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Cross-Encoder (CE) and Dual-Encoder (DE) models are two fundamental approaches for query-document relevance in information retrieval. To predict relevance, CE models use joint query-document embeddings, while DE models maintain factorized query and document embeddings; usually, the former has higher quality while the latter benefits from lower latency. Recently, late-interaction models have been proposed to realize more favorable latency-quality tradeoffs, by using a DE structure followed by a lightweight scorer based on query and document token embeddings. However, these lightweight scorers are often hand-crafted, and there is no understanding of their approximation power; further, such scorers require access to individual document token embeddings, which imposes an increased latency and storage burden. In this paper, we propose novel learnable late-interaction models (LITE) that resolve these issues. Theoretically, we prove that LITE is a universal approximator of continuous scoring functions, even for relatively small embedding dimension. Empirically, LITE outperforms previous late-interaction models such as ColBERT on both in-domain and zero-shot re-ranking tasks. For instance, experiments on MS MARCO passage re-ranking show that LITE not only yields a model with better generalization, but also lowers latency and requires 0.25x storage compared to ColBERT.

Variational Physics-Informed Neural Networks (VPINNs) utilize a variational loss function to solve partial differential equations, mirroring Finite Element Analysis techniques. Traditional hp-VPINNs, while effective for high-frequency problems, are computationally intensive and scale poorly with increasing element counts, limiting their use in complex geometries. This work introduces FastVPINNs, a tensor-based advancement that significantly reduces computational overhead and improves scalability. Using optimized tensor operations, FastVPINNs achieve a 100-fold reduction in the median training time per epoch compared to traditional hp-VPINNs. With proper choice of hyperparameters, FastVPINNs surpass conventional PINNs in both speed and accuracy, especially in problems with high-frequency solutions. Demonstrated effectiveness in solving inverse problems on complex domains underscores FastVPINNs' potential for widespread application in scientific and engineering challenges, opening new avenues for practical implementations in scientific machine learning., Comment: 31 pages, 19 figures, 4 algorithms