This paper introduces Honor of Kings Arena, a reinforcement learning (RL) environment based on Honor of Kings, one of the world's most popular games at present. Compared to other environments studied in most previous work, ours presents new generalization challenges for competitive reinforcement learning. It is a multiagent problem with one agent competing against its opponent; and it requires the generalization ability as it has diverse targets to control and diverse opponents to compete with. We describe the observation, action, and reward specifications for the Honor of Kings domain and provide an open-source Python-based interface for communicating with the game engine. We provide twenty target heroes with a variety of tasks in Honor of Kings Arena and present initial baseline results for RL-based methods with feasible computing resources. Finally, we showcase the generalization challenges imposed by Honor of Kings Arena and possible remedies to the challenges.

Domain Generalization (DG) aims to enable models to generalize to unseen target domains by learning from multiple source domains. Existing DG methods primarily rely on convolutional neural networks (CNNs), which inherently learn texture biases due to their limited receptive fields, making them prone to overfitting source domains. While some works have introduced transformer-based methods (ViTs) for DG to leverage the global receptive field, these methods incur high computational costs due to the quadratic complexity of self-attention. Recently, advanced state space models (SSMs), represented by Mamba, have shown promising results in supervised learning tasks by achieving linear complexity in sequence length during training and fast RNN-like computation during inference. Inspired by this, we investigate the generalization ability of the Mamba model under domain shifts and find that input-dependent matrices within SSMs could accumulate and amplify domain-specific features, thus hindering model generalization. To address this issue, we propose a novel SSM-based architecture with saliency-based token-aware transformation (namely START), which achieves state-of-the-art (SOTA) performances and offers a competitive alternative to CNNs and ViTs. Our START can selectively perturb and suppress domain-specific features in salient tokens within the input-dependent matrices of SSMs, thus effectively reducing the discrepancy between different domains. Extensive experiments on five benchmarks demonstrate that START outperforms existing SOTA DG methods with efficient linear complexity.

This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context, we show that the corresponding optimization problem can be reformulated as a non-negative penalized linear regression problem. This reformulation allows us to propose novel algorithms inspired from inverse problems and nonnegative matrix factorization. In particular, we consider majorization-minimization which leads in our setting to efficient multiplicative updates for a variety of penalties. Furthermore, we derive for the first time an efficient algorithm to compute the regularization path of UOT with quadratic penalties. The proposed algorithm provides a continuity of piece-wise linear OT plans converging to the solution of balanced OT (corresponding to infinite penalty weights). We perform several numerical experiments on simulated and real data illustrating the new algorithms, and provide a detailed discussion about more sophisticated optimization tools that can further be used to solve OT problems thanks to our reformulation.

Paul Pierce explains how LeBron's absence has actually been good for the Lakers. Los Angeles Lakers shooting guard Bronny James has been the center of debate from the moment he was drafted in June. The 20-year-old said he tries to filter it all out, but he sees it all. "My first thought about everything is I always try to just let it go through one ear and out the other, put my head down and come to work and be positive every day. I see everything that people are saying, and people think, like, I'm a f---ing robot, like I don't have any feelings or emotions," James said via The Athletic.

PCA: We show that under strict conditions, the PCA vectors applied on an intermediate layer where the principle components are used as concept vectors, maximizes the completeness score. We note that the assumptions for this proposition are extremely stringent, and may not hold in general. When the isometry and other assumptions do not hold, PCA no longer maximizes the completeness score as the lowest reconstruction in the intermediate layer do not imply the highest prediction accuracy in the output. In fact, DNNs are shown to be very sensitive to small perturbations in the input [Narodytska and Kasiviswanathan, 2017] - they can yield very different outputs although the difference in the input is small (and often perceptually hard to recognize to humans). Thus, even though the reconstruction loss between two inputs are low at an intermediate layer, subsequent deep nonlinear processing may cause them to diverge significantly.

Human explanations of high-level decisions are often expressed in terms of key concepts the decisions are based on. In this paper, we study such concept-based explainability for Deep Neural Networks (DNNs). First, we define the notion of completeness, which quantifies how sufficient a particular set of concepts is in explaining a model's prediction behavior based on the assumption that complete concept scores are sufficient statistics of the model prediction. Next, we propose a concept discovery method that aims to infer a complete set of concepts that are additionally encouraged to be interpretable, which addresses the limitations of existing methods on concept explanations. To define an importance score for each discovered concept, we adapt game-theoretic notions to aggregate over sets and propose ConceptSHAP. Via proposed metrics and user studies, on a synthetic dataset with apriori-known concept explanations, as well as on real-world image and language datasets, we validate the effectiveness of our method in finding concepts that are both complete in explaining the decisions and interpretable.

We thank all reviewers for their constructive comments. We fixed the architecture g in our previous experiments to a two layer neural network. We discussed how to select the layer choice and its impact above. The computational cost is low since the pretrained model is fixed, and we only optimize for g and c. We didn't test on Imagenet since we can't visualize results for all 1000 classes.