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Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order.

CFQ is the only realistic benchmark that comprehensively measure compositional generalization.

Language models pretrained on large collections of tabular data have demonstrated their effectiveness in several downstream tasks.However, many of these models do not take into account the row/column permutation invariances, hierarchical structure, etc. that exist in tabular data. To alleviate these limitations, we propose HyTrel, a tabular language model, that captures the permutation invariances and three more structural properties of tabular data by using hypergraphs--where the table cells make up the nodes and the cells occurring jointly together in each row, column, and the entire table are used to form three different types of hyperedges. We show thatHyTrel is maximally invariant under certain conditions for tabular data, i.e., two tables obtain the same representations via HyTreliff the two tables are identical up to permutation. Our empirical results demonstrate that HyTrel consistently outperforms other competitive baselines on four downstream tasks with minimal pretraining, illustrating the advantages of incorporating inductive biases associated with tabular data into the representations. Finally, our qualitative analyses showcase that HyTrel can assimilate the table structure to generate robust representations for the cells, rows, columns, and the entire table.

Learning set functions becomes increasingly important in many applications like product recommendation and compound selection in AI-aided drug discovery. The majority of existing works study methodologies of set function learning under the function value oracle, which, however, requires expensive supervision signals. This renders it impractical for applications with only weak supervisions under the Optimal Subset (OS) oracle, the study of which is surprisingly overlooked. In this work, we present a principled yet practical maximum likelihood learning framework, termed as EquiVSet, that simultaneously meets the following desiderata of learning neural set functions under the OS oracle: i) permutation invariance of the set mass function being modeled; ii) permission of varying ground set; iii) minimum prior and iv) scalability. The main components of our framework involve: an energy-based treatment of the set mass function, DeepSet-style architectures to handle permutation invariance, mean-field variational inference, and its amortized variants. Thanks to the delicate combination of these advanced architectures, empirical studies on three real-world applications (including Amazon product recommendation, set anomaly detection, and compound selection for virtual screening) demonstrate that EquiVSet outperforms the baselines by a large margin.

In many machine learning problems the output should not depend on the order of the inputs. Such ``permutation invariant'' functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recursive architectures. Existing solutions (e.g., DeepSets) mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to learning functions which are semi permutation invariant, e.g.

We investigate machine learning approaches to approximating the \emph{domination number} of graphs, the minimum size of a dominating set. Exact computation of this parameter is NP-hard, restricting classical methods to small instances. We compare two neural paradigms: Convolutional Neural Networks (CNNs), which operate on adjacency matrix representations, and Graph Neural Networks (GNNs), which learn directly from graph structure through message passing. Across 2,000 random graphs with up to 64 vertices, GNNs achieve markedly higher accuracy ($R^2=0.987$, MAE $=0.372$) than CNNs ($R^2=0.955$, MAE $=0.500$). Both models offer substantial speedups over exact solvers, with GNNs delivering more than $200\times$ acceleration while retaining near-perfect fidelity. Our results position GNNs as a practical surrogate for combinatorial graph invariants, with implications for scalable graph optimization and mathematical discovery.