论文检索

Theory · Optimization

MINH DUC DO, Thao Do, Minh Hoang, Anh Le Duc Tran, Daeyoung Kim, Huy L Nguyen

Differentially private (DP) training protects individual examples by adding noise to gradients, but the injected noise interacts nontrivially with adaptive optimizers. Recent DP methods temporally filter privatized gradients to reduce variance; however, filtering also changes the DP noise statistics seen by AdamW’s second-moment accumulator. As a result, bias corrections derived for unfiltered DP noise (e.g., subtracting $\sigma_w^2$) can become miscalibrated when filtering is present. We propose FIBER, a DP optimizer designed for temporally filtered privatized gradients. FIBER (i) performs denoising in innovation space by filtering the residual stream and integrating it to form the filtered gradient estimate, (ii) decouples the two-point observation geometry from the innovation gain to enable independent tuning, and (iii) introduces a filter-aware second-moment calibration that subtracts the attenuated DP noise contribution $A(\omega)\sigma_w^2$, where $A(\omega)$ is derived in closed form for the innovation filter and can be computed for general stable linear filters. Across vision and language benchmarks, FIBER consistently demonstrates substantial improvements in the performance of DP optimizers, surpassing state-of-the-art results under equivalent privacy constraints on multiple tasks.

Applications · Computer Vision

Weize Li, Yang Li, Quan Yuan, Xiaoyuan Fu, Guiyang Luo, Jinglin Li

Collaborative perception enhances environment understanding through multi-agent information sharing, but its performance in real-world scenarios is constrained by heterogeneous sensor modalities and model architectures. Recent protocol-based two-stage methods alleviate this problem by mapping heterogeneous features into a shared protocol space; however, independently trained modality-specific converters often generate modality-specific pseudo-protocol distributions, leading to semantic inconsistency and error accumulation, which is particularly pronounced in scenarios with large modality discrepancies. To address this issue, we propose CauseCollab, a causal unified and modality-agnostic network. CauseCollab formulates representation learning in the protocol space from a causal perspective, explicitly disentangling semantic factors from modality-specific statistical confounders via causal metric learning. Meanwhile, CauseCollab adopts context-guided Unified Converter for heterogeneous modalities to ensure cross-modal semantic consistency. In addition, integrating new modalities only requires training adapters with minimal parameters. Extensive experiments on the OPV2V and DAIR-V2X datasets demonstrate that CauseCollab achieves state-of-the-art performance, with more significant gains in scenarios involving large modality gaps.

Applications · Time Series

Yangyou Liu, Zezhi Shao, Xinyu Chen, Hu Chen, Fei Wang, Yuankai Wu

Time series forecasting under non-stationarity faces a fundamental tension between capturing stable representations and adapting to distribution shifts. Existing methods implicitly rely on static historical assumptions, leading to a critical failure mode we term Phase Amnesia, where models become blind to the evolving global context. To resolve this, we formalize non-stationary dynamics through three physical hypotheses: Wold decomposition, dynamical phase evolution, and heteroscedastic manifold generation. These principles inspire PULSE, a physics-informed, plug-and-play framework adopting a Disentangle--Evolve--Simulate design philosophy. Specifically, PULSE utilizes phase-anchored disentanglement to resolve optimization interference caused by dominant trends, employs a Phase Router to actively generate future trajectories, and introduces Statistic-Aware Mixup (SAM) to ensure robustness against out-of-distribution volatility. Empirically, PULSE enables a simple MLP backbone to consistently outperform state-of-the-art Transformers across 12 real-world benchmarks. This validates that a correct physics-informed inductive bias is far more critical than raw architectural complexity for non-stationary forecasting.

Applications · Time Series

Guikang Du, Haoran Li, Xinyu Liu, Zhibo Zhang, Xiaoli Gong, Jin Zhang

Cross-subject generalization in biomedical time-series (BTS) refers to training on data from some subjects and testing on unseen subjects. The key challenge is to suppress subject-specific variability in BTS representations. Most existing methods implicitly suppress the variability through model building or subject adversarial learning, but rarely model it explicitly. We introduce \textit{\textbf{spectral drift}} as a new perspective to characterize subject-specific variability. Specifically, BTS signals under the same label often share consistent oscillatory structure, yet exhibit subject-dependent magnitude or phase shifts in specific frequency components, which we interpret as subject-specific variability. Building on this insight, we propose \textbf{BioFormer}. At its core is a Frequency-Band Alignment Module (FBAM) that generates band-wise modulation factors from the spectral distribution and adaptively adjusts amplitude and phase to align spectral structure, thereby mitigating variability. We further pair FBAM with Sample-Conditional Layer Normalization, which infers normalization parameters from intrinsic signal statistics rather than subject identity, stabilizing cross-subject representations. Extensive experiments on six datasets demonstrate that BioFormer outperforms 12 baselines, yielding absolute F1-score improvements of 6\%.

Social Aspects · Robustness

Kuheli Pratihar, Debdeep Mukhopadhyay

Large language models generate text through probabilistic token sampling, a mechanism increasingly leveraged for inference-time watermarking to verify AI-generated content. We present an information-theoretic framework that characterizes the trade-off between robustness to text editing and detectability by keyless observers, where detectability bounds are information-theoretic and computational attainability depends on detector access. Central to our analysis is an additive, usable Kullback-Leibler (KL) information budget that governs hypothesis testing separability between watermarked and unwatermarked outputs subject to a stealth constraint. This budget induces a hierarchy of detectability across watermark families: distribution-preserving schemes exhibit zero statistical drift, while probability-modifying schemes at both token and sentence levels accumulate detectable signal with sequence length. When text editing is modeled as a noise process, the usable KL budget contracts quadratically with edit rate for token-level schemes and according to an induced semantic flip rate for sentence-level schemes. These contraction laws reveal an irreducible trilemma among robustness, stealth, and reliable verification. Guided by these limits, we propose a hybrid watermarking strategy that selects among distribution-preserving, semantic-level, and token-level methods based on anticipated editing regimes. Experiments on Llama-2-7B and Mistral-7B under paraphrasing attacks corroborate theoretical predictions and confirm that the hybrid strategy is empirically near-Pareto across evaluated edit regimes.

Applications · Computer Vision

Pengfei zhang, Jian Ji

Evaluation metrics establish a standard assessment framework for models, playing a pivotal role in model optimization and advancement. However, widely adopted pixel-wise metrics (e.g., IoU, Dice) rely heavily on pixel-level statistics, often failing to capture the structural integrity of predictions. While the S-measure ($S_m$) incorporates structural perception to some extent, it struggles to differentiate critical structural violations and remains insensitive to background false positives and small objects. To address these limitations, we propose the Topology-aware measure ($T_m$), a novel metric designed to explicitly quantify topological consistency. $T_m$ employs the Fuzzy Jaccard Index as a foundational score, integrates a Topological Integrity term ($I_{topo}$) to penalize critical structural fragmentation, and utilizes a Boundary Alignment term ($\mathcal{A}_{bdy}$) to evaluate boundary alignment. These three components synergize to achieve robust evaluation of prediction maps at the topological level. We establish a rigorous Meta-Measure validation framework and benchmark our method against nine mainstream metrics across diverse complex scenarios. Extensive experiments demonstrate that $T_m$ performs exceptionally in downstream tasks and maintains high consistency with human visual perception.

Probabilistic Methods · Monte Carlo and Sampling Methods

Yu Wang, Jie Ding, Jonathan Huggins

Tuning stochastic gradient methods such as stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD) for approximate sampling and uncertainty quantification remains challenging, particularly in relevant settings using a large batch size or when the model is misspecified. Existing theory that provides tuning guidance relies on continuous-time limits or strong statistical assumptions, which can become quantitatively inaccurate in these regimes. We address these shortcomings by proposing a new discrete-time approximations to SG(L)D with and without momentum, which enables accurate predictions of the stationary covariance, iterate average covariance, and integrated autocorrelation time. Moreover, we prove quantitative, non-asymptotic error bounds showing that these estimates are sufficiently accurate for practical tuning and uncertainty quantification. Numerical experiments demonstrate that our theory yields improved tuning guidance across a range of models and data-generating distributions where existing approaches fail, including when using the $\beta$-divergence rather than log-loss to obtain statistically robust inferences.

Probabilistic Methods · Everything Else

Qi Kuang, Bowen Gang, Yin Xia

We propose a unified framework to enhance the power of online multiple hypothesis testing procedures based on $e$-values. While $e$-value-based methods offer robust online False Discovery Rate (FDR) control under minimal assumptions, they often suffer from power loss by discarding evidence that exceeds the rejection threshold. We address this inefficiency via the **S**equential **C**ontrol with **O**vershoot **R**efund for **E**-values (SCORE) framework, which leverages the inequality $\mathbb{I}(y \ge 1) \le y - (y-1)_+$ to reclaim this otherwise ``wasted'' evidence. This simple yet powerful insight yields a unified principle for improving a broad class of online testing algorithms. Building on this framework, we develop SCORE-enhanced versions of several state-of-the-art procedures, including SCORE-LOND, SCORE-LORD, and SCORE-SAFFRON, all of which strictly dominate their original counterparts while preserving valid finite-sample FDR control. Furthermore, under mild assumptions, SCORE permits retroactive updates of alpha‑wealth by using the latest decision twice: first to determine its reward or loss, and then to refresh past wealth. Such a mechanism enables more aggressive testing strategies while maintaining valid FDR control, thereby further improving statistical power. The effectiveness of the proposed methods is validated through extensive simulation and real-data experiments.

Probabilistic Methods · Monte Carlo and Sampling Methods

Bin Yang, Xiaojie Wang

Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning. Langevin Monte Carlo (LMC) algorithms are among the most widely used sampling methods in high dimensional settings. This paper introduces a novel higher-order and Hessian-free LMC sampling algorithm based on an efficient stochastic Runge-Kutta method of strong order $1.5$ for the overdamped Langevin dynamics. In contrast to the existing Runge-Kutta type LMC (Li et al.,2019) involved with three gradient evaluations, the newly proposed algorithm is computationally cheaper and requires only two gradient evaluations for one iteration. Under certain log-smooth conditions, non-asymptotic error bounds of the proposed algorithms are analyzed in $\mathcal{W}_2$-distance. In particular, a uniform-in-time convergence rate of order $O(d ^{\frac32} h^{\frac32})$ is derived in a non-log-concave setting, matching the convergence rate proved in the aforementioned work but under the log-concavity condition. Numerical experiments are finally presented to demonstrate the effectiveness of the new sampling algorithm.

General Machine Learning · Supervised Learning

Zhiwen Cao, Yanfeng Li, Shudong Huang, Yalan Ye, Shuyin Xia, Yi Wang, Jiancheng Lv

Recent class-incremental learning (CIL) methods built on large pre-trained vision models have shown that strong performance can be retained even under strict data access constraints. This raises a fundamental question: which properties of pre-trained representations make such recovery possible in the class-incremental setting? In this work, we show that class-level feature statistics play a central role in enabling effective CIL under strong pre-training. When the visual backbone is frozen, maintaining simple class-wise statistics—such as prototypes and low-order distributional information—can recover a substantial fraction of the performance achieved by static joint training across diverse benchmarks. We make this observation explicit through deliberately minimal reference points built on frozen CLIP representations. In particular, we demonstrate that competitive performance can be obtained even without continual training, by performing inference directly from accumulated class-level statistics. Our findings suggest that class-level statistics constitute an important and previously underemphasized component of recent CIL approaches based on pre-trained models, offering a complementary perspective for understanding their strong empirical performance.

Social Aspects · Accountability, Transparency, and Interpretability

Maxime Méloux, François Portet, Maxime Peyrard

Mechanistic Interpretability (MI) aims to reverse-engineer model behaviors by identifying functional sub-networks. Yet, the scientific validity of these findings depends on their stability. In this work, we argue that circuit discovery is not a standalone task but a statistical estimation problem built upon causal mediation analysis (CMA). We uncover a fundamental instability at this base layer: exact, single-input CMA scores exhibit high intrinsic variance, implying that the causal effect of a component is a volatile random variable rather than a fixed property. We then demonstrate that circuit discovery pipelines inherit this variance and further amplify it. Fast approximation methods, such as Edge Attribution Patching and its successors, introduce additional estimation noise, while aggregating these noisy scores over datasets leads to fragile structural estimates. Consequently, small perturbations in input data or hyperparameters yield vastly different circuits. We systematically decompose these sources of variance and advocate for more rigorous MI practices, prioritizing statistical robustness and routine reporting of stability metrics.

Optimization · Non-Convex

Chenyu Gao, Zhexian Yang, Ziping Zhao

Estimating statistical parameters from quantized data has received significant attention in recent years, as recovering information from quantized measurements has numerous applications across signal processing, communications, and data analysis. In this work, we focus on maximum likelihood (ML) estimation of statistical parameters from quantized samples. Directly solving the ML problem is challenging, as the likelihood function involves multiple integrals that are difficult to evaluate. To address this challenge, we propose an expectation-conditional-maximization (ECM) algorithm under a general distributional framework. Our approach generalizes the quantization model to multi-bit settings and allows the underlying signal to follow any distribution within the normal mean-variance mixture family. By designing suitable surrogate functions, the ECM algorithm ensures that all model parameters can be updated in closed form at each iteration. Leveraging the ECM framework, we provide convergence guarantees, and under specific distributional assumptions, we further derive bounds on the convergence rate and the statistical error. Extensive experiments demonstrate the effectiveness of our method in recovering statistical parameters from quantized data.

Probabilistic Methods · Bayesian Models and Methods

John-Joseph Brady, Nikolas Nüsken, Yunpeng Li

Latent state space systems are ubiquitous in statistical modelling, arising naturally when a time-series is observed through a noisy measurement function, however training deep state space models (DSSM) at scale remains difficult. Two largely distinct strategies and literatures have developed around the training of DSSMs. Firstly, auto-encoding DSSMs train generative DSSMs by optimising a variational lower bound. Secondly, DSSMs trained by back-propagating the outputs of a classical sequential Monte Carlo algorithm (SMC). Such approaches can train DSSMs for discriminative as well as generative tasks, however, due to the sequentiality of their forward pass, scale poorly on modern hardware. We propose a new training method _Parallel Variational Monte Carlo_ (PVMC) that bridges the gap between the paradigms, and can be used robustly to train DSSMs for both discriminative and generative tasks. Our method achieves state-of-the-art or better results on a set of baseline experiments and trains $10\times$ faster than the fastest competing SMC approach.

General Machine Learning · Supervised Learning

Guanliang Liu, Wenchao Chen, Long Tian, Xuefei Cao, Hongwei Liu, Bo Chen

Long-tailed recognition suffers from extreme class imbalance, where scarce tail data leads to biased and fragile feature distributions that exacerbate confusion with semantically or visually similar classes. Prior feature-space reconstruction methods transfer head-class structure or train conditional generators to synthesize tail features, yet the resulting statistical updates are often heuristic and can degrade multi-class separability when tail estimates are unreliable. Given this issue, we propose Risk-Bounded Distribution Reconstruction (RBDR), an offline statistic calibration framework for the two-stage long-tailed pipeline, grounded in an analysis of rival-induced discriminative directions. RBDR performs (i) risk-aware mean calibration by softly projecting any candidate update onto a supportive set such that a surrogate discriminative-risk upper bound does not increase, and (ii) covariance control by shrinking dispersion in a rival subspace while preserving diversity in orthogonal components. These plug-and-play modules transform heuristic reconstruction signals into controllable updates, improving performance and stability across multiple long-tailed benchmarks.

General Machine Learning · Causality

Rémi Khellaf, Aurélien Bellet, julie Josse

Causal inference typically assumes centralized access to individual-level data. Yet, in practice, data are often decentralized across multiple sites, making centralization infeasible due to privacy, logistical, or legal constraints. We address this problem by estimating the Average Treatment Effect (ATE) from decentralized observational data via a Federated Learning (FL) approach, allowing inference through the exchange of aggregate statistics rather than individual-level data. We propose a novel method to estimate propensity scores via a federated weighted average of local scores using Membership Weights (MW), defined as probabilities of site membership conditional on covariates. MW can be flexibly estimated with parametric or non-parametric classification models using standard FL algorithms. The resulting propensity scores are used to construct Federated Inverse Propensity Weighting (Fed-IPW) and Augmented IPW (Fed-AIPW) estimators. In contrast to meta-analysis methods, which fail when any site violates positivity, our approach exploits heterogeneity in treatment assignment across sites to improve overlap. We show that Fed-IPW and Fed-AIPW perform well under site-level heterogeneity in sample sizes, treatment mechanisms, and covariate distributions. Theoretical analysis and experiments on simulated and real-world data demonstrate clear advantages over meta-analysis and related approaches.

General Machine Learning · Causality

Alek Fröhlich, Vladimir Kostic, Karim Lounici, Daniel Rodrigues Perazzo, Daniel Tiezzi, Massimiliano Pontil

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity. Kernel methods using partial covariance operators offer a more principled approach but suffer from limited adaptivity, slow convergence, and poor scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of partial covariance operators and use them to construct a simple test statistic. We also introduce a bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Experiments on real and synthetic data suggest that this approach offers a principled and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

Yiyan Edgar, Sifei Liu, Weitong Zhang

Score-based and flow-based generative models exhibit remarkable expressive capacity in capturing complex distributions, and have been extensively deployed in tasks ranging from image generation to reinforcement learning. Nevertheless, these models suffer from prolonged inference latency, which imposes a significant computational bottleneck in RL with iterative sampling. To overcome this limitation, we propose a new framework named *Moment Matching Q-Learning* (MoMa QL), which utilizes a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD) that intend to match all orders of statistics between the original and target distribution. By enforcing strong regularization on all moment statistics, this algorithm guarantees distribution-level convergence for conditional score function and remains stable under various hyperparameters. Empirically, we show that our method MoMa QL is more computationally efficient with a comparable if not competitive performance in various D4RL tasks. Remarkably, by accelerating the action sampling process for flow-based policies, MoMa QL demonstrates superior performance in offline-to-online RL tasks because of faster and stronger adaptability for online interactive finetuning.

General Machine Learning · Transfer, Multitask and Meta-learning

Jean-Baptiste Fermanian, Batiste Le Bars, Aurélien Bellet

Personalized Federated Learning enables a collection of agents to collaboratively learn individual models without sharing raw data. We propose a new approach in which each agent optimizes a weighted combination of all agents' empirical risks, with the weights learned from data rather than specified a priori. The novelty of our method lies in formulating the estimation of these collaborative weights as a kernel mean embedding estimation problem with multiple data sources, leveraging tools from multi-task averaging to capture statistical relationships between agents. This perspective yields a fully adaptive procedure that requires no prior knowledge of data heterogeneity and automatically transitions between global and local learning regimes. By recasting the objective as a high-dimensional mean estimation problem, we derive finite-sample guarantees on local excess risks for a broad class of distributions, explicitly quantifying the statistical gains of collaboration. To address communication constraints inherent to federated settings, we also propose a practical implementation based on random Fourier features, which allows one to trade communication cost for statistical efficiency. Numerical experiments validate our theoretical results.

Deep Learning · Large Language Models

Jianxiang Zang, Yongda Wei, Ruxue Bai, Shiyu Jiang, Nijia Mo, Binhong Li, Qiang Sun, Hui Liu

Reliable reward models (RMs) are critical for ensuring the safe alignment of large language models (LLMs). However, current RM evaluation methods focus solely on preference perception accuracies in given specific scenarios, obscuring the critical vulnerabilities of RMs in real-world scenarios. We identify the true challenge lies in assessing a novel dimension: Suitability, defined as conditional reliability under specific real-world perturbations. To this end, we introduce Reward Auditor, a hypothesis-testing framework specifically designed for RM suitability inference. Rather than answering “How accurate is the RM's preference perception for given samples?”, it employs scientific auditing to answer: “Can we infer RMs exhibit systematic vulnerabilities in specific real-world scenarios?". Under real-world perturbed scenarios, Reward Auditor quantifies statistical significance and effect size by auditing distribution degradation of RM preference perception confidence. This enables inference of both the certainty and severity of RM vulnerabilities across diverse real-world scenarios, thereby laying a solid foundation for building next-generation LLM alignment systems that are verifiably safe, more robust, and trustworthy.

General Machine Learning · Representation Learning

Juntang Wang, Hao Wu, Yihan Wang, Dongmian Zou, Shixin Xu

Clustering-based features are widely used in machine learning, but most methods must choose a resolution---a choice that is global, fixed, and ad hoc. Recent work shows that varying the resolution parameter produces only a finite set of structurally stable partitions, known as configurations. Based on this, we introduce Configuration-Mixed Prediction (CMP), a setting where models learn to adaptively weight these configurations per sample for downstream prediction. We propose MixConfig, a plug-and-play feature augmentation module that extracts configurations from any embedding and learns energy-aware mixing weights via a novel selector that jointly reasons about sample context, cluster assignments, and stability statistics. Experiments across tabular, molecular, vision, and text domains demonstrate consistent improvements over single-resolution and static baselines across diverse predictor architectures, with gains particularly pronounced in low-data regimes.