This paper targets at improving the generalizability of hypergraph neural networks in the low-label regime, through applying the contrastive learning approach from images/graphs (we refer to it as HyperGCL). We focus on the following question: How to construct contrastive views for hypergraphs via augmentations? We provide the solutions in two folds. First, guided by domain knowledge, we fabricate two schemes to augment hyperedges with higher-order relations encoded, and adopt three vertex augmentation strategies from graph-structured data. Second, in search of more effective views in a data-driven manner, we for the first time propose a hypergraph generative model to generate augmented views, and then an end-to-end differentiable pipeline to jointly learn hypergraph augmentations and model parameters. Our technical innovations are reflected in designing both fabricated and generative augmentations of hypergraphs. The experimental findings include: (i) Among fabricated augmentations in HyperGCL, augmenting hyperedges provides the most numerical gains, implying that higher-order information in structures is usually more downstream-relevant; (ii) Generative augmentations do better in preserving higher-order information to further benefit generalizability; (iii) HyperGCL also boosts robustness and fairness in hypergraph representation learning.

Multi-channel learning has gained significant attention in recent applications, where neural networks with t-product layers (t-NNs) have shown promising performance through novel feature mapping in the transformed domain. However, despite the practical success of t-NNs, the theoretical analysis of their generalization remains unexplored. We address this gap by deriving upper bounds on the generalization error of t-NNs in both standard and adversarial settings. Notably, it reveals that t-NNs compressed with exact transformed low-rank parameterization can achieve tighter adversarial generalization bounds compared to non-compressed models. While exact transformed low-rank weights are rare in practice, the analysis demonstrates that through adversarial training with gradient flow, highly over-parameterized t-NNs with the ReLU activation can be implicitly regularized towards a transformed low-rank parameterization under certain conditions. Moreover, this paper establishes sharp adversarial generalization bounds for t-NNs with approximately transformed low-rank weights. Our analysis highlights the potential of transformed low-rank parameterization in enhancing the robust generalization of t-NNs, offering valuable insights for further research and development.

A.1 Proof of Theorem 1 To prove Theorem 1, we need the help of the following Lemma See Proposition 7.1 in [3]. Now we can prove our Theorem 1. Proof. For games with only one step (normal-form games, functional-form games), there is only one fixed state. Therefore, the distribution of state-action is equivalent to the distribution of the action. A.2 Proof of Theorem 2 Let us restate our Theorem 2 Theorem 2. For a given empirical payoff matrix A RM N and the reward vector aM+1 for policy M + ||(I A>(A>))aM+1||2, (18) where (A>) is the Moore-Penrose pseudoinverse of A>, and σmin(A) is the minimum singular value of A. Proof. The last equation comes from the analytic calculation of min1>β=1 ||β (A>) aM+1||2 using Lagrangian.

Measuring and promoting policy diversity is critical for solving games with strong non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). With that in mind, maintaining a pool of diverse policies via open-ended learning is an attractive solution, which can generate auto-curricula to avoid being exploited. However, in conventional open-ended learning algorithms, there are no widely accepted definitions for diversity, making it hard to construct and evaluate the diverse policies. In this work, we summarize previous concepts of diversity and work towards offering a unified measure of diversity in multi-agent open-ended learning to include all elements in Markov games, based on both Behavioral Diversity (BD) and Response Diversity (RD).

We introduce the problem of Bayesian optimization with cost-varying variable subsets (BOCVS) where in each iteration, the learner chooses a subset of query variables and specifies their values while the rest are randomly sampled. Each chosen subset has an associated cost. This presents the learner with the novel challenge of balancing between choosing more informative subsets for more directed learning versus leaving some variables to be randomly sampled to reduce incurred costs. This paper presents a novel Gaussian process upper confidence bound-based algorithm for solving the BOCVS problem that is provably no-regret. We analyze how the availability of cheaper control sets helps in exploration and reduces overall regret. We empirically show that our proposed algorithm can find significantly better solutions than comparable baselines with the same budget.

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