SchoenbAt: Rethinking Attention with Polynomial basis

Kernelized attention extends the attention mechanism by modeling sequence correlations through kernel functions, making significant progresses in optimizing attention. Under the guarantee of harmonic analysis theory, kernel functions can be expanded with basis functions, inspiring random feature-based approaches to enhance the efficiency of kernelized attention while maintaining predictive performance. However, current random feature-based works are limited to the Fourier basis expansions under Bochner's theorem. We propose Schoenberg's theorem-based attention (SchoenbAt), which approximates dot-product kernelized attention with the polynomial basis under Schoenberg's theorem via random Maclaurin features and applies a two-stage regularization to constrain the input space and restore the output scale, acting as a drop-in replacement of dot-product kernelized attention. Our theoretical proof of the unbiasedness and concentration error bound of SchoenbAt supports its efficiency and accuracy as a kernelized attention approximation, which is also empirically validated under various random feature dimensions. Evaluations on real-world datasets demonstrate that SchoenbAt significantly enhances computational speed while preserving competitive performance in terms of precision, outperforming several efficient attention methods.

IRRGN: An Implicit Relational Reasoning Graph Network for Multi-turn Response Selection

The task of response selection in multi-turn dialogue is to find the best option from all candidates. In order to improve the reasoning ability of the model, previous studies pay more attention to using explicit algorithms to model the dependencies between utterances, which are deterministic, limited and inflexible. In addition, few studies consider differences between the options before and after reasoning. In this paper, we propose an Implicit Relational Reasoning Graph Network to address these issues, which consists of the Utterance Relational Reasoner (URR) and the Option Dual Comparator (ODC). URR aims to implicitly extract dependencies between utterances, as well as utterances and options, and make reasoning with relational graph convolutional networks. ODC focuses on perceiving the difference between the options through dual comparison, which can eliminate the interference of the noise options. Experimental results on two multi-turn dialogue reasoning benchmark datasets MuTual and MuTual+ show that our method significantly improves the baseline of four pretrained language models and achieves state-of-the-art performance. The model surpasses human performance for the first time on the MuTual dataset.