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新论文 · v1arXiv:2611.04341

Pairwise Distortion Distribution with Graph-Based Importance Sampling for Quantization Error and Intrinsic Dimension Estimation

Xi Chen, Carl Nuzman, Shirin Jalali

原文摘要

Quantifying the dimensionality of data is a fundamental need in machine learning and signal processing applications such as representation learning, data compression, and inverse problems, where the extrinsic dimension in which the data is presented can be very different from the intrinsic dimension that determines the operational performance. Various concepts, such as Rényi information dimension, rate-distortion dimension, and quantization dimension are useful here. Despite their theoretical significance, estimating these measures are challenging given their asymptotic definitions. Recent research has shown that analyzing the pairwise distortion distribution (PDD) of a data source can provide a tractable lower bound on the distortion of random codebook quantization, from which a tractable notion of intrinsic dimension can be derived. In this paper we extend this line of research in three main ways. First, we develop a related upper bound on distortion of random codebook quantization. Second, we improve the computability of both the lower and upper bounds, using a graph-based adaptive importance sampling approach. Third, we leverage the bounds to define new notions of intrinsic dimension which form upper and lower bounds on the Rényi information dimension, rate-distortion dimension, and quantization dimension, and which can be empirically estimated from unknown data sources. We illustrate the concepts by analyzing several artificial and empirical distributions.

cs.IT · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2605.13986

TabPFN-3: Technical Report

Léo Grinsztajn, Klemens Flöge, Oscar Key, Felix Birkel, Philipp Jund, Brendan Roof, Mihir Manium, Shi Bin Hoo 等 41 位作者

原文摘要

Tabular data underpins most high-value prediction problems in science and industry, and TabPFN has driven the foundation model revolution for this modality. Designed with feedback from our users, TabPFN-3 builds on this foundation to scale state-of-the-art performance to datasets with 1M training rows and substantially reduce training and inference time. Pretrained exclusively on synthetic data from our prior, TabPFN-3 dramatically pushes the frontier of tabular prediction and brings substantial gains on time series, relational, and tabular-text data. On the standard tabular benchmark TabArena, a forward pass of TabPFN-3 outperforms all other models, including tuned and ensembled baselines, by a significant margin, and pareto-dominates the speed/performance frontier. On more diverse datasets, TabPFN-3 ranks first on datasets with many classes, and beats 8-hour-tuned gradient-boosted-tree baselines on datasets up to 1M training rows and 200 features. TabPFN-3 introduces test-time compute scaling to tabular foundation models. Our API offering TabPFN-3-Plus (Thinking) exploits this to beat all non-TabPFN models by over 200 Elo on TabArena, rising to 420 Elo on the largest data subset, and outperforms AutoGluon 1.5 extreme while being 10x faster, without using LLMs, real data, internet search or any other model besides TabPFN. TabPFN-3 extends the capabilities of our models, enabling SOTA prediction on relational data (new SOTA foundation model on RelBenchV1) and tabular-text data (SOTA on TabSTAR via TabPFN-3-Plus); and improves existing integrations: a specialized checkpoint, TabPFN-TS-3, ranks 2nd on the time-series benchmark fev-bench, and SHAP-value computation is up to 120x faster. TabPFN-3 achieves this performance while being up to 20x faster than TabPFN-2.5. In addition, a reduced KV cache and row-chunking scale to 1M rows on one H100 with fast inference speed.

cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04307

Nearly Linear-Time Follow-the-Perturbed-Leader for Weakly Observable Graph Bandits

Jongyeong Lee, Hyundam Yoo

原文摘要

We study online learning with directed weakly observable feedback graphs and propose a Follow-the-Perturbed-Leader (FTPL) policy that achieves best-of-both-worlds guarantee with nearly linear expected time complexity. To preserve the simple structure of FTPL, we develop a novel graph-based loss estimator that combines forced exploration, conditional geometric resampling and adaptive learning rates with surrogate probabilities. Our policy achieves $\tilde{\mathcal{O}}(δ_*^{1/3} T^{2/3})$ regret for adversarial regimes as well as $\tilde{\mathcal{O}}(δ_* \log T / Δ_{\min}^2)$ regret for stochastic regimes, where $δ_*$ and $Δ$, respectively, denote the fractional weak domination number and the suboptimality gap. These results show that refined guarantees for problems with minimax regret of $Θ(T^{2/3})$ can be obtained through appropriately designed adaptive learning rates and loss estimators without sacrificing the simplicity of FTPL.

stat.ML · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2511.13025

Recovering Geodesic Distances from Noisy Observations

Charles Fefferman, Jonathan Marty, Kevin Ren

原文摘要

Let $(M,d,μ)$ be a nice geodesic probability space (such as a manifold) and $X=\{x_i\}_{i\in [N]} \subset M$ a finite $μ$-i.i.d. sample. Suppose we observe noisy distance random variables $d'(x_i,x_j)$. When can the true distances be recovered to small additive error? This question has attracted interest in two disparate fields: latent-space graph models and boundary-value inverse problems. We first show that, taking $N \asymp ε^{-2d-2}|\logε|$ and using runtime $O(N^{2.5+o_d (1)})$, we can recover all distances in $X$ to additive error $O(ε|\logε|)$ with high probability, assuming $\mathbb{E} d'(x_i, x_j) = F(d(x_i,x_j))$ for an unknown, increasing bilipschitz $F$ and with the $d'(x_i,x_j)$ allowed to be arbitrarily heterogeneous in their distribution as long as they are bounded in subgaussian norm. This generalizes existing work, which required $F$ to be known and made strict assumptions on the distribution of $d'(x_i, x_j)$. Achieving this generalization required a novel ``ruler-building'' procedure to learn $F$. We extend our results to a missing data case where we randomly lose access to noisy distances. Our second result uses ideas from the first to tackle a partial observability case: $X = Y \cup Z$ with $Z$ sampled from $M$ and $Y$ sampled from an observer subset satisfying visibility conditions that model the assumptions made on the boundary in boundary-value inverse problems. In this setting, we recover all pairwise distances in $Z$ to additive error $O(ε)$ with $|Z| \asymp ε^{-2d-2}|\logε|$, $|Y| \asymp ε^{-\max\{d_ν,4\}}$ with $d_ν$ determined by the volume-growth properties of the probability measure on the observer set, and runtime $O(|Z|^3)$. This is, to our knowledge, the first quantitative guarantee for this observer/observed split under noise, which complements existing stability results for boundary data.

stat.ML · cs.LG · math.DG · math.PR

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04292

How Risky Is Your Data-Driven Policy?

Omar Besbes, Alon Rieger

原文摘要

Data-driven algorithms are ubiquitous across industries, and there is an extensive literature on analyzing their \emph{average} performance. The risk profile of such algorithms, while critical, is much less understood. This paper quantifies the risk of data-driven policies and isolates its sources. We evaluate a policy through the conditional value-at-risk (CVaR) of its loss over the training sample, any policy randomization, and the future outcome, at a fixed unknown distribution. Regret against an oracle that knows the distribution decomposes into expected post-sample regret (PS), the average outcome-only CVaR gap of the selected action, and a sample-risk premium (SR), the additional tail risk omitted by averaging those evaluations. The analogous premium vanishes under expected loss. We characterize when the premium vanishes and how large it is relative to post-sample regret. For losses with a continuous density near the tail cutoff, we identify conditions under which both components decay at the same rate, yet the limiting ratio of the premium to post-sample regret can reach the thousands. When a probability mass at the cutoff moves with the action, the premium can decay more slowly and dominate post-sample regret. We establish conditions under which sample average approximation learns the oracle action at rate $n^{-1/2}$ in both settings, but its combined-risk regret is of order $n^{-1}$ in the first and $n^{-1/2}$ in the second. In finite-sample numerical examples of SAA in both settings, the premium accounts for approximately $74\%$--$97\%$ of regret.

stat.ML · cs.LG · math.OC

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04256

OmniST: Topology-Invariant Spatiotemporal Forecasting with Guaranteed-Coverage Uncertainty at Unseen Sensor Locations

Praveg Vashishtha

原文摘要

Standard spatiotemporal graph convolutional networks need a fixed-size adjacency matrix, coupling model weights to a specific sensor count N; they cannot produce any output at a sensor absent from training. We present OmniST, a topology-invariant forecaster whose computation has zero structural dependency on the number of nodes, and which, composed with inductive split-conformal calibration, gives distribution-free, coverage-guaranteed prediction intervals at arbitrary (including never-seen) sensor locations, preserving that guarantee as sensors are added or removed. Topology invariance follows from coordinate-based tokenization, k-nearest-neighbor attention from geographic coordinates at each forward pass, and per-node temporal processing via a bidirectional GRU. On real Delhi air-quality data (37 stations, 2019-2023), OmniST attains a 30-day PM2.5 MAE of 31.0 ug/m3 and degrades at most 1.1 percent when 40 percent of stations are removed. Its inductive forecasts at unseen stations beat nearest-neighbor interpolation (about 12 percent) and a learned kriging GNN (IGNNK, about 21 percent), and, unlike either, carry a finite-sample coverage guarantee. The guarantee holds at 90 percent or above under 30-50 percent node dropout across four real datasets over three domains (Delhi and Beijing air quality, NOAA GHCN weather, Caltrans PeMSD7-M traffic), and still holds at 325 real sensors (full PeMS-BAY). We also fix a temporal-drift failure: static conformal under-covers over time (about 0.50 late), but a rolling adaptive-conformal estimator restores target coverage (0.89 overall, 0.96 late) at the cost of wider intervals.

cs.LG · cs.AI · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04211

Two-Layer Random ReLU Networks Can Separate Disjoint Classes

Yichen Liu, Jianbin Yang

原文摘要

Set separation by continuous linear functionals is fundamental in functional analysis and convex optimization and underlies binary classification in machine learning. Support vector machines provide maximum-margin affine separators for linearly separable data, while kernel methods represent nonlinear decision rules through linear separation in a reproducing-kernel Hilbert space. We study when two classes, not necessarily convex or linearly separable in the input space, can be separated with positive margin by finite ReLU networks and by random ReLU features. At the deterministic level, we prove that positive-margin separation by a finite ReLU network is equivalent to the existence of finite closed convex covers whose opposite-label members have positive pairwise distances, and exactly two hidden layers suffice. For random separation, suppose each class is represented as a finite union of nonempty closed convex cells, possibly unbounded. If every opposite-label cell pair has positive distance and its closed difference cone is pointed, then two independent random ReLU layers yield a common positive-margin affine separator with high probability. The first layer separates the feature image of each negative cell from the feature image of the positive class by a hyperplane through the origin. It also controls all cross-class distances uniformly. The second layer combines cellwise scores through Chebyshev polynomials and realizes the resulting polynomial using Gaussian Hermite features, followed by a uniform finite-width approximation. With the remaining geometric, bias, and confidence parameters fixed, each sufficient width is quadratic in the largest Gaussian width of a spherical difference-cone section, hence at most linear in its span dimension. An example shows that this squared Gaussian-width dependence is sharp for both layers.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04207

Point interpolation and distributional universality in flow-based generative models

Antonio Álvarez-López, Jingpu Cheng, Liyan Zhang, Qianxiao Li

原文摘要

Motivated by the expressive power of neural ordinary differential equations in flow-based generative modeling, we study the approximation of probability measures by pushforwards generated by parameterized families of Lipschitz vector fields. For Wasserstein distances, we establish a quantitative relationship between finite-sample point interpolation and distributional approximation, and derive universality criteria based on $L^p$-approximation of transport maps. In particular, affine-invariant families containing a non-affine vector field are universal from compactly supported absolutely continuous base measures. For total variation, we show that coordinate-wise dynamics are insufficient in dimensions $d\geq 2$ and establish sufficient conditions based on one-dimensional Sobolev approximation and shear-type mixing. We further examine the role of point interpolation, establishing when different regimes relate to one another and when approximate interpolation can be made exact.

stat.ML · cs.LG · math.OC

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04193

Statistical Machine Learning for Medicinal Plant Leaves Classification

Jayani P. Gamage, Thiyanga S. Talagala

原文摘要

Medicinal plants are usually identified using practitioners' experience, but reproducible, image based methods can complement this knowledge. We present MEDIPI (MEDIcinal Plant Identification), a statistical machine learning approach that classifies medicinal plant leaves from photographs. From each leaf image we extract 52 interpretable features covering shape, texture, color, and a new scagnostics category. We then classify leaves using a three level hierarchy: shape, then edge type, then species. We also release MedLEA, an open R package with 1,099 leaf images of 31 Sri Lankan medicinal plant species. On this dataset, a hierarchical Random Forest achieved the best overall accuracy (100%) in our comparison of hierarchical and non-hierarchical approaches and eight algorithms: Random Forest, XGBoost, Gradient Boosting, linear discriminant analysis, k-nearest neighbor, support vector machine, probabilistic neural network, and artificial neural network. Adding texture, color, and scagnostic features to shape features raised shape level accuracy from 90% to 97%. Linear discriminant analysis plots show how the trained model separates leaf shapes. Accuracy dropped sharply (23-50%) when training and test data came from different datasets, so generalization across datasets remains a challenge.

cs.CV · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04171

Descending Everest, Part II: Oracle Complexity of Minimizing a Sum of Convex $(L_0,L_1)$-Smooth Functions

Mikhail Rudomanov, Ivan Fomin, Alexander V. Gasnikov, Fedor S. Stonyakin

原文摘要

We study the minimization of the average of $n$ convex $(L_0,L_1)$-smooth functions: the Hessian norm of each function is bounded by an affine function of its gradient norm. We assume known upper bounds $R$ on the distance from the starting point to a minimizer and $δ$ on the difference between the minimum of the average and the average of the infima of the components. We derive upper and lower bounds on the oracle complexity of reaching accuracy $\varepsilon$ in function value in expectation. Up to logarithmic factors, both bounds are of order $n(1+(L_1R)^{2/3}) +\sqrt{\frac{n(L_0+L_1^2δ)R^2}{\varepsilon}+n(L_1R)^2}$. The upper bound is attained by the proposed method YETI. The method combines ideas of accelerated proximal methods and variance reduction methods with a heuristic for choosing additional points. The number of oracle calls made by the heuristic is bounded, which preserves the upper bound on the total number of queries needed to reach the target accuracy. In the experiments, YETI is compared with first-order methods on synthetic problems and Poisson regression problems. We also examine the stopping criterion and the effect of the heuristic separately. The lower bound is obtained by an explicit construction of families of instances that are hard for any first-order method.

math.OC · cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04157

Nonparametric GARCH: An Iterated Neural Estimator

Ruizhi Deng, Guohao Shen, Ngai Hang Chan

原文摘要

We study nonparametric estimation and forecasting for GARCH-type processes and propose an iterated neural estimator that alternates between estimating the recursion map and updating the unobserved conditional variances. Under mild conditions, we establish finite-sample bounds for the time-averaged in-sample variance-path error and show that the estimator is minimax rate-optimal up to logarithmic factors. Under stationarity and mixing conditions, we establish the same rate for recursion-map estimation and derive finite-sample bounds for out-of-sample variance forecasts and expected excess Gaussian quasi-likelihood (QLIKE) loss. The convergence rates depend on the true lag orders and remain unchanged when the fitted orders are overspecified. Simulation studies illustrate the effectiveness of our estimators under nonlinear and time-varying volatility dynamics. Real-data applications suggest that our neural methods perform competitively and can incorporate option-price and high-frequency information.

stat.ML · cs.LG · math.ST · stat.ME

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arXiv ↗PDF ↗
版本更新 · v5arXiv:2604.24749

The Optimal Sample Complexity of Multiclass and List Learning

Chirag Pabbaraju

原文摘要

While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification had remained open. The appropriate complexity parameter for multiclass classification is the DS dimension, and despite significant efforts, a gap of $\sqrt{\text{DS}}$ had persisted between the upper and lower bounds on sample complexity. Recent work by Hanneke et al. (2026) shows a novel algebraic characterization of multiclass hypothesis classes in terms of their DS dimension. Building up on this, we show that the maximum hypergraph density of any multiclass hypothesis class is upper-bounded by its DS dimension. This proves a longstanding conjecture of Daniely and Shalev-Shwartz (2014). As a consequence, we determine the optimal dependence of the sample complexity on the DS dimension for multiclass as well as list learning.

cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2609.09981

Optimal Value Inference for Reinforcement Learning

Nan Lu, Ethan Lee, Ruicheng Ao, David Simchi-Levi, Junwei Lu

原文摘要

We study offline inference for the optimal value in reinforcement learning under finite state and action spaces. Two new nuisances are derived as fixed points of a self-induced Bellman equation, in which we approximate the maximum Bellman operator by its softmax correspondence. We propose a debiased estimator through the Neyman orthogonality and establish its asymptotic normality under diverging horizons even when the behavior policy changes with time, as long as the nuisances have the statistical rates that can be achieved by many machine learning methods. We provide a concrete estimating procedure for these nuisances and show they can lead to valid inference. Synthetic experiments validate the numerical performance of our inference method, and we implement it in real-life decision-making problems, including bike repositioning and AI agentic tool use.

stat.ML · cs.LG · stat.ME

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2605.05179

Estimating the expected output of wide random MLPs more efficiently than sampling

Wilson Wu, Victor Lecomte, Michael Winer, George Robinson, Jacob Hilton, Paul Christiano

原文摘要

By far the most common way to estimate an expected loss in machine learning is to draw samples, compute the loss on each one, and take the empirical average. However, sampling is not necessarily optimal. Given an MLP at initialization, we show how to estimate its expected output over Gaussian inputs without running samples through the network at all. Instead, we produce approximate representations of the distributions of activations at each layer, leveraging tools such as cumulants and Hermite expansions. We show both theoretically and empirically that for sufficiently wide networks, our estimator achieves a target mean squared error using substantially fewer FLOPs than Monte Carlo sampling. We find moreover that our methods perform particularly well at estimating the probabilities of rare events, and additionally demonstrate how they can be used for model training. Together, these findings suggest a path to producing models with a greatly reduced probability of catastrophic tail risks.

cs.LG · cond-mat.dis-nn · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04066

Graph-Localized Coverage for Conformal Prediction on Inductive Graphs

Jinwen Xu, Qin Lu, Georgios B. Giannakis

原文摘要

Conformal prediction (CP) provides marginal coverage guarantees, but marginal coverage does not determine where prediction errors occur on a graph. Queries from different graph neighborhoods can exhibit substantially different levels of uncertainty even when aggregate coverage remains near its target. We introduce GLocalCP, an online CP framework for inductive node classification and edge prediction that combines marginal and graph-local calibration with uncertainty-adaptive prediction sets. Specifically, GLocalCP puts forth a novel uncertainty-adaptive nonconformality score that relies on the mutual information obtained from Monte-Carlo (MC) dropout based prediction. Then, it augments a global online threshold with a kernel-based local correction that propagates coverage feedback among similar graph queries. On the theoretical horizon, we establish pathwise $O(N^{-1/2})$ marginal calibration error without exchangeability or stationarity and, for the exact-kernel formulation, an explicit $O(N^{-1/2})$ graph-localized calibration guarantee. Experiments on seven node-classification and seven edge-prediction benchmarks show that similar marginal coverage can conceal substantially different local reliability. Our proposed GLocalCP maintains coverage near the target while consistently reducing graph-local calibration error. Uncertainty scaling in GLocalCP further reduces prediction-set size across all evaluated node and edge datasets while leaving marginal coverage essentially unchanged.

cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2503.01036

Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis

Bamdad Hosseini, Alexander Hsu, Yasamin Jalalian, Juan Felipe Osorio Ramirez, Houman Owhadi

原文摘要

We introduce a novel kernel-based framework for learning differential equations and their solution maps. The framework is efficient in its data requirements in terms of the number of observed states and the amount of data available per state. Our formulation also allows us to employ efficient Gauss-Newton-type optimization algorithms in the training procedure to improve accuracy and speed of the training procedure. We also support our algorithm with rigorous theoretical guarantees in the form of quantitative worst-case error bounds for the learned equation that can be extended to the subsequent solution operators under smoothness assumptions. Numerical benchmarks demonstrate significant improvements in computational complexity and robustness while achieving one to two orders of magnitude improvements in terms of accuracy compared to certain state-of-the-art algorithms.

stat.ML · cs.LG · math.NA

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04062

StreamLTT: Risk Certification for Policy Selection under Stream Dependence

Jinwen Xu, Qin Lu

原文摘要

Learn-then-Test (LTT) provides a general framework for certifying deployment policies against a prescribed risk target, but its standard formulation targets a fixed population risk estimated from calibration losses. In sequential deployment, losses may instead be dependent and nonstationary, so the risk of a fixed policy can evolve with the observed history. We introduce StreamLTT, which replaces this fixed population risk with average predictable risk, defined by conditioning each decision's loss on the information available before its outcome is revealed. Conditional centering turns empirical deviations from this target into a martingale sum, enabling both a test that adapts to predictable variance and a finite-sample Hoeffding alternative. Combined with family-wise error rate control, StreamLTT yields a simultaneously certified policy region that supports subsequent deployment selection. Across seven forecasting datasets and seven deployment risks, StreamLTT places the certified frontier substantially closer to the prescribed risk target than IID, robust-variance, block-bootstrap, and concentration-based alternatives, while empirical family-wise error closely follows the prescribed level. A finite-sample ablation further shows that the predictable-risk formulation drives the tighter risk frontier, while adaptation to predictable variance makes more effective use of the available family-wise error budget. StreamLTT therefore extends risk-certified policy selection to dependent deployment streams by addressing both what risk should be certified and how it should be tested.

cs.LG · math.ST · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04043

Denoising Is Stein: Moment Access and a Resource Hierarchy for Learning Hidden Structure in Diffusion Models

Rui Wang

原文摘要

We study score learning from denoising pairs when the data contain a hidden non-Gaussian component. If covariance reveals the component, its subspace can be recovered directly. If covariance is isotropic, the first distinguishing moment has order $k^\ast$, and the learner must extract that moment from clean points and their noisy views. Correlations in the denoising loss are Stein discrepancies against a baseline; for polynomial fields they determine exactly the corresponding moment differences. Averaging fresh noisy views conditional on a clean point gives an exact moment query on the clean distribution. In the covariance-matched regime, orientation-independent dictionaries satisfying an $L^4/L^2$ condition need order $d^{k^\ast-1}$ features, and the stated dot-product kernel ridge models need the same power in samples. Small-step online SGD on one unit has this exponent up to logarithms. A two-stage learner uses the curvature of a smoothed denoising loss to recover the hidden direction, then sharpens it and fits a scalar readout. For every even $k^\ast$, it obtains a fixed score gain over the Gaussian baseline from $O(d^{k^\ast/2}\log d)$ clean points. In the covariance-visible regime, the frozen-feature threshold occurs at $d^J/J!$, while projection onto principal components makes the fitted-model, score-risk and generated-law distributions independent of ambient dimension. In the covariance-matched experiments, the measured partial-trace overlaps are consistent with the proposed spectral transition. A width-8 network trained with clean-point reuse shows a $d^2$-like training-set threshold over $d=64$--$192$, with fixed validation and calibration overhead.

cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.03614

Benchmark Prediction with Sparse and Unpaired Cached Responses

Hayden Helm, Avijit Ghosh, Ben Johnson, Carey Priebe

原文摘要

Evaluating a generative model on all queries from all available benchmark tasks is prohibitively expensive. As such, models are often evaluated on different subsets of tasks and/or different subsets of queries from a given task. The resulting collection of responses and the corresponding (model, task) score matrix are sparse and unpaired. In this paper, we introduce the Product Kernel Perspective Space (PKPS), a collection of low-dimensional representations of models based on their embedded responses. PKPS generalizes existing methods for representing black-box generative models by comparing responses to similar -- rather than just identical -- queries and is therefore able to utilize sparse and unpaired information. Theoretically, we show that benchmark prediction using PKPS is query-efficient relative to methods that only use information from dense and paired portions of the evaluation data. Empirically, we show that PKPS-based methods outperform baselines on benchmark prediction across two large benchmark suites.

cs.LG · stat.ME · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.03612

Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches

Rileigh Bandy, Teresa Portone, Mohammad Khalil, Eric Crislip, Kyle Neal

原文摘要

Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require rapid evaluations for fast design iterations. Closure models address this challenge by approximating unresolved effects in reduced or incomplete dynamical systems. Data-driven closures offer a flexible mechanism for improving model accuracy and applicability, but approaches that embed the closure within a computational model for construction and training phases can be computationally expensive and cause numerical instabilities in the computational model during training. To avoid the challenges posed by embedded approaches, staged approaches to closure-model learning have been developed. The first stage uses data assimilation to infer state and closure trajectories from observations. The second stage trains a machine learning closure model offline using the assimilated data, thereby avoiding repeated simulator calls during training. In this work, we investigate the cost and accuracy tradeoffs between embedded and staged data-driven closure modeling approaches for a synthetic epidemiological SIQR model with a nonlinear state-dependent quarantine closure. The results illustrate a practical accuracy-efficiency trade-off: for this exemplar, embedded training provides the strongest average accuracy, while the staged approach yields comparable qualitative behavior with a moderate increase in error, substantially fewer model evaluations, and improved optimization robustness.

cs.LG · math.DS · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.03512

ST-GFM: Spectral-Temporal Graph Forecasting with Measured Perturbation Bounds and Masked Spectral Reconstruction

Aashish Bohra, Vivek Vijay

原文摘要

Graph forecasters for sensor networks are trained in one regime and deployed in others, where sensor coupling and signal frequency content both change. We split this spectral shift into an operator channel and a frequency channel, each with a dimensionless measure. ST-GFM (Spectral-Temporal Graph Forecasting Model) filters every input step with Chebyshev and bidirectional diffusion filters on one learned, non-symmetric operator and alternates them with per-node temporal attention. For the operator channel we prove Frobenius-norm perturbation bounds for both graph branches, show that the Chebyshev bound is attained to first order, and compute its constant from the trained weights and the measured operator norm: 17.9 on METR-LA and 21.5 on PEMS-BAY. Under random edge dropout the trained layer moves by 2.0% to 3.1% of this bound. Masked Spectral Reconstruction (MSR), a self-supervised loss active in the first 40 epochs, matches the log power spectrum of the encoder output to that of the input. For small log-spectral residuals on unclamped bins it is proportional to an Itakura-Saito divergence to leading order. Removing it raises the 60-minute MAE by 0.30 on METR-LA, close to the 0.33 lost when all three self-supervised losses go. Under one shared evaluation pipeline, the 60-minute MAE of ST-GFM is 3.5% below a retrained STAEformer on METR-LA and 13.0% below it on PEMS-BAY. Its 60-minute MAE is 3.0980.017 on METR-LA (five seeds) and 1.5760.006 on PEMS-BAY (three seeds), the lowest PEMS-BAY MAE among twelve published baselines.

cs.LG · eess.SP · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.09166

Lower Bounds for Parallel Diffusion Sampling

Yiwen Kou, Yimeng Wang

原文摘要

Standard diffusion samplers generate samples through sequential evaluations of a learned score function, with each query depending on previous answers. Parallel samplers seek to accelerate this process by making multiple score queries simultaneously. We ask how many adaptive rounds are necessary when each round allows polynomially many queries. We establish the first polynomial lower bounds on the round complexity of diffusion sampling with approximate scores satisfying a mean-square accuracy guarantee. Specifically, we prove (1) a $\widetildeΩ(d^{1/3})$-round lower bound for sampling smooth, near-isotropic Gaussian mixtures in $\mathbb{R}^d$, and (2) a tight $Ω(d)$-round lower bound for uniform sampling from anisotropic axis-aligned boxes contained in the unit ball. Both bounds hold for arbitrary randomized algorithms making polynomially many queries per round at arbitrary locations and noise levels, with inverse-polynomial score error and constant total variation accuracy. Our near-isotropic construction follows the blockwise approach of earlier lower bounds for parallel matroid search and discrete sampling \cite{KUW85,AGR24}. We use independent coordinate blocks containing random codebooks with well-separated rates and construct approximate score oracles whose responses in each block depend on consistency tests in earlier blocks. Together, the rate separation and these tests ensure that each round reveals information about at most one additional block with high probability.

cs.DS · cs.AI · cs.CC · cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.17749

Testable and Actionable Calibration for Full Swap Regret

Konstantina Bairaktari, Lunjia Hu, Huy L. Nguyen, Jonathan Ullman

原文摘要

AI generated predictions increasingly inform decision making in critical tasks, and therefore must be trustworthy. One widely used measure of trustworthiness is calibration, which requires that the predictions match the true frequencies and can be treated like real probabilities of a given outcome. However, defining calibration is subtle, and designing good measures of calibration error has been an active topic of recent research. The first goal is to find calibration measures that are actionable, meaning they can inform decision makers about their utility loss when predictions are treated as true probabilities, which is known as swap regret. The second goal is to find calibration measures that are testable, meaning that calibration error can be measured from a small sample of predictions and outcomes. Although these are very basic requirements, there is no existing calibration measure that fully satisfies both properties, and all existing measures relax actionability by bounding a weaker notion of swap regret, or relax testability by having suboptimal estimation error. We introduce a new calibration measure, Soft-Binned Calibration Decision Loss (SCDL), which we prove is fully actionable without weakening either requirement, and testable with nearly optimal error rate. In addition, SCDL satisfies other desired properties such as continuity and consistency. We also provide a set of experiments confirming that the theoretical advantages of SCDL compared to other measures lead to better performance in practice.

cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.03472

Tilted Convexity and an Exact Offline-Online Separation

Mohammad Pedramfar, Rajiv Khanna, Christopher John Quinn, Vaneet Aggarwal

原文摘要

Convexity has three equivalent descriptions: support by affine functions, monotonicity of the subdifferential, and increasing secant slopes. We weaken all three by one distortion with parameter $γ\in(0,1]$, which multiplies positive changes by $γ$ and divides negative ones by $γ$. The resulting classes are the convex functions at $γ=1$ and, for $γ<1$, are distinct and nested, with the parameter dropping by at most a square along the chain. For proper lower semicontinuous functions in these classes, the effective domain is convex, local minimizers are global, and the function is locally Lipschitz on the relative interior of its domain. The classes separate offline from online optimization over compact convex sets with efficient projection, with access to function values and bounded support vectors. A smooth member of any class can be minimized to additive accuracy $\varepsilon$ with $\mathrm{poly}(1/\varepsilon)$ first-order queries and projections. Online, with nonpositive losses and $α$-regret measured against $α$ times the best fixed point, a polynomial-time algorithm achieves $γ$-regret $O(\sqrt T)$ on the largest class. For every fixed, effectively specified $γ\in(0,1)$ and every $α\in(γ,1]$, no randomized polynomial-time algorithm has sublinear expected $α$-regret unless $\mathbf{NP}=\mathbf{RP}$, already for smooth concave polynomial losses in the smallest class, each minimized by one linear optimization. Thus, unless $\mathbf{NP}=\mathbf{RP}$, $γ$ is the exact online coefficient of each class, while the offline coefficient is one.

cs.LG · cs.CC · math.OC · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2510.20094

On the Structure of Stationary Solutions to McKean-Vlasov Equations with Applications to Noisy Transformers

Krishnakumar Balasubramanian, Sayan Banerjee, Philippe Rigollet

原文摘要

We study stationary solutions of McKean-Vlasov equations on the circle. We establish an exact equivalence between solutions of the stationary McKean-Vlasov equation and an infinite-dimensional quadratic system of equations over Fourier coefficients, allowing explicit characterization of stationary states in a sequence space rather than a function space. This framework provides a transparent description of local bifurcations, their periodicity and resonance structures, while accommodating singular potentials. We derive analytic expressions for the emergence, form and shape (supercritical, critical, subcritical or transcritical) of bifurcations involving possibly multiple Fourier modes and connect them with discontinuous phase transitions. We also characterize, under suitable assumptions, the detailed structure of the stationary bifurcating solutions through leading small-amplitude coefficients for arbitrarily many fixed Fourier modes. At the global level, we establish regularity and concavity properties of the free energy landscape, proving existence, compactness, and coexistence of globally minimizing stationary measures, and identifying discontinuous phase transitions with points of non-differentiability of the minimum free energy map. We apply the theory to the Noisy Mean-Field Transformer model, where we show how changing the inverse temperature $β$ affects the geometry of the infinitely many bifurcations from the uniform measure. We also discuss how increasing $β$ motivates the study of approximate multi-mode stationary profiles as candidates for a separate metastability analysis; persistence times require additional dynamical estimates. Moreover, we determine the exact threshold $β_0\simeq2.447$ separating continuous and discontinuous phase transitions in this model. The same threshold marks the change of the first bifurcation from supercritical to subcritical.

math.PR · cs.AI · cs.LG · math.AP · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2601.06514

Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matching

Jinyuan Chang, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Yi Xu, Jerry Zhijian Yang

原文摘要

Inference-time alignment for diffusion models aims to adapt a pre-trained reference diffusion model toward a target distribution without retraining the reference score network, thereby preserving the generative capacity of the reference model while enforcing desired properties at inference time. A central mechanism for achieving such alignment is guidance, which modifies the sampling dynamics through an additional drift term. In this work, we introduce variationally stable Doob's matching, a novel framework for provable guidance estimation grounded in Doob's $h$-transform. Our approach formulates guidance as the gradient of the logarithm of an underlying Doob's $h$-function and employs gradient-regularized regression to simultaneously estimate both the $h$-function and its gradient, resulting in a consistent estimator of the guidance. Theoretically, we establish non-asymptotic convergence rates for the estimated guidance. Moreover, we analyze the resulting controllable diffusion processes and prove non-asymptotic convergence guarantees for the generated distributions in the Wasserstein-2 distance. Finally, we show that variationally stable guidance estimators are adaptive to unknown low dimensionality, effectively mitigating the curse of dimensionality under low-dimensional linear subspace assumptions. Numerical experiments demonstrate the effectiveness of our proposed method and show the advantages compared to the baselines.

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

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.03445

Error Accumulation in Second-Order Sequential Machine Unlearning

Chen Shang, Haolin Zou, Binghe Zhu, Arian Maleki

原文摘要

Machine unlearning seeks to remove the influence of deleted training data without full retraining. In the sequential setting, deletion requests arrive over time, and repeated updates can accumulate approximation errors. In this paper, we study error accumulation in high dimensions, where parameter count $p$ is proportional to sample size $n$, for second-order unlearning methods under two privacy settings: (i) \emph{partial unlearning}, which allows unpublished internal states to be retained while certified versions of the model are released; and (ii) \emph{perfect unlearning}, which retains only published models and no hidden states. We also distinguish pointwise and pathwise certification, depending on whether the certification guarantee applies to each released model or the whole released sequence. We analyze conjugate gradient (CG) as an efficient solver for the inverse Hessian-vector product (IHVP) in Newton iterations. Our theory shows that a maximum of 1/2/2/3 Newton--CG updates suffice for successful certification and vanishing population-risk degradation of the published model, for pointwise partial, pathwise partial, pointwise perfect and pathwise perfect certification, respectively. Numerical experiments demonstrate accurate sequential tracking and substantial computational gains of Newton-based methods combined with conjugate gradient, over gradient-based updates, especially for ill-conditioned problems.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.03442

Subpolynomial-Query Proximal Sampling Beyond Log-Concavity

Wei Guo, Bo Yuan, Ye He, Jiaming Liang, Molei Tao, Yongxin Chen

原文摘要

We study the gradient query complexity of sampling from a density $π(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ has a $β$-Lipschitz gradient but need not be convex. Our approach uses the proximal sampler, which alternates Gaussian perturbation with sampling a position conditional on the noisy observation. We implement its observation chain using the high-order noisy conditional sampler of [OpenAI 2026], obtaining improved dimension dependence under functional inequalities. If $π$ satisfies a log-Sobolev inequality (LSI) with constant $α$, then for every fixed $ν>0$, there is a finite constant $C_ν$ depending only on $ν$ such that the algorithm returns a sample within total-variation distance $\varepsilon$ using at most $C_νκ(d+κ+\varepsilon^{-1}+\|\nabla V(x_0)\|^2/β)^ν$ queries, where $κ=β/α$ and $x_0$ is an arbitrary reference point for initialization. The analysis controls center-dependent local errors along exact proximal histories and removes the final observation noise by conditional decoding. Under a Poincaré inequality (PI), we obtain a corresponding guarantee from a warm start with a known bound on its Rényi divergence. An oracle lower bound shows that a stationary point alone, which suffices under LSI, is insufficient under PI.

stat.ML · cs.CC · cs.LG · math.ST

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2602.05786

Selecting Hyperparameters for Tree-Boosting

Floris Jan Koster, Fabio Sigrist

原文摘要

Tree-boosting is a widely used machine learning technique for tabular data. However, its out-of-sample accuracy is critically dependent on multiple hyperparameters. In this article, we empirically compare several popular methods for hyperparameter optimization for tree-boosting including random grid search, the tree-structured Parzen estimator (TPE), Gaussian-process-based Bayesian optimization (GP-BO), Hyperband, the sequential model-based algorithm configuration (SMAC) method, and deterministic full grid search using $59$ regression and binary classification data sets. We find that the SMAC method clearly outperforms all the other considered methods on average, and it gives stable performance across a diverse collection of tabular data sets under a fixed tuning budget, which is relevant for users who cannot afford extensive manual trial-and-error tuning. We further observe that (i) a relatively large number of trials larger than $100$ is typically required for accurate tuning, (ii) using default values for hyperparameters or a full search over a small grid often yields very inaccurate models, (iii) all considered hyperparameters can have a material effect on the accuracy of tree-boosting, i.e., there is no small set of hyperparameters that is more important than others, and (iv) choosing the number of boosting iterations using early stopping yields more accurate results compared to including it in the search space for regression tasks.

cs.LG · stat.AP · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.03308

LLMs Depend on Specialist Tools for Out-of-Distribution Generalization in MS/MS Structural Elucidation

Gabriel Asher, Cailum M. K. Stienstra, Tomo Oga, Devesh Shah Antonio H. de O. Fonseca, Niall O'Connor, Michael Widrich

原文摘要

A frontier language model was recently reported to solve 1D NMR structural elucidation without tools. We ask whether this capability transfers to tandem mass spectrometry (MS/MS) in the de novo setting, where the model must propose a structure directly from the spectrum without a candidate list or reference library. To separate reasoning from recall, we build a 100-analyte benchmark from MassSpecGym, split by each analyte's textual footprint into in-distribution (well documented in literature) and out-of-distribution (essentially undocumented) arms. We hold the model, harness, and output format fixed and vary only the LLM's access to domain-specific tools. Without tools, a frontier LLM reaches 52% Top-1 accuracy in-distribution but only 2% out-of-distribution. Only access to de novo structure generators improves out-of-distribution accuracy, raising it to as much as 38% Top-1, and the resulting agent outperforms the standalone de novo models both in and out of distribution. These results suggest that LLMs are not effective at de novo MS/MS structural elucidation on their own, and that further gains depend on the specialist tools available to the agent rather than on the LLM itself.

cs.LG · cs.AI · cs.CL · stat.ML

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arXiv ↗PDF ↗