A Coulomb Particle Model for Learning Kernel Attention in Transformers

Randomized features provide a scalable approximation to kernel machines, but their performance depends strongly on the choice of feature distribution. We propose a particle-based method that learns this distribution by optimizing kernel-target alignment while regularizing particles with a Riesz/Coulomb repulsive potential. The resulting Hamiltonian yields diverse, task-adaptive random features and admits a mean-field description through a McKean--Vlasov equation. We instantiate the method in linearized Transformer attention by learning positive random-feature maps in a first alignment phase, then freezing the kernel and training the remaining network parameters with cross-entropy. Experiments on synthetic classification and sentence-level benchmarks show that learned kernelized attention can improve accuracy, calibration, and robustness for several feature maps while preserving linear-attention inference complexity.

Progressive Refinement of E-commerce Search Ranking Based on Short-Term Activities of the Buyer

In e-commerce shopping, aligning search results with a buyer's immediate needs and preferences presents a significant challenge, particularly in adapting search results throughout the buyer's shopping journey as they move from the initial stages of browsing to making a purchase decision or shift from one intent to another. This study presents a systematic approach to adapting e-commerce search results based on the current context. We start with basic methods and incrementally incorporate more contextual information and state-of-the-art techniques to improve the search outcomes. By applying this evolving contextual framework to items displayed on the search engine results page (SERP), we progressively align search outcomes more closely with the buyer's interests and current search intentions. Our findings demonstrate that this incremental enhancement, from simple heuristic autoregressive features to advanced sequence models, significantly improves ranker performance. The integration of contextual techniques enhances the performance of our production ranker, leading to improved search results in both offline and online A/B testing in terms of Mean Reciprocal Rank (MRR). Overall, the paper details iterative methodologies and their substantial contributions to search result contextualization on e-commerce platforms.