-CM, sex and race contributed to disparities in tafamidis initiation and survival, underscoring compounded disparities in both access and outcomes.

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

PointDiffusion: Diffusion-Based Scene Completion in the Point Cloud Domain

Reconstructing dense 3D scenes from sparse LiDAR point clouds is a fundamental challenge in autonomous driving, where latent diffusion models offer a promising solution. However, existing approaches rely on object-level autoencoders that collapse into unstable global representations at outdoor scale and suffer from ground truth data corrupted by odometry drift that systematically degrades supervision quality. Furthermore, multi-step diffusion inference incurs prohibitive latency for real-time deployment. We propose a novel multi-token Gaussian VAE with cross-attention pooling for stable scene-scale LiDAR compression, combined with an anchor-based ICP ground truth refinement pipeline that eliminates drift-induced noise from training supervision. Together, these components enable a scaffold-free single-step diffusion completion model that achieves an approximately 16x reduction in squared Chamfer distance on SemanticKITTI seq. 08 (0.396 m^2 to 0.024 m^2), surpasses LiDiff and ScoreLiDAR by 17-19% and 10-11%, respectively, and operates at 25-143x lower inference latency. Our results demonstrate that data quality dominates model design in this regime and that multi-token latent spaces provide a stable first stage for latent diffusion-based scene completion.

15.
arXiv (math.PR) 2026-06-17

Absolute continuity, supports and idempotent splitting in categorical probability

arXiv:2308.00651v5 Announce Type: replace Abstract: Markov categories have recently turned out to be a powerful high-level framework for probability and statistics. They accommodate purely categorical definitions of notions like conditional probability and almost sure equality, as well as proofs of fundamental results such as the Hewitt–Savage 0/1 Law, the de Finetti Theorem and the Ergodic Decomposition Theorem. In this work, we develop additional relevant notions from probability theory in the setting of Markov categories. This comprises improved versions of previously introduced definitions of absolute continuity and supports, as well as a detailed study of idempotents and idempotent splitting in Markov categories. Our main result on idempotent splitting is that every idempotent measurable Markov kernel between standard Borel spaces splits across another standard Borel space, and we derive this as an instance of a general categorical criterion for idempotent splitting in Markov categories.

16.
medRxiv (Medicine) 2026-06-10

Gendered pathways to adolescent mental health: An empirical assessment of a new conceptual framework

Introduction Gender norms and roles are important determinants of physical and mental health in the key period of adolescence. Yet, the gendered pathways to mental health in adolescents are not fully understood. Using a conceptual framework for global adolescent mental health that we developed based on a Delphi process, we empirically investigated the associations between six gender-related constructs and adolescent mental health. Methods We used cross-sectional Gender and Adolescence: Global Evidence (GAGE) data from Ethiopia (2020) to explore the associations between sex, gender norms, psychological competencies, gender attitudes, gender roles, with the latter two also serving as mediators, and psychological distress (GHQ-12), using Structural Equation Modelling (SEM). Results The SEM model contained measurements from 1,584 adolescents, including 843 girls and 741 boys, with a median age of 13 years. Out of 14 pathways tested, we found statistically significant associations between psychological competencies and psychological distress; sex and gender attitudes; and between gender norms and psychological competencies, gender attitudes, and gender roles. Hence, the gender-related constructs were mostly associated with each other, rather than with psychological distress. Conclusion The gender-related constructs are strongly interrelated, thereby attenuating their individual effects on psychological distress. The interplay of gender-related constructs should be considered when developing interventions to promote mental health in adolescents.

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

Not all Jensen-Shannon Divergence Estimators are Equal

arXiv:2606.16411v1 Announce Type: new Abstract: The Jensen-Shannon divergence is widely reported as a scalar measure of fidelity for synthetic tabular data. Yet, in practice, it is estimated from finite samples using protocols that are often underspecified. This creates a measurement problem. Although the population divergence is well defined, the empirical value depends on the estimator family, sampling protocol, calibration, dimensionality, and class balance. We show that different protocols can yield non-comparable values: marginal-based estimators ignore dependencies in the joint distribution and can severely underestimate divergence, while classifier-based estimators capture joint structure but exhibit strong estimator dependence. We systematically study this behavior across controlled settings with reference divergences and real-world synthetic tabular benchmarks. Our analysis reveals dependence blindness in marginal estimators, prior-shift bias under class imbalance, and estimator sensitivity in high dimensions. To address prior shift, we derive a closed-form posterior correction for classifier-based Jensen-Shannon estimation. Our results show that empirical Jensen-Shannon divergence values are inherently protocol-dependent, making explicit specification of the estimation procedure necessary for meaningful comparison. We provide practical guidelines and an open-source tool for estimator-aware Jensen-Shannon evaluation.

18.
arXiv (quant-ph) 2026-06-19

The use of Peres lattices in periodically driven systems

arXiv:2606.20009v1 Announce Type: new Abstract: We demonstrate the strength of the method of Peres lattices in periodically driven quantum systems. The method, which has previously been used mostly in stationary systems, enables us to efficiently detect resonances in the driven system, to monitor the onset of chaos, and to recognize critical properties of the Floquet modes. It also allows quick comparisons of the spectra of Floquet modes for various driving Hamiltonians and transparent tests of the iterative approximation techniques based on effective stationary Hamiltonians.

19.
arXiv (quant-ph) 2026-06-16

Ultrastrongly coupled open systems and fine grained time

arXiv:2606.16634v1 Announce Type: new Abstract: We study the dynamics of a d-level quantum system coupled to a bosonic reservoir when the coupling constant is large. It is known that in the limit of infinite coupling strength, the system undergoes an instantaneous nonselective measurement, resulting in the immediate decoherence in the measurement basis, followed by a unitary Zeno dynamics. Here we resolve this dynamical process by introducing a fine grained scaling regime of short times proportional to the inverse coupling. We provide a rigorous derivation of the open system dynamics in this regime of ultrastrong coupling and demonstrate how decoherence unfolds continuously in the new time scale. We show that Markovian dynamics which are not given by semigroups arise naturally, in contrast to what happens in the weak coupling theory.

20.
arXiv (CS.CL) 2026-06-18

Rethinking Reward Supervision: Rubric-Conditioned Self-Distillation

Post-training of reasoning language models is commonly driven by supervised distillation and reinforcement learning with verifiable rewards. Distillation often relies on chain-of-thought annotations that are expensive to obtain and may themselves be noisy, incomplete, or partially incorrect; even when the final solution is correct, an imperfect rationale can interfere with learning. Reinforcement learning with verified rewards, on the other hand, typically compresses evaluative feedback into a scalar signal, obscuring which aspects of a response should be improved. We propose Rubric-Conditioned Self-Distillation, a framework that incorporates rubrics as structured, fine-grained feedback for on-policy self-distillation. Our method conditions the teacher model on criterion-level rubrics and uses it to provide token-level guidance on the student's own sampled trajectories. This design avoids treating a single reference rationale as the sole supervision target. Instead, rubrics specify what a strong response should satisfy, enabling more fine-grained credit assignment over the reasoning process than scalar reward optimization. We instantiate this framework with a two-stage pipeline that first learns to generate task-specific rubrics and then trains a rubric-guided reasoner. We evaluate on a diverse suite of science reasoning benchmarks and results show that rubric-conditioned self-distillation effectively converts rubric-level criteria into token-level guidance over the reasoning process, surpassing GRPO by 1.0 points and OPSD by 0.9 points on average.

21.
arXiv (quant-ph) 2026-06-17

Unveiling Hierarchical Invariants in Multiphoton Linear Optics

arXiv:2506.12857v2 Announce Type: replace Abstract: Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.

22.
arXiv (CS.LG) 2026-06-16

Repeated Bilateral Trade: The Quest for Fairness

arXiv:2606.15369v1 Announce Type: new Abstract: We study repeated bilateral trade from a fairness perspective. At each round, a fresh seller-buyer pair arrives, and the platform posts a price before observing the traders' valuations. Trade occurs only if both agents accept the price. Rather than maximizing only the gain from trade, we consider platforms that seek balanced divisions of the generated surplus. We show that natural fairness desiderata lead to a one-parameter Rawls-to-Nash family of fair-gain objectives, obtained by aggregating the seller's and buyer's net gains through nonpositive Hölder means. Unlike the standard gain-from-trade objective and the Rawlsian fair-gain objective studied in prior work, our proposed objectives induce a new statistical structure in which expected rewards are recovered from threshold feedback through a two-dimensional singular-kernel integral identity. This leads to a nonstandard pure-exploration problem whose natural estimators are rectangular double sums with row-column dependence and singular weights. Assuming independent i.i.d. seller and buyer valuation sequences with arbitrary unknown marginals, we characterize the optimal learning rates for the whole Rawls-to-Nash family of fair-gain objectives, giving matching fixed-confidence sample-complexity and regret bounds up to polylogarithmic factors.

23.
arXiv (CS.CL) 2026-06-12

Select to Think: Unlocking SLM Potential with Local Sufficiency

Small language models (SLMs) offer efficient deployment, yet they often lag behind their larger counterparts (LLMs) in reasoning. Existing remedies either invoke an LLM at points of reasoning divergence, incurring substantial latency and cost, or rely on standard distillation, which is limited by the SLM's capacity to accurately mimic the LLM's complex generative distribution. We address this dilemma by identifying local sufficiency: at divergence points, the LLM's preferred token often resides within the SLM's top-K next-token predictions, even when failing to emerge as the SLM top-1 choice. We therefore propose Select to Think (S2T), which reframes the LLM's role from open-ended generation to selection among the SLM's proposals, simplifying the supervision signal to discrete candidate rankings. Leveraging this, we introduce S2T-Local, which distills the selection logic into the SLM, empowering it to perform autonomous re-ranking without inference-time LLM dependency. Empirically, a 1.5B SLM's top-8 candidates contain the 32B LLM's choice with a 95% hit rate, and S2T-Local improves the 1.5B SLM's Math Avg. over greedy decoding by 24.1% relative gain, matching the efficacy of 8-path self-consistency with single-trajectory efficiency.

24.
arXiv (CS.LG) 2026-06-18

Regular Fourier Features for Nonstationary Gaussian Processes

arXiv:2602.23006v2 Announce Type: replace-cross Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation and treating the spectral density as a probability distribution suitable for Monte Carlo approximation. Although this probabilistic interpretation is valid for stationary processes, it is overly restrictive for the nonstationary case, where spectral densities are generally not probability measures. We propose regular Fourier features for harmonizable processes to avoid this limitation. Our method discretizes the spectral representation directly, preserving the correlation structure among spectral weights without requiring probability assumptions. Under a finite-spectral-support assumption, this yields an efficient low-rank approximation that is consistent and positive semi-definite by construction. When the spectral density is unknown, the framework extends naturally to kernel learning from data. We demonstrate the method on locally stationary and harmonizable mixture kernels, the latter with a complex-valued spectral density, and apply the kernel-learning extension to real and synthetic data.

25.
bioRxiv (Bioinfo) 2026-06-21

GENATATORs: ab initio Gene Annotation With DNA Language Models

Inference of gene structure and location from genome sequences - known as de novo gene annotation - is a fundamental task in biological research. However, sequence grammar encoding gene structure is complex and poorly understood, often requiring costly transcriptomic data for accurate gene annotation. In this work, we benchmark current solutions and develop new methods of gene annotation. We show that pretrained DNA language model (DNA LM) embeddings do not capture the features necessary for precise gene segmentation, and that task-specific fine-tuning remains essential. We comprehensively evaluate the impact of model architecture, training strategy, receptive field size, dataset composition, and data augmentations on gene segmentation performance. We revisit standard evaluation protocols, showing that commonly used per-token and per-sequence metrics fail to capture the challenges of real-world gene annotation. We introduce and theoretically justify new biologically grounded metrics, along with benchmarking datasets that better capture annotation quality. We show that fine-tuned DNA LMs outperform existing annotation tools, generalizing across species separated by hundreds of millions of years from those seen during training, and providing segmentation of previously intractable non-coding transcripts and untranslated regions of protein-coding genes. Our results thus provide a foundation for new biological applications centered on accurate gene annotation.