In this paper, we leverage stochastic projection and lossy compression to establish new conditional mutual information (CMI) bounds on the generalization error of statistical learning algorithms. It is shown that these bounds are generally tighter than the existing ones. In particular, we prove that for certain problem instances for which existing MI and CMI bounds were recently shown in Attias et al. [2024] and Livni [2023] to become vacuous or fail to describe the right generalization behavior, our bounds yield suitable generalization guarantees of the order of $\mathcal{O}(1/\sqrt{n})$, where $n$ is the size of the training dataset. Furthermore, we use our bounds to investigate the problem of data memorization raised in those works, and which asserts that there are learning problem instances for which any learning algorithm that has good prediction there exist distributions under which the algorithm must memorize'' a big fraction of the training dataset. We show that for every learning algorithm, there exists an auxiliary algorithm that does not memorize and which yields comparable generalization error for any data distribution. In part, this shows that memorization is not necessary for good generalization.

We study online learning in finite-horizon episodic Markov decision processes (MDPs) under the challenging \textit{aggregate bandit feedback} model, where the learner observes only the cumulative loss incurred in each episode, rather than individual losses at each state-action pair. While prior work in this setting has focused exclusively on worst-case analysis, we initiate the study of \textit{best-of-both-worlds} (BOBW) algorithms that achieve low regret in both stochastic and adversarial environments. We propose the first BOBW algorithms for episodic tabular MDPs with aggregate bandit feedback. In the case of known transitions, our algorithms achieve $O(\log T)$ regret in stochastic settings and ${O}(\sqrt{T})$ regret in adversarial ones. Importantly, we also establish matching lower bounds, showing the optimality of our algorithms in this setting. We further extend our approach to unknown-transition settings by incorporating confidence-based techniques. Our results rely on a combination of FTRL over occupancy measures, self-bounding techniques, and new loss estimators inspired by recent advances in online shortest path problems. Along the way, we also provide the first individual-gap-dependent lower bounds and demonstrate near-optimal BOBW algorithms for shortest path problems with bandit feedback.

Symbolic regression (SR) seeks interpretable analytical expressions that uncover the governing relationships within data, providing mechanistic insight beyond'black-box' models. However, existing SR methods often suffer from two key limitations: (1) *redundant representations* that fail to capture mathematical equivalences and higher-order operand relations, breaking permutation invariance and hindering efficient learning; and (2) *sparse rewards* caused by incomplete incorporation of constraints that can only be evaluated on full expressions, such as constant fitting or physical-law verification. To address these challenges, we propose a unified framework, **Graph-based Symbolic Regression (GSR)**, which compresses the search space through the permutation-invariant representations, expression graphs (EGs), that intrinsically encode expression equivalences via a term-rewriting system (TRS) and a directed acyclic graph (DAG) structure. GSR mitigates reward sparsity by employing a hybrid neural-guided Monte Carlo tree search (hnMCTS) on EGs, where constraint-informed neural guidance enables the direct incorporation of expression-level constraint priors, and an adaptive $\epsilon$-UCB policy balances exploration and exploitation. Theoretical analyses establish the uniqueness of our proposed EG representation and the convergence of the hnMCTS algorithm. Experiments on synthetic and real-world scientific datasets demonstrate the efficiency and accuracy of GSR in discovering underlying expressions and adhering to physical laws, offering practical solutions for scientific discovery.

Large Language Models (LLMs) excel at natural language processing tasks, but their massive size leads to high computational and storage demands. Recent works have sought to reduce their model size through layer-wise structured pruning. However, they tend to ignore retaining the capabilities in the pruned part. In this work, we re-examine structured pruning paradigms and uncover several key limitations: 1) notable performance degradation due to direct layer removal, 2) incompetent linear weighted layer aggregation, and 3) the lack of effective post-training recovery mechanisms. To address these limitations, we propose CoMe, including a progressive layer pruning framework with a Concatenation-based Merging technology and a hierarchical distillation post-training process. Specifically, we introduce a channel sensitivity metric that utilizes activation intensity and weight norms for fine-grained channel selection. Subsequently, we employ a concatenation-based layer merging method to fuse the most critical channels in the adjacent layers, enabling a progressive model size reduction. Finally, we propose a hierarchical distillation protocol, which leverages the correspondences between the original and pruned model layers established during pruning, enabling efficient knowledge transfer. Experiments on seven benchmarks show that CoMe achieves state-of-the-art performance; when pruning 30% of LLaMA-2-7b's parameters, the pruned model retains 83% of its original average accuracy.

While RLHF has demonstrated promising results, many algorithms are highly sensitive to misspecifications in the underlying preference model (e.g., the Bradley-Terry model), the reference policy, or the reward function, resulting in undesirable fine-tuning. To address model misspecification, we propose a doubly robust preference optimization algorithm that remains consistent when either the preference model or the reference policy is correctly specified (without requiring both). Our proposal demonstrates superior and more robust performance than state-of-the-art algorithms, both in theory and in practice.

The softmax-contaminated mixture of experts (MoE) model is deployed when a large-scale pre-trained model, which plays the role of a fixed expert, is fine-tuned for learning downstream tasks by including a new contamination part, or prompt, functioning as a new, trainable expert. Despite its popularity and relevance, the theoretical properties of the softmax-contaminated MoE have remained unexplored in the literature. In the paper, we study the convergence rates of the maximum likelihood estimator of gating and prompt parameters in order to gain insights into the statistical properties and potential challenges of fine-tuning with a new prompt. We find that the estimability of these parameters is compromised when the prompt acquires overlapping knowledge with the pre-trained model, in the sense that we make precise by formulating a novel analytic notion of distinguishability. Under distinguishability of the pre-trained and prompt models, we derive minimax optimal estimation rates for all the gating and prompt parameters. By contrast, when the distinguishability condition is violated, these estimation rates become significantly slower due to their dependence on the prompt convergence rate to the pre-trained model. Finally, we empirically corroborate our theoretical findings through several numerical experiments.

The fundamental challenge of long video understanding, e.g., question answering, lies in the extensive number of frames, making it infeasible to densely understand the local details while comprehensively digest the global contexts, especially within a limited context length. To address this problem, our insight is to process short video segments individually and combine these segment-level analyses into a final response. This intuition is noted in the well-established MapReduce principle in big data processing and is naturally compatible with inference scaling at the system level. Motivated by this, we propose MR. Video (pronounced as mister video), a long video understanding framework adopting the MapReduce principle. We define the standard operations of MapReduce in a long video understanding context: the Map steps conduct independent and sequence-parallel dense perception on short video segments, covering local details, while the Reduce steps comprehensively aggregate the segment-level results into an answer with global contexts.

Test-time adaptation (TTA) for Vision-Language Models (VLMs) aims to enhance performance on unseen test data. However, existing methods struggle to achieve robust and continuous knowledge accumulation during test time. To address this, we propose Statistics Caching test-time Adaptation (SCA), a novel cache-based approach. Unlike traditional feature-caching methods prone to forgetting, SCA continuously accumulates task-specific knowledge from all encountered test samples. By formulating the reuse of past features as a least squares problem, SCA avoids storing raw features and instead maintains compact, incrementally updated feature statistics. This design enables efficient online adaptation without the limitations of fixed-size caches, ensuring that the accumulated knowledge grows persistently over time. Furthermore, we introduce adaptive strategies that leverage the VLM's prediction uncertainty to reduce the impact of noisy pseudo-labels and dynamically balance multiple prediction sources, leading to more robust and reliable performance. Extensive experiments demonstrate that SCA achieves compelling performance while maintaining competitive computational efficiency.

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Perturbation-based explanations are widely utilized to enhance the transparency of machine-learning models in practice. However, their reliability is often compromised by the unknown model behavior under the specific perturbations used. This paper investigates the relationship between uncertainty calibration - the alignment of model confidence with actual accuracy - and perturbation-based explanations. We show that models systematically produce unreliable probability estimates when subjected to explainability-specific perturbations and theoretically prove that this directly undermines global and local explanation quality. To address this, we introduce ReCalX, a novel approach to recalibrate models for improved explanations while preserving their original predictions. Empirical evaluations across diverse models and datasets demonstrate that ReCalX consistently reduces perturbation-specific miscalibration most effectively while enhancing explanation robustness and the identification of globally important input features.