arXiv Machine Learning
Sep 21

Diagonalized Attention for Individualized Regression: Latent-Row Localization and Prediction

The paper introduces an individualized sparse regression framework for matrix‑valued covariates, where each observation has its own relevant rows while regression effects are shared across the population. It proposes a diagonalized attention mechanism that uses query–key scores to localize sample‑specific signal rows and a value matrix for downstream regression, achieving a parameter dimension independent of sample size. The authors provide existence theorems guaranteeing recovery of latent rows under score‑separation and concentration conditions, and demonstrate strong prediction, localization, and classification performance in simulations and real sentiment analysis.

By Borui Peng, Liwei Lin, Feifei Wang, Long Feng
arXiv Machine Learning
Sep 25

Beyond Pairwise Attention: Higher-Order Modular Attention for Efficient Sequence Learning

The paper introduces Higher-Order Modular Attention (HOMA), a new attention mechanism that combines standard pairwise self‑attention with an explicit triadic attention pathway. HOMA uses overlapping blocks, local windows, and a low‑rank projection to make triadic interactions tractable. Experiments on controlled PARITY and MATCH3 tasks, as well as TAPE benchmarks, show that HOMA matches or outperforms matched pairwise and purely triadic baselines, especially when dependencies extend beyond triadic order, and it often converges faster and uses parameters more efficiently.

By Shirin Amiraslani, Xin Gao