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

arXiv: https://arxiv.org/abs/2602.07206 · HTML: https://mlsanity.com/paper/2602.07206/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 13 of 13)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [DORO: Distributional and Outlier Robust Optimization](https://mlsanity.com/paper/2106.06142/) (2021)
- [Empowering Collaborative Filtering with Principled Adversarial Contrastive Loss](https://mlsanity.com/paper/2310.18700/) (2023)
- [Lower-Left Partial AUC: An Effective and Efficient Optimization Metric for Recommendation](https://mlsanity.com/paper/2403.00844/) (2024)
- [PSL: Rethinking and Improving Softmax Loss from Pairwise Perspective for Recommendation](https://mlsanity.com/paper/2411.00163/) (2024)
- [Breaking the Top-K Barrier: Advancing Top-K Ranking Metrics Optimization in Recommender Systems](https://mlsanity.com/paper/2508.05673/) (2025)
- [Towards Resolving Propensity Contradiction in Offline Recommender Learning](https://mlsanity.com/paper/1910.07295/) (2019)
- [Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications](https://mlsanity.com/paper/2311.05054/) (2023)

## Abstract (arXiv)

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.