Bandit multiple hypothesis testing has broad applications in biological sciences, clinical testing for drug discovery, and online A/B/n testing. The framework utilizes an adaptive sampling strategy for multiple testing which aims to maximize statistical power while ensuring anytime false discovery rate control. This paper proposes a robust approach for bandit multiple testing, allowing for at most an epsilon fraction of arbitrary distribution corruption, as in Huber’s contamination model. Specifically, we introduce two adaptive sampling strategies designed to minimize the number of samples required to exceed a target true positive rate, while providing anytime control over the false discovery rate. We analyze the sample complexity of our proposed methods and perform numerical simulations to demonstrate their efficiency and robustness. Furthermore, we extend our methods to address scenarios where distributions have infinite variance and situations involving multiple agents collaborating on the same bandit task.
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Many optimization tasks involve streaming data with unknown concept drifts, posing a significant challenge as Streaming Data-Driven Optimization (SDDO). Existing methods, while leveraging surrogate model approximation and historical knowledge transfer, are often under restrictive assumptions such as fixed drift intervals and fully environmental observability, limiting their adaptability to diverse dynamic environments. We propose TRACE, a TRAnsferable Concept-drift Estimator that effectively detects distributional changes in streaming data with varying time scales. TRACE leverages a principled tokenization strategy to extract statistical features from data streams and models drift patterns using attention-based sequence learning, enabling accurate detection on unseen datasets and highlighting the transferability of learned drift patterns. Further, we showcase TRACE's plug-and-play nature by integrating it into a streaming optimizer, facilitating adaptive optimization under unknown drifts. Comprehensive experimental results on diverse benchmarks demonstrate the superior generalization, robustness, and effectiveness of our approach in SDDO scenarios.
Ordinal classification has been widely applied in many high-stakes applications, e.g., medical imaging and diagnosis, where reliable uncertainty quantification (UQ) is essential for decision making. Conformal prediction (CP) is a general UQ framework that provides statistically valid guarantees, which is especially useful in practice. However, prior ordinal CP methods mainly focus on heuristic algorithms or restrictively require the underlying model to predict a unimodal distribution over ordinal labels. Consequently, they provide limited insight into coverage–efficiency trade-offs, or a model-agnostic and distribution-free nature favored by CP methods. To this end, we fill this gap by propose an ordinal-CP method that is model-agnostic and provides instance-level optimal prediction intervals. Specifically, we formulate conformal ordinal classification as a minimum-length covering problem at the instance level. To solve this problem, we develop a sliding-window algorithm that is optimal on each calibration data, with only a linear time complexity in K, the # of label candidates. The local optimality per instance further also improves predictive efficiency in expectation. Moreover, we propose a length-regularized variant that shrinks prediction set size while preserving coverage. Experiments on four benchmark datasets from diverse domains are conducted to demonstrate the significantly improved predictive efficiency of the proposed methods over baselines (by 15%↓ on average over four datasets).
Model-heterogeneous federated tuning (MHFT) enables the privacy-preserving fine-tuning of foundation models in heterogeneous systems by allowing clients and the server to adopt different model architectures. Depth partial training—where each client updates only a subset of the model's layers—alleviates system heterogeneity but exacerbates client drift, which stems from clients optimizing different objectives and therefore degrades overall performance. Beyond the well-known statistical bias—where non-IID data leads to client drift—we identify a structural bias arising from clients deploying only partial layers of the global model, which serves as an important cause of drift. We further provide a theoretical analysis showing that the possible range of structural bias expands linearly with the number of missing layers. To counter this effect, we introduce FedBRICK (Federated Bias Recovery via Inserted Calibrative Kernels), which inserts tiny BRICKs into each client’s subnetwork. We employ a dual-end layer-wise distillation scheme to train these blocks using both client-side local data and a small public proxy set on the server. This design effectively mitigates the structural bias caused by layer dropping, reduces client drift, and remains practical for storage-constrained devices. Extensive experiments on federated learning benchmarks confirm that FedBRICK delivers up to a 5% average accuracy gain while requiring no more than 1.44% extra storage per client.
Multi-annotator learning traditionally aggregates diverse annotations to approximate a single “ground truth”, treating disagreements as noise. However, this paradigm faces fundamental challenges: subjective tasks often lack absolute ground truth, and sparse annotation coverage makes aggregation statistically unreliable. We introduce a paradigm shift from sample-wise aggregation to annotator-wise behavior modeling. By treating annotator disagreements as valuable information rather than noise, modeling annotator-specific behavior patterns can reconstruct unlabeled data to reduce annotation cost, enhance aggregation reliability, and explain annotator decision behavior. To this end, we propose QuMAB (Query-based Multi-Annotator Behavior Pattern Learning), which uses lightweight queries to model individual annotators while capturing inter-annotator correlations as implicit regularization, preventing overfitting to sparse individual data while maintaining individualization and improving generalization, with a visualization of annotator focus regions offering an explainable analysis of behavior understanding. We contribute two large-scale datasets with dense per-annotator labels: STREET (4,300 labels/annotator) and AMER (average 3,118 labels/annotator), the first multimodal multi-annotator dataset. Extensive experiments demonstrate the superiority of our QuMAB in modeling individual annotators’ behavior patterns, their utility for consensus prediction, and applicability under sparse annotations.
CastX: Cohort-Level Causal Inference Meets Statistical Testing for Faithful and Reliable GNN Explanations
PDF ↗Explainability plays a critical role in understanding the workings of Graph Neural Networks (GNNs). While recent methods have introduced causal inference into GNN explanation, they predominantly rely on individual-level interventions and lack rigorous statistical causality testing, resulting in unfaithful and unreliable explanations. To address these challenges, we propose CastX that integrates cohort-level causal analysis with statistical causality testing for GNN explanations. Specifically, CastX formulates the discovery of explanatory subgraphs as a dynamic edge pruning task guided by Conditional Average Treatment Effect (CATE) estimation. A reinforcement learning agent is employed to iteratively eliminate spurious edges and identify causally informative substructures. To further enhance reliability, we introduce an i.i.d.-agnostic non-parametric permutation test that assesses the statistical significance of each target edge. Extensive experiments on real-world datasets demonstrate that our CastX outperforms existing methods in yielding explanatory subgraphs that are concise, faithful, reliable, and statistically supported.
Multi-task test-time adaptation (MT-TTA) aims to adapt pre-trained models to dynamic environments during multi-task inference by leveraging unlabeled test data. This task is particularly challenging as different tasks respond divergently to distribution shifts, and mixed input streams containing both in-distribution (ID) and out-of-distribution (OOD) samples make the models after test-time adaptation prone to catastrophic forgetting of ID knowledge. Although the existing methods like M-TENT extend the classic test entropy minimization (TENT) by minimizing multi-task entropies and employing task-average gradient to adapt a model, it suffers from two key limitations: 1) the average gradient strategy proposed by M-TENT may exacerbate multi-task test-time optimization conflicts, harming individual tasks when gradients are directionally non-consensual; 2) aggressive updates on mixed ID/OOD data cause severe forgetting of ID knowledge. In this paper, we theoretically establish a formal connection between multi-task loss differences and test-time performance under the first-order Taylor analysis, demonstrating that consensual multi-task entropy reductions are likely to increase the performance, while non-consensual ones might decrease the performance. To this end, we propose Consensus-driven Constrained Multi-Task Test-Time Adaptation (CoCo-MT-TTA), consisting of 1) multi-task gradient consensus adaptation, which aligns cross-task gradient directions to seek a consensus gradient; 2) multi-task plasticity-constraint adaptation, which constrains parameter updates using second-moment statistics to preserve ID knowledge. Extensive experiments on benchmark datasets, including CelebA and PlantData, demonstrate that our method achieves an absolute improvement of up to 16.02% in mean ID/OOD F1-score (Mean I&O) under domain shifts over non-adapted models, outperforming the recent baselines.
REMISVFU: Vertical Federated Unlearning via Representation Misdirection for Intermediate Output Feature
PDF ↗Data-protection regulations such as the GDPR grant every participant in a federated system a right to be forgotten. Federated unlearning has therefore emerged as a research frontier, aiming to remove a specific party's contribution from the learned model while preserving the utility of the remaining parties. However, most unlearning techniques focus on Horizontal Federated Learning (HFL), where data are partitioned by samples. In contrast, Vertical Federated Learning (VFL) allows organizations that possess complementary feature spaces to train a joint model without sharing raw data. The resulting feature-partitioned architecture renders HFL-oriented unlearning methods ineffective. In this paper, we propose ReMisVFU, a plug-and-play representation-misdirection framework that enables fast, client-level unlearning in splitVFL systems. When a deletion request arrives, the forgetting party collapses its encoder output to a randomly sampled anchor on the unit sphere, severing the statistical link between its features and the global model. To maintain utility for the remaining parties, the server jointly optimizes a retention loss and a forgetting loss, aligning their gradients via orthogonal projection to eliminate destructive interference. Evaluations on public benchmarks show that ReMisVFU suppresses back-door attack success to the natural class-prior level and sacrifices only about 2.5% points of clean accuracy, outperforming state-of-the-art baselines.
The Dragonfly network, with its high-radix and low-diameter structure, is a leading interconnect in high-performance computing. A major challenge is workload interference on shared network links. Parallel discrete event simulation (PDES) is commonly used to analyze workload interference. However, high-fidelity PDES is computationally expensive, making it impractical for large-scale or real-time scenarios. Hybrid simulation that incorporates data-driven surrogate models offers a promising alternative, especially for forecasting application runtime, a task complicated by the dynamic behavior of network traffic. We present SMART, a surrogate model that combines graph neural networks (GNNs) and large language models (LLMs) to capture both spatial and temporal patterns from port level router data. SMART outperforms existing statistical and machine learning baselines, enabling accurate runtime prediction and supporting efficient hybrid simulation of Dragonfly networks.
Partial linear models (PLM) have attracted much attention for regression estimation and variable selection due to their feasibility on utilizing linear and nonlinear approximations jointly. However, theoretical understanding of how they control the false discovery rate (FDR) during variable selection remains limited. To address this issue, we formulate a new integral-based knockoffs (IKO) inference scheme for controlled variable selection in PLM, where integral-based knockoff statistics are used to measure the variable importance and B-splines (or random Fourier features) are employed for approximating nonlinear components. In theory, FDR control is guaranteed for both linear and nonlinear parts, and the statistical analysis for its power is established. Empirical evaluations validate the effectiveness of our proposed approach.
Selecting an appropriate look-back horizon remains a fundamental challenge in time series forecasting (TSF), particularly in federated learning scenarios where data is decentralized, heterogeneous, and often non-independent. While recent work has explored horizon selection by preserving forecasting-relevant information in an intrinsic space, these approaches are primarily restricted to centralized and independently distributed settings. This paper presents a principled framework for adaptive horizon selection in federated time series forecasting through an intrinsic space formulation. We introduce a synthetic data generator that captures essential temporal structures in client data, including autoregressive dependencies, seasonality, and trend, while incorporating client-specific heterogeneity. Building on this model, we define a transformation that maps time series windows into an intrinsic representation space with well-defined geometric and statistical properties. We then derive a decomposition of the forecasting loss into a Bayesian term, which reflects irreducible uncertainty, and an approximation term, which accounts for finite-sample effects and limited model capacity. Our analysis shows that while increasing the look-back horizon improves the identifiability of deterministic patterns, it also increases approximation error due to higher model complexity and reduced sample efficiency. We prove that the total forecasting loss is minimized at the smallest horizon where the irreducible loss starts to saturate, while the approximation loss continues to rise. This work provides a rigorous theoretical foundation for adaptive horizon selection for time series forecasting in federated learning.
The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis, suggesting that typical worst-case analysis does not provide practical guarantees. A natural step for analysis is thus to assume the manifold hypothesis and derive bounds that are independent of any ambient dimensions that the data may be embedded in. Theoretical implications in this direction have recently been explored in terms of generalization of ReLU networks and convergence of Langevin methods. In this work, we consider optimal uniform approximations with functions of finite statistical complexity. While upper bounds on uniform approximation exist in the literature using ReLU neural networks, we consider the opposite: lower bounds to quantify the fundamental difficulty of approximation on manifolds. In particular, we demonstrate that the statistical complexity required to approximate a class of bounded Sobolev functions on a compact manifold is bounded from below, and moreover that this bound is dependent only on the intrinsic properties of the manifold, such as curvature, volume, and injectivity radius.
Optimization Method for Surrogate Function in Spiking Neural Networks Based on Membrane Potential Distribution
PDF ↗Spiking Neural Networks (SNNs) offer promising energy efficiency and temporal sparsity for edge intelligence, but their training remains difficult due to gradient mismatch, membrane potential drift, and discretization errors. In this paper, we propose a membrane potential-guided surrogate optimization(MPO) framework that dynamically aligns the surrogate function with the membrane potential distribution to enhance the gradient propagation. Specifically, we introduce a KL-divergence-based regularization to stabilize membrane potential dynamics, and an adaptive width constraint to synchronize the surrogate gradient range with neural activity statistics. Additionally, we design a spike discretization error metric and a correction strategy to mitigate temporal discretization effects. Experiments on CIFAR-10, CIFAR-100, and ImageNet show our method achieves 94.76%, 74.20%, and 65.70% top-1 accuracy respectively, while improving gradient stability and energy efficiency. This work provides a principled optimization scheme for robust and scalable SNN training in practical neuromorphic systems.
Graph Neural Networks (GNNs) are expressive architectures for learning from complex graph-structured data. However, their practical use is often limited by the high computational cost of neighborhood aggregation. Recent efforts have focused on knowledge distillation from GNNs to inference-efficient Multi-Layer Perceptrons (MLPs). However, most existing works treat this distillation as an embedding alignment problem, overlooking the need to replicate the topology-aware smoothing behavior that arises from message passing in GNNs. Moreover, existing methods are primarily performance driven, ignoring critical real-world requirements such as fairness. In this work, we make two key observations: (1) state-of-the-art distillation methods fail to capture the heterogeneous smoothness patterns of GNNs, limiting structural awareness in MLPs, and (2) they introduce significant individual and group fairness violations. We introduce FAITH, the first fair and structurally aware GNN-to-MLP distillation framework with graph-free inference. To improve structural awareness in MLPs, we propose a neighborhood-guided energy alignment objective that transfers not only node-level energy, but also the distribution of energies across local neighborhoods. To improve individual fairness, FAITH introduces a novel ℓ2,1-norm objective that preserves structured similarity in the learned representations. Additionally, we incorporate a counterfactual invariance objective that explicitly encourages the model to learn representations that are statistically independent of the sensitive attribute. We provide a comprehensive theoretical analysis of FAITH, interpreting it through a novel instantiation of the Information Bottleneck principle. Extensive experiments on 11 benchmark datasets show that FAITH achieves stronger structural awareness and delivers a better trade-off between utility and fairness than existing methods.
FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification
PDF ↗Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete observations. Existing methods commonly employ fixed interpolation schemes, which impose simplistic geometric assumptions that often misrepresent the underlying data manifold, particularly under high missingness. We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow. Rather than merely connecting observations, FlowPath constructs a continuous and data-adaptive manifold, guided by invertibility constraints that enforce information-preserving and well-behaved transformations. This inductive bias distinguishes FlowPath from prior unconstrained learnable path models. Empirical evaluations on 18 benchmark datasets and a real-world case study demonstrate that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures. These results highlight the importance of modeling not only the dynamics along the path but also the geometry of the path itself, offering a robust and generalizable solution for learning from irregular time series.
Existing drift detection methods focus on designing sensitive test statistics. They treat the detection threshold as a fixed hyperparameter, set once to balance false alarms and late detections, and applied uniformly across all datasets and over time. However, maintaining model performance is the key objective from the perspective of machine learning, and we observe that model performance is highly sensitive to this threshold. This observation inspires us to investigate whether a dynamic threshold could be provably better. In this paper, we prove that a threshold that adapts over time can outperform any single fixed threshold. The main idea of the proof is that a dynamic strategy, constructed by combining the best threshold from each individual data segment, is guaranteed to outperform any single threshold that apply to all segments. Based on the theorem, we propose a Dynamic Threshold Determination algorithm. It enhances existing drift detection frameworks with a novel comparison phase to inform how the threshold should be adjusted. Extensive experiments on a wide range of synthetic and real-world datasets, including both image and tabular data, validate that our approach substantially enhances the performance of state-of-the-art drift detectors.
Adversarial attacks pose a major challenge to distributed learning systems, prompting the development of numerous robust learning methods. However, most existing approaches suffer from the curse of dimensionality, i.e. the error increases with the number of model parameters. In this paper, we make a progress towards high dimensional problems, under arbitrary number of Byzantine attackers. The cornerstone of our design is a direct high dimensional semi-verified mean estimation method. The idea is to identify a subspace with large variance. The components of the mean value perpendicular to this subspace are estimated using corrupted gradient vectors uploaded from worker machines, while the components within this subspace are estimated using auxiliary dataset. As a result, a combination of large corrupted dataset and small clean dataset yields significantly better performance than using them separately. We then apply this method as the aggregator for distributed learning problems. The theoretical analysis shows that compared with existing solutions, our method gets rid of sqrt{d} dependence on the dimensionality, and achieves minimax optimal statistical rates. Numerical results validate our theory as well as the effectiveness of the proposed method.
The housing market, also known as one-sided matching market, is a classic exchange economy model where each agent on the demand side initially owns an indivisible good (a house) and has a personal preference over all goods. The goal is to find a core-stable allocation that exhausts all mutually beneficial exchanges among subgroups of agents. While this model has been extensively studied in economics and computer science due to its broad applications, little attention has been paid to settings where preferences are unknown and must be learned through repeated interactions. In this paper, we propose a statistical learning model within the multi-player multi-armed bandit framework, where players (agents) learn their preferences over arms (goods) from stochastic rewards. We introduce the notion of core regret for each player as the market objective. We study both centralized and decentralized approaches, proving O (log T / △^2) upper bounds on regret, where T is the time horizon and △ is the minimum preference gap among players. For the decentralized setting, we also establish a matching lower bound, demonstrating that our algorithm is order-optimal.
Missing data presents a widespread challenge in real-world data collection. In this paper, our goal is to impute missing entries while accurately reflecting the uncertainty associated with them. We introduce U-VAE, a method that employs a non-parametric distributional learning strategy to parameterize the likelihood of missing values. To address the infeasibility of directly estimating the underlying conditional distributions due to data incompleteness, we incorporate stochastic re-masking and un-masking techniques during training. Specifically, we replace the conventional reconstruction loss with the continuous ranked probability score (CRPS), a strictly proper scoring rule, and theoretically demonstrate that the discrepancy between the underlying conditional distribution and our imputer is upper-bounded. We evaluate the performance of U-VAE on 11 real-world datasets, showing its effectiveness in both single and multiple imputations, while also enhancing post-imputation performance and supporting valid statistical inference.
Pseudo-random number generators (PRNGs) are high-nonlinear processes, and they are key blocks in optimization of Large language models. Transformers excel at processing complex nonlinear relationships. Thus it is reasonable to generate high-quality pseudo-random numbers based on transformers. In this paper, we explore this question from both theoretical and practical perspectives, highlighting the potential benefits and implications of Transformer in PRNGs. We theoretically demonstrate that decoder-only Transformer models with Chain-of-Thought can simulate both the Linear Congruential Generator (LCG) and Mersenne Twister (MT) PRNGs. Based on this, we conclude that the log-precision decoder-only Transformer can represent non-uniform AC0. Our simulative theoretical findings are validated through experiments. The random numbers generated by Transformer-based PRNGs successfully pass the majority of NIST tests, whose heat maps exhibit clear statistical randomness. Finally, we assess their capability in prediction attacks.