Snapshot compressive imaging (SCI) recovers high-dimensional (3D) data cubes from a single 2D measurement, enabling diverse applications like video and hyperspectral imaging to go beyond standard techniques in terms of acquisition speed and efficiency. In this paper, we focus on SCI recovery algorithms that employ untrained neural networks (UNNs), such as deep image prior (DIP), to model source structure. Such UNN-based methods are appealing as they have the potential of avoiding the computationally intensive retraining required for different source models and different measurement scenarios. We first develop a theoretical framework for characterizing the performance of such UNN-based methods. The theoretical framework, on the one hand, enables us to optimize the parameters of data-modulating masks, and on the other hand, provides a fundamental connection between the number of data frames that can be recovered from a single measurement to the parameters of the untrained NN. We also employ the recently proposed bagged-deep-image-prior (bagged-DIP) idea to develop SCI Bagged Deep Video Prior (SCI-BDVP) algorithms that address the common challenges faced by standard UNN solutions. Our experimental results show that in video SCI our proposed solution achieves state-of-the-art among UNN methods, and in the case of noisy measurements, it even outperforms supervised solutions.

Graph Neural Networks (GNNs) have demonstrated remarkable performance across a spectrum of graph-related tasks, however concerns persist regarding their vulnerability to adversarial perturbations. While prevailing defense strategies focus primarily on pre-processing techniques and adaptive message-passing schemes, this study delves into an under-explored dimension: the impact of weight initialization and associated hyper-parameters, such as training epochs, on a model's robustness.We introduce a theoretical framework bridging the connection between initialization strategies and a network's resilience to adversarial perturbations. Our analysis reveals a direct relationship between initial weights, number of training epochs and the model's vulnerability, offering new insights into adversarial robustness beyond conventional defense mechanisms. While our primary focus is on GNNs, we extend our theoretical framework, providing a general upper-bound applicable to Deep Neural Networks.Extensive experiments, spanning diverse models and real-world datasets subjected to various adversarial attacks, validate our findings. We illustrate that selecting appropriate initialization not only ensures performance on clean datasets but also enhances model robustness against adversarial perturbations, with observed gaps of up to 50\% compared to alternative initialization approaches.

Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop a theoretical framework for graph classification problems in the partial observation setting (i.e., subgraph samplings). Equipped with insights from graph limit theory, we propose a new graph classification model that works on a randomly sampled subgraph and a novel topology to characterize the representability of the model. Our theoretical framework contributes a theoretical validation of mini-batch learning on graphs and leads to new learning-theoretic results on generalization bounds as well as size-generalizability without assumptions on the input.

Optimistic exploration is central to improving sample efficiency in reinforcement learning with human feedback, yet existing exploratory bonus methods to incentivize exploration often fail to realize optimism. We provide a theoretical analysis showing that current formulations, under KL or $α$-divergence regularization, unintentionally bias exploration toward high-probability regions of the reference model, thereby reinforcing conservative behavior instead of promoting discovery of uncertain regions. To address this pitfall, we introduce the General Exploratory Bonus (GEB), a novel theoretical framework that provably satisfies the optimism principle. GEB counteracts divergence-induced bias via reference-dependent reward regulation and unifies prior heuristic bonuses as special cases, while extending naturally across the full $α$-divergence family. Empirically, GEB consistently outperforms baselines on alignment tasks across multiple divergence settings and large language model backbones. These results demonstrate that GEB offers both a principled and practical solution for optimistic exploration in RLHF.

Existing reinforcement learning (RL)-based post-training methods for large language models have advanced rapidly, yet their design has largely been guided by heuristics rather than systematic theoretical principles. This gap limits our understanding of the properties of the gradient estimators and the associated optimization algorithms, thereby constraining opportunities to improve training stability and overall performance. In this work, we provide a unified theoretical framework that characterizes the statistical properties of commonly used policy-gradient estimators under mild assumptions. Our analysis establishes unbiasedness, derives exact variance expressions, and yields an optimization-loss upper bound that enables principled reasoning about learning dynamics. Building on these results, we prove convergence guarantees and derive an adaptive learning-rate schedule governed by the signal-to-noise ratio (SNR) of gradients. We further show that the variance-optimal baseline is a gradient-weighted estimator, offering a new principle for variance reduction and naturally enhancing stability beyond existing methods. These insights motivate Optimal Baseline and Learning-Rate Policy Optimization (OBLR-PO), an algorithm that jointly adapts learning rates and baselines in a theoretically grounded manner. Experiments on Qwen3-4B-Base and Qwen3-8B-Base demonstrate consistent gains over existing policy optimization methods, validating that our theoretical contributions translate into practical improvements in large-scale post-training.

Ensemble learning improves classification performance by combining multiple base classifiers. While increasing the number of classifiers generally enhances accuracy, excessively large ensembles can lead to computational inefficiency and diminishing returns. This paper investigates the relationship between ensemble size and performance through the lens of linear independence among classifier votes in data streams. We propose that ensembles composed of linearly independent classifiers maximize representational capacity, particularly under a geometric model. We then generalize the importance of linear independence to the weighted majority voting problem. By modeling the probability of achieving linear independence among classifier outputs, we derive a theoretical framework that explains the trade-off between ensemble size and accuracy. Our analysis leads to a theoretical estimate of the ensemble size required to achieve a user-specified probability of linear independence. We validate our theory through experiments on both real-world and synthetic datasets using two ensemble methods, OzaBagging and GOOWE. Our results confirm that this theoretical estimate effectively identifies the point of performance saturation for robust ensembles like OzaBagging. Conversely, for complex weighting schemes like GOOWE, our framework reveals that high theoretical diversity can trigger algorithmic instability. Our implementation is publicly available to support reproducibility and future research.

We thank the reviewers for their valuable comments and for pointing out the typos and clarity issues. We first explain the novelty and significance of our work and then answer the questions of each reviewer. We will clarify our contributions in the revision. But more careful analysis are needed to obtain similar convergence rate without projection. Here we adopt Gaussian policy for simplicity.

Marine invasive species spread through global shipping and generate substantial ecological and economic impacts. Traditional risk assessments require detailed records of ballast water and traffic patterns, which are often incomplete, limiting global coverage. This work advances a theoretical framework that quantifies invasion risk by combining environmental similarity across ports with observed and forecasted maritime mobility. Climate-based feature representations characterize each port's marine conditions, while mobility networks derived from Automatic Identification System data capture vessel flows and potential transfer pathways. Clustering and metric learning reveal climate analogues and enable the estimation of species survival likelihood along shipping routes. A temporal link prediction model captures how traffic patterns may change under shifting environmental conditions. The resulting fusion of environmental similarity and predicted mobility provides exposure estimates at the port and voyage levels, supporting targeted monitoring, routing adjustments, and management interventions.

Elicited performance requirements need to be quantified for compliance in different engineering tasks, e.g., configuration tuning and performance testing. Much existing work has relied on manual quantification, which is expensive and error-prone due to the imprecision. In this paper, we present LQPR, a highly efficient automatic approach for performance requirements quantification.LQPR relies on a new theoretical framework that converts quantification as a classification problem. Despite the prevalent applications of Large Language Models (LLMs) for requirement analytics, LQPR takes a different perspective to address the classification: we observed that performance requirements can exhibit strong patterns and are often short/concise, therefore we design a lightweight linguistically induced matching mechanism. We compare LQPR against nine state-of-the-art learning-based approaches over diverse datasets, demonstrating that it is ranked as the sole best for 75% or more cases with two orders less cost. Our work proves that, at least for performance requirement quantification, specialized methods can be more suitable than the general LLM-driven approaches.

Reservoir computing is a powerful framework for real-time information processing, characterized by its high computational ability and quick learning, with applications ranging from machine learning to biological systems. In this paper, we investigate how the computational ability of reservoir recurrent neural networks (RNNs) scales with an increasing number of readout neurons. First, we demonstrate that the memory capacity of a reservoir RNN scales sublinearly with the number of readout neurons. To elucidate this observation, we develop a theoretical framework for analytically deriving memory capacity that incorporates the effect of neuronal correlations, which have been ignored in prior theoretical work for analytical simplicity. Our theory successfully relates the sublinear scaling of memory capacity to the strength of neuronal correlations. Furthermore, we show this principle holds across diverse types of RNNs, even those beyond the direct applicability of our theory. Next, we numerically investigate the scaling behavior of nonlinear computational ability, which, alongside memory capacity, is crucial for overall computational performance. Our numerical simulations reveal that as memory capacity growth becomes sublinear, increasing the number of readout neurons successively enables nonlinear processing at progressively higher polynomial orders. Our theoretical framework suggests that neuronal correlations govern not only memory capacity but also the sequential growth of nonlinear computational capabilities. Our findings establish a foundation for designing scalable and cost-effective reservoir computing, providing novel insights into the interplay among neuronal correlations, linear memory, and nonlinear processing.