Set Representation Auxiliary Learning with Adversarial Encoding Perturbation and Optimization

Sets are a fundamental data structure, and learning their vectorized representations is crucial for many computational problems. Existing methods typically focus on intra-set properties such as permutation invariance and cardinality independence. While effective at preserving basic intra-set semantics, these approaches may be insufficient in explicitly modeling inter-set correlations, which are critical for tasks requiring fine-grained comparisons between sets. In this work, we propose SRAL, a Set Representation Auxiliary Learning framework for capturing inter-set correlations that is compatible with various downstream tasks. SRAL conceptualizes sets as high-dimensional distributions and leverages the 2-Sliced-Wasserstein distance to derive their distributional discrepancies into set representation encoding. More importantly, we introduce a novel adversarial auxiliary learning scheme. Instead of manipulating the input data, our method perturbs the set encoding process itself and compels the model to be robust against worst-case perturbations through a min-max optimization. Our theoretical analysis shows that this objective, in expectation, directly optimizes for the set-wise Wasserstein distances, forcing the model to learn highly discriminative representations. Comprehensive evaluations across four downstream tasks examine SRAL’s performance relative to baseline methods, showing consistent effectiveness in both inter-set relation-sensitive retrieval and intra-set information-oriented processing tasks.