SEARCH · Search arXiv

Results for “stat.OT”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

328 recordsLinked to original sources

arXiv2026

GeoGR^2:Zero-Shot Geospatial Inference via Geostatistically-Guided Iterative Refinement with LLMs

Standard large language model prompting treats geospatial inference as independent, instance-wise prediction, ignoring the fundamental spatial dependencies that govern geographic reality. Consequently, even advanced models struggle with spatial consistency and exhibit severe biases toward populous regions. To bridge this gap, we propose GeoGR^2 (Geospatial Graph Refine Reasoning), a framework that formalizes zero-shot geospatial prediction as an iterative message-passing process on a dynamically constructed graph. Unlike static retrieval methods, GeoGR^2 instantiates three dynamic operators via collaborating operators: (1) a Topology Operator that constructs graph topology to enforce the Spatial Markov property; (2) a Feature Operator that enriches nodes with task-relevant semantic covariates; and (3) an Update Operator that performs natural language message passing to iteratively minimize spatial discrepancy. Theoretically, we frame this refinement as a contraction mapping that approximates the fixed point of a global consistency equation. Empirically, we validate GeoGR^2 on diverse physical and socioeconomic tasks. Results demonstrate that by explicitly embedding geostatistical inductive biases, GeoGR^2 significantly outperforms standard prompting baselines, while effectively mitigating systematic geographic bias. Our framework leverages large language models' intrinsic capacity for understanding spatial correlations through explicit topological scaffolding, without resorting to general graph reasoning paradigms. The code of GeoGR^2 is available at https://github.com/JinfanTang/GeoGRR.

cs.AI↗

arXiv2026

Differential Privacy Meets Invariant Statistics: Some Conundrums in Quantifying Trade-Offs

This work was inspired by the question of whether data swapping, a popular form of statistical disclosure control used to protect many data products including three recent US Decennial Censuses, can satisfy differential privacy (DP). Given the existence of more than 200 formulations of DP (and counting), as a precondition to answering this question one must precisely specify what it actually means to be DP. Motivated by this observation, we first conduct a theoretical investigation into DP's fundamental essence, resulting in a five-building-block system explicating the who, where, what, how and how much aspects of DP. Instantiating this system in the context of the US Decennial Census, we then demonstrate the broad applicability and relevance of DP by comparing a swapping strategy like that used in 2010 with the TopDown Algorithm--the main DP method adopted in the 2020 Census. This chapter provides nontechnical summaries of these two pieces of work (developed elsewhere), as well as extended discussions on a number of issues they unearth that complicate the formulation and the navigation of the so-called privacy-utility trade-off: How can greater awareness of the five building blocks thwart privacy theatrics? How can invariants (statistics that are released as is, without any privacy protection) align with DP's philosophy of relative privacy? How do our results bridging traditional statistical disclosure control and DP allow a data custodian to reap the benefits of both these fields? And how can removing the implicit reliance on aleatoric uncertainty lead to new generalizations of DP? Our ultimate goal with these discussions is to deepen the theoretical basis, broaden the practical applicability, and reduce the misperception of DP--all without shaking its core foundations.

cs.CR↗

arXiv2026

FIS-OT: Feature-Induced Optimal Transport for Unsupervised Action Segmentation

Unsupervised action segmentation is a challenging task. It involves finding action categories and boundaries in videos without labels. Existing Optimal Transport (OT) methods use global constraints. This causes them to overlook the use of local information. Furthermore, existing Optimal transport architectures are prone to confirmation bias because they overly trust the pseudo-labels they generate. This causes models to learn from noise in the early training stages. To address these issues, we propose FIS-OT. It is a novel Feature-Induced Structured Optimal Transport framework. First, we introduce a Feature Enhanced Generator (FEG) module. It serves as an internal regularizer. By using triplet loss, FEG captures local consistency. It provides robust supervision that is independent of noisy pseudo-labels. Second, we propose a Feature-Induced Residual Structural Prior. This combines a fixed temporal backbone with dynamic feature similarities. This design ensures temporal continuity. It also allows the solver to adapt to complex action structures. Finally, we establish a cyclic optimization loop. This aligns local feature learning with global structural alignment. Extensive experiments on the three datasets show the effectiveness of our method.

cs.CV↗

arXiv2026

BIRDS: Characterizing and Understanding Biodiversity Impact of Large Language Model Serving

Large language model (LLM) serving creates environmental impacts beyond carbon and water, including ecosystem damage through biodiversity-related pathways. We present BIRDS, a framework for Biodiversity Impact of Request-Driven LLM Serving. BIRDS defines request-level functional units, quantifies operational and embodied biodiversity impact, and introduces Quality-Normalized Biodiversity Impact (QNBI) to jointly analyze ecological impact and response quality. Across diverse workloads, models, GPUs, and regions, BIRDS reveals that biodiversity impact accumulates at scale and exposes quality-aware serving tradeoffs. The code is available at https://github.com/TianyaoShi/BIRDS.

q-bio.OT↗

arXiv2026

Importance and methods to control, vary, and characterize mud strength for studying locomotion

Animals and robots encounter mud at the water-land interface. Like sand, mud can stay solid or flow like a fluid. Unlike sand, the yield strength of mud at which solid-fluid transitions occur depends on not only the amount of solid relative to fluid (water in mud, air in dry sand), but also how much coarse grains and fine clay are within the solid. Despite understanding of locomotion on/within dry sand dominated by coarse grains with repulsive normal forces and friction, little is known for mud dominated by fine clay with strong cohesion. Here, we developed methods to prepare uniform mud of controlled, variable yield strength and characterize and track its drift from water evaporation. Compared to other flowable substrates, mud strength measured by upward force during penetration is weaker and can vary more, and mud sticks more during extraction to pull downward, making it more challenging for locomotion.

physics.bio-ph↗

arXiv2026

See the Change, Keep the Flow: Unsupervised Action Segmentation via Spectral-Temporal Representation Learning

Unsupervised action segmentation aims to discover latent action categories and their temporal organization without action annotations. Optimal transport-based methods provide structured frame-to-action assignments, however, their pseudo-label quality is fundamentally conditioned on the representation space used to construct the transport cost. We argue that reliable OT pseudo-labeling requires a representation geometry that is simultaneously sensitive to discriminative action changes and coherent along local temporal progressions. Based on this insight, we propose SpecT-OT, a spectral-temporal representation learning framework built upon an unbalanced optimal transport pseudo-labeling concept. SpecT-OT introduces a Spectral Reparameterization Projector (SRP), which parameterizes projector weights with fixed Fourier bases and learnable coefficients to improve the modeling of rapidly varying discriminative features, and Temporal Affinity Regularization (TAR), which imposes distance-aware, label-free constraints on pairwise frame affinities to stabilize local temporal structure. The two components jointly produce more discriminative and temporally stable transport costs, yielding more reliable pseudo-labels for iterative representation learning. Experiments on four benchmarks demonstrate strong performance compared with state-of-the-art methods. SpecT-OT achieves the best results on 13 of 15 metrics, including 4.1-point MoF and 7.4-point F1 gains over the baseline on Breakfast and Desktop Assembly, respectively.

cs.CV↗

arXiv2026

Aletheia: An Offline-First Clinical Decision Support System for Differential Diagnosis in Low-Resource Healthcare Settings

Access to specialist clinical expertise remains severely limited across sub-Saharan Africa, where physician-to-patient ratios can fall below 1:25,000 in rural settings. Existing AI-assisted diagnostic tools predominantly require reliable internet connectivity and high-specification hardware, rendering them impractical for frontline healthcare workers in district hospitals and health centres. This paper presents Aletheia, an offline-first clinical decision support system designed for low-resource healthcare contexts across sub-Saharan Africa. Aletheia is built upon Qwen2.5-3B-Instruct, fine-tuned using Quantised Low-Rank Adaptation (QLoRA) on a curated dataset of 27,000 clinical reasoning samples spanning 50 disease conditions with elevated prevalence in East Africa. Evaluation demonstrates a Top-1 diagnostic accuracy of 80% (8 of 10 cases; 95% CI: 49.0-94.3%), Top-3 accuracy of 100% (10 of 10 cases; 95% CI: 72.2-100%), BERTScore-F1 of 0.909, and METEOR of 0.467. These diagnostic figures are computed over a deliberately small set of ten representative clinical case categories, one case each, and are therefore indicative rather than statistically robust; the wide confidence intervals should be read alongside them. The system achieves an Expected Calibration Error (ECE) of 0.275 and passes the Africa Deep Tech Challenge 2026 (ADTC 2026) memory budget constraint of 7168 MB, achieving a peak inference RAM of approximately 3630 MB on the standardised benchmark laptop. These results demonstrate the feasibility of deploying large language model-based clinical reasoning at the primary care level in resource-constrained settings without cloud infrastructure.

cs.AI↗

arXiv2026

CAT-Flow: Curvature-Adaptive sTeps for Flow Matching

Flow Matching has emerged as a leading framework for generative modeling, powering state-of-the-art systems such as FLUX and Stable Diffusion 3.5. However, the iterative nature of its ODE-based sampling process creates a fundamental efficiency bottleneck: the quality of generated samples is highly sensitive to the choice of step-sizes, and current models typically require 20 to 30 steps for good quality. In this work, we propose two lightweight, training-free algorithms, CAT-OV and CAT-OT that adapt step-sizes at inference time based on a novel connection between Flow Matching sampling and gradient flow. Our algorithms are computed efficiently by not requiring additional neural function evaluations. Specifically, CAT-OT estimates curvature over time via a finite-difference approximation of the time-derivative of the vector field, while CAT-OV approximates curvature over the state space via a gradient of the vector field. Under suitable conditions, both methods have truncation error bounds of constant order. Empirically, CAT-OV and CAT-OT outperform existing step-size heuristics in image quality metrics across four text- to-image Flow Matching models, reducing the number of generation steps required to reach comparable quality by up to 40%.

cs.LG↗

arXiv2026

Optimizer Memory Schedules for Outscaling the Overtraining Axis

We investigate how optimizers scale across the overtraining axis and show that relative optimizer performance and optimal hyperparameters change substantially with training horizon. In particular, we study how matrix-preconditioned methods (Muon and SOAP) and a momentum-scheduled method (ADANA) scale relative to AdamW. We compare these four optimizers across models from 51M to 253M parameters and overtraining (OT) factors from 1x to 256x, sweeping the base learning rate at every setting. The preferred learning rate schedule can reverse across the overtraining axis, the best weight decay coefficient scales approximately as sqrt(OT), and longer horizons generally favor longer fixed memory. ADANA's scaling advantage over AdamW persists after tuning AdamW's fixed memory separately at each horizon. Log-time weight decay and momentum cooldown provide substantial gains for ADANA that compound as training increases. With this treatment, ADANA outscales AdamW with an exponent advantage close to that predicted by DANA theory on power-law random features. Muon and SOAP instead provide roughly constant token-efficiency advantages over AdamW across most of the measured range, although SOAP may gain further at the highest overtraining factors. ADANA begins behind both matrix-preconditioned optimizers but closes the gaps as training increases, surpassing Muon and becoming competitive with SOAP at our highest OT factors. These results establish training horizon as an essential axis for optimizer evaluation and design.

cs.LG↗

arXiv2026

DrainSinkhorn: Safe Elimination for Batched Entropic Optimal Transport

Fast entropic optimal transport backends reduce the cost of each Sinkhorn update, but static batches still run at full width until the slowest problem finishes. We introduce DrainSinkhorn, a verifier-gated active-packing layer for batches of independent Sinkhorn problems. It combines candidate-axis packing, a Sinkhorn-specific one-sided screen, verifier-gated retirement under the backend's configured two-sided residual check, and physical compaction of all candidate-indexed state. The EOT objective, per-instance Sinkhorn map, and stopping rule are unchanged; later kernels run only on unfinished problems. We characterize the removable work exactly. If completion depths differ within a packed window, active execution removes the padding between the static batch rectangle and the observed survival curve. A quotient nonlinear Perron-Frobenius analysis gives a local explanation for these finite-tolerance depth differences: convergence depends on the full modal spectrum and proposal alignment, not only on the slowest mode. DrainSinkhorn achieves state-of-the-art execution performance on the tested heterogeneous batched-EOT workloads within matched backend families. The complete Flash-backed OT path is 4.110x faster on MetroPT-3, 3.798x faster on ImageNet-32 feature couplings, and 1.250-1.270x faster across a five-tolerance Packer19 sweep. Independent implementations reach 2.600x on ImageNet-32 with OTT-JAX, 3.174x on A2D2 LiDAR with PyKeOps, and 1.415x on large ImageNet-32 PyKeOps couplings. End-to-end speedups remain 4.074x on MetroPT-3 and 2.786x on ImageNet-32 feature-space OT flow matching, with all reported residual, consumer-output, and training-quality checks passing.

cs.DC↗

arXiv2026

SketchFlow: Zero-Shot Vector Sketch Generation via GMM Prior Flow in CLIP Latent Space

Vector sketches remain one of the most concise and immediate mediums for abstract human expression. However, generating high-quality vector strokes that exhibit human-like drawing styles remains an open challenge due to the severe scarcity of fine-grained, high-quality text-to-sketch paired data. Existing text-conditioned generation methods often rely on unstable, time-consuming optimization or struggle to generalize to unseen categories in a zero-shot manner. To address these limitations, we present SketchFlow, a novel generative framework rooted in Optimal Transport (OT) theory and flow matching. By leveraging pre-trained CLIP models to bypass labor-intensive image-level text annotations, we formulate cross-modal alignment as a continuous mapping problem directly within the CLIP latent space. To bridge the inevitable modality gap between discrete text concepts and continuous sketch features, we first inject noise into discrete category embeddings to construct a continuous Gaussian Mixture Model (GMM) prior. We then utilize an Optimal Transport Conditional Flow Matching (OT-CFM) model to learn a deterministic vector field mapping from this continuous GMM prior to the target sketch feature distribution. Finally, a Hybrid Diffusion Decoder, fusing 1D U-Net and Transformer architectures, is designed to decode these features into fast and high-fidelity stroke trajectories. Extensive experiments demonstrate that SketchFlow substantially outperforms existing baselines in visual quality and adherence to natural human drawing styles. Furthermore, our geometry-preserving framework demonstrates promising local zero-shot synthesis for prompts beyond the QuickDraw training vocabulary, including unseen concept labels and semantic modifiers, while enabling smooth, continuous semantic interpolation between distinct concepts. Source code is available at: https://github.com/doudin404/SketchFlow.

cs.CV↗

arXiv2026

A simple derivation of the Kalman filter

In this lecture note, we present a concise and self-contained derivation of the discrete-time Kalman filter equations that requires only a basic understanding of least squares estimation. The treatment is designed to minimize mathematical overhead while preserving both rigor and generality.

math.OC↗

arXiv2026

Beyond Straightness: Non-Crossing Flow Matching via Quantile AlignTree Coupling

The performance of Flow Matching largely depends on the quality of the coupling between the source and target distributions. However, independent coupling often leads to path crossings and local velocity ambiguity, while OT-based couplings typically incur high construction costs. To address this challenge, we propose Quantile AlignTree Flow Matching (QAT-FM), an efficient structured coupling strategy that constructs a hierarchical coupling between a Gaussian prior and the target data distribution via a quantile-aligned tree structure. QAT-FM constructs the coupling in $\mathcal{O}(Nd\log N)$ time and supports per-pair source sampling with $\mathcal{O}(d)$ complexity, enabling scalable training for large-scale high-dimensional generative tasks. Theoretically, we prove that the QAT coupling satisfies marginal consistency, induces non-crossing linear interpolation paths, and consistently improves path separation at intermediate times compared with independent coupling, thereby alleviating local velocity ambiguity. QAT-FM further extends naturally to conditional generation, enabling structured conditional coupling while preserving global Gaussian alignment. Experiments across diverse benchmark datasets demonstrate that QAT-FM achieves competitive generative performance while substantially reducing coupling construction cost.

cs.LG↗

arXiv2026

Clustering Three-Way Data with Outliers

Matrix-variate distributions are a relatively recent addition to the model-based clustering literature, thereby making it possible to analyze data in matrix form with complex structure such as images and time series. Due to its recent appearance, there is limited literature on matrix-variate data, with even less on dealing with outliers in these models. An approach for clustering matrix-variate normal data with outliers is discussed. The approach, which uses the distribution of subset log-likelihoods, extends the OCLUST algorithm to matrix-variate normal data and uses an iterative approach to detect and trim outliers.

stat.ML↗

arXiv2026

Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests

Symbolic regression has emerged as a powerful tool for artificial intelligence-driven scientific discovery by learning interpretable analytical expressions that reveal governing relationships directly from data. Existing methods, however, often rely on heuristic search, struggle to balance predictive accuracy with expression complexity in noisy settings, and offer limited characterization of symbolic uncertainty. Probabilistic approaches that address these challenges in a unified manner remain underexplored. We introduce a probabilistic symbolic regression framework that represents mathematical expressions as ensembles of symbolic trees. A regularizing prior over tree topology controls expression complexity, while an Occam's window-based posterior summary captures uncertainty across multiple plausible symbolic models. Given the limited existing theoretical treatment of symbolic regression, we develop posterior concentration guarantees when symbolic expressions approximate the underlying relationship arbitrarily well, with a near-parametric rate when an exact finite formula exists. Additionally, we establish a sharp oracle concentration result under symbolic misspecification. Comparisons of our proposed framework with state-of-the-art competitors demonstrate superior predictive accuracy, optimal symbolic complexity, and stable structural recovery when learning benchmark scientific equations, together with the identification of scientifically interpretable descriptor formulas in a challenging materials discovery application.

stat.ME↗

arXiv2026

A complete characterization of sequential testability and change detectability in i.i.d. models

We give a necessary and sufficient condition for the existence of power-one sequential tests in an i.i.d. composite testing problem. A level-$α$ test with power one against every alternative exists if and only if the alternatives are separated from the null by a countable family of finite-block events. We provide other equivalent conditions using randomized fixed-sample tests, bounded finite-block scores, e-processes, reduced-filtration test supermartingales, and a countable cover whose finite-block weak-$*$ closed convex hulls are positively separated in total variation. As a bonus, the constructive proof yields tests have pointwise expected sample size $O_Q(\log(1/α))$. Exactly the same conditions also characterize i.i.d.\ change detectability under optional-horizon average-run-length control: for every $η>0$, they are equivalent to an alarm family $(T_γ)_{γ\ge1}$ satisfying $\Prob_{P^\infty}(T_γ\leσ)\le \E_{P^\infty}σ/γ$ for every null law and every stopping time $σ$. In fact, when these conditions hold, we can construct a single e-detector such that every null-law average run length lies between $γ$ and $(1+η)γ+1$, and having robust Lorden delay $O_Q(\logγ)$.

math.ST↗

arXiv2026

Diagonal Attenuation: A Finite-Sample Correction for PCA

Principal component analysis (PCA) can rotate away from its population target when a covariance matrix is estimated from limited data. We introduce diagonal attenuation, which preserves sample cross-covariances while reducing coordinatewise sample variances. The method is revealed exactly by averaging a linear full-output reconstruction loss over random input masks; studying the correction directly extends it beyond the range attainable by masking. We isolate the part of the random coupling between retained and omitted population directions that is contributed by sample-variance errors, and show how attenuation can reduce the resulting rotation. Under balanced marginal variances, we derive an explicit expected-risk theorem, uniform over the attenuation path for all sufficiently large finite samples, and obtain the asymptotically risk-minimizing strength. For general covariances, we characterize when attenuation leaves the population PCA subspace unchanged and give a risk theorem that also accounts for changing eigengaps and the population cost when the target moves. Simulations track this tradeoff from exact preservation back to PCA. Across local image patches, speech spectra, and smartphone acceleration, both mask-derived and direct attenuation improve PCA under two fitting-sample budgets, and one of them has the largest mean gain among seven methods in every data--budget cell. The full path selects strengths beyond the mask-derived boundary on $63\%$--$95\%$ of the subsamples.

stat.ML↗

arXiv2026

Bias-Corrected Subspace Intersection: Minimax-Optimal Shared Subspace Estimation in Multi-View Data

Estimating a low-dimensional subspace shared across noisy data matrices is a fundamental problem in multi-view matrix estimation. We study this problem under the two-view JIVE model, where each data matrix contains shared and view-specific low-rank components. We demonstrate that standard plug-in subspace intersection, including AJIVE, suffers from a second-order bias caused by direction-dependent leakage of the empirical singular vectors. We propose bias-corrected subspace intersection (BCSI), which removes this bias before estimating the shared subspace. We establish finite-sample risk bounds for BCSI that accommodate unequal view dimensions, signal strengths, and view-specific ranks and require no condition-number assumptions on the signal matrices. When the shared and view-specific ranks are comparable, these bounds match our minimax lower bounds up to universal constants. The resulting minimax rate contains a new second-order term, arising from quadratic leakage perturbations relative to the shrinking spectral gap when the view-specific subspaces are nearly aligned. This term is absent from previous JIVE minimax lower bounds. Numerical experiments demonstrate the advantage of BCSI over AJIVE when the leakage bias is pronounced. Along the way, we establish a nonasymptotic concentration result for the bias-corrected leakage Gram matrix of a rectangular spiked matrix, which may be of independent interest.

stat.ME↗