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Geophysical systems are inherently complex and span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially pronounced for extreme events, which are primarily governed by their instantaneous properties rather than their average characteristics. Advances in dynamical systems theory, including the development of local dynamical indices such as local dimension and inverse persistence, have provided powerful tools for studying these short-lasting phenomena. However, existing applications of such indices often rely on predefined fixed spatial domains and scales, with limited discussion on the influence of spatial scales on the results. In this work, we present a novel spatially multiscale methodology that applies a sliding window method to compute dynamical indices, enabling the exploration of scale-dependent properties. Applying this framework to high-impact European summertime heatwaves, we reconcile previously different perspectives, thereby underscoring the importance of spatial scales in such analyses. Furthermore, we emphasize that our novel methodology has broad applicability to other atmospheric phenomena, as well as to other geophysical and spatio-temporal systems.

Large language models (LLMs) have exhibited remarkable few-shot learning capabilities and unified the paradigm of NLP tasks through the in-context learning (ICL) technique. Despite the success of ICL, the quality of the exemplar demonstrations can significantly influence the LLM's performance. Existing exemplar selection methods mainly focus on the semantic similarity between queries and candidate exemplars. On the other hand, the logical connections between reasoning steps can be beneficial to depict the problem-solving process as well. In this paper, we proposes a novel method named Reasoning Graph-enhanced Exemplar Retrieval (RGER). RGER first quires LLM to generate an initial response, then expresses intermediate problem-solving steps to a graph structure. After that, it employs graph kernel to select exemplars with semantic and structural similarity. Extensive experiments demonstrate the structural relationship is helpful to the alignment of queries and candidate exemplars. The efficacy of RGER on math and logit reasoning tasks showcases its superiority over state-of-the-art retrieval-based approaches. Our code is released at //github.com/Yukang-Lin/RGER.

Sampling from high dimensional, multimodal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics based machine learning. In this paper, we propose Annealing Flow, a continuous normalizing flow based approach designed to sample from high dimensional and multimodal distributions. The key idea is to learn a continuous normalizing flow based transport map, guided by annealing, to transition samples from an easy to sample distribution to the target distribution, facilitating effective exploration of modes in high dimensional spaces. Unlike many existing methods, AF training does not rely on samples from the target distribution. AF ensures effective and balanced mode exploration, achieves linear complexity in sample size and dimensions, and circumvents inefficient mixing times. We demonstrate the superior performance of AF compared to state of the art methods through extensive experiments on various challenging distributions and real world datasets, particularly in high-dimensional and multimodal settings. We also highlight the potential of AF for sampling the least favorable distributions.

In planning and reinforcement learning, the identification of common subgoal structures across problems is important when goals are to be achieved over long horizons. Recently, it has been shown that such structures can be expressed as feature-based rules, called sketches, over a number of classical planning domains. These sketches split problems into subproblems which then become solvable in low polynomial time by a greedy sequence of IW$(k)$ searches. Methods for learning sketches using feature pools and min-SAT solvers have been developed, yet they face two key limitations: scalability and expressivity. In this work, we address these limitations by formulating the problem of learning sketch decompositions as a deep reinforcement learning (DRL) task, where general policies are sought in a modified planning problem where the successor states of a state s are defined as those reachable from s through an IW$(k)$ search. The sketch decompositions obtained through this method are experimentally evaluated across various domains, and problems are regarded as solved by the decomposition when the goal is reached through a greedy sequence of IW$(k)$ searches. While our DRL approach for learning sketch decompositions does not yield interpretable sketches in the form of rules, we demonstrate that the resulting decompositions can often be understood in a crisp manner.

In multi-agent reinforcement learning, optimal control with robustness guarantees are critical for its deployment in real world. However, existing methods face challenges related to sample complexity, training instability, potential suboptimal Nash Equilibrium convergence and non-robustness to multiple perturbations. In this paper, we propose a unified framework for learning \emph{stochastic} policies to resolve these issues. We embed cooperative MARL problems into probabilistic graphical models, from which we derive the maximum entropy (MaxEnt) objective optimal for MARL. Based on the MaxEnt framework, we propose \emph{Heterogeneous-Agent Soft Actor-Critic} (HASAC) algorithm. Theoretically, we prove the monotonic improvement and convergence to \emph{quantal response equilibrium} (QRE) properties of HASAC. Furthermore, HASAC is provably robust against a wide range of real-world uncertainties, including perturbations in rewards, environment dynamics, states, and actions. Finally, we generalize a unified template for MaxEnt algorithmic design named \emph{Maximum Entropy Heterogeneous-Agent Mirror Learning} (MEHAML), which provides any induced method with the same guarantees as HASAC. We evaluate HASAC on seven benchmarks: Bi-DexHands, Multi-Agent MuJoCo, Pursuit-Evade, StarCraft Multi-Agent Challenge, Google Research Football, Multi-Agent Particle Environment, Light Aircraft Game. Results show that HASAC consistently outperforms strong baselines in 34 out of 38 tasks, exhibiting improved training stability, better sample efficiency and sufficient exploration. The robustness of HASAC was further validated when encountering uncertainties in rewards, dynamics, states, and actions of 14 magnitudes, and real-world deployment in a multi-robot arena against these four types of uncertainties. See our page at \url{//sites.google.com/view/meharl}.

A mainstream type of current self-supervised learning methods pursues a general-purpose representation that can be well transferred to downstream tasks, typically by optimizing on a given pretext task such as instance discrimination. In this work, we argue that existing pretext tasks inevitably introduce biases into the learned representation, which in turn leads to biased transfer performance on various downstream tasks. To cope with this issue, we propose Maximum Entropy Coding (MEC), a more principled objective that explicitly optimizes on the structure of the representation, so that the learned representation is less biased and thus generalizes better to unseen downstream tasks. Inspired by the principle of maximum entropy in information theory, we hypothesize that a generalizable representation should be the one that admits the maximum entropy among all plausible representations. To make the objective end-to-end trainable, we propose to leverage the minimal coding length in lossy data coding as a computationally tractable surrogate for the entropy, and further derive a scalable reformulation of the objective that allows fast computation. Extensive experiments demonstrate that MEC learns a more generalizable representation than previous methods based on specific pretext tasks. It achieves state-of-the-art performance consistently on various downstream tasks, including not only ImageNet linear probe, but also semi-supervised classification, object detection, instance segmentation, and object tracking. Interestingly, we show that existing batch-wise and feature-wise self-supervised objectives could be seen equivalent to low-order approximations of MEC. Code and pre-trained models are available at //github.com/xinliu20/MEC.

Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.

Representation learning on a knowledge graph (KG) is to embed entities and relations of a KG into low-dimensional continuous vector spaces. Early KG embedding methods only pay attention to structured information encoded in triples, which would cause limited performance due to the structure sparseness of KGs. Some recent attempts consider paths information to expand the structure of KGs but lack explainability in the process of obtaining the path representations. In this paper, we propose a novel Rule and Path-based Joint Embedding (RPJE) scheme, which takes full advantage of the explainability and accuracy of logic rules, the generalization of KG embedding as well as the supplementary semantic structure of paths. Specifically, logic rules of different lengths (the number of relations in rule body) in the form of Horn clauses are first mined from the KG and elaborately encoded for representation learning. Then, the rules of length 2 are applied to compose paths accurately while the rules of length 1 are explicitly employed to create semantic associations among relations and constrain relation embeddings. Besides, the confidence level of each rule is also considered in optimization to guarantee the availability of applying the rule to representation learning. Extensive experimental results illustrate that RPJE outperforms other state-of-the-art baselines on KG completion task, which also demonstrate the superiority of utilizing logic rules as well as paths for improving the accuracy and explainability of representation learning.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.