Stochastic optimal control methods often struggle in complex non-convex landscapes, frequently becoming trapped in local optima due to their inability to learn from historical trajectory data. This paper introduces Memory-Augmented Potential Field Theory, a unified mathematical framework that integrates historical experience into stochastic optimal control. Our approach dynamically constructs memory-based potential fields that identify and encode key topological features of the state space, enabling controllers to automatically learn from past experiences and adapt their optimization strategy. We provide a theoretical analysis showing that memory-augmented potential fields possess non-convex escape properties, asymptotic convergence characteristics, and computational efficiency. We implement this theoretical framework in a Memory-Augmented Model Predictive Path Integral (MPPI) controller that demonstrates significantly improved performance in challenging non-convex environments. The framework represents a generalizable approach to experience-based learning within control systems (especially robotic dynamics), enhancing their ability to navigate complex state spaces without requiring specialized domain knowledge or extensive offline training.

Traditional reinforcement learning (RL) assumes the agents make decisions based on Markov decision processes (MDPs) with one-step transition models. In many real-world applications, such as energy management and stock investment, agents can access multi-step predictions of future states, which provide additional advantages for decision making. However, multi-step predictions are inherently high-dimensional: naively embedding these predictions into an MDP leads to an exponential blow-up in state space and the curse of dimensionality. Moreover, existing RL theory provides few tools to analyze prediction-augmented MDPs, as it typically works on one-step transition kernels and cannot accommodate multi-step predictions with errors or partial action-coverage. We address these challenges with three key innovations: First, we propose the Bayesian value function to characterize the optimal prediction-aware policy tractably. Second, we develop a novel BellmanJensen Gap analysis on the Bayesian value function, which enables characterizing the value of imperfect predictions. Third, we introduce BOLA (Bayesian Offline Learning with Online Adaptation), a two-stage model-based RL algorithm that separates offline Bayesian value learning from lightweight online adaptation to real-time predictions. We prove that BOLA remains sample-efficient even under imperfect predictions.

Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent covariance matrix for the response, failing to capture the underlying correlation structure. However, spatio-temporal GPs suffer from issues of scalability and various forms of approximation bias resulting from restrictive assumptions of the covariance kernel function. We propose STACI, a novel framework consisting of a variational Bayesian neural network approximation of non-stationary spatio-temporal GP along with a novel spatio-temporal conformal inference algorithm. STACI is highly scalable, taking advantage of GPU training capabilities for neural network models, and provides statistically valid prediction intervals for uncertainty quantification. STACI outperforms competing GPs and deep methods in accurately approximating spatio-temporal processes and we show it easily scales to datasets with millions of observations.

Harnessing the event-driven characteristic, Spiking Neural Networks (SNNs) present a promising avenue toward energy-efficient Transformer architectures. However, existing Spiking Transformers still suffer significant performance gaps compared to their Artificial Neural Network counterparts. Through comprehensive analysis, we attribute this gap to these two factors. First, the binary nature of spike trains limits Spiking Self-attention (SSA)'s capacity to capture negative-negative and positive-negative membrane potential interactions on Querys and Keys. Second, SSA typically omits Softmax functions to avoid energy-intensive multiplyaccumulate operations, thereby failing to maintain row-stochasticity constraints on attention scores.

Dynamic coreset selection is a promising approach for improving the training efficiency of deep neural networks by periodically selecting a small subset of the most representative or informative samples, thereby avoiding the need to train on the entire dataset. However, it remains inherently challenging due not only to the complex interdependencies among samples and the evolving nature of model training, but also to a critical coreset representativeness degradation issue identified and explored in-depth in this paper, that is, the representativeness or information content of the coreset degrades over time as training progresses. Therefore, we argue that, in addition to designing accurate selection rules, it is equally important to endow the algorithms with the ability to assess the quality of the current coreset. Such awareness enables timely re-selection, mitigating the risk of overfitting to stale subsets-a limitation often overlooked by existing methods. To this end, this paper proposes an Efficient Representativeness-Aware Coreset Selection (ERACS) method for deep neural networks, a lightweight framework that enables dynamic tracking and maintenance of coreset quality during training.

The computational sparsity of Mixture-of-Experts (MoE) models enables sublinear growth in compute cost as model size increases, thus offering a scalable path to training massive neural networks. However, existing implementations suffer from low GPU utilization, significant latency overhead, and a fundamental inability to leverage task locality, primarily due to CPU-managed scheduling, host-initiated communication, and frequent kernel launches. To overcome these limitations, we develop FlashMoE, a fully GPU-resident MoE operator that fuses expert computation and inter-GPU communication into a single persistent GPU kernel. FlashMoE enables fine-grained pipelining of dispatch, compute, and combine phases, eliminating launch overheads and reducing idle gaps. Unlike existing work, FlashMoE obviates bulk-synchronous collectives for one-sided, device-initiated, inter-GPU (R)DMA transfers, thus unlocking payload efficiency, where we eliminate bloated or redundant network payloads in sparsely activated layers. When evaluated on an 8-H100 GPU node with MoE models having up to 128 experts and 16K token sequences, FlashMoE achieves up to 9 higher GPU utilization, 6 lower latency, 5.7 higher throughput, and 4 better overlap efficiency compared to state-of-the-art baselines--despite using FP32 while baselines use FP16. FlashMoE shows that principled GPU kernel-hardware co-design is key to unlocking the performance ceiling of large-scale distributed ML.

Time series forecasting plays a pivotal role in critical domains such as energy management and financial markets. Although deep learning-based approaches (e.g., MLP, RNN, Transformer) have achieved remarkable progress, the prevailing "longsequence information gain hypothesis" exhibits inherent limitations. Through systematic experimentation, this study reveals a counterintuitive phenomenon: appropriately truncating historical data can paradoxically enhance prediction accuracy, indicating that existing models learn substantial redundant features (e.g., noise or irrelevant fluctuations) during training, thereby compromising effective signal extraction. Building upon information bottleneck theory, we propose an innovative solution termed Adaptive Masking Loss with Representation Consistency (AMRC), which features two core components: 1) Dynamic masking loss, which adaptively identified highly discriminative temporal segments to guide gradient descent during model training; 2) Representation consistency constraint, which stabilized the mapping relationships among inputs, labels, and predictions. Experimental results demonstrate that AMRC effectively suppresses redundant feature learning while significantly improving model performance. This work not only challenges conventional assumptions in temporal modeling but also provides novel theoretical insights and methodological breakthroughs for developing efficient and robust forecasting models. We have made our code available at https://github.com/MazelTovy/AMRC.

This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task.

Test-time scaling (TTS) enhances the performance of large language models (LLMs) by allocating additional compute resources during inference. However, existing research primarily investigates TTS in single-stage tasks; while many real-world problems are multi-stage complex tasks, composed of a sequence of heterogeneous subtasks with each subtask requires LLM of specific capability. Therefore, we study a novel problem: the test-time compute-optimal scaling in multi-stage complex tasks, aiming to select suitable models and allocate budgets per subtask to maximize overall performance. TTS in multi-stage tasks introduces two fundamental challenges: (i) The combinatorial search space of model and budget allocations, combined with the high cost of inference, makes brute-force search impractical.

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.