DSL: Understanding and Improving Softmax Recommender Systems with Competition-Aware Scaling

TL;DR

This paper introduces Dual-scale Softmax Loss (DSL), a novel loss function for recommender systems that adapts competition sharpness based on sampled negatives, leading to significant improvements in accuracy, robustness, and fairness.

Contribution

DSL is a new loss function that infers effective sharpness from competition, reshaping negative sampling and temperature to enhance recommender system training.

Findings

DSL improves accuracy by over 10% in several benchmarks.

DSL enhances robustness under popularity shifts, averaging 9.31% gains.

Theoretical analysis shows DSL reshapes robust payoff and KL deviation.

Abstract

Softmax Loss (SL) is being increasingly adopted for recommender systems (RS) as it has demonstrated better performance, robustness and fairness. Yet in implicit-feedback, a single global temperature and equal treatment of uniformly sampled negatives can lead to brittle training, because sampled sets may contain varying degrees of relevant or informative competitors. The optimal loss sharpness for a user-item pair with a particular set of negatives, can be suboptimal or destabilising for another with different negatives. We introduce Dual-scale Softmax Loss (DSL), which infers effective sharpness from the sampled competition itself. DSL adds two complementary branches to the log-sum-exp backbone. Firstly it reweights negatives within each training instance using hardness and item--item similarity, secondly it adapts a per-example temperature from the competition intensity over a constructed competitor slate. Together, these components preserve the geometry of SL while reshaping the competition distribution across negatives and across examples. Over several representative benchmarks and backbones, DSL yields substantial gains over strong baselines, with improvements over SL exceeding $10%$ in several settings and averaging $6.22%$ across datasets, metrics, and backbones. Under out-of-distribution (OOD) popularity shift, the gains are larger, with an average of $9.31%$ improvement over SL. We further provide a theoretical, distributionally robust optimisation (DRO) analysis, which demonstrates how DSL reshapes the robust payoff and the KL deviation for ambiguous instances. This helps explain the empirically observed improvements in accuracy and robustness.