跳到正文
研踪PaperTrail

论文库

检索计算机领域论文，按研究方向、作者或关键词筛选。

部分采集异常
正在读取账号与研究记录…

全站更新概况

+0新增论文
+0其中 AI 相关
+0已有论文修订
+93新增 AI 导读

arXiv 最近完成扫描：2026-11-16 01:34 · 全站最近入库：2026-11-14 15:09各信源进度 →

统计口径与数据新鲜度

统计 2026-11-15 07:15 — 2026-11-16 07:15（北京时间） · 点击数字查看对应简报；AI 相关包含在新增论文内。

最近完成检查：2026-11-16 01:34最近发现新增版本：2026-11-14 15:09库内论文最新更新时间：2026-11-13 02:59

每分钟刷新已保存的数据。空检查不代表采集异常；新收录可能包含历史论文。AI 导读按新增版本计数。

23,348 已收录论文19,580 AI 相关6,729 有修订112 HF 社区发现

浏览论文库

研究日报 / 周报 →按信源浏览 →

时间范围跟随排序：版本更新、本站收录或首次发表。最新收录可能包含历史论文。部分信源异常，查看状态 →

找到 769 篇论文 · 按版本更新时间排序上轮扫描起点 2026-11-16 01:33（北京时间）
版本更新 · v2arXiv:2605.19557

Density-Ratio Losses for Post-Hoc Learning to Defer

Alexander Soen, Ragnar Thobaben, Joakim Jaldén, Richard Nock

原文摘要

We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low task loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer. For KL-based ideal distributions, our deferral rule recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior---which incorporates the expert's performance---depending on if the ideal distributions are marginal or joint distributions. This leads to two variants of the DR CPE losses, with the joint variant being computationally convenient in practice. We establish consistency properties of the joint DR CPE losses when considering the zero-one task loss and strongly proper composite CPE losses. Experimentally, our approach is competitive compared to common baselines and is more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio estimation between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.

stat.ML · cs.LG

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2604.12497

Allocating Human Oversight in AI-Enabled Analytics

Zikun Ye, Jiameng Lyu, Rui Tao

原文摘要

Artificial intelligence provides low-cost predictions for many analytics tasks, but their reliability and the value of another human label vary across tasks. We study how to allocate a shared human-validation budget when task-level uncertainty is unknown and each acquired label informs both estimation and subsequent allocation. For known difficulty levels, the benchmark follows a cost-adjusted Neyman rule that accounts for task importance and label cost. Within our Tuned Rectification-Difficulty framework, we develop an upper-confidence-bound policy that jointly learns the correction coefficients of tuned prediction-powered inference and the resulting difficulties from paired human labels and predictions, and establish an allocation-regret guarantee for the confidence-radius policy. In synthetic experiments and a real digital-twin survey with 68 tasks and over 2,000 respondents, our method closes most of the gap to the oracle on the allocation objective. It matches the estimation error of uniform allocation with up to 22.7% and 4.5% fewer human labels, respectively. The same allocation structure extends beyond scalar means to vector-valued decision models, including regression and choice/conjoint estimation, by replacing the scalar residual variance with a scalarized sandwich covariance. The value of AI depends not only on model accuracy but also on the operational policy that targets human oversight where it matters most.

cs.LG · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13973

On the Spectral Estimation of VARMA Processes

Bin Zhu, Mattia Zorzi

原文摘要

We consider the problem of estimating the power spectral density of a Vector-valued Autoregressive Moving-Average (VARMA) process. A well-established approach to accomplishing this task consists of formulating a moment problem that selects the spectral density maximizing an entropy-like index while matching certain moments of the underlying process. However, existing methods assume that the moving-average (MA) component is either fixed or scalar, thereby reducing the class of ARMA models over which the optimal spectral density is sought. In this paper, we propose a new moment problem, based on the notion of transportation entropy, for learning the spectral density of a VARMA process without fixing the MA component or restricting it to be scalar.

stat.ML · cs.LG · math.OC

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2502.15118

Do we really need the Rademacher complexities?

Daniel Bartl, Shahar Mendelson

原文摘要

We study the fundamental problem of learning with respect to the squared loss in a convex class. In the subgaussian setting, the sharpest known sample complexity bounds are characterised via fixed points associated with the limiting gaussian process. In more general settings (for example, heavier-tailed scenarios) the state-of-the-art bounds rely on localised Rademacher complexities, which are often difficult to control and can be considerably larger than their limiting gaussian counterparts. We show that if one has access to coarse information on the covariance structure of the underlying class, it is possible to derive an upper bound on the sample complexity that matches the state-of-the-art rates in the gaussian setting---even in heavy-tailed regimes. As a consequence, under rather minimal assumptions, learning problems that share the same $L_2$-structure---even those involving heavy-tailed distributions---admit the same upper bound on the sample complexity as if the problem were fully gaussian. This constitutes the first universality result for general convex learning problems. The proof is based on a novel learning procedure, and its performance is studied by combining optimal mean estimation techniques for real-valued random variables with Talagrand's generic chaining method.

math.ST · cs.LG · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13935

MEOW: Medical Open-World Interactive Segmentation

Philip Matthias Winter, Maria Wimmer, Bernhard Schäfl, David Major, Dimitrios Lenis, Astrid Berg, Theresa Neubauer, Ariharasudhan Muthusami 等 11 位作者

原文摘要

In open-world recognition, machine learning models not only make predictions on unknown structures ("generalized open-set"), but also continually learn and improve from those predictions over time. Interactive segmentation, despite its access to user feedback, has so far remained confined to the open-set setting. In this work we introduce MEOW, the first framework that turns non-interactive segmentation backbones into interactive open-world learners without updating learnable model parameters. MEOW combines parameter-free transductive reasoning with memory consolidation to accumulate knowledge and thereby improve future performance. Focusing on medical data, we show that MEOW consistently improves its own predictions on classes never seen during training, and transfers zero-shot to unfamiliar domains, including micro-CT data and other imaging modalities.

cs.CV · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2605.11841

Minimax Rates and Spectral Distillation for Tree Ensembles

Binh Duc Vu, David S. Watson

原文摘要

Tree ensembles such as random forests (RFs) and gradient boosting machines (GBMs) are among the most widely used supervised learners, yet their theoretical properties remain incompletely understood. We adopt a spectral perspective on these algorithms, with two main contributions. First, we derive minimax-optimal convergence for RF regression, showing that, under mild regularity conditions on tree growth, the eigenvalue decay of the induced kernel operator governs the statistical rate. Second, we exploit this spectral viewpoint to develop compression schemes for tree ensembles. For RFs, leading eigenfunctions of the kernel operator capture the dominant predictive directions; for GBMs, leading singular vectors of the smoother matrix play an analogous role. Learning nonlinear maps for these spectral representations yields distilled models that are orders of magnitude smaller than the originals while maintaining competitive predictive performance. Our methods compare favorably to state of the art algorithms for forest pruning and rule extraction, with applications to resource constrained computing.

stat.ML · cs.AI · cs.LG

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13869

Outliers and the Hard-Margin Linear SVM in High-Dimension, Low-Sample-Size Settings

Yugo Nakayama

原文摘要

We study how outliers affect the hard-margin linear support vector machine when the dimension grows while the sample sizes remain fixed. For one-sided contamination, the centered Gram matrix converges to a constant inlier block plus an outlier-diagonal component, and the limiting dual problem has a closed-form solution. All outliers act through one effective distance. This representation yields explicit thresholds for loss of inlier support, margin shrinkage. intercept displacement, and asymptotic misclassification. We then treat contamination in both classes. The limiting intercept is the multiplier of the class-balance constraint, and the two classes pull it in opposite directions. Consequently, at most one class can collapse or be asymptotically misclassified, whereas symmetric contamination leaves the limiting discriminant function unchanged even though the margin shrinks. Seven numerical experiments verify the dual allocation, phase transitions, and discriminant limits.

stat.ML · cs.LG

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.09919

Eigenvalues of the Hessian in Deep Learning: The Origin of Symmetry and Its Breaking

Yossi Arjevani

原文摘要

Hessian spectra at trained models in deep learning exhibit a persistent pattern: eigenvalues organize into distinct clusters, including a large bulk near zero and a few isolated outliers. This paper shows that a natural account of these spectral phenomena emerges when the original setting is understood as a departure from a nearby, otherwise hidden, highly symmetric reference. Modifications, including changes to the architecture, data distribution, or parameter metric, expose a nearby reference configuration whose Hessian exhibits rich invariances-ones not accounted for by weight symmetries. There, symmetry enables a precise description of the spectra, forcing high-dimensional kernels and eigenvalues of large multiplicity. Returning to the original configuration breaks the Hessian symmetry and thereby produces the observed hierarchy of clusters and outliers. The framework is developed in some generality, with a detailed analysis of three-layer ReLU networks and applications to convolutional, graph, and transformer models, as well as to the NTK. The same mechanism is further shown to yield analogous spectral structures in layerwise Hessians and the Gauss-Newton matrix.

cs.LG · math.OC · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13765

Beyond Interaction Scores: Selecting Feature Interactions via Independent Replication

Jincheng Gao, Shuo Sun

原文摘要

Learning feature interactions is essential for accurate prediction and interpretable modeling, yet a high interaction score may reflect fitting noise rather than a reproducible pattern. Ranking methods score feature pairs but leave the cutoff to the user; testing methods set the cutoff but rely on repeated model refits or a model of the joint feature distribution. We present LENS, a model-agnostic framework for selecting feature interactions through independent replication. LENS trains two models with the same learning algorithm on disjoint data and accesses them only through predictions. For each feature pair, it removes main effects from the joint-effect surface to isolate an interaction pattern, ranks pairs by its strength, and tests whether the second model reproduces it at a meaningful strength. A single multiple-testing correction determines which pairs to retain, using only two model fits regardless of the number of features. We prove that a replication ratio alone can retain arbitrarily weak patterns shared by both fits, whereas a strength floor restores selection consistency, and we characterize when normalization in Friedman's $H^2$ reverses interaction rankings. On 16 synthetic designs, LENS matches leading model-specific ranking methods (e.g., TreeSHAP) and recovers 91% of material interactions, against 45% for the knockoff-based DIAMOND, without selecting false pairs; with 1,225 candidate pairs and no interactions, it makes substantially fewer false discoveries. On large-scale French motor insurance data, it identifies interactions documented in the actuarial literature and recovers 90% of the deviance gain obtained using all pairs. On two credit datasets, LENS selects few pairs while maintaining or slightly improving predictive performance over the additive baseline.

cs.LG · cs.DB · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.19291

Factor Augmented High-Dimensional SGD

Shubo Li, Yuefeng Han, Xiufan Yu

原文摘要

Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations in high-dimensional learning tasks. Unlike standard two-stage dimension reduction approaches that rely on offline representation learning and full data storage, a key novelty of FSGD is that it operates purely on streaming data, making it scalable to large-scale and high-dimensional problems. Furthermore, we establish the first theoretical framework that explicitly incorporates latent factor estimation error into the analysis of SGD, and provide moment convergence in $\ell^s$ norm under decaying step sizes and mini-batch updates. Our results provide a new foundation for employing SGD reliably and scalably in high-dimensional machine learning systems.

stat.ML · cs.LG · math.ST

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2608.08743

A Distribution Mapping Approach to Counterfactually Fair Reinforcement Learning

Jianhan Zhang, Jitao Wang, John D. Piette, Donglin Zeng, Chengchun Shi, Zhenke Wu

原文摘要

Reinforcement learning (RL) seeks to optimize sequential decisions to maximize population-level benefits over time. However, when deployed in high-stakes settings such as healthcare, RL decisions might systematically restrict some subpopulation's access to valuable services in a manner contrary to the values and goals of stakeholders. Counterfactual fairness (CF) offers a promising framework to address this problem based on causal reasoning. This paper develops a data preprocessing algorithm that, when used in tandem with policy learning, enables CF in RL. Our algorithm relies on a novel quantile distribution mapping method for sequentially estimating the counterfactual states and rewards in the data preprocessing step, subsuming common additivity assumptions used for counterfactual prediction as a special case. We theoretically prove that the per-step level of counterfactual unfairness and infinite-horizon suboptimality gap can be bounded under mild regularity conditions. We also empirically test our algorithm in numerical experiments as well as in application to a real-world interventional digital health dataset.

stat.ML · cs.CY · cs.LG · stat.ME

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.14586

Finite-Cadence Refresh Equilibria for Streaming Prior-Anchored Ridge: A Closed-Form Forgetting Window and Spectral Correction

Mrigank Shekhar Singh

原文摘要

Recursive estimators on drifting streams must forget stale data fast enough to track the target, yet slowly enough to average out noise. In prior-anchored ridge regression, this trade-off admits a closed-form spectral decomposition in which each eigen-direction interpolates between the data solution and the prior with pull weight $s_i = ρ/ (μ_i + ρ)$. When the anchor is refreshed every $k$ steps, we show that the moving-frame offset converges to a finite-cadence equilibrium that lags the pure-leaky path by an explicit $Δ_k(s)$ while reducing estimation variance by a factor $Ψ(s, r_k)$. Minimizing the cycle-averaged risk gives $ω^* = (4ν^2 Σ/ c')^{1/3}$, $c' = σ^2 d_{\mathrm{eff}}(ρ)$, and the plug-in strength $ρ^* = σ^2 / (nδ^2)$. A random-matrix deterministic equivalent extends both laws to finite dimension, renormalizing the anchor to $ρ_{\mathrm{eff}} = ρ(e^{ζq} - 1) / (ζq)$; it matches simulation within 5% at fixed operating points and within 13% at the method's own, and rank-deficient populations reduce exactly to their active subspace. The resulting method, SPAR, calibrates window and strength online from residuals. On a 27-configuration grid the calibrated window opens on drift without divergence, and the grid defaults transfer to an hourly electricity stream and to BCI IV 2b. The core algebra, refresh chain, and regret bounds are formalized in Lean 4.

stat.ML · cs.AI · cs.GT · cs.LG

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13647

CP-MLPs: A Tensor-Rank Theory of Tied and Untied MLP Blocks

Md Rifat Arefin, Farzaneh Heidari, Irina Rish, Guillaume Rabusseau

原文摘要

Transformer feed-forward blocks combine several design choices: squared activations, gating, and tied versus untied parameter sharing, whose separate contributions to expressivity remain poorly understood. We introduce CP-MLPs, a tensor framework in which each multiplicative unit contributes a rank-1 interaction with three roles: detecting an input feature, reading a value, and writing to the output. Tied gated blocks such as ReLU$^2$ force the detector and value roles to share the same direction; untied gated blocks such as ReGLU and SwiGLU let them differ. We show that this distinction yields exact, degree-wise tensor-rank separations: untied detector-value units are strictly more width-efficient for indefinite quadratic interactions and role-asymmetric monomials, while tied units are structurally matched to symmetric pure-power targets. The width advantage of untying therefore depends on the target structure. Experiments show loss plateaus below the exact-representation width, but these plateaus alone do not establish a positive approximation gap: arbitrarily accurate approximation is governed by border rank. In trained gated MLPs, untied blocks retain an advantage in selected comparisons at matched input-projection budget. Code is available at https://github.com/rarefin/CP-MLPs.

cs.LG · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13565

Investigating Composite Modeling in Multi-Objective Bayesian Optimization for Scientific Design

Ricky Ye, Sahas Goli, Muhammad Ali, Poompol Buathong, Peter I. Frazier

原文摘要

Scientific design often requires balancing competing objectives that are expensive to evaluate through experiments or simulations. Multi-objective Bayesian optimization (MOBO) addresses this challenge by using probabilistic models to guide the selection of promising designs. In many applications, tunable inputs map to observable intermediate responses, which are then combined through known functions to compute the final objectives. Prior work on Bayesian optimization of composite functions shows that learning from these intermediate responses, which we call Composite modeling, can substantially improve sampling efficiency in single-objective optimization, compared to methods that condition only on black-box observations of the objective function. The benefits of Composite modeling in MOBO, however, remain understudied. In this work, we study the benefits of Composite modeling in MOBO and investigate the factors driving variation in its gains. We first establish single-objective conditions under which intermediate observations provide no additional predictive information beyond objective values, where composite and black box methods use the same warped Gaussian process prior. Controlled numerical experiments with versions of four MOBO methods across eight synthetic and application-inspired scientific-design benchmarks examine how these conditions relate to optimization gains in the multi-objective setting, where the black box approach models the objective functions with a standard multi-output Gaussian process. Both investigations support the claim that composite modeling tends to help more when the function mapping intermediate responses to final objectives is non-bijective and non-affine.

cs.LG · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13545

Closing the BF16-FP16 Convergence Speed Gap in RL Post-Training with Stochastic Rounding

Mahdi Nazemi, Oleg Rybakov, Tijmen Blankevoort, Asit Mishra, Carlo del Mundo

原文摘要

BF16 is widely used to pretrain large language models because it has the same dynamic range as FP32 and converges similarly to FP32 training. However, in reinforcement learning with verifiable rewards, where learning rates are typically low, we find that standard mixed-precision BF16 training converges more slowly than FP16 training at the same learning rate. We attribute this gap to weight sticking: when FP32 shadow weights are quantized to BF16 using round-to-nearest, small updates often leave the BF16 weights used for rollout generation and training unchanged. Consequently, several optimizer steps may be needed before updates to the shadow weights are reflected in the BF16 weights. Raising the BF16 learning rate reduces weight sticking and matches FP16's convergence speed, but it also increases the KL divergence from the reference model. We instead apply stochastic rounding when quantizing the FP32 shadow weights to BF16. This approach matches FP16's convergence speed across different models and datasets while reducing the KL divergence relative to BF16 training with a larger learning rate. Unlike FP16, it keeps BF16's wider dynamic range and needs no loss scaling.

cs.LG · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13489

Simultaneous Near-Optimal Region Identification in Continuous Simulation Optimization: Minimax Complexity and Adaptive Sampling

Yilin Zheng, Haowei Wang, Wenjia Wang, Szu Hui Ng

原文摘要

Simulation optimization typically returns a single estimated optimal point. When decisions also depend on criteria evaluated independently of simulation, such as resource cost, the decision maker instead needs the set of designs whose expected performance lies within a tolerance of the optimum, often choosing the tolerance only after seeing the tradeoffs. We study how to identify these near-optimal regions on a continuous design space, simultaneously for all tolerances up to a prescribed maximum $T$, with region estimation error at most $η$. We show that region identification is not a by-product of optimization. Specifically, when $α>ν$, any procedure, even one given the optimal design in advance, needs at least $Ω\bigl(η^{-(2+d/ν)}\min\{1,KT^{d/α}\}\bigr)$ simulation evaluations, where $d$ is the dimension, $ν$ the smoothness, and $(K,α)$ the covering parameters that describe the geometry of the near-optimal designs. We propose SASORI, which returns an estimated optimal point and the regions for all tolerances from the same evaluations, matching this lower bound up to logarithmic factors. SASORI also achieves the optimal tradeoff between region estimation error and cumulative regret, and reduces to a minimax-optimal simulation optimization procedure at zero tolerance. Numerical experiments illustrate the effectiveness of our proposed method.

stat.ML · cs.LG

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13485

Differentially Private Statistical Inference for Rankings from Pairwise Comparisons

Xintao Xia, Jia Gu

原文摘要

Reliable inference for rankings of large language models based on human pairwise comparisons must preserve the privacy of individual preference records. To meet this need, we develop methods for score and rank inference under the Bradley-Terry model with edge differential privacy. For an objective-perturbed estimator, a new leave-one-out analysis establishes finite-sample bounds on Euclidean and entrywise estimation errors. For sufficiently dense comparison graphs, the error bounds extend to smaller privacy budgets, including regimes in which its privacy term dominates its statistical term. A uniform asymptotic expansion yields asymptotically valid confidence intervals for individual scores and pairwise score differences. To improve finite-sample performance, we account for both regularization bias and privacy-induced randomness by combining a plug-in ridge-bias correction with Gaussian-Laplace calibration. We further establish a bootstrap procedure for simultaneous rank inference, providing asymptotically valid confidence sets for individual ranks and tests of top-$K$ membership. When the comparison probability is public and known, all proposed inferential procedures require no additional privacy budget. We evaluate finite-sample performance through simulations and apply the proposed methods to rank large language models for creative writing.

stat.ML · cs.LG · stat.ME

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.11652

Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces

Jeunghun Oh, Jaeyong Lee, Lizhen Lin, Kyeongwon Lee

原文摘要

We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation for KANs from a Bayesian point of view. We show that sparse Bayesian KANs equipped with spike-and-slab-type sparsity priors attain a near-minimax posterior contraction rate. In particular, the contraction rate depends on the intrinsic anisotropic smoothness of the underlying function. Moreover, by placing a hyperprior on a single model-size parameter, the resulting posterior adapts to unknown anisotropic smoothness and still achieves the corresponding near-minimax rate. A distinctive feature of our results, compared with those for standard multilayer perceptrons, is that the KAN depth can be kept fixed: owing to the expressive power of learnable spline edge functions, the required approximation complexity is controlled through the network width, the range and size of the spline grid, and parameter sparsity. Our analysis develops theoretical tools tailored to sparse spline-edge architectures, including approximation and complexity bounds for Bayesian KANs. We then extend to compositional Besov spaces and show that the contraction rates depend on layerwise smoothness and effective dimension of the underlying compositional structure, thereby effectively avoiding the curse of dimensionality. Together, these results advance the theoretical understanding of Bayesian neural networks and establish rigorous Bayesian guarantees for KANs.

stat.ML · cs.LG · math.ST

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2408.16852

The Star Geometry of Critic-Based Regularizer Learning

Oscar Leong, Eliza O'Reilly, Yong Sheng Soh

原文摘要

Variational regularization is a classical technique to solve statistical inference tasks and inverse problems, with modern data-driven approaches parameterizing regularizers via deep neural networks showcasing impressive empirical performance. Recent works along these lines learn task-dependent regularizers. This is done by integrating information about the measurements and ground-truth data in an unsupervised, critic-based loss function, where the regularizer attributes low values to likely data and high values to unlikely data. However, there is little theory about the structure of regularizers learned via this process and how it relates to the two data distributions. To make progress on this challenge, we initiate a study of optimizing critic-based loss functions to learn regularizers over a particular family of regularizers: gauges (or Minkowski functionals) of star-shaped bodies. This family contains regularizers that are commonly employed in practice and shares properties with regularizers parameterized by deep neural networks. We specifically investigate critic-based losses derived from variational representations of statistical distances between probability measures. By leveraging tools from star geometry and dual Brunn-Minkowski theory, we illustrate how these losses can be interpreted as dual mixed volumes that depend on the data distribution. This allows us to derive exact expressions for the optimal regularizer in certain cases. Finally, we identify which neural network architectures give rise to such star body gauges and when do such regularizers have favorable properties for optimization. More broadly, this work highlights how the tools of star geometry can aid in understanding the geometry of unsupervised regularizer learning.

cs.LG · math.MG · math.OC · math.ST · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13383

Settling the Burn-in Gap: Sharp Risk Bounds for Tail-Averaged SGD in Linear Regression

Qingyue Zhao, Xuheng Li, Quanquan Gu

原文摘要

We study the excess risk of constant-stepsize online stochastic gradient descent (SGD) with tail-averaging for high-dimensional linear regression. Building on the instance-dependent spectral framework of Zou et al. (2021), we establish matching initialization-explicit upper and lower bounds on the total excess risk of tail-averaged SGD in terms of the population covariance spectrum $\mathbf{H}$ and initialization $\mathbf{w}_0-\mathbf{w}^*$ whenever a trajectory spectral feedback condition holds. Existing analyses exhibit a fundamental gap in the effective variance: the upper bound of Zou et al. (2021) retains an undamped contribution from the initial error in the head eigenspace $\mathbf{I}_{0:k^\dagger}$, whereas their lower bound omits the variance induced by the head initialization altogether. We show that both the existing upper and lower bounds are loose: the single-hop fast-mode variance contribution from the head initialization is exponentially damped during the burn-in phase, whereas fourth-moment energy scattered from the head initialization into slow spectral modes during the early burn-in steps survives undamped into the averaging window. We prove that our spectral feedback condition is satisfied in two concrete constant-stepsize regimes: (i) for arbitrary covariance spectra $\mathbf{H}$ and any finite horizon, under an explicit horizon-dependent stepsize chosen prior to execution; and (ii) for polynomially decaying spectra $λ_i\asymp i^{-a}$ ($a>1$), under a single horizon-independent positive stepsize. Finally, we complement these positive results with explicit one- and two-dimensional separation constructions proving an exponential-versus-polynomial gap in the lower bound of Zou et al. (2021) and showing why fourth-moment assumptions alone cannot determine the asymptotic exponential decay rate without additional structural conditions.

cs.LG · math.OC · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v4arXiv:2603.23398

Graph Energy Matching: Transport-Aligned Energy-Based Modeling for Graph Generation

Michal Balcerak, Suprosanna Shit, Chinmay Prabhakar, Sebastian Kaltenbach, Michael S. Albergo, Yilun Du, Bjoern Menze

原文摘要

Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design. In these domains, probabilistic inference is particularly valuable, as it enables composable generation and principled incorporation of desired constraints, such as structural or functional properties. Energy-based models naturally support this goal by capturing relative likelihoods and enabling composable inference by directly enforcing constraints during inference. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities, resulting in a fidelity gap compared to discrete diffusion models. To address this gap, we introduce Graph Energy Matching (GEM), a discrete generative framework inspired by the Jordan-Kinderlehrer-Otto (JKO) transport-map optimization perspective. GEM learns a permutation-invariant potential energy that simultaneously guides discrete transport from noise toward high-likelihood graph regions and refines samples within these regions. We further introduce a sampling protocol leveraging an energy-based switching strategy, seamlessly bridging rapid, gradient-guided transport and a local mixing regime for effective exploration. On molecular graph benchmarks, GEM matches or surpasses strong discrete diffusion baselines on most reported metrics. Beyond improving generation quality, GEM's relative likelihood modeling enables targeted exploration, facilitating compositional generation, property-constrained sampling, and interpolation between graphs. Project page: https://michalbalcerak.ai/graph-energy-matching/.

cs.LG · cs.AI · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2605.21489

Variance Reduction for Gradients from Diffusion Teachers

Jesse Bettencourt, Xindi Wu, Matan Atzmon, James Lucas, Jonathan Lorraine

原文摘要

Pretrained diffusion models serve as frozen teachers for pipelines such as text-to-3D, single-step distillation, and data attribution. The teacher gradients these pipelines consume are expectations over noise levels and Gaussian noise, estimated by Monte Carlo (MC). Each MC draw requires expensive upstream work (rendering, simulation, encoding), so estimator variance dominates compute cost. We introduce CARV, a compute-aware variance-accounting framework that casts these gradients as a classical two-stage sampling problem with asymmetric per-level costs. This motivates a hierarchical MC estimator that amortizes each expensive upstream computation by reusing it across cheap diffusion draws, with within-unit variance further reduced by timestep importance sampling (IS) and stratified inverse-CDF sampling. CARV delivers 2 to 3x effective compute multipliers on text-to-3D and data attribution without changing the objective. In text-to-3D, reuse provides most of the gain and IS with stratification adds about 25%. In single-step distillation, the same techniques cut gradient variance by an order of magnitude but do not improve downstream FID, marking the regime where MC variance is no longer the bottleneck.

cs.LG · cs.AI · cs.CV · stat.CO · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13337

VC-Dimension and Generalization in Geometric Machine Learning with Applications to Active Learning

Gokul Bhusal, Delanna Do, Ekaterina Merkurjev, Kevin Miller, Stephan Wojtowytsch

原文摘要

We compute the VC-dimension of metric ball classifiers in the model spaces of Riemannian geometry (Euclidean, spherical, hyperbolic) and present upper and lower bounds on the VC-dimension of metric balls in several other situations, including general normed vector spaces (potentially infinite VC-dimension), vector spaces with $\ell^p$-norms (VC-dimension grows at least linearly in the dimension, faster than Euclidean for $p=1$), flat tori, and general Riemannian manifolds (arbitrarily large VC-dimension after a conformal change). In several situations where the VC-dimension is large or even infinite, we prove generalization bounds under additional assumptions on the data distribution using covering arguments. Both in the VC-dimension and covering setting, we consider data on low-dimensional subsets of high-dimensional Euclidean spaces. As an application, we consider coverage-based algorithms in active learning.

stat.ML · cs.LG · math.DG

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2611.02340

On Stochastic Continuous-Time Linear System Identification for Adaptive Stabilization

Reza Sadeghi Hafshejani, Mohamad Kazem Shirani Faradonbeh

原文摘要

System identification studies the canonical problem of reliably learning system-dynamics from state and input trajectories. One of its important applications consists of estimating a feedback gain matrix that can stabilize an unknown system. This paper focuses on the analysis of such adaptive stabilization schemes for multivariate linear time-invariant state-space models. The system instability practically renders trajectories short, i.e., the observed data is notably limited. So, it is crucial to tightly consider effects of \emph{all} involved quantities including length and number of trajectories, dimension, controllability Gramian, and signal-to-noise ratio. We put forward a simple, practical, and reliable relationship between the chance that adaptive stabilization (based on system identification) fails to stabilize the system, in terms of all the above-mentioned quantities. Our findings show that despite exponential effects of all other quantities on failure probability, such effects do not hold for signal-to-noise ratio. More specifically, this study shows that the strength of the excitation signal helps stabilization only \emph{logarithmically}; a very important phenomenon that we explain under the term \emph{signal saturation}.

stat.ML · cs.LG

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13295

Time Series Change Point Detection with Gaussian Processes

Olga Isupova, Danil Kuzin, Fredrik Gustafsson, Lyudmila Mihaylova

原文摘要

This paper proposes a novel general Gaussian process framework for change point detection in time series. A change is defined as an alteration of the hyperparameters of the Gaussian process prior. We formulate the problem in the context of statistical hypothesis testing and demonstrate its performance over both offline and online multiple change points detection. The approach provides theoretical guaranties of its performance. An important advantage of the developed framework is that it does not need a detailed specification of the time series function before and after a change. The hyperparameter values are learned from the data. Comprehensive evaluation of the proposed framework is provided both on synthetic and real data and its efficiency is demonstrated.

stat.ML · cs.LG · math.ST · stat.ME

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13228

Continuous Horizon Forecasting

Malcolm Wolff, Elliott Zackrone, Souhaib Ben Taieb, Michael W. Mahoney, Kin G. Olivares

原文摘要

Multi-horizon forecasting has been dominated by discrete forecast strategies that treat model outputs as fixed-vectors or recurrently create them. In this paper, we introduce the Continuous Horizon (CH) strategy that generalizes upon recursive, direct, and multi-step strategies by redefining forecasts as a continuous operator and the forecast horizon as a query variable rather than an index. We present the theoretical foundations for the CH strategy, a Universal Operator Approximation Theorem, and a continuous-horizon bias-variance decomposition that formally proves the estimation variance improvements of CH over the discrete strategies. We validate the CH strategy empirically through a simulation study, and on 16 large-scale datasets from the M-series benchmark, showing how CH achieves competitive RMSE accuracy, while uniquely enabling parallel inference, targeted horizon querying, and interpolation and extrapolation across unseen horizons.

stat.ML · cs.LG · math.ST

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2602.22847

Decentralized Ranking Aggregation via Gossip: Convergence and Robustness

Kerrian Le Caillec, Anna Van Elst, Igor Colin, Stephan Clémençon

原文摘要

The concept of ranking aggregation plays a central role in preference analysis, and numerous algorithms for calculating median rankings, often originating in social choice theory, have been documented in the literature, offering theoretical guarantees in a centralized setting, \textit{i.e.}, when all the ranking data to be aggregated can be brought together in a single computing unit. For many technologies (\textit{e.g.} peer-to-peer networks, IoT, multi-agent systems), extending the ability to calculate consensus rankings with guarantees of convergence and resilience to potential contamination in a decentralized setting, when preference data is initially distributed across a communicating network, remains a major methodological challenge. Indeed, in recent years, the literature on decentralized computation has mainly focused on computing or optimizing statistics such as arithmetic means using gossip algorithms. The purpose of this article is precisely to study how to achieve reliable and resilient consensus on collective rankings in a decentralized setting, thereby raising new questions, robustness to corrupted nodes, and scalability through reduced communication costs in particular. The approach proposed and analyzed here relies on the robustness guarantees offered by random gossip communication, which allows autonomous agents to compute a global ranking consensus using local interactions only, without coordination or a central authority.

cs.LG · cs.AI · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.13210

Near-Optimal Sample Complexity of Deterministic Agnostic PAC Learning

Shai Ben-David, Steve Hanneke, Farnam Mansouri, Amirreza Shaeiri

原文摘要

We study the problem of agnostic PAC learning under deterministic labels, where the examples are labeled by an arbitrary deterministic function, which need not belong to the concept class $C$. This model captures misspecification without stochastic label noise and lies between the realizable and fully agnostic settings. Prior work showed that, when $C$ has finite diameter $K$ and VC dimension $d$, deterministic labels can improve the sample complexity upper bound from the classical agnostic guarantee $O(d/\varepsilon^2)$ to $\widetilde{O}(K/\varepsilon)$, but left a large gap between upper and lower bounds. Our main result sharpens this picture. We prove that every class of VC dimension $d$ and finite diameter $K$ is learnable with sample complexity $\widetilde{O}\left( \frac{K^{1/3} \, d^{2/3}}{\varepsilon} \right)$, and we construct classes for which this bound is tight up to logarithmic factors. We also study the online analogue of this problem and show that the minimax regret is again partly controlled by the diameter of the class. Technically, our upper bounds are obtained via memorization-based learning algorithms that exploit the deterministic label structure.

stat.ML · cs.LG

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2604.08116

A unifying view of contrastive learning, importance sampling, and bridge sampling for energy-based models

Luca Martino

原文摘要

In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in EBMs is challenging for conventional inference methods. This work is a review paper that brings together these different methodological contributions within a unified framework, highlighting the connections among noise contrastive estimation (NCE), reverse logistic regression (RLR), Bennett's acceptance-ratio (BAR) method, multiple importance sampling (MIS), and bridge sampling within the context of EBMs. Some of them are equivalent under specific conditions. This unified perspective clarifies relationships among existing methods and enables the development of new estimators, with the potential to improve statistical and computational efficiency. Furthermore, this study helps elucidate the success of NCE in terms of its flexibility and robustness, while also identifying scenarios in which its performance can be further improved. Our aim is to provide a self-contained and accessible treatment, with clear and straightforward derivations, that brings together these contributions within a common framework and makes the main results and their underlying ideas understandable to a broader readership. The contribution is twofold. First, this work serves as a comprehensive tutorial for researchers entering the field, introducing the fundamental concepts and derivations. Second, it offers a thorough review for experienced practitioners. The code used in the numerical experiments is available to support the reproducibility of the results.

cs.CE · eess.SP · stat.CO · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.18298

Disentangling Forced and Internal Climate Variability in Single Realizations using Dynamic Mode Decomposition with Control

Nathan Mankovich, Andrei Gavrilov, Gustau Camps-Valls

原文摘要

Separating externally forced trends from internal climate variability is a fundamental challenge in climate science, particularly when analyzing observational records that exist only as a single realization. We show that a single climate realization can be decomposed into forced and internal components by treating external forcing as a dynamical driver within a linear stochastic system, an idea grounded in pullback attractor theory. This addresses a central challenge for climate projection and for detecting and attributing the forced response. Existing single-realization methods rely on linear inverse models (LIMs), which ignore forcing, or linear regression, which omits dynamics. Here we introduce PullbackDMDc, a method grounded in non-autonomous dynamical systems theory and dynamic mode decomposition with control (DMDc), incorporating pullback attractor estimation to decompose a single climate realization into spatial modes and their associated forced and internal components, yielding a physically interpretable picture of the underlying dynamics. After testing on a synthetic system with a known forced response, we illustrate the utility of PullbackDMDc for Earth System Model (ESM) evaluation by applying it to near-surface air temperature and sea-level pressure from reanalysis and four ESM large ensembles. PullbackDMDc estimates the forced response with skill matching or exceeding established baselines and helps select forcing predictors against model-based ground truth. Its internal-variability components reveal that ESMs qualitatively capture interannual and decadal modes while exhibiting systematic differences relative to each other and to observations. Skillful forced-response estimation and a novel decomposition position PullbackDMDc as a practical tool for single-realization climate analysis and ESM evaluation.

stat.ML · cs.LG · physics.ao-ph

查看论文
arXiv ↗PDF ↗