Extended Stability Runge-Kutta (ESRK) methods are crucial for solving large-scale computational problems in science and engineering, including weather forecasting, aerodynamic analysis, and complex biological modelling. However, balancing accuracy, stability, and computational efficiency remains challenging, particularly for high-order, low-storage schemes. This study introduces a hybrid Genetic Algorithm (GA) and Reinforcement Learning (RL) approach for automated heuristic discovery, optimising low-storage ESRK methods. Unlike traditional approaches that rely on manually designed heuristics or exhaustive numerical searches, our method leverages GA-driven mutations for search-space exploration and an RL-inspired state transition mechanism to refine heuristic selection dynamically. This enables systematic parameter reduction, preserving fourth-order accuracy while significantly improving computational efficiency.The proposed GA-RL heuristic optimisation framework is validated through rigorous testing on benchmark problems, including the 1D and 2D Brusselator systems and the steady-state Navier-Stokes equations. The best-performing heuristic achieves a 25\% reduction in IPOPT runtime compared to traditional ESRK optimisation processes while maintaining numerical stability and accuracy. These findings demonstrate the potential of adaptive heuristic discovery to improve resource efficiency in high-fidelity simulations and broaden the applicability of low-storage Runge-Kutta methods in real-world computational fluid dynamics, physics simulations, and other demanding fields. This work establishes a new paradigm in heuristic optimisation for numerical methods, opening pathways for further exploration using Deep RL and AutoML-based heuristic search less

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound. less

Multivariate time series anomaly detection (MTS-AD) is critical in domains like healthcare, cybersecurity, and industrial monitoring, yet remains challenging due to complex inter-variable dependencies, temporal dynamics, and sparse anomaly labels. We introduce mTSBench, the largest benchmark to date for MTS-AD and unsupervised model selection, spanning 344 labeled time series across 19 datasets and 12 diverse application domains. mTSBench evaluates 24 anomaly detection methods, including large language model (LLM)-based detectors for multivariate time series, and systematically benchmarks unsupervised model selection techniques under standardized conditions. Consistent with prior findings, our results confirm that no single detector excels across datasets, underscoring the importance of model selection. However, even state-of-the-art selection methods remain far from optimal, revealing critical gaps. mTSBench provides a unified evaluation suite to enable rigorous, reproducible comparisons and catalyze future advances in adaptive anomaly detection and robust model selection. less

Large Language Models (LLMs) have become indispensable in real-world applications. However, their widespread adoption raises significant safety concerns, particularly in responding to socially harmful questions. Despite substantial efforts to improve model safety through alignment, aligned models can still have their safety protections undermined by subsequent fine-tuning - even when the additional training data appears benign. In this paper, we empirically demonstrate that this vulnerability stems from the sensitivity of safety-critical low-rank subspaces in LLM parameters to fine-tuning. Building on this insight, we propose a novel training-free method, termed Low-Rank Extrapolation (LoX), to enhance safety robustness by extrapolating the safety subspace of an aligned LLM. Our experimental results confirm the effectiveness of LoX, demonstrating significant improvements in robustness against both benign and malicious fine-tuning attacks while preserving the model's adaptability to new tasks. For instance, LoX leads to 11% to 54% absolute reductions in attack success rates (ASR) facing benign or malicious fine-tuning attacks. By investigating the ASR landscape of parameters, we attribute the success of LoX to that the extrapolation moves LLM parameters to a flatter zone, thereby less sensitive to perturbations. The code is available at github.com/VITA-Group/LoX. less

Offline reinforcement learning (offline RL) algorithms often require additional constraints or penalty terms to address distribution shift issues, such as adding implicit or explicit policy constraints during policy optimization to reduce the estimation bias of functions. This paper focuses on a limitation of the Advantage-Weighted Regression family (AWRs), i.e., the potential for learning over-conservative policies due to data corruption, specifically the poor explorations in suboptimal offline data. We study it from two perspectives: (1) how poor explorations impact the theoretically optimal policy based on KL divergence, and (2) how such poor explorations affect the approximation of the theoretically optimal policy. We prove that such over-conservatism is mainly caused by the sensitivity of the loss function for policy optimization to poor explorations, and the proportion of poor explorations in offline datasets. To address this concern, we propose Corruption-Averse Advantage-Weighted Regression (CAWR), which incorporates a set of robust loss functions during policy optimization and an advantage-based prioritized experience replay method to filter out poor explorations. Numerical experiments on the D4RL benchmark show that our method can learn superior policies from suboptimal offline data, significantly enhancing the performance of policy optimization. less

Graph Neural Networks (GNNs) have achieved remarkable success across various domains. However, recent theoretical advances have identified fundamental limitations in their information propagation capabilities, such as over-squashing, where distant nodes fail to effectively exchange information. While extensively studied in static contexts, this issue remains unexplored in Spatiotemporal GNNs (STGNNs), which process sequences associated with graph nodes. Nonetheless, the temporal dimension amplifies this challenge by increasing the information that must be propagated. In this work, we formalize the spatiotemporal over-squashing problem and demonstrate its distinct characteristics compared to the static case. Our analysis reveals that counterintuitively, convolutional STGNNs favor information propagation from points temporally distant rather than close in time. Moreover, we prove that architectures that follow either time-and-space or time-then-space processing paradigms are equally affected by this phenomenon, providing theoretical justification for computationally efficient implementations. We validate our findings on synthetic and real-world datasets, providing deeper insights into their operational dynamics and principled guidance for more effective designs. less

Rule-based rewards offer a promising strategy for improving reinforcement learning from human feedback (RLHF), but current approaches often rely on manual rule engineering. We present AutoRule, a fully automated method for extracting rules from preference feedback and formulating them into rule-based rewards. AutoRule extraction operates in three stages: it leverages a reasoning model to interpret user preferences, identifies candidate rules from the reasoning chain of these interpretations, and synthesizes them into a unified rule set. Leveraging the finalized rule set, we employ language-model verifiers to compute the fraction of rules satisfied by each output, using this metric as an auxiliary reward alongside the learned reward model during policy optimization. Training a Llama-3-8B model with AutoRule results in a 28.6\% relative improvement in length-controlled win rate on AlpacaEval2.0, and a 6.1\% relative gain in second-turn performance on a held-out MT-Bench subset, compared to a GRPO baseline trained with the same learned reward model but without the rule-based auxiliary reward. Our analysis confirms that the extracted rules exhibit good agreement with dataset preference. We find that AutoRule demonstrates reduced reward hacking compared to a learned reward model when run over two episodes. Finally, our case study suggests that the extracted rules capture unique qualities valued in different datasets. The extracted rules are provided in the appendix, and the code is open-sourced at https://github.com/cxcscmu/AutoRule. less