Bucher Sahyouni

Preprint - 2026

DSL - Dual-scale Softmax Loss

A competition-conditioned softmax objective for implicit-feedback recommendation.

Recommender systemsImplicit feedbackLearning objectivesDistribution shift
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Overview

Dual-scale Softmax Loss (DSL) rethinks sampled softmax from a competition-first perspective. It conditions the training objective on the competition induced by the sampled negative set, allowing the loss to adapt locally between negatives and globally between training examples.

Problem

In implicit-feedback recommendation, missing interactions are not reliable negatives. Sampled negative sets can therefore contain very different levels of competition: some are weak, while others include relevant or informative alternatives. A single global temperature and uniform negative weighting can be poorly matched to these differences and make optimisation brittle.

Method

DSL operates at two scales. Within each instance, it reweights negatives using hardness and item-item similarity, concentrating learning on relevant competitors. Across instances, it constructs a competitor slate and adjusts the effective temperature according to its competition intensity. The method retains the log-sum-exp structure and scalability of sampled softmax while adapting its gradient allocation to each training example.

Key contributions

  • Per-negative reweighting based on hardness and relevance proxies, normalised within each example.
  • Per-example temperature adaptation using pseudo-slates of top sampled competitors.
  • Evaluation across multiple recommender backbones and real-world datasets.
  • Ablations, hyperparameter sensitivity analysis, and evaluation under out-of-distribution popularity shift.

Results / findings

Across the evaluated datasets, metrics, and backbones, DSL improved over standard softmax loss by an average of 6.22%, with gains above 10% in several settings. Under out-of-distribution popularity shift, the average improvement over softmax increased to 9.31%. The analysis attributes most of the gain to better recommendation of rare, less-popular items and reports smaller improvements for dominant head items. A distributionally robust optimisation analysis provides theoretical support for the observed accuracy and robustness changes.

Citation

Bucher Sahyouni, Matthew Vowels, Liqun Chen, and Simon Hadfield. “DSL: Understanding and Improving Softmax Recommender Systems with Competition-Aware Scaling.” arXiv:2602.07206, 2026.