Papers

Visual search on large e-commerce catalogs must serve both "similarity" queries that ask for items resembling an uploaded image and "modifier" queries that comprise an image and text describing a desired modification (e.g. a color change or style swap). The latter is the setting known as composed image retrieval (CIR). Existing CIR methods, however, treat relevance as binary and train on triplets with a single positive target - a poor fit for real catalogs where many candidates partially satisfy a user query and ranking across that partial-match spectrum drives the customer experience. We propose a methodology for training CIR retrievers on graded relevance, consisting of: (i) a VLM to curate training data, generating both queries (object detection + modifier synthesis) and 4-level relevance labels without manual annotation, (ii) an iterative relevance-feedback loop that expands the training set by mining hard negatives from the in-training retriever, and (iii) a hierarchy-aware angular objective to train the retriever directly on the graded labels rather than collapsing them to a binary split. We call this methodology GradCIR and instantiate it on a PaliGemma2 bi-encoder trained on 3.5M graded pairs curated from raw Walmart catalog data. A controlled graded-vs-binary ablation isolates the supervision granularity and shows lift of 4.9%-5.9% in NDCG@10. The same recipe applied to other multimodal encoders lifts early-fusion backbones by up to 8.5% NDCG@10. On the public FashionIQ benchmark, GradCIR (applied to PaliGemma2) reaches 0.6703 average recall when fine-tuned, slightly ahead of the strongest peer-reviewed supervised baseline we compare against, and matching or exceeding all published CLIP-L-class zero-shot CIR methods. The system is deployed in production at Walmart, where it's serving live visual-search user traffic.

Four-dimensional (4D) Radar has emerged as a key sensor for environmental perception, providing range, azimuth, elevation, and Doppler measurements while remaining robust to illumination changes and adverse weather conditions. However, conventional Radar preprocessing methods, such as constant false alarm rate (CFAR) detection, select measurements primarily based on signal-level criteria and may therefore discard information valuable for downstream perception during point cloud generation. In addition, existing 4D Radar perception pipelines typically optimize Radar data processing and downstream perception independently, preventing task objectives from directly guiding the preprocessing stage. To address these limitations, we propose a Scene- and Task-Aware Radar (STAR) Preprocessor together with an end-to-end training framework. The STAR Preprocessor incorporates scene context and downstream task objectives to generate task-relevant Radar points, enabling the Radar representation to be optimized directly for perception. On the K-Radar benchmark, the proposed method achieves 74.3 AP, outperforming the previous state of the art by 5.6 AP points. Furthermore, applying the task-relevant points generated by STAR to various existing 3D detectors improves detection performance in most evaluation settings and yields an overall positive average gain over point clouds produced by conventional preprocessing.

Speculative decoding accelerates large language model (LLM) inference by using a lightweight draft model to generate multiple candidate tokens that are verified by the target model in a single forward pass. Its speedup is largely determined by the acceptance length, yet existing draft-model training methods mainly optimize cross-entropy or Kullback-Leibler (KL) divergence as proxies. These objectives encourage distribution matching but do not directly optimize acceptance length, and the acceptance mechanism also differs between greedy and sampling-based decoding. In this work, we propose acceptance-length-aware training losses that directly optimize the expected number of accepted tokens within a speculative window. For greedy verification, we derive an expected accepted length (EAL) loss that explicitly maximizes expected acceptance length. For sampling-based decoding, we introduce a window total variation (WTV) loss that optimizes the overlap between temperature-scaled draft and target distributions while accounting for sequential acceptance dependencies. Both objectives can be further combined with a group-relative reinforcement learning stage (GRPO) using simulated acceptance length as the reward. Experiments across different target and draft models, tasks, and decoding settings show that our losses consistently improve acceptance length over KL-based training. WTV provides particularly strong gains under sampling-based decoding, while EAL better matches greedy verification. These results show that directly optimizing the acceptance objective, with losses tailored to the decoding mode, is more effective than conventional distribution-matching objectives.

We study the fixed-$q$ right-edge asymptotics of the ordinary $q$-Krawtchouk ensemble. For $0<q<1$, finite polynomial duality gives a direct proof of convergence of the correlation kernels to an explicit limiting kernel. The local Jacobi limit is a shifted continuous $q^{-1}$-Hermite expression with an indeterminate moment problem, so the limiting Jacobi expression does not determine a unique self-adjoint operator. A single spectral atom, asymptotically saturating the mass bound, selects the realization and yields strong-resolvent convergence. The limiting kernel represents its positive spectral projection and admits spectral-series, Christoffel–Darboux, and partial-theta representations. After a ground-state transformation, the associated dual operator agrees with a two-step spatial Markov operator of Borodin–Corwin. For $q>1$, the limiting Jacobi operator is of Al-Salam–Carlitz~I type and is essentially self-adjoint.

If $f$ is a tuple of functions satisfying an algebraic ODE and $P\in{\mathbb C}(x)[f]$, it is common in applications to transcendental number theory to consider upper bounds for the order of zero of $P(x,f)$ at a given point in terms of $\operatorname{deg}_x P,\operatorname{deg}_f P$. Nesterenko introduced a condition known as the D-property, which holds in many applications, and proved essentially optimal bounds under this condition. We prove a global form of this result, where the field $\mathbb C(x)$ is replaced by a number field $K$ and $\operatorname{deg}_x P$ is replaced by the logarithmic height $\operatorname{h}(P)$. Under an analogous global D-property, we prove essentially optimal bounds for the number of zeroes, counted with multiplicities, in a fixed compact set. Applications of this result to point-counting theorems are developed in a separate joint paper with Hirata-Kohno and Kawashima.

Characterizing the phonon distribution of trapped-ion motional states is essential for many applications in quantum information processing, but existing methods become ill-conditioned beyond the Lamb-Dicke regime. We overcome this limitation by recasting phonon-state reconstruction as a filter-function inversion problem. Using composite pulses on the carrier and multiple sidebands, we engineer well-conditioned filters in phonon space to characterize pure and mixed states, study heating dynamics, and reconstruct Fock states up to $n=250$.

Language model agents are increasingly used to simulate social interaction, and the resulting transcripts read as though the agents understand one another. We ask whether that appearance rests on a model of the partner's mind or on the surface record of what the partner said. We build a social simulation in which both questions have exact answers: 40 multi-issue negotiations whose hidden preference weights and whose full Pareto frontier are known by construction. Two model families negotiate across 160 dyads, every transcript is frozen before any measurement, and 2880 counterfactual probes then hold the evidence byte identical while moving one factor at a time: the reader's own stake, the partner's tone, an identity label, and the order of recursion. The agents are socially fluent and economically poor. They reach agreement in 96.2% of dyads with 0 protocol failures, yet only 0.7% of deals land on the Pareto frontier, they leave 20.5% of the available joint value unclaimed, and they miss the one issue on which their interests are perfectly aligned in 76.6% of deals; on the frontier and on that aligned issue, a package drawn at random from the set both sides would accept does as well. The probes locate the failure. Swapping only the reader's own payoff sheet, while the partner's words and offers stay identical, moves the inferred top priority by 15.0 percentage points, which is egocentric projection rather than inference, while a tone rewrite moves it by 5.3 percentage points and an identity label by 0.0. Most tellingly, an agent predicts what its partner believes about it 72.5% of the time while that partner's belief is itself correct only 51.2% of the time: the agents track the conversation far better than they track the mind behind it.

We present MimicAgent, a prompt-to-trajectory generation framework for learning dynamic quadruped skills. Although reward shaping is extensively used when training quadruped policies, navigating the resulting reward landscape is notoriously difficult, requiring hours of "graduate student descent". Eureka attempts to automate reward design with LLMs, but we find that it struggles to generalize across diverse skills and morphologies. Our key observation is that it is far easier for a human - and by association, an LLM - to generate reference motions than to shape reward functions. Our hypothesis is motivated by the success of example-guided RL for humanoids, which exploits large-scale motion capture datasets as references for training locomotion policies. Unlike humanoids, quadrupeds lack such reference motion data. Towards this end, we propose MimicAgent, an agentic harness that, given a skill prompt, generates quadruped reference trajectories with coding agents. These coarse reference trajectories are then used to train example-guided RL policies that are deployable in simulation and in the real-world. Notably, we find that when prompting Claude Fable 5.1 within our agentic harness, 87% of prompts yield semantically aligned reference trajectories.

Group-relative reinforcement learning compares rollouts of the same prompt, but independent environment noise can obscure these comparisons. We study paired rollouts, which share an event-keyed noise schedule within each group while preserving each rollout's marginal distribution. Pairing removes the between-schedule component of reward-contrast variance, but need not reduce gradient variance. For one-sided grader noise, we derive an exact condition for reduction and give a counterexample in which reward contrasts improve while gradient variance increases. A controlled study trains a 2B tool-use agent under tool faults and grader flips, with three seeds per design. The protocol was registered with a disclosed, previously completed pilot. Under tool faults, pairing improves final noisy-test success by +5.1 percentage points on average, with all three seed differences positive, but misses the registered learning-curve criterion. The criterion is also missed under grader flips: the validation-AUC difference is +0.003 (95% interval [-0.029, +0.033]). A gradient probe on eight distinct checkpoints from two fault-trained trajectories finds lower mean-centered covariance traces under both noise types: 21 to 30% for grader flips and 40 to 63% for tool faults. These finite-sample measurements support the variance mechanism without establishing a general learning-speed benefit. The results distinguish improving reward comparisons, reducing estimator variance, and improving learning.

In this paper, we develop a preconditioner that is robust with respect to both the mesh size and the interaction horizon for finite element discretizations of volume-constrained nonlocal diffusion problems. Motivated by the Fourier multiplier of the nonlocal operator, we construct the preconditioner $B_h=G_h+\beta\delta^2D_h^{-1}$, where $G_h$ is a symmetric local Poisson solver, $D_h$ is the lumped mass matrix, and $\beta$ is a kernel-dependent constant. We rigorously prove that the spectrum of the $B_h$-preconditioned system is bounded above and away from zero uniformly with respect to the mesh size and horizon. Moreover, we develop a pair-cell assembly for the finite element matrix that preserves the symmetry and positive definiteness required by the preconditioner and PCG, and establish an $L^2$-error estimate for the finite element discretization. Finally, we use a single symmetric geometric multigrid V-cycle for $G_h$ in the numerical experiments, and the corresponding numerical results confirm the predicted convergence rate and show bounded condition numbers and PCG iteration counts over the tested meshes, horizons, and kernels.

We propose a local-cohomology obstruction to the existence of small Cohen–Macaulay modules over completed section rings of surfaces. Let $Y$ be a smooth connected complex projective surface, and let $H$ be an ample globally generated divisor with $K_Y\equiv4H$ numerically. Put $c(Y,H)=15H^2/8-\chi(\OO_Y)$. The main claim is that, when $c(Y,H)>0$, every nonzero finite reflexive module $M$ over the completed vertex local ring of $\bigoplus_{n\geq0}H^0(Y,\OO_Y(nH))$ satisfies $\dim_\C H^2_\mm(M)\geq c(Y,H)\rk M$. The argument combines elementary transformations of reflexive extensions, Harder–Narasimhan slopes, Bogomolov's inequality, and a two-section Koszul estimate. A fixed-source kernel estimate transfers the resulting cohomology to the punctured spectrum without requiring a grading on $M$. For the degree-six member of the six-line Hirzebruch–Kummer family, $H^2=1080$ and $\chi(\OO_Y)=1926$, so the bound is $99\rk M$. We give an explicit complete-intersection model for this application and spell out the argument leading to the claimed nonexistence of nonzero finite maximal Cohen–Macaulay modules.

On-policy distillation (OPD) pays twice for each fresh batch: the student generates trajectories and a stronger teacher scores them. Existing methods improve which trajectories are scored and how the teacher signal is constructed, but usually consume it with one actor update. We introduce CLOOPD, a closed-loop framework separating teacher-signal acquisition from student-side realization. CLOOPD selects an adaptive $\alpha$ waypoint inside a KL envelope, freezes the scored batch and its advantages, re-forwards the student after each actor pass, measures realization, and allocates actor work under a separate token budget. The framework includes deterministic two- and three-pass policies, token-priced CLOOPD-TPMR, and a budget-matched control. Across six 300-step runs on an 8-H20 node, every CLOOPD policy improves the one-pass TOP-D anchor at comparable teacher-token scale: macro accuracy rises from 15.41 to 17.78 with CLOOPD-Fixed2 and 19.36 with CLOOPD-Fixed3. At step 100, CLOOPD-Fixed3 reaches 15.35, nearly matching TOP-D at step 300 while using 67.2% fewer teacher-scored tokens and 28.0% fewer GPU-hours. Earlier 8-A100 ablations show adaptive $\alpha$ eliminates observed trust-envelope violations; a third pass adds headroom. These results position CLOOPD as a framework for budgeting how fully students learn from teacher-scored tokens.

Neural-rendering-based SLAM relies on rendered RGB-D residuals for camera tracking and map optimization, but the reliability of these predictions can vary substantially because of sensor noise, limited observation coverage, and incomplete map representations. Without an explicit reliability estimate, unreliable residuals may adversely affect pose optimization, while frames already well explained by the current map may trigger redundant mapping updates. In this paper, we present BayesianGS-SLAM, an uncertainty-aware 3D Gaussian Splatting SLAM framework that estimates predictive color and depth uncertainty during mapping and consistently reuses it across the SLAM pipeline. Our tractable probabilistic formulation combines a sensor-noise uncertainty component with an opacity-induced map-representation component propagated through the rendering process. The resulting predictive uncertainty is used to augment mapping, normalize tracking residuals through a robust pose objective, and evaluate incoming frames using a predictive-surprise-based keyframe criterion. Unlike prior uncertainty-aware neural-rendering SLAM methods that primarily consider color uncertainty or use uncertainty only during mapping, our framework estimates predictive uncertainty for both color and depth and integrates it into mapping, tracking, and keyframe selection. Evaluations on real-world RGB-D datasets demonstrate substantially improved depth uncertainty-error ranking compared with existing uncertainty-aware SLAM methods. Moreover, the proposed keyframe-selection strategy reduces the number of selected keyframes and mapping calls while maintaining competitive tracking and rendering performance.

An imperfect many-body revival does not by itself certify the entanglement of the returning state. We give a finite-record protocol for graph-edge localizable entanglement along scar wavepackets of a graph-dressed PXP chain. The target cluster state has nonzero energy variance, so neither an exact target eigenstate nor a dark-state embedding is assumed. Fresh binary probes of the undeformed Hamiltonians Pauli terms have a fully separable explanation, even within the dressed blockade sector. Adding local graph-stabilizer probes makes established entanglement witnesses accessible with simultaneous confidence bounds. For a specified square-root instrument, an imposed worst-case disturbance budget fixes the strength that minimizes the equal-allocation Hoeffding sufficient sampling cost. A local commutator bound accounts for finite-duration ancilla pulses while the Hamiltonian remains active. We test the protocol on chains through twenty spins, under perturbed dynamics, and with independent implementations. At the first twenty-spin return, synthetic weak records certify all nineteen graph edges. Generator, two-color, bounded-weight, and full-group benchmarks separate this localizable resource from genuine multipartite certification. The protocol measures recoverable entanglement in a known scar wavepacket, with explicit calibration and limits on its physical and statistical interpretation.

Generative models have recently demonstrated considerable promise in speech super-resolution (SSR). Nevertheless, the majority of existing work has concentrated on standard or versatile SSR configurations, leaving the extreme setting with severely limited spectral inputs largely unexplored. In this regime, current approaches exhibit marked performance degradation, underscoring the need for dedicated solutions. To bridge this gap, we introduce P2Flow, a phoneme-aware progressive flow matching (FM) framework designed for extreme SSR with three main strategies. First, our model leverages phonetic information to reconstruct missing spectral components. Furthermore, it employs a progressive architectural design that hierarchically restores distinct frequency regions. Finally, we incorporate post-training of the vocoder to enhance overall waveform fidelity. Extensive experiments are conducted on the TIMIT and VCTK datasets under both 1 kHz to 16 kHz and 2 kHz to 16 kHz settings, demonstrating that P2Flow yields state-of-the-art results across multiple evaluation metrics.

Traditional data systems face profound limitations in the AI era, relying on human-crafted pipelines, lacking semantic understanding of heterogeneous data, and operating through rigid, reactive processing. To address these challenges, we propose a new paradigm called the Data Agent, designed to manage, process, and analyze data with minimal human intervention. Data agents autonomously execute a wide range of data-related tasks, transforming traditional data systems by shifting from manual design to autonomous orchestration, from literal manipulation to semantic interpretation, and from reactive to proactive processing. Our Data Agent system includes six components: semantic data organization, semantic operators, agentic pipeline orchestration and optimization, feedback-driven refinement, memory management, and proactive adaptation. Building on this foundation, we also develop two specialized agents: the data analytics agent and the data science agent. Experiments on real benchmarks demonstrate significant performance gains of our data agent over state-of-the-art methods. We identify open challenges to guide future research in building fully autonomous data systems.

Brain-to-image retrieval seeks to identify the visual stimulus that elicited a non-invasive neural response. Candidate images are typically represented by pretrained vision models, whose internal representations vary in abstraction across depth. Existing methods usually train the neural encoder to recover a fixed final-layer visual target. Under this formulation, the visual hierarchy is reduced to a single prescribed endpoint, preventing representations at other depths from directly shaping the visual target. This limitation motivates learning how information across visual depths should contribute to the retrieval target. To this end, we introduce NeuroGlyph, which learns a trial-independent visual target from multiple depths of a frozen visual backbone. NeuroGlyph decomposes the target into factor-specific subspaces. Each subspace learns an image-conditioned allocation over visual depth. The resulting subspaces are fused into a single embedding for retrieval. Across THINGS-EEG and THINGS-MEG, NeuroGlyph outperforms final-layer supervision in all controlled comparisons. It also surpasses the post hoc best fixed-layer oracle in three of four comparisons. Parameter-matched ablations support both factorized target construction and image-conditioned depth allocation. Under comparable 200-way retrieval protocols, NeuroGlyph achieves the strongest system-level performance in six of eight reported metrics. These results support learning retrieval targets across the visual hierarchy rather than prescribing one visual depth.

We establish the full version of a conjecture of Guth and Zahl, giving a lower bound for the volume of a semialgebraic set that has a large intersection with a collection of $\delta$-separated $\delta$-tubes. Our proof uses o-minimal methods to simplify the proof of Katz and Rogers, who proved the conjecture up to a small factor. We also establish that the constants depend polynomially on the complexity of the semialgebraic set, and more generally in the #o-minimal setting.

The open-source text-to-image (T2I) ecosystem enables rapid model development and sharing, but also hosts models intentionally tailored for harmful services, which we call Monets. Prior work has examined specific types of harmful T2I models on individual platforms, but a Monet does not exist in isolation. The broader Monet ecosystem, spanning model characteristics, cross-platform propagation, governance evasion, monetization, and downstream deployment, remains poorly understood. In this study, we present the first systematic, ecosystem-level measurement of Monets. Grounded in the policies of real-world model hubs, we construct a taxonomy of ten harmful service categories and identify 23,947 Monets across eight major T2I model hubs, with the most popular exceeding 19 million downloads. While some developers employ anti-theft mechanisms against unauthorized re-uploading, Monets propagate across platforms at scale, with 40.76% mirrored across hubs. Such propagation further enables governance evasion via cross-platform archiving, keeping 11.99% of Monets accessible after bans on their original platforms, alongside other evasion strategies including keyword obfuscation and model-level safeguard circumvention. Monets also anchor coordinated commercial campaigns—one spanning 668 models with 914 completed commissions and another advertising gray-market account-farming service—and reach users through GitHub projects and inference APIs, raising downstream child safety concerns. These findings expose the limitations of platform-siloed defenses and highlight the need for cross-platform threat intelligence, coordinated governance, and technical safeguards.

Recent advances in humanoid robotics and embodied intelligence have enabled robots to perform increasingly complex manipulation tasks. However, musical instrument performance remains a formidable benchmark, demanding not only collision-free trajectory execution but also precise contact timing, asymmetric bimanual coordination, and target acoustic outcomes on physical instruments. The guqin, a seven-string fretless zither, presents unique manipulation challenges due to its millimetric string spacing, transient right-hand plucking, and sustained left-hand harmonic contacts. In this work, we present a physical heterogeneous dual-arm robotic system for phrase-level autonomous guqin performance. We formulate guqin playing as a hybrid discrete–continuous execution problem and develop a hierarchical planning framework that coordinates working finger assignment, configuration continuity, obstacle avoidance, and tight bimanual contact schedules across consecutive musical events. The system integrates vision-guided instrument localization, tactile-based harmonic contact monitoring, and auditory feedback-informed plucking parameter calibration. Real-world experiments on a 25-event phrase demonstrate that the system reliably executes coordinated open-string and seventh-hui harmonic sequences on a physical guqin, achieving 93.6% and 96.8% event correctness across repeated trials.

Learning the full Pauli profile of the virtually distilled quantum state $\rho^m/\text{tr}(\rho^m)$ has so far required exponentially many copies of $\rho$. We show that all $4^n$ squared Pauli moments $[\text{tr}(P\rho^m)]^2$ can be learned to additive error $\varepsilon$ with confidence $1-\delta$ from one $2m$-replica measurement setting using $O(m[n+\log(1/\delta)]/\varepsilon^2)$ copies. This is an exponential speedup in the system size $n$ over previous protocols. For $m = 2$, we propose the coherent Bell difference sampling circuit that realizes this measurement on current devices. The speedup originates from paired replicas that cancel the anticommutation signs of Pauli operators, collapsing the incompatibility of the Pauli family. We certify this collapse by introducing the quantum Bernstein norm, a computable incompatibility measure for nonlinear functionals. A further information-theoretic $m$-replica protocol recovers the signed moments $\text{tr}(P\rho^m)$ using $O(m[n+\log(1/\delta)]/\varepsilon^4)$ copies. For fixed $m$ in the stated lower-bound regime, it attains the optimal replica number, since any protocol with fewer replicas requires exponentially many copies.

Let $K \subset \mathbb{R}^N$ be a convex body containing the origin in its interior. In this work, we study the diameters of random sections of $K$ and derive upper and lower bounds for them in terms of geometric parameters of $K$. Our bounds hold with large probability, and they offer new insights into this widely studied subject. Our upper bound complements the so-called low $M^*$-estimate and in many cases it is much sharper. The two lower bounds that we give are each of a different nature: depending on the body in question each time, either could be better, and in many interesting cases it matches the upper bound too. Subsequently, we apply our results to determine random diameters of $p$-ellipsoids (images of $\ell_p$ balls under diagonal operators), improving upon previously known results and achieving sharp estimates in many cases. One notable application is to Information-Based Complexity Theory, where we manage to establish a simple (and essentially optimal) dichotomy in response to a very natural conjecture posed by Hinrichs, Prochno and Sonnleitner in 2023. Our solution settles precisely when it is useful to replace the optimal information used for the recovery of vectors from a $p$-ellipsoid with random (Gaussian) information, which can be more practical to obtain.

LLM agents can change their own future behavior, raising a basic control question of which self-generated changes should be allowed to persist. We formulate this as admission control for self-modification. The agent may propose changes to its operating instructions, while an external runtime gate controls persistence. We implement this principle as a model-agnostic self-healing harness that runs a Detect, Notice, Heal, Validate loop around an otherwise unmodified agent. The agent authors candidate behavioral rules in an external workspace, where they receive provisional execution authority during evaluation and acquire persistent cross-episode authority only after measured improvement on the triggering failure without regression beyond a fixed margin on protected cases. Replay provides matched evidence when available, forward trials provide a weaker fallback, and a corpus-level guard re-tests the accumulated active rule set. Across 16 matched Baseline and Harness runs spanning AppWorld, Terminal-Bench, and $\tau^2$-Bench, the gate rejected 383 replay-decided proposals. Of these, 211 (55%) improved their triggering failure while degrading a case that previously worked. This shows that locally beneficial self-modifications can introduce collateral regressions often enough to materially affect gate decisions, providing direct empirical motivation for external admission control. Task-completion score is higher under the Harness in all 16 pairs, with two paired bootstrap intervals excluding zero, while repeated-trial reliability is higher in 12 pairs, tied in 4, and lower in none. Because adaptation modifies the policy-inducing context while leaving model weights fixed, admitted changes remain inspectable, reversible, and compatible with closed-weight models.

Uncu and Zudilin studied reflections of finite forms of the modulo nine Kanade–Russell identities under $q\mapsto q^{-1}$, leading to ten conjectural sum–product evaluations, including two proposed by Warnaar. Hickerson conjectured four further identities in his study of contiguous relations for the associated parameterized double sums. By constructing finite forms of Hickerson's sums and studying their reflections, Konenkov proposed two additional product identities, whose conjugates give two more. In this paper, we prove all eighteen conjectural identities by combining Nahm-sum dual evaluations established by the author with parameterized divided-difference identities. For the symmetric reflections, Schur-type decompositions and finite rational identities reduce the required evaluations to nonsingular two-by-two linear systems. The asymmetric and cyclotomic cases are treated through $q$-Airy–theta connection formulas, whereas the Hickerson identities are derived from low-order divided differences.

LLM judges evaluate candidate language models through pairwise comparisons of their responses. Judge-aware Bradley–Terry models aggregate pairwise comparisons by jointly estimating candidate scores and judge-specific sensitivities (how strongly each judge responds to quality differences), often interpreted as reliability. We show that this reading fails when judges prefer a display position. Even under balanced display orders or swap-and-average, omitting position attenuates fitted judge sensitivity by approximately the factor $1-D^2$ near equal quality, where $D$ is the judge's net first-slot preference between equally good responses. We propose OSCAR, which jointly estimates candidate scores, judge sensitivities and judge-specific position, length and family effects, and provides confidence intervals for pairwise win probabilities that account for dependence within prompts. On held-out data, observed attenuation closely matches the prediction $1-D^2$ (correlation of log ratios 0.99). Across four datasets, position adjustment lowers held-out log loss by 14-23% and changes which judges would be dropped for low sensitivity on three datasets. On MT-Bench, it ranks GPT-4 first instead of claude-v1, matching human votes. Simulations with known parameters show improved recovery of judge sensitivities and candidate rankings, with 94.4-95.2% confidence interval coverage. Low estimated sensitivity alone is therefore not evidence of an unreliable judge.

Atomic activity understanding aims to recognize and localize structured traffic behaviors that jointly encode motion patterns and their grounding in road topology. Unlike conventional action recognition, atomic activities are multi-agent, multi-label, and topology-aware: multiple activities co-occur while many agents remain inactive. We introduce Action-Slot, a structured action-centric representation learning framework. Slot attention is widely used for object-centric decomposition, but its permutation-invariant design and object-level inductive bias are misaligned with atomic activity semantics. We reformulate slot learning as structured activity decomposition through three designs: (1) category-aligned action slots that anchor slots to predefined activity categories, (2) parallel spatio-temporal slot updating for holistic video-level reasoning, and (3) background and negative-slot regularization that enforces competition between foreground activities and irrelevant regions. Together these establish an activity-centric inductive bias that disentangles concurrent and asynchronous activities directly from raw video. Beyond recognition, the learned representations encode transferable spatio-temporal grounding signals. We further propose an attention-difference-based pseudo mask selection framework that suppresses false positives by measuring attention changes before and after candidate region removal, enabling weakly supervised localization without dense annotations. To support systematic evaluation, we introduce TACO, a balanced synthetic dataset with full atomic activity coverage and pixel-level annotations. Experiments on OATS, TACO, and annotated nuScenes show superior recognition, strong sim-to-real transfer, and state-of-the-art weakly supervised localization.

Black-box machine learning models increasingly deliver strong predictions, but extracting useful information from them, such as a set of important features, remains challenging. Existing model-agnostic methods primarily estimate feature importance or conduct inference on it rather than directly selecting features, whereas many feature selection methods are model-specific or rely on the model-X assumption. We introduce LOCO-guided Adaptive Minipatch Sampling (LAMPS), a model-agnostic ensemble framework that uses any black-box regression algorithm as its base learner to select features important for predicting the response. The base learner need only produce predictions and need not perform feature selection itself. LAMPS operates within a minipatch ensemble framework that subsamples both observations and features, allowing leave-one-covariate-out (LOCO) feature importance scores to be easily computed. It adaptively concentrates minipatch sampling on features with high LOCO scores while maintaining exploration. The resulting sampling probabilities rapidly separate signal from noise features after a few iterations, enabling selection through simple thresholding. We establish that LAMPS achieves exact feature selection in high-dimensional settings, provided that the base predictive models are sufficiently well trained on average. Extensive experiments on synthetic and real data show that LAMPS outperforms state-of-the-art feature selection methods, with particularly strong performance in the presence of correlated features.

Contrastive self-supervised learning has achieved strong performance by learning representations from multiple augmented views of the same image. However, most existing methods construct positive pairs using independently sampled stochastic augmentations, which may alter semantic content and ignore the intrinsic geometry of the data distribution. In this work, we propose OTCLR, an optimal transport-aware framework for contrastive learning representations that generates geometry-consistent positive samples. Instead of directly contrasting two randomly augmented views, we construct intermediate views between the original image and its augmented variants through entropic optimal-transport displacement interpolation. These transport-interpolated samples serve as positive views that better preserve image structure while explicitly modeling spatial distributional geometry. To further promote smooth representation learning, we evaluate auxiliary Sinkhorn regularization terms that encourage transport-interpolated views to remain consistent with their endpoint images. The proposed method can be incorporated into standard contrastive learning pipelines without modifying the encoder architecture. Experiments on multiple benchmark datasets show that our approach improves representation quality and transfer learning performance compared with conventional augmentation-based contrastive learning baselines.

Active perception and manipulation are crucial for robots to interact with complex scenes. Existing benchmarks struggle to evaluate how robots effectively acquire and maintain information in memory in an active manner. To this end, we introduce ActiveArena-Sim, an active-perception simulator with controllable viewpoints and large-scale workspaces as the foundation. Built on this, we propose ActiveArena-Bench, which comprises 35 tasks across 5 fine-grained categories, covering visual exploration and interactive information acquisition. Each task is difficult to solve from passive observations alone, requiring multi-round evidence acquisition and memory-based reasoning. The benchmark provides rich memory annotations, standardized training data, and ID/OOD protocols featuring disjoint scenes, unseen distractor configurations, and novel backgrounds. Moreover, we present ActiveArena-VLA, a modular suite of 13 vision-language-action configurations for controlled studies of memory writing, memory capacity, proprioceptive state, subtask supervision, and high-level planning in active perception. Benchmark results reveal a substantial ID-OOD gap: uniform memory sampling, increased memory capacity under reliable write policies, proprioceptive inputs, and subtask supervision improve OOD generalization, while planner-guided memory management and decision-making achieve performance close to the best-performing configuration using only sparse memory. ActiveArena thus provides a unified testbed to develop and diagnose models for active perception and manipulation.

We prove that the solution functor from bounded good filtered complexes of coherent D-modules on a smooth rigid-analytic variety to modules over the positive almost de Rham period sheaf is fully faithful. On filtered vector bundles with flat connection satisfying Griffiths transversality, the construction recovers, up to duality and extension of scalars, Scholze's horizontal sections functor. As an application, we obtain a notion of de Rham Zariski-constructible sheaves, generalising the classical notion of de Rham local systems.