The least-squares ReLU neural network method (LSNN) was introduced and studied for solving linear advection-reaction equation with discontinuous solution in \cite{Cai2021linear,cai2023least}. The method is based on an equivalent least-squares formulation and employs ReLU neural network (NN) functions with a $\lceil \log_2(d+1)\rceil+1$ layer representation for approximating the solution. In this paper, we show theoretically that the method is also capable of approximating a non-constant jump along the discontinuous interface of the underlying problem that is not necessarily a straight line. Numerical results for test problems with various non-constant jumps and interfaces show that the LSNN method with $\lceil \log_2(d+1)\rceil+1$ layers approximates the solution accurately with DoFs less than that of mesh-based methods and without the common Gibbs phenomena along the discontinuous interface.
Graph-based kNN algorithms have garnered widespread popularity for machine learning tasks, due to their simplicity and effectiveness. However, the conventional kNN graph's reliance on a fixed value of k can hinder its performance, especially in scenarios involving complex data distributions. Moreover, like other classification models, the presence of ambiguous samples along decision boundaries often presents a challenge, as they are more prone to incorrect classification. To address these issues, we propose the Preferential Attached k-Nearest Neighbors Graph (paNNG), which combines adaptive kNN with distribution-based graph construction. By incorporating distribution information, paNNG can significantly improve performance for ambiguous samples by "pulling" them towards their original classes and hence enable enhanced overall accuracy and generalization capability. Through rigorous evaluations on diverse benchmark datasets, paNNG outperforms state-of-the-art algorithms, showcasing its adaptability and efficacy across various real-world scenarios.
We consider structural equation models (SEMs), in which every variable is a function of a subset of the other variables and a stochastic error. Each such SEM is naturally associated with a directed graph describing the relationships between variables. When the errors are homoscedastic, recent work has proposed methods for inferring the graph from observational data under the assumption that the graph is acyclic (i.e., the SEM is recursive). In this work, we study the setting of homoscedastic errors but allow the graph to be cyclic (i.e., the SEM to be non-recursive). Using an algebraic approach that compares matroids derived from the parameterizations of the models, we derive sufficient conditions for when two simple directed graphs generate different distributions generically. Based on these conditions, we exhibit subclasses of graphs that allow for directed cycles, yet are generically identifiable. We also conjecture a strengthening of our graphical criterion which can be used to distinguish many more non-complete graphs.
In contemporary self-supervised contrastive algorithms like SimCLR, MoCo, etc., the task of balancing attraction between two semantically similar samples and repulsion between two samples from different classes is primarily affected by the presence of hard negative samples. While the InfoNCE loss has been shown to impose penalties based on hardness, the temperature hyper-parameter is the key to regulating the penalties and the trade-off between uniformity and tolerance. In this work, we focus our attention to improve the performance of InfoNCE loss in SSL by studying the effect of temperature hyper-parameter values. We propose a cosine similarity-dependent temperature scaling function to effectively optimize the distribution of the samples in the feature space. We further analyze the uniformity and tolerance metrics to investigate the optimal regions in the cosine similarity space for better optimization. Additionally, we offer a comprehensive examination of the behavior of local and global structures in the feature space throughout the pre-training phase, as the temperature varies. Experimental evidence shows that the proposed framework outperforms or is at par with the contrastive loss-based SSL algorithms. We believe our work (DySTreSS) on temperature scaling in SSL provides a foundation for future research in contrastive learning.
Evolutionary reinforcement learning (ERL) algorithms recently raise attention in tackling complex reinforcement learning (RL) problems due to high parallelism, while they are prone to insufficient exploration or model collapse without carefully tuning hyperparameters (aka meta-parameters). In the paper, we propose a general meta ERL framework via bilevel optimization (BiERL) to jointly update hyperparameters in parallel to training the ERL model within a single agent, which relieves the need for prior domain knowledge or costly optimization procedure before model deployment. We design an elegant meta-level architecture that embeds the inner-level's evolving experience into an informative population representation and introduce a simple and feasible evaluation of the meta-level fitness function to facilitate learning efficiency. We perform extensive experiments in MuJoCo and Box2D tasks to verify that as a general framework, BiERL outperforms various baselines and consistently improves the learning performance for a diversity of ERL algorithms.
With the breakthrough of AlphaGo, deep reinforcement learning becomes a recognized technique for solving sequential decision-making problems. Despite its reputation, data inefficiency caused by its trial and error learning mechanism makes deep reinforcement learning hard to be practical in a wide range of areas. Plenty of methods have been developed for sample efficient deep reinforcement learning, such as environment modeling, experience transfer, and distributed modifications, amongst which, distributed deep reinforcement learning has shown its potential in various applications, such as human-computer gaming, and intelligent transportation. In this paper, we conclude the state of this exciting field, by comparing the classical distributed deep reinforcement learning methods, and studying important components to achieve efficient distributed learning, covering single player single agent distributed deep reinforcement learning to the most complex multiple players multiple agents distributed deep reinforcement learning. Furthermore, we review recently released toolboxes that help to realize distributed deep reinforcement learning without many modifications of their non-distributed versions. By analyzing their strengths and weaknesses, a multi-player multi-agent distributed deep reinforcement learning toolbox is developed and released, which is further validated on Wargame, a complex environment, showing usability of the proposed toolbox for multiple players and multiple agents distributed deep reinforcement learning under complex games. Finally, we try to point out challenges and future trends, hoping this brief review can provide a guide or a spark for researchers who are interested in distributed deep reinforcement learning.
Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This allows one to reason about the effects of changes to this process (i.e., interventions) and what would have happened in hindsight (i.e., counterfactuals). We categorize work in \causalml into five groups according to the problems they tackle: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, (5) causal reinforcement learning. For each category, we systematically compare its methods and point out open problems. Further, we review modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Conventionally, spatiotemporal modeling network and its complexity are the two most concentrated research topics in video action recognition. Existing state-of-the-art methods have achieved excellent accuracy regardless of the complexity meanwhile efficient spatiotemporal modeling solutions are slightly inferior in performance. In this paper, we attempt to acquire both efficiency and effectiveness simultaneously. First of all, besides traditionally treating H x W x T video frames as space-time signal (viewing from the Height-Width spatial plane), we propose to also model video from the other two Height-Time and Width-Time planes, to capture the dynamics of video thoroughly. Secondly, our model is designed based on 2D CNN backbones and model complexity is well kept in mind by design. Specifically, we introduce a novel multi-view fusion (MVF) module to exploit video dynamics using separable convolution for efficiency. It is a plug-and-play module and can be inserted into off-the-shelf 2D CNNs to form a simple yet effective model called MVFNet. Moreover, MVFNet can be thought of as a generalized video modeling framework and it can specialize to be existing methods such as C2D, SlowOnly, and TSM under different settings. Extensive experiments are conducted on popular benchmarks (i.e., Something-Something V1 & V2, Kinetics, UCF-101, and HMDB-51) to show its superiority. The proposed MVFNet can achieve state-of-the-art performance with 2D CNN's complexity.
Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.
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.