With the advancement of artificial intelligence (AI) and increasing integrated circuit (IC) design complexity, efficient chip design through electronic design automation (EDA) has become critical. Fast and accurate congestion prediction in chip layout and routing can significantly enhance automated design performance. Existing congestion modeling methods are limited by (i) ineffective processing and fusion of multi-view circuit data information, and (ii) insufficient reliability and interpretability in the prediction process. To address these challenges, we propose the Multi-view Interpretable Hypergraph for Chip (MIHC), a trustworthy multi-view hypergraph neural network framework that (i) processes both graph and image information in unified hypergraph representations, capturing topological and geometric circuit data; (ii) implements a novel subgraph Information Bottleneck mechanism, identifying critical congestion-correlated regions to guide predictions. This work is the first attempt to incorporate such interpretability into congestion prediction through informative graph reasoning. Experiments show that the MIHC method reduces NMAE by 16.67% and 8.57% in cell-based and grid-based predictions on ISPD2015, and 5.26% and 2.44% on CircuitNet-N28, respectively, compared to state-of-the-art methods. Rigorous cross-design generalization experiments further validate our method's capability to handle entirely unseen circuit designs.

Clustering is a fundamental task in both machine learning and data mining. Among various methods, edge-colored clustering (ECC) has emerged as a useful approach for handling categorical data. Given a hypergraph with (hyper)edges labeled by colors, ECC aims to assign vertex colors to minimize the number of edges where the vertex color differs from the edge's color. However, traditional ECC has inherent limitations, as it enforces a nonoverlapping and exhaustive clustering. To tackle these limitations, three versions of ECC have been studied: LOCALECC and GLOBALECC, which allow overlapping clusters, and ROBUSTECC, which accounts for vertex outliers.

Heterogeneous hypergraph is a kind of structural data that contains multiple types of nodes and multiple types of hyperedges. Each hyperedge type corresponds to a specific multi-ary relation (called hyper-relation) among subsets of nodes, which goes beyond traditional pair-wise relations in simple graphs. Existing representation learning methods for heterogeneous hypergraphs typically learn embeddings for nodes and hyperedges based on graph neural networks. Although achieving promising performance, they are still limited in capturing more complex structural features and richer semantics conveyed by the composition of various hyper-relations. To fill this research gap, in this work, we propose the concept of hyper-meta-path for heterogeneous hypergraphs, which is defined as the composition of a sequence of hyper-relations. Besides, we design an attention-based heterogeneous hypergraph neural network (HHNN) to automatically learn the importance of hyper-meta-paths. By exploiting useful ones, HHNN is able to capture more complex structural features to boost the model's performance, as well as leverage their conveyed semantics to improve the model's interpretability. Extensive experiments show that HHNN can achieve significantly better performance than state-of-the-art baselines, and the discovered hyper-meta-paths bring good interpretability for the model predictions.

Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent extensions of graph neural network (GNN) architectures to hypergraphs. Most of these architectures rely on message-passing to encode higher-order information. In this paper, we propose to instead use hypergraph-level encodings based on characteristics such as hypergraph Laplacians and discrete curvature notions. These encodings can be used on datasets that are naturally parametrized as hypergraphs and on graph-level datasets, which we reparametrize as hypergraphs to compute encodings.

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension.

Heterogeneous hypergraph is a kind of structural data that contains multiple types of nodes and multiple types of hyperedges. Each hyperedge type corresponds to a specific multi-ary relation (called hyper-relation) among subsets of nodes, which goes beyond traditional pair-wise relations in simple graphs. Existing representation learning methods for heterogeneous hypergraphs typically learn embeddings for nodes and hyperedges based on graph neural networks. Although achieving promising performance, they are still limited in capturing more complex structural features and richer semantics conveyed by the composition of various hyper-relations. To fill this research gap, in this work, we propose the concept of hyper-meta-path for heterogeneous hypergraphs, which is defined as the composition of a sequence of hyper-relations. Besides, we design an attention-based heterogeneous hypergraph neural network (HHNN) to automatically learn the importance of hyper-meta-paths. By exploiting useful ones, HHNN is able to capture more complex structural features to boost the model's performance, as well as leverage their conveyed semantics to improve the model's interpretability. Extensive experiments show that HHNN can achieve significantly better performance than state-of-the-art baselines, and the discovered hyper-meta-paths bring good interpretability for the model predictions.

Hypergraphs provide a principled framework for modeling polyadic interactions, with applications in recommendation systems, social networks, and molecular modeling. Hypergraph generation remains challenging because incidence structures are discrete, sparse, and governed by heterogeneous higher-order interactions. Existing generators often rely on implicit latent spaces or continuous incidence decoders, which provide limited mechanistic interpretation of how node-hyperedge incidences arise. To address these limitations, we propose HYVINT, an intensity-driven hypergraph generative framework. Our key innovations are twofold: (i) we develop an intensity-driven incidence formation mechanism for hypergraphs that links latent interaction strength to binary incidence, and (ii) we derive a tractable lower-bound variational estimator for learning latent representations. We provide generation error bounds with asymptotic convergence rates and empirically show that HYVINT achieves strong fidelity while maintaining substantial novelty and diversity on synthetic and real-world hypergraphs.

Pairwise Fisher graphs capture local covariance information, but they cannot distinguish an irreducible multi-observable radiation pattern from a collection of ordinary pairwise correlations. We show that this missing structure is naturally supplied by higher-order Fisher tensors. In a finite basis of binned EECs, ECFs, or EFPs, and in the natural exponential-family coordinates generated by that basis, the same local tensor has three equivalent interpretations: a coefficient in the local Kullback-Leibler expansion, a connected cumulant of the chosen correlator observables, and a signed weight on a hyperedge linking those observables. This gives an exact Fisher-correlator-hypergraph triality in the local exponential-family embedding. The triality provides a direct construction of physics-informed hypergraphs from correlator data. Extending the quadratic Fisher matrix to the first non-trivial higher tensor identifies genuinely connected multi-observable radiation patterns, supplies hyperedge weights for higher-order Laplacians and message passing, and gives a principled criterion for compressing observable bases beyond pairwise information. We develop these constructions and spell out why the exact cumulant interpretation is special to natural exponential-family coordinates. We illustrate the framework in four applications. In a minimal local-KL study, the cubic Fisher tensor reduces the KL truncation error and isolates the dominant triplet structure. In a two-versus-three prong jet substructure benchmark, the hypergraph selector improves compressed-basis classification. In a 33-observable basis-design problem, the Fisher hypergraph retains more third-order local response at twelve observables. A low-capacity learning benchmark then shows how the same Fisher hyperedges can be used as an interpretable inductive bias for message passing on correlator observables.

Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose \HEDGE, a generative model defined directly on relaxed incidence matrices via a structured stochastic diffusion. The forward process combines a hypergraph-specific two-sided heat operator with an Ornstein--Uhlenbeck component, preserving structure-aware noising near the data while yielding an explicit Gaussian terminal law. Conditional on an observed hypergraph, this forward process is linear-Gaussian, so conditional means, covariances, scores, and reverse-drift targets are available in closed form. We therefore learn a permutation-equivariant state-only reverse-drift field in incidence space by regressing onto exact conditional targets, and generate samples by simulating a learned reverse-time SDE from the Gaussian base law. We establish exactness in the ideal state-only setting together with finite-horizon stability guarantees, and empirically show improved hypergraph generation quality relative to strong baselines.