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Probabilistic Methods · Everything Else

Ege Onur Taga, Samet Oymak, Shubhanshu Shekhar

We develop horizon-aware anytime-valid tests and confidence sequences for bounded means under a strict deadline $N$. Using the betting/e-process framework, we cast horizon-aware betting as a finite-horizon optimal control problem with state space $(t, \log W_t)$, where $t$ is the time and $W_t$ is the test martingale value. We first show that in certain interior regions of the state space, policies that deviate significantly from Kelly betting are provably suboptimal, while Kelly betting reaches the threshold with high probability. We then identify sufficient conditions showing that outside this region, more aggressive betting than Kelly can be better if log-wealth is low or time is short, and less aggressive can be better if log-wealth is high. Taken together these results suggest a simple phase diagram in the $(t, \log W_t)$ plane, delineating regions where Kelly, fractional Kelly, and aggressive betting may be preferable. Guided by this phase diagram, we introduce a Deep Reinforcement Learning approach based on a universal Deep Q-Network (DQN) agent that learns a single policy from synthetic experience and maps simple statistics of past observations to bets across horizons and null values. In limited-horizon experiments, the learned DQN policy outperforms state-of-the-art baselines.

Theory · Learning Theory

Peiyuan Zhang, Syamantak Kumar, Kevin Tian, Purnamrita Sarkar

Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\\mathbf{\Sigma}$, whose top eigenvector $\\mathbf{v} \in \\mathbb{R}^d$ is $s$-sparse. Existing sparse PCA algorithms can be broadly categorized into (1) combinatorial algorithms (e.g., diagonal or elementwise covariance thresholding) and (2) SDP-based algorithms. While combinatorial algorithms are much simpler, they are typically only analyzed under the spiked identity model (where $\\mathbf{\Sigma} \propto \\mathbf{I}_d + \gamma \\mathbf{v}\\mathbf{v}^\top$ for some $\gamma > 0$), whereas SDP-based algorithms require no additional assumptions on $\\mathbf{\Sigma}$. We demonstrate explicit counterexample covariances $\\mathbf{\Sigma}$ against the success of standard combinatorial algorithms for sparse PCA, when moving beyond the spiked identity model. In light of this discrepancy, we give the first combinatorial method for sparse PCA that provably succeeds for general $\\mathbf{\Sigma}$ using $\\mathsf{poly}(s, \log(d))$ samples and $d^2 \cdot \\mathsf{poly}(s, \log(d))$ time, by providing a global convergence guarantee on the truncated power method of Yuan and Zhang (JMLR, 2013). We provide a natural generalization of our method to recovering $k$ sparse principal components. Finally, we evaluate our method on synthetic and real-world sparse PCA datasets.

General Machine Learning · Sequential, Network, and Time Series Modeling

Enver Menadjiev, Jihyeon Seong, Jisu Yeo, Jaesik Choi

Sequential conformal prediction (CP) provides valid uncertainty quantification under the assumption of residual exchangeability. However, this assumption is often violated in real-world time series due to temporal dependencies and distributional shifts. While recent methods attempt to approximate exchangeability through reweighting, identifying optimal weights remains an open challenge. To address this limitation, we propose [DistMatch](https://anonymous.4open.science/r/distmatch/), a binning-based method that recursively partitions residuals within a binary tree using the Kolmogorov–Smirnov (KS) statistic. We theoretically show that this partitioning induces approximately exchangeable leaves, thereby avoiding the need for reweighting. By applying quantile regression with online updates within each leaf, DistMatch enables locally adaptive inference and improves robustness to distributional shifts. Extensive experiments demonstrate that DistMatch outperforms existing sequential CP methods.

Deep Learning · Foundation Models

Zhe Cheng, Wenyu Chen, Fode Zhang, Dehuan Shen

Large vision-language models (LVLMs) often hallucinate content that is fluent yet unsupported by the image, limiting their reliability in real-world deployment. We show that a key failure mode arises from route competition: even when visual tokens receive attention, the final token decision can be dominated by the textual pathway, causing the decoder to follow linguistic priors over visual evidence. To mitigate this, we propose a training-free, decision-aligned intervention that decomposes each attention head into a visual route and a text route, and estimates their token-level effects using an efficient one-forward/one-gradient approximation. These estimates reveal route conflict within heads and identify prior-dominant ones, enabling selective suppression of only the text route while keeping the visual route intact. Across five benchmarks spanning discriminative and generative settings, our method consistently reduces hallucination-related errors across models with limited impact on overall multimodal performance, while incurring a modest inference-time overhead.

Theory · Domain Adaptation and Transfer Learning

Zhe Cheng, Fode Zhang, Lingrui Wang, Yifan Zhu, Jiaolong Wang

We study unsupervised domain adaptation (UDA) where measuring cross-domain discrepancy is critical. Most UDA approaches fix a single $f$-divergence a priori, which can be suboptimal across heterogeneous shifts. We propose a framework that (i) tightens the variational lower bound of an $f$-divergence by inserting a learnable, monotone $L$-Lipschitz transform $\tau$ (Tighter-VR), and (ii) selects the divergence family adaptively from data via a likelihood-based criterion. The resulting estimator yields more informative and statistically efficient discrepancy estimates while recovering prior fixed-divergence methods as special cases. Theoretically, we derive a target-risk bound whose three components are a transformed source risk, a Tighter-VR discrepancy between domains, and an ideal-hypothesis residual; we further provide finite-sample guarantees using standard complexity measures. Empirically, on Office-31, Office-Home, Digits, and VisDA-2017, our method consistently improves accuracy over strong baselines, demonstrating that coupling Tighter-VR with adaptive divergence selection yields tangible gains in UDA.

Applications · Robotics

Hanxin Zhang, Mingshuo Xu, Abdulqader Dhafer, Shigang Yue, Hongbiao Dong, Zhou Daniel Hao

Vision–Language–Action (VLA) policies often fail under distribution shift, suggesting that decisions may depend on spurious visual correlations rather than task-relevant causes. We formulate visual–action attribution as an interventional estimation problem. Accordingly, we introduce the **Interventional Significance Score (ISS)**, an interventional masking procedure for estimating the causal influence of visual regions on action predictions, and the **Nuisance Mass Ratio (NMR)**, a scalar measure of attribution to task-irrelevant features. We analyze the statistical properties of ISS and show that it admits unbiased estimation, and we characterize conditions under which action prediction error provides a valid proxy for causal influence. Experiments across diverse manipulation tasks indicate that NMR predicts generalization behavior and that ISS yields more faithful explanations than existing interpretability methods. These results suggest that interventional attribution provides a simple diagnostic approach for identifying causal misalignment in embodied policies.

General Machine Learning · Supervised Learning

Shuqi Liu, Yuzhou Cao, Lei Feng, Bo An, Luke Ong

Learning to Defer (L2D) enables a classifier to abstain from predictions and defer to an expert, and has recently been extended to multi-expert settings. In this work, we show that multi-expert L2D is fundamentally more challenging than the single-expert case. With multiple experts, the classifier's underfitting becomes inherent, which seriously degrades prediction performance, whereas in the single-expert setting it arises only under specific conditions. We theoretically reveal that this stems from an intrinsic expert identifiability issue: learning which expert to trust from a diverse pool, a problem absent in the single-expert case and renders existing underfitting remedies failed. To tackle this issue, we propose PiCCE (**Pi**ck the **C**onfident and **C**orrect **E**xpert), a surrogate-based method that adaptively identifies a reliable expert based on empirical evidence. PiCCE effectively reduces multi-expert L2D to a single-expert–like learning problem, thereby resolving multi-expert underfitting. We further prove its statistical consistency and ability to recover class probabilities and expert accuracies. Extensive experiments across diverse settings, including real-world expert scenarios, validate our theoretical results and demonstrate improved performance.

Deep Learning · Large Language Models

G M Shahariar, Erfan Shayegani, Ali Nazari, Nael Abu-Ghazaleh

Large Reasoning Models (LRMs) solve complex tasks by generating long Chain-of-Thought (CoT) sequences; however, the emergent dynamics governing reasoning trajectories are not well understood and can lead to inconsistencies and reasoning pathologies. In this work, we propose to approximate LRM's emerging hierarchical reasoning dynamics as a trajectory within a Finite State Machine (FSM) transitioning among six abstract cognitive states. We demonstrate that these states and transitions can be captured in the latent state of the model. We believe that this representation can have different applications in the interpretability and optimization of LRM models. For example, by analyzing the topology of these transitions, we identify statistical shifts in reasoning strategies that help identify effective reasoning chains from those that fail. To illustrate these potential advantages, we propose $Q$-Value guided steering, a training-free inference-time control method that treats reasoning as a planning problem. We estimate the long-horizon utility of state transitions and apply sparse, orthogonal activation steering at sentence boundaries to align the CoT generation with optimal reasoning policies. Experiments across four benchmarks (AIME25, MATH-500, GSM8k, and GPQA Diamond) using three state-of-the-art open reasoning models demonstrate that $Q$-Value steering policy achieves significant performance gains with "surgical'' efficiency, often requiring $25\times$ fewer interventions than greedy and weighted baselines, which suggests that reasoning can be effectively controlled by guiding high-level cognitive dynamics rather than micro-managing token generation.

Social Aspects · Accountability, Transparency, and Interpretability

Soyeon Kim, Seongwoo Lim, Kyowoon Lee, Jaesik Choi

Feature attribution is central to diagnosing and trusting deep neural networks, and Integrated Gradients (IG) is widely used due to its axiomatic properties. However, IG can yield unreliable explanations when the integration path between a baseline and the input passes through regions with noisy gradients. While Guided Integrated Gradients reduces this sensitivity by adaptively updating low-gradient-magnitude features, input-space guidance still produces intermediate inputs that deviate from the data manifold. To address this limitation, we propose **Manifold-Aligned Guided Integrated Gradients** (MA-GIG), which constructs attribution paths in the latent space of a pre-trained variational autoencoder. By ensuring that decoded intermediate images remain aligned with the data manifold, MA-GIG constrains gradient evaluation to statistically valid regions. Through qualitative and quantitative evaluations, we demonstrate that MA-GIG produces faithful explanations by aggregating gradients on path features proximal to the input. Consequently, our method suppresses off-manifold noise and outperforms prior path-based attribution methods across multiple datasets and classifiers.

General Machine Learning · Sequential, Network, and Time Series Modeling

Xiaokai Luo, Haotian Xu, Carlos Misael Madrid Padilla, OSCAR HERNAN MADRID PADILLA

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains underexplored in the machine learning and statistics literature. We propose a method that uses low-rank matrices to represent the multivariate Poisson intensity functions, resulting in an adaptive nonparametric detection procedure. Our algorithm is single-pass and requires only constant computational cost per new observation, independent of the elapsed length of the time series. We provide theoretical guarantees to control the overall false alarm probability and characterize the detection delay under temporal dependence. We also develop a new Matrix Bernstein inequality for temporally dependent Poisson point process time series, which may be of independent interest. Numerical experiments demonstrate that our method is both statistically robust and computationally efficient.

Optimization · Stochastic

Tianjin Huang, Zhangyang “Atlas” Wang, Haotian Hu, Zhenyu Zhang, Gaojie Jin, Xiang Li, Li Shen, Jiaxing Shang, Tianlong Chen, Ke Li 等

Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence. Widely used safeguards such as gradient clipping mitigate these failures but require threshold tuning and indiscriminately truncate large updates. We propose **GradientStabilizer**, a lightweight, drop-in gradient transform that *preserves the instantaneous gradient direction* while replacing the update magnitude with a statistically stabilized estimate derived from running gradient-norm statistics. We prove that the resulting stabilized magnitude is uniformly bounded on spike steps, independent of the spike size, and show how this boundedness controls optimizer state evolution in adaptive methods. Across LLM pre-training (FP16), quantization-aware pre-training (FP4), ImageNet classification, reinforcement learning, and time-series forecasting, **GradientStabilizer** consistently improves training stability, widens stable learning-rate regions, and reduces divergence relative to clipping-based baselines, even substantially reducing Adam’s sensitivity to weight-decay strength.

General Machine Learning · Evaluation

Andrew Klearman, Radu Revutchi, Rohin Garg, Rishav Chakravarti, Samuel Denton, Yuan Xue

Retrieval quality is the primary bottleneck for accuracy and robustness in retrieval-augmented generation (RAG). Current evaluation relies on heuristically constructed query sets, which introduce a hidden intrinsic bias. We formalize retrieval evaluation as a statistical estimation problem, showing that metric reliability is fundamentally limited by the evaluation-set construction. We further introduce \emph{semantic stratification}, which grounds evaluation in corpus structure by organizing documents into an interpretable global space of entity-based clusters and systematically generating queries for missing strata. This yields (1) formal semantic coverage guarantees across retrieval regimes and (2) interpretable visibility into retrieval failure modes. Experiments across multiple benchmarks and retrieval methods validate our framework. The results expose systematic coverage gaps, identify structural signals that explain variance in retrieval performance, and show that stratified evaluation yields more stable and transparent assessments while supporting more trustworthy decision-making than aggregate metrics.

Dennis Frauen, Athiya Deviyani, Mihaela van der Schaar, Stefan Feuerriegel

Evaluating the performance of large language models (LLMs) from human preference data is crucial for obtaining LLM leaderboards. However, many existing approaches either rely on restrictive parametric assumptions or lack valid uncertainty quantification when flexible machine learning methods are used. In this paper, we propose a nonparametric statistical framework, called DMLRank, for comparing and ranking LLMs from preference data using debiased machine learning (DML). For this, we introduce generalized average ranking scores (GARS), which generalize commonly used ranking models, including the Bradley-Terry model or PageRank/ Rank centrality with complex human responses such as ties. \framework comes with the following advantages: (i)~It produces statistically efficient estimates of GARS ranking scores. (ii) It naturally allows to incorporate black-box machine learning methods for estimation. (iii) It can be combined with pre-trained LLM evaluators (e.g., using LLM-as-a-judge). (iv) It suggests optimal policies for collecting preference data under budget constraints. We demonstrate these advantages both theoretically and empirically using both synthetic and real-world preference datasets. In summary, our framework provides practitioners with powerful, state-of-the-art methods for comparing or ranking LLMs for leaderboards.

Deep Learning · Large Language Models

Zhixiong Zhao, Zukang Xu, Zhixuan Chen, Xing Hu, Zhe jiang, Dawei Yang

Large language models (LLMs) exhibit exceptional general language processing capabilities, but their memory and compute costs hinder deployment. Ternarization has emerged as a promising compression technique, offering significant reductions in model size and inference complexity. However, existing methods struggle with heavy-tailed activation distributions and therefore keep activations in high precision, fundamentally limiting end-to-end inference acceleration. To overcome this limitation, we propose **TWLA** (**T**ernarized **W**eights and **L**ow-bit **A**ctivations), a post-training quantization (PTQ) framework that achieves 1.58-bit weight compression and 4-bit activation quantization while maintaining high accuracy. TWLA comprises three components: (1) Euclidean-to-Manifold Asymmetric Ternary Quantizer (E2M-ATQ) minimizes layer-output error under weight ternarization via a two-stage optimization from Euclidean initialization to manifold relocation; (2) Kronecker Orthogonal Tri-Modal Shaping (KOTMS) applies a Kronecker-structured orthogonal rotation to reshape weights into ternary-friendly tri-modal distributions, while the shared rotation statistically suppresses activation outliers; and (3) Inter-Layer Aware Activation Mixed Precision (ILA-AMP) explicitly introduces adjacent-layer second-order interaction costs in bit allocation and jointly optimizes for the layer-wise disparity of activation quantization gains induced by the shared orthogonal transform, preventing cascades triggered by a few weak layers. Extensive experiments demonstrate that TWLA is a PTQ method that maintains high accuracy under the **W1.58A4** configuration, while delivering significant inference acceleration. The code is available at [TWLA](https://anonymous.4open.science/r/TWLA-0212/).

Deep Learning · Algorithms

Reena Elangovan, Charbel Sakr, Anand Raghunathan, Brucek Khailany

Post-training quantization (PTQ) is a promising approach to reducing the storage and computational requirements of large language models (LLMs) without additional training cost. Recent PTQ studies have primarily focused on quantizing only weights to sub-$8$-bits while maintaining activations at $8$-bits or higher. Accurate sub-8-bit quantization for both weights and activations without relying on quantization-aware training remains a significant challenge. We propose a novel quantization method called block clustered quantization (BCQ) wherein each operand tensor is decomposed into blocks (a block is a group of contiguous scalars), blocks are clustered based on their statistics, and a dedicated optimal quantization codebook is designed for each cluster. As a specific embodiment of this approach, we propose a PTQ algorithm called Locally-Optimal BCQ (LO-BCQ) that iterates between the steps of block clustering and codebook design to greedily minimize the quantization mean squared error. When weight and activation scalars are encoded to W4A4 format (with $0.5$-bits of overhead for storing scaling factors and codebook selectors), we advance the current state-of-the-art by demonstrating $<1$\% loss in inference accuracy across several LLMs and downstream tasks.

Applications · Neuroscience, Cognitive Science

Yifan Wang, Yijia Ma, Wen Li, Chenyu You

High-fidelity EEG generation is critical for alleviating data scarcity and addressing privacy constraints in large-scale neural modeling. Despite recent progress, most existing approaches formulate EEG generation via discrete denoising objectives, which inadequately reflect the inherently continuous temporal dynamics and spectral structure of neural activity. As a result, these methods often struggle to preserve long-range temporal dependencies and exhibit mismatches in the spectral and temporal structure of the generated signals. In this work, we argue that effective EEG generation requires models that operate directly on the continuous evolution of neural signals. We introduce Just EEG Transformer (JET), a generative framework based on conditional flow matching that models EEG as raw sequences evolving along continuous trajectories. By learning a smooth vector field that transports noise to the EEG data distribution, JET captures temporal continuity and transient dynamics without relying on discretized denoising schemes or domain-specific representations. To ensure that the learned dynamics remain consistent with key properties of EEG signals, we introduce principled constraints that preserve spectral structure, temporal stationarity, and signal-level statistics. Across three large-scale benchmarks, JET consistently achieves state-of-the-art performance, reducing TS-FID by over 40\% compared to strong baselines. Extensive analyses show that JET captures key structural properties of neural dynamics, providing a scalable and principled approach to EEG generation.

General Machine Learning · Online Learning, Active Learning and Bandits

Mengtong Hu, Ziyang Gong, Xu Shi, Ling Zhou, Peter Song

Online learning for the Cox model is challenging because its partial likelihood is non-decomposable, with each risk set requiring a summation over all samples. We propose Collaborative Operation of Linked Survival Analysis (COLSA), an online learning framework that replaces the partial likelihood with the full likelihood using sieve approximation of the baseline hazard. The proposed likelihood function is decomposable and eliminates the need to store historical data in memory, enabling efficient online updates. Moreover, COLSA maintains sufficient statistics for a higher-order basis and employs data-driven basis projection to adaptively scale model complexity to the effective sample size. Unlike existing online Cox methods, COLSA achieves asymptotic normality and attains the same statistical efficiency as the pooled-data partial likelihood estimator, without accessing full data and only requiring constant memory. Simulation studies and application to kidney transplant data demonstrate that COLSA outperforms existing online methods and matches the performance of full-data estimation.

Hoang Pham, The-Anh Ta, Long Tran-Thanh

Pruning at Initialisation methods discover sparse, trainable subnetworks before training, but their theoretical mechanisms remain elusive. Existing analyses are often limited to finite-width statistics, lacking a rigorous characterisation of the global sparsity patterns that emerge as networks grow large. In this work, we connect discrete pruning heuristics to graph limit theory via graphons, establishing the *graphon limit of PaI masks*. We introduce a *Factorised Saliency Model* that encompasses popular pruning criteria and prove that, under regularity conditions, the discrete masks generated by these algorithms converge to deterministic bipartite graphons. This limit framework establishes a novel topological taxonomy for sparse networks: while unstructured methods (e.g., Random, Magnitude) converge to homogeneous graphons representing uniform connectivity, data-driven methods (e.g., SNIP, GraSP) converge to heterogeneous graphons that encode implicit feature selection. Leveraging this continuous characterisation, we derive two fundamental theoretical results: (i) a Universal Approximation Theorem for sparse networks that depends only on the intrinsic dimension of active coordinate subspaces; and (ii) a Graphon-NTK generalisation bound demonstrating how the limit graphon modulates the kernel geometry to align with informative features. Our results transform the study of sparse neural networks from combinatorial graph problems into a rigorous framework of continuous operators, offering a new mechanism for analysing expressivity and generalisation in sparse neural networks.

Deep Learning · Large Language Models

Yueying Li, Yuanfan Chen, Jiayang Chen, Esha Choukse, Haoran Qiu, Edward Suh, Rodrigo Fonseca, Ziv Scully, Udit Gupta

LLM serving exhibits extreme length variability, making size-based scheduling difficult in practice. Recent LLM schedulers approximate SJF/SRPT using predicted decode lengths or rank and primarily report mean-centric metrics (e.g., TTFT/TBT). We show these prediction-driven policies can be fragile under distribution shifts, bursty arrivals, and GPU memory pressure, and still offer limited control over tail latency (P90–P99) that dominates user experience—even with perfect decode-length knowledge. We introduce a distribution-aware, prediction-free scheduling framework that replaces explicit length prediction with soft, $\gamma$-parameterized priority boosting driven by lightweight statistical signals. Our design co-optimizes scheduling with cache-aware preemption to account for memory-coupled decode dynamics that vary across workload mixes. Evaluated on Azure production traces, our method achieves a P99 TTLT up to 35--50\% lower than SRPT with perfect length prediction and a TTFT 34--47\% lower across various workloads, including reasoning-heavy and chat-heavy tasks, demonstrating a robust alternative for tail-latency optimization in online LLM serving.

Deep Learning · Theory

Fares Mehouachi, Saif Jabari

Neural operators learn mappings between function spaces, enabling fast PDE surrogates. Despite architectural diversity, these methods often share a common input representation: raw coordinate-value pairs. This ignores the differential structure that defines the underlying physics. We study whether derivative features can improve neural operator learning. Through Picard iteration on mild solutions, we show that derivatives of the input naturally enter PDE solution operators, and we prove that providing them improves approximation rates substantially. But the optimal derivative order is not what one might expect. We show that the statistically optimal order is strictly less than the PDE order, for any finite sample size. This gap arises from a bias-variance tradeoff: higher-order derivatives carry more information but amplify noise. We characterize this tradeoff in closed form and show that learning the derivative order from data achieves automatic spectral regularization. We introduce $\partial$-NO (derivative-augmented neural operators), a simple augmentation that provides learnable fractional derivative features to any neural operator backbone. Across benchmarks, this consistently improves accuracy. Learned orders reflect dominant PDE structure while adapting to finite-sample constraints, confirming the theory.