Most methods for finding a Nash equilibrium rely on procedures that operate over the entire action space, making them infeasible for settings with too many actions to be searched exhaustively. Randomised search heuristics such as coevolutionary algorithms offer benefits in such settings, however they lack many of the theoretical guarantees established for exhaustive methods such as zero-regret learning. We address this by developing a method for proving necessary and sufficient conditions for a coevolutionary algorithm to be stable, in the sense that it reliably retains a Nash equilibrium following discovery. As the method provides bounds that are adapted to both application and algorithm instance, it can be used as a practical tool for parameter configuration. We additionally show how bounds on regret may be deduced from our results and undertake corresponding empirical analysis.

Designing de novo 3D molecules with desirable properties remains a fundamental challenge in drug discovery and molecular engineering. While diffusion models have demonstrated remarkable capabilities in generating high-quality 3D molecular structures, they often struggle to effectively control complex multi-objective constraints critical for real-world applications. In this study, we propose an uncertaintyaware Reinforcement Learning (RL) framework to guide the optimization of 3D molecular diffusion models toward multiple property objectives while enhancing the overall quality of the generated molecules. Our method leverages surrogate models with predictive uncertainty estimation to dynamically shape reward functions, facilitating balance across multiple optimization objectives. We comprehensively evaluate our framework across three benchmark datasets and multiple diffusion model architectures, consistently outperforming baselines for molecular quality and property optimization. Additionally, Molecular Dynamics (MD) simulations and ADMET profiling of top generated candidates indicate promising drug-like behavior and binding stability, comparable to known Epidermal Growth Factor Receptor (EGFR) inhibitors. Our results demonstrate the strong potential of RL-guided generative diffusion models for advancing automated molecular design.

When applied sequentially to video, frame-based networks often exhibit temporal inconsistency--for example, outputs that flicker between frames. This problem is amplified when the network inputs contain time-varying corruptions. In this work, we introduce a general approach for adapting frame-based models for stable and robust inference on video. We describe a class of stability adapters that can be inserted into virtually any architecture and a resource-efficient training process that can be performed with a frozen base network. We introduce a unified conceptual framework for describing temporal stability and corruption robustness, centered on a proposed accuracy-stability-robustness loss. By analyzing the theoretical properties of this loss, we identify the conditions where it produces well-behaved stabilizer training.

As deep learning models continue to scale, the growing computational demands have amplified the need for effective coreset selection techniques. Coreset selection aims to accelerate training by identifying small, representative subsets of data that approximate the performance of the full dataset. Among various approaches, gradient-based methods stand out due to their strong theoretical underpinnings and practical benefits, particularly under limited data budgets. However, these methods face challenges such as na ıve stochastic gradient descent (SGD) acting as a surprisingly strong baseline and the breakdown of representativeness due to loss curvature mismatches over time. In this work, we propose a novel framework that addresses these limitations. First, we establish a connection between posterior sampling and loss landscapes, enabling robust coreset selection even in high-data-corruption scenarios. Second, we introduce a smoothed loss function based on posterior sampling onto the model weights, enhancing stability and generalization while maintaining computational efficiency. We also present a novel convergence analysis for our sampling-based coreset selection method. Finally, through extensive experiments, we demonstrate how our approach achieves faster training and enhanced generalization across diverse datasets than the current state of the art.

We study matching markets with ties, where workers on one side of the market may have tied preferences over jobs, determined by their matching utilities. Unlike classical two-sided markets with strict preferences, no single stable matching exists that is utility-maximizing for all workers. To address this challenge, we introduce the Optimal Stable Share (OSS)-ratio, which measures the ratio of a worker's maximum achievable utility in any stable matching to their utility in a given matching. We prove that distributions over only stable matchings can incur linear utility losses, i.e., an Ω(N) OSS-ratio, where N is the number of workers. To overcome this, we design an algorithm that efficiently computes a distribution over (possibly non-stable) matchings, achieving an asymptotically tight O(logN) OSS-ratio. When exact utilities are unknown, our second algorithm guarantees workers a logarithmic approximation of their optimal utility under bounded instability. Finally, we extend our offline approximation results to a bandit learning setting where utilities are only observed for matched pairs. In this setting, we consider worker-optimal stable regret, design an adaptive algorithm that smoothly interpolates between markets with strict preferences and those with statistical ties, and establish a lower bound revealing the fundamental trade-off between strict and tied preference regimes.

Recurrent neural networks (RNNs) trained on neuroscience-inspired tasks offer powerful models of brain computation. However, typical training paradigms rely on open-loop, supervised settings, whereas real-world learning unfolds in closed-loop environments. Here, we develop a mathematical theory describing the learning dynamics of linear RNNs trained in closed-loop contexts. We first demonstrate that two otherwise identical RNNs, trained in either closed-or open-loop modes, follow markedly different learning trajectories. To probe this divergence, we analytically characterize the closed-loop case, revealing distinct stages aligned with the evolution of the training loss. Specifically, we show that the learning dynamics of closed-loop RNNs, in contrast to open-loop ones, are governed by an interplay between two competing objectives: short-term policy improvement and long-term stability of the agent-environment interaction. Finally, we apply our framework to a realistic motor control task, highlighting its broader applicability. Taken together, our results underscore the importance of modeling closed-loop dynamics in a biologically plausible setting.

Reuse of data in adaptive workflows poses challenges regarding overfitting and the statistical validity of results. Previous work has demonstrated that interacting with data via differentially private algorithms can mitigate overfitting, achieving worstcase generalization guarantees with asymptotically optimal data requirements. However, such past work assumes data is static and cannot accommodate situations where data grows over time. In this paper we address this gap, presenting the first generalization bounds for adaptive analysis on dynamic data. We allow the analyst to adaptively schedule their queries conditioned on the current size of the data, in addition to previous queries and responses. We also incorporate time-varying empirical accuracy bounds and mechanisms, allowing for tighter guarantees as data accumulates. In a batched query setting, the asymptotic data requirements of our bound grows with the square-root of the number of adaptive queries, matching prior works' improvement over data splitting for the static setting. We instantiate our bound for statistical queries with the clipped Gaussian mechanism, where it empirically outperforms baselines composed from static bounds.

Algorithm configuration, which involves selecting algorithm parameters based on sampled problem instances, is a crucial step in applying modern algorithms such as SAT solvers. Although prior work has attempted to understand the theoretical foundations of algorithm configuration, we still lack a comprehensive understanding of why practical algorithm configurators exhibit strong generalization performances in real-world scenarios. In this paper, through the lens of machine learning theory, we provide an algorithm-dependent generalization bound for the widely used model-based algorithm configurators under mild assumptions. Our approach is based on the algorithmic stability framework for generalization bounds. To the best of our knowledge, this is the first generalization bound that applies to a model closely approximating practical model-based algorithm configurators.

Motivated by the geometric advantages of quaternions in representing rotations and postures, we propose a quaternion-valued supervised learning Hopfield-structured neural network (QSHNN) with a fully connected structure inspired by the classic Hopfield neural network (HNN). Starting from a continuous-time dynamical model of HNNs, we extend the formulation to the quaternionic domain and establish the existence and uniqueness of fixed points with asymptotic stability. For the learning rules, we introduce a periodic projection strategy that modifies standard gradient descent by periodically projecting each 4 4block of the weight matrix onto the closest quaternionic structure in the least-squares sense. This approach preserves both convergence and quaternionic consistency throughout training. Benefiting from this rigorous mathematical foundation, the experimental model implementation achieves high accuracy, fast convergence, and strong reliability across randomly generated target sets. Moreover, the evolution trajectories of the QSHNN exhibit well-bounded curvature, i.e., sufficient smoothness, which is crucial for applications such as control systems or path planning modules in robotic arms, where joint postures are parameterized by quaternion neurons. Beyond these application scenarios, the proposed model offers a practical implementation framework and a general mathematical methodology for designing neural networks under hypercomplex or non-commutative algebraic structures.

In this work, we first empirically demonstrate the instability and suboptimal performance of existing popular MU methods when deployed in different scenarios. To address this issue, we propose Dual Optimizer (DualOptim), which incorporates adaptive learning rate and decoupled momentum factors. Empirical and theoretical evidence demonstrates that DualOptim contributes to effective and stable unlearning. Through extensive experiments, we show that DualOptim can significantly boost MU efficacy and stability across diverse tasks, including image classification, image generation, and large language models, making it a versatile approach to empower existing MU algorithms.