Computer Vision
Papers
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All of arXiv
Wednesday 7 October
Whole slide image (WSI) analysis in computational pathology follows a multiple instance learning (MIL) pipeline where patch embeddings are extracted independently and aggregated for slide-level prediction, but within-slide variance from staining, scanner, and local texture can overwhelm the discriminative signal. We propose Masked Feature Encoding for Multiple Instance Learning (MFE-MIL), a feature-space masking framework that trains a lightweight MLP adapter jointly with a window-based masked reconstruction branch and a MIL classification head. The two objectives are complementary. Classification guides the adapter to suppress within-slide patch variance, while window-based masked reconstruction provides an auxiliary regularizer for the adapted features without using patch coordinates, coordinate graphs, or segmentation preprocessing. The raster patch-extraction order is used only as a weak implicit prior. At inference, the decoder is removed, leaving only the adapter and MIL head. Across CAMELYON16/17, PANDA, and TCGA-BRCA with four diverse encoders, MFE-MIL improves ACC/F1 for nearly all tested aggregator-encoder settings and AUC in most, outperforms coordinate-based spatial methods (CAMIL), and achieves higher AUC than 2DMamba on three of four datasets (UNI). On five TCGA survival cohorts it improves the average concordance index for every aggregator tested, its most consistent gain. Code is available at https://github.com/AtlasAnalyticsLab/MFE-MIL.
Other Statistics
Generative AI in Publishing: An Editors' Panel on Ethics and Policies
Generative artificial intelligence (GenAI) is reshaping scholarly research faster than journals have developed stable norms for its use. This article presents an edited thematic account of a 2026 Joint Statistical Meetings panel that brought together editorial perspectives from mathematical statistics, data science, biomedical statistics, and general statistical scholarship. The discussion examines journal policies, disclosure, authorship and research integrity, peer-review confidentiality, researcher training, editorial workload, access, and possible future models of scholarly publishing. Panelists shared commitments to human accountability, the protection of confidential submissions, and disclosure of consequential assistance, while offering different recommendations on assistance with research ideas and proofs, disclosure requirements, automated review, and policy enforcement. By distinguishing shared principles from unresolved implementation questions, the article clarifies the choices facing statistical publishing and outlines an agenda for evaluating policies and practices as GenAI evolves. The account seeks to foster continued discussion of GenAI in scientific communication and encourage statistical organizations to develop more robust operational standards.
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Statistics Applications
Neutral Is Not Free: Evaluating Downside Risk in Neutral Launches
Evaluating "neutral launches" (e.g., infrastructure upgrades) using traditional confidence interval overlap is flawed: it is dangerously permissive with scarce data and excessively restrictive with abundant data. To resolve this, this paper introduces Expected Bayesian Loss (EBL), a continuous metric that quantifies both the probability and expected severity of metric degradation. Computable directly from standard frequentist estimates, EBL explicitly penalizes empirical noise and high-variance experiments. Validated against expert decisions, EBL provides experimentation platforms with a rigorous, tunable guardrail that aligns statistical safety with institutional risk appetite.
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Machine Learning
Evaluating Sequence Assembly Strategies for Differentially Private Synthetic Time-Series Forecasting
Differentially private time-series generators commonly produce fixed-length synthetic windows, whereas downstream forecasting models often require long continuous training sequences. How these windows are assembled after generation can therefore alter the effective synthetic data presented to a forecaster, even when the trained generator remains unchanged. We study this post-generation sequence assembly process by systematically varying overlap rates and window-weighting schemes and evaluating the resulting sequences in terms of boundary continuity, statistical and temporal fidelity, and Train-on-Synthetic-Test-on-Real (TSTR) forecasting utility. Across four types of public datasets (ETTh1, ETTm1, Weather, and Appliances) and five forecasting models, the results reveal a clear forecaster-dependent assembly principle: downstream TSTR utility is jointly shaped by the forecaster, overlap rate, and window-weighting scheme, leading to distinct assembly preferences across forecasting models. Increased overlap generally improves boundary continuity, but improvements in continuity or individual fidelity diagnostics do not consistently reduce forecasting error, indicating that these diagnostics alone are insufficient for selecting assembly configurations. Complete five-forecaster assembly grids, together with matched Train-on-Real-Test-on-Real (TRTR) references, further characterize these regularities and quantify assembly-dependent utility relative to real-data training. We then validate the identified principles through additional analyses of robustness and generator variability.
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Combinatorics
The Domination Reciprocal Mean Square Index
We introduce the Domination Reciprocal Mean Square index \(DRMS\), a new domination-degree-based topological index obtained by replacing the ordinary degree in the reciprocal mean square index with the domination degree. We establish elementary bounds in terms of graph size and extremal domination degrees, derive a one-parameter family of sharp lower bounds via the power mean, and obtain sharp bounds in terms of several well-known domination-degree-based indices, with a full characterization of the equality cases. We also compute closed-form expressions for \(DRMS\) on several standard graph families and for the corona product of two graphs.
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Quantum Physics
Dynamics of Work Extraction in Multipartite Atomic Systems: Role of Correlations and Relative Entropy
We investigate the dynamics of quantum ergotropy in a multipartite system of two-level atoms interacting with a quantized field. The role of multipartite quantum mutual information and quantum relative entropy is analyzed to understand how correlations and the distinguishability between the passive state and the product of local states affect the extractable work. Numerical results for systems containing two to five atoms show that the maximum ergotropy does not increase linearly with the system size, while the intervals of zero ergotropy are gradually modified and suppressed for larger systems. We also study the effect of the average thermal photon number and different initial atomic states. Increasing the thermal photon number mainly reduces the relative-entropy contribution, whereas the initial state strongly influences both the magnitude and persistence of ergotropy. Among the considered states, the partially entangled state provides the largest and more persistent extractable work, while the mixed GHZ state gives the smallest ergotropy. These results highlight the importance of multipartite correlations, thermal effects, and state preparation in controlling quantum work extraction and may be useful for future studies of quantum batteries and quantum power.
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High Energy Physics (Phenomenology)
Is the Light Neutralino Dark Matter Still Viable in the MSSM After the LZ-2024 Results?
In the Minimal Supersymmetric Standard Model with heavy sfermions, a sub-hundred-GeV Bino-like neutralino can thermally achieve the observed dark matter abundance only through $h$- or $Z$-resonant annihilation. Since the couplings governing these resonances simultaneously determine the spin-independent and spin-dependent scattering off nucleons, reproducing the relic density imposes irreducible lower envelopes on the scattering cross sections. We evaluate these bounds including the complete one-loop corrections to these vertices, which enhance the direct-detection rates by up to $50\%$ and $30\%$, respectively, adopt the FLAG-2024 nucleon matrix elements with their most adverse $3\sigma$ shifts, and confront the predictions with a likelihood-based recast of the LZ data. We find that the LZ-2024 results exclude both resonant scenarios at conservative one-sided significances exceeding $5.9\sigma$ and $4.1\sigma$, respectively, irrespective of whether the neutralino constitutes all or only part of the dark matter, and independently of LHC electroweakino searches.
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Machine Learning
Finite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows
Wasserstein gradient flow extends gradient descent to probability measures. Its Hessian-guided perturbed variant (PWGF) adds Gaussian perturbations to escape saddle points in nonconvex problems. We investigate when its approximation by finitely many interacting particles remains accurate over growing time horizons. Our analysis retains the curvature accumulated along the population-driven reference path: negative curvature can amplify approximation errors, while subsequent positive curvature can damp their influence. This captures favorable scenarios in which temporary instability is compatible with accurate tracking over growing horizons. Under regularity assumptions and a prescribed common perturbation schedule, we prove particle and objective-value tracking bounds on a high-probability event for reference paths satisfying explicit conditions on accumulated curvature. To handle state-dependent Gaussian jumps, we construct a population-first coupling that preserves the reference particles' conditional independence and reduces jump errors to covariance comparison. We verify the conditions in a variance-plus-cosine model, where curvature recovery yields a growing-horizon tracking guarantee. We also establish local attraction, transverse descent, and positive second variation in two regions of a regularized matrix-factorization model, motivating a positive-negative-positive curvature pattern.
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Quantum Physics
Engineering of Chirped Apodized Sources for Quantum Spectroscopy
Quantum sources of light are of paramount importance for the development of photonic quantum technologies. The growing demand for bright, efficient, and spectrally engineered photonic sources for applications in quantum sensing, spectroscopy, and imaging has motivated the development of tailored nonlinear crystals. Here, we report on the development and characterization of chirped, apodized KTP crystals specifically engineered for quantum spectroscopy. Our source exhibits an unprecedented bandwidth in a highly non-degenerate configuration, demonstrating its potential to support quantum spectroscopy protocols over broad spectral ranges while enabling significantly shorter measurement times.
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Differential Geometry
Extremal Sasaki manifolds and weighted K-stability
We remove the log-concavity assumption on the weight in the analytic weighted Yau–Tian–Donaldson correspondence established in [arXiv:2406.10939, arXiv:2407.09929, arXiv:2503.22183] and discuss applications to Sasaki and conformally Kähler Einstein–Maxwell geometries.
Cosmology and Nongalactic Astrophysics
Angular Baryon Acoustic Oscillations with DESI DR1
We present the angular BAO analysis using DESI DR1 data as a complementary approach to DESI's primary 3D BAO analysis. We perform the analysis using the two-point angular correlation function $w(\theta)$ in tomographic redshift shells of $\delta z = 0.02, 0.05$, spanning the redshift range $0.4 < z < 2.1$ using the DESI tracers: LRG1, LRG2, LRG3+ELG1, ELG2 and QSO. The main benefit is that it requires no fiducial cosmology to convert redshifts into distances and yields a direct measurement of the transverse dilation parameter $\alpha_{\perp}(z)$. We fit each tracer with a single shared $\alpha_{\perp}(z)$ using templates constructed in a fiducial cosmology and a mock-based covariance from 1000 EZmock realisations. We measure $\alpha_\perp$ to $2.5$ – $4.2\%$ precision in each tracer bin. Compared to the $D_M/r_{\rm d}$ measurements obtained from the DESI DR1 3D analysis for the same tracers, our results are consistent within the statistical precision. We find no evidence for a shift in the transverse BAO scale between the 2D and 3D analyses. Flat $\Lambda$CDM fits to $\alpha_\perp(z)$ alone give $\Omega_{\rm m} = 0.198^{+0.045}_{-0.068}$, $1.6\sigma$ below the DESI 3D value, and the pull is dominated by the $z =1.49$ QSO bin, whose $\alpha_\perp(z=1.49)=1.058\pm0.028$ sits $\sim 2\sigma$ above the fiducial. Restricting to LRGs and ELGs only, our $\Omega_{\rm m}$ and $H_0 r_{\rm d}$ agree with the 3D transverse-only fit over the same bins to better than $0.1\sigma$. With an additional BBN prior, the full 2D sample gives $H_0 = 63.9^{+1.9}_{-3.3}\, {\rm km\,s^{-1}\,Mpc^{-1}}$. This pipeline is implementable on forthcoming DESI data releases, where the increase in volume and sampling density will determine if the QSO offset persists and will also tighten 2D BAO constraints.
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Machine Learning (Statistics)
RoBART: Bayesian Additive Regression Trees with Tree-Specific Rotations
Bayesian additive regression trees (BART) can require many splits to approximate boundaries misaligned with the predictor axes. RoBART assigns each tree a rotation shared by all internal nodes, retaining axis-aligned splits in rotated coordinates and constant leaves. We jointly propose a Givens rotation sequence and cutpoints on the resulting grid by Metropolis-Hastings and establish reversibility with respect to the conditional posterior with leaf means integrated out. For additive functions with component-specific rotations and anisotropic Hölder smoothness, we prove posterior contraction in empirical $L_2$ distance and for the noise standard deviation. Under the stated prior, design, and grid conditions, with fixed numbers of predictors, trees, and components and no more components than trees, the rate is a sum of componentwise rates determined by smoothness and the number of rotated coordinates used. We also establish a posterior contraction lower bound showing that there exist functions for which RoBART adapts to the intrinsic dimension but axis-aligned BART does not.
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Machine Learning
Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems
A natural strategy for inverse problems with scarce labelled data is to transfer relational structure learned from abundant forward-simulation data. We show this strategy fails systematically, even when it satisfies the standard theoretical justification for why structure should help. We prove that approximate structure provides estimation-error benefits whenever the edge error satisfies $\Delta < n^2 - kn$, reducing sample complexity from $O(n^2)$ to $O(kn+\Delta)$. Structure learned via Neural Relational Inference (NRI) from dynamics prediction satisfies this condition, yet on a source-localisation task across 180 CFD-simulated hydrogen-leak scenarios and 180 acoustic scenarios, it degrades performance by 116% and 201% relative to a flexible, task-optimised attention baseline, while a physics-based prior (Green's function) degrades by only 69-72%. Four independent lines of evidence show this is not a tuning failure: NRI improves only 0.5% when given 18x more training data (versus 16.6% for the task-optimised baseline, $p<0.001$); performance is insensitive to the NRI edge threshold across a wide range; the dynamics-learned graph overlaps the task-optimal graph on only 6% of edges; and two further dynamics-derived structure estimators (correlation- and mutual-information-based) show no measurable benefit over a structure-free baseline, with the correlation-based estimator performing markedly worse. We formalise this gap as a statement about approximation error that the edge-accuracy condition cannot control, and we provide a lightweight transferability test (Jaccard similarity against a partially-observed target-task graph) that separates successful from failed transfer in all four domain/structure pairs we evaluate, using under an hour of computation and 15-20% of target-domain data; we present this as a heuristic calibrated on few cases, not a validated general threshold.
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Number Theory
Intersecting a curve in an abelian variety with multiples of another curve
Levin asked what can be said about the locus of points lying on a given curve in $\mathbb{G}_m^n$ that have a non-zero integer power on another given curve in $\mathbb{G}_m^n$ for $n \geq 3$. We give a definite answer to the abelian analog of Levin's question, proving what is predicted by the Zilber-Pink conjecture in this case. An important ingredient in our proof is a strengthening of a height inequality by Vojta and Rémond.
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Information Theory
Sequential Random Sampling PIR with Multiple Colluding Servers in DNA-Based Data Storage
As DNA-based data storage evolves, protecting user privacy during data retrieval has become increasingly important. We study sequential random sampling DNA private information retrieval (SRS DNA PIR) with multiple colluding random sampling servers, where the database is partitioned into servers of equal size. We investigate the tradeoff between the download cost, defined as the expected number of queries, and the privacy leakage, measured by mutual information. We derive lower bounds on this tradeoff, including a bound given by an optimization problem. This bound is tight when each server stores two files, and we construct schemes that attain it. For servers of any size, we construct schemes that apply a single-server scheme to a randomly selected subset of servers.
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Machine Learning
OrthoGen: A Generative Orthogonal Learner for Time-Varying Treatments
Estimating conditional distributional potential outcomes (CDPOs) over time is important in medicine (e.g., to estimate patient-specific risks under different treatment sequences). However, this task is challenging because of time-varying confounding, yet existing adjustment strategies for this task are limited. In this paper, we aim to learn CDPOs under time-varying treatments using flexible generative models. Our contributions are two-fold. (1) We introduce a tailored adjustment strategy for our setting, namely, generative recursive g-computation. Our adjustment strategy recursively propagates full conditional outcome distributions rather than conditional means, modeling the variables of interest directly rather than full trajectories. Building on our adjustment strategy, we formulate simple generative learners for CDPO estimation. However, these learners can be sensitive to nuisance estimation errors, which motivates an orthogonal learner. (2) We thus introduce OrthoGen, a Neyman-orthogonal and doubly robust generative learner. Importantly, we show that OrthoGen further achieves rate double robustness and quasi-oracle efficiency under suitable conditions. Our learners are flexible and can be instantiated with different generative backbones (e.g., normalizing flows and diffusion models). Across experiments with synthetic, semi-synthetic and real-world datasets, we find that OrthoGen is highly effective. To the best of our knowledge, we are the first to propose a generative orthogonal learner for estimating CDPOs under time-varying treatments.
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Logic
Points and their multiples on curves in powers of simple abelian varieties
Let $G$ be a simple abelian variety of dimension $g \in \mathbb{N}$ defined over $\mathbb{Q}^\mathrm{alg}$ and let $C_1, C_2 \subseteq G^N(\mathbb{C})$ be irreducible closed algebraic curves with $N \geq 3$. Further assume that at least one of $C_1$ and $C_2$ is not defined over $\mathbb{Q}^\mathrm{alg}$. Suppose that there does not exist an algebraic subgroup $H_1 \subseteq G^N(\mathbb{C})$ of dimension $g$ such that $C_1 \subseteq H_1$ and that there does not exist an algebraic subgroup $H_2 \subseteq G^N(\mathbb{C})$ of dimension $2g$ such that $C_1 \cup C_2 \subseteq H_2$. Denoting $\mathcal{N} = \{n \in \mathbb{N} \ | \ [n]C_1 \subseteq C_2\}$, we prove that $\bigcup_{n \in \mathbb{N} \setminus \mathcal{N}}\{x \in C_1 \ | \ nx \in C_2\}$ is finite.
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Sound
CARES: A Controlled Synthetic Benchmark of Speaker Reactions to Sound
Automatic audio scene description turns a recording into a text account of a situation. One difficulty is deciding which elements of the audio should be kept, since a description cannot include them all. Annotators disagree about this, making a ground truth hard to obtain. In this work, we first define the ground truth, then generate the data. We focus on audio events and define sound salience with a simple rule: a sound is salient when a speaker audibly reacts to it. For scale and variety, a controlled set of scenarios fixes the ground truth, and a language model writes the dialogues. The resulting corpus, CARES, contains 10,000 two-speaker scenes. We then benchmark six audio-language models on three tasks: identifying the scene, tagging the sounds present, and classifying reactions. We show that these models hear the sounds but miss how the speakers react to them.
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Theoretical Economics
Identifiable Preference Types and Optimal Menu-Choice Experiments
A planner wants to elicit partial information about a subject's preference relation. Preferences are grouped into “types" relevant to the planner's purpose. Can the planner identify the subject's type through menu-choice data or experiment, without distinguishing preferences within the same type? We provide a complete answer by characterizing identifiable type spaces. The characterization uses a novel geometric condition, called face consistency, which governs distinctions within and across square and hexagonal faces of the permutohedron. For every identifiable type space, we explicitly construct the unique irreducible identifying experiment from its boundary. This experiment is optimal among all identifying experiments under any cost criterion for which adding menus cannot reduce cost. Using the equivalence between identifiability and elicitation with acts, as shown in Azrieli et al. (2021), we study symmetric policies requesting unranked shortlists that contain only acceptable products, include every product preferred to a selected one, and are nonempty whenever an acceptable product exists. Only two such policies are elicitable with acts: requesting the favorite acceptable product or the entire acceptable set.
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Geometric Topology
Computations of the slice genus and the unknotting number of links via machine learning
Links are disjoint unions of circles smoothly embedded in $S^3$. We use reinforcement learning and Bayesian optimisation to obtain new upper bounds on several link invariants that are not known to be algorithmically computable: the slice genus and the unknotting number for links, and the strong slice genus for algebraically split links. We also compute lower bounds using known invariants. Combining the upper and lower bounds, we obtain new exact values in many cases. Our unknotting agents can reproduce the non-additivity of the unknotting number for several counterexamples due to Brittenham and Hermiller, in some cases finding new unknotting trajectories.
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Optimization and Control
Breaking the Odd Cycle: Regularization and First-Order Optimization for the Maximum $s$-Plex Problem
Building on a new regularized continuous formulation which avoids spurious solutions of the maximum $s$-plex problem, we develop a tailored block-coordinate first-order method that combines away-step Frank-Wolfe updates on the standard simplex with linear optimization over the fractional $b$-matching polytope. We establish finite stabilization of the auxiliary variables, convergence to stationary points, and finite support identification under suitable conditions. Numerical experiments on standard benchmark graphs show that, also in practice, regularization avoids the support-identification failures observed with the original cubic formulation and enables the proposed method to quickly find high-quality $s$-plexes.
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Atmospheric and Oceanic Physics
Three-dimensional Lagrangian ecosystems: carbon dynamics and potential for artificial fertilization
Transient supplies of nutrients to the surface ocean, both natural and artificial, stimulate blooms of phytoplankton and the formation of organic matter, driving air-sea gradients and uptake of CO$_2$. However, quantifying the associated carbon budget remains challenging, as it requires tracking the coupled biophysical evolution of water masses while they are transported, stretched and diluted. Here, we present an idealized three-dimensional model that describes biomass production and carbon dynamics within a Lagrangian patch in the ocean. The framework reproduces observed biogeochemical patterns from an artificial fertilization experiment and provides integrated metrics for the local carbon budget. Utilizing large ensembles of simulations, we examine the sensitivity of patch-scale primary production and carbon uptake to biochemical and physical factors. Our results show that patch dilution can enhance the ecosystem response, and how carbon uptake is sensitive to initial injected area, horizontal divergence and vertical diffusivity. In the context of renewed interest in ocean fertilization strategies for climate mitigation, our approach can thus provide quantitative tools to assess their efficacy and potential.
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Machine Learning
How to train your model organism
Model organisms of alignment-relevant behaviors (e.g., backdoors, sycophancy, spurious correlations) have emerged as a key tool for evaluating whitebox interpretability techniques. We argue that the prevailing practice of training model organisms to a single objective of installing the target behavior is insufficient and propose validating model organisms with respect to three objectives with associated metrics: target-behavior installation, general-capability preservation (i.e., parametric knowledge, chat quality), and output naturalness (i.e., CoT and activations). We re-visit two publicly released organism suites using this validation framework and show that (1) chat quality and CoT naturalness degrade substantially across training recipes, and (2) validation metrics predict how well interpretability methods recover the installed behavior, e.g., a logit lens readout covaries with an organism's general capabilities. We introduce a multi-objective training approach based on model merging to train more realistic model organisms. Finally, on a new suite of model organisms targeting demographic biases in clinical reasoning, we compare training recipes and find that DPO training stays closer to the base model than supervised finetuning, and the proposed model optimization approach better preserves capabilities and naturalness. Auditing this suite with an investigator agent, we again observe validation metrics tracking bias recovery. In sum, training methods shape the interpretability conclusions an organism supports, and we argue that one should consider multiple objectives to draw generalizable conclusions about interpretability methods using (realistic) model organisms.
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Quantum Algebra
Chiral Extensions of Cotangent Yangian
We construct chiral extensions of the cotangent Yangian using vertex algebroids. At zero level, the construction yields a vertex algebra with a compatible coproduct, whose Zhu reduction recovers the cotangent Yangian of Abedin and Niu. We also construct vertex algebra extensions at non-zero levels and study level-additive coproducts. The zero-level vertex algebra admits two natural quasi-conformal structures. We compute the corresponding sphere one-point conformal blocks and equip each block space with an associative product induced by the coproduct. For the first quasi-conformal structure, the blocks space can be identified with the dual of a certain Lie algebroid homology; for the second, we describe the block algebra and its classical limit in terms of mini-twistor geometry.
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Artificial Intelligence
GAGR-Lab: Evaluating Joint Spatial-Geometric and Analytic Function Reasoning
Joint spatial-geometric and analytic function reasoning requires translating a perceived spatial configuration into a symbolic function whose executed curve satisfies geometric constraints. We present GAGR-Lab, a framework for measuring this capability through Cartesian game scenes, explicit function semantics, and authoritative Rust trajectory execution. It distinguishes spatial perception, metric grounding, geometric relations, function interpretation, function construction, and constrained synthesis. We specify four configurable scene-difficulty presets and a prospective 24-cell diagnostic design, while reporting only the subset actually evaluated. A bounded pilot of one hosted model (Llama 3.2 11B Vision Instruct) using two API credentials as execution replicas yields 72 balanced games with 432 attempts, 429 valid provider responses, and no target hits; exploratory ordinary-function prompt variants also fail to hit, while the structured localization interface yields no scoreable outputs. A privileged analytic search control independently succeeds on 600 directional cases from 300 generated scenes, with exact repeatability and 1,200 successful vertical-reflection or translation checks. The framework separates serving reliability, symbolic compliance, and geometric success, and preserves exact model-visible inputs and realized paths. A staged protocol outlines diagnostic calibration, held-out replication, multi-model comparison, and paired robustness tests. The contribution is an operational research framework with an executed pilot and a clearly identified prospective study plan; the full difficulty matrix and comparative model results remain untested.
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Commutative Algebra
On an ideal membership problem
Suppose $f_1, \dots, f_{n+1}$ are elements of a regular ring $R$, where $n := \dim R$. The first author proved that $f_1^n \cdots f_{n+1}^n \in (f_1^{n+1}, \dots, f_{n+1}^{n+1})R$; this uses the Brian\c con-Skoda theorem — no simpler proof is known, as far as we are aware. We show here that this result is optimal in many respects. On the other hand, when the $f_i$ are homogeneous general polynomials of a fixed degree in $R := \mathbb{F}[x_1,\dots,x_n]$, for $\mathbb{F}$ a field of characteristic zero, we prove that $f_1 \cdots f_{n+1} \in (f_1^2, \dots, f_{n+1}^2)R$.
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Machine Learning
Robust Decentralized Fairness Auditing
Emerging legislation requires large language models (LLMs) to be audited for compliance with regulatory standards, particularly fairness. Such black-box audits typically assume a single auditor with access to a large, representative set of queries. In practice, it can be difficult for an auditor to obtain such a query set, but multiple auditors can together cover the relevant demographic groups by auditing the LLM collaboratively with their individual query sets. However, relying on multiple auditors raises a fundamental trust problem, as they may act on behalf of the LLM provider to portray a misleading appearance of fairness, i.e., fairwashing. We propose Auditopus, a novel approach for robust decentralized fairness auditing. In Auditopus, auditing proceeds in rounds without a central server. In each round, every auditor issues a fixed number of queries to the LLM, and sends only cumulative statistics vectors of its query results to other auditors instead of sensitive queries in clear. The fairness of the audited LLM is then estimated by aggregating all the vectors. We show theoretically and empirically that even a single adversarial auditor in the network can steer this estimate by fabricating the vectors it sends, making an unfair LLM appear fair. To address this threat, Auditopus has each honest auditor locally down-weight any auditor whose cumulative statistics vectors are statistically inconsistent with previous ones. We implement Auditopus and compare it to robust aggregation baselines on two datasets with two pre-trained LLMs. Against an attacker that optimizes the vectors it sends to make the LLM appear fair, Auditopus reduces audit error by up to 78% on average relative to no defense and at least 62% relative to the robust aggregation baselines. Even when 49% of the auditors are adversarial, Auditopus never lets a very unfair or moderately unfair LLM pass as fair.
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Robotics
Benchmarking Behavioral Steerability in Behavior Foundation Models
Behavior Foundation Models (BFMs) are emerging as a paradigm for translating human intentions into executable humanoid behaviors. As these models evolve beyond behavior generation toward general-purpose behavioral systems, a fundamental question arises: can they be reliably steered according to user intentions? In this paper, we introduce the concept of behavioral steerability, defined as the ability of BFMs to faithfully generate behaviors that satisfy user-specified intentions. To study this capability, we present RoboSteer, the first benchmark for behavioral steerability in BFMs. RoboSteer organizes behavioral steerability into a three-level hierarchy-Conditional Steering, Constraint Steering, and Compositional Steering-and establishes a unified evaluation framework supported by a large-scale multimodal motion corpus. Using RoboSteer, we conduct the first large-scale empirical study of behavioral steerability across 9 existing BFMs. We view behavioral steerability as more than a capability for controlling motion: it concerns how embodied systems translate human intentions into purposeful actions. We hope RoboSteer will advance research on intention realization as a foundation for general-purpose embodied intelligence.
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Computer Vision
VolCo: Volumetric Contact for High-Fidelity Human Grasp Generation
Accurate contact modeling is fundamental to understanding hand-object interaction, yet existing contact representations are typically restricted to object surfaces and rely on hand-crafted rules to recover contact details, leading to severe penetrations and implausible results. To better exploit the rich detail in motion-capture data, we introduce Volumetric Contact (VolCo), a representation that expands surface points to a set of 3D volumetric grids. VolCo encodes 3D contact that allows precise hand part recovery, and is organized in an inherent hierarchy: local contact details within each volume and global hand geometry across all volumes. Our framework, VolCoDiff, employs two modules to capture local and global features following this hierarchy. For local contact details, we use a 3D variational autoencoder to model the possible hand configurations conditioned on the local object signed distance field (SDF). For global hand geometry, we design a prior-guided diffusion model that learns the distribution of compressed latent features aggregated from the volumetric grids. We evaluate our method on two benchmark datasets and demonstrate state-of-the-art performance in penetration and stability, indicating the capability to generate tight grasps with much less severe penetrations. Our code is available at https://github.com/chzh9311/volco.
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Computer Vision
HuLiGen: Human LiDAR Generation from Parametric Body Models
LiDAR point clouds of humans are extremely expensive to collect and annotate, thus represent a scarce resource that hinders the development of human analysis using this modality. To alleviate this scarcity, prior work relies on simulated human LiDAR, but such samples do not fully reflect the geometry and sensing characteristics of real observations. In contrast, we introduce HuLiGen, a generative model that generates human LiDAR point clouds from a parametric body model, using a point transformer trained with a flow-matching objective. We show that our generated point clouds are closer to the real capture distribution. Using HuLiGen to generate synthetic data, we propose a synthetic-only pretraining scheme for LiDAR-based HPE that achieves state-of-the-art performance, with even larger gains in low-annotation and low-data regimes, where MPJPE is reduced by up to 50%. Code, models and generated samples are available at https://github.com/valeoai/HuLiGen.