# On the Effectiveness of Sampled Softmax Loss for Item Recommendation

arXiv: https://arxiv.org/abs/2201.02327 · HTML: https://mlsanity.com/paper/2201.02327/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2022.

## Built on by (most cited first, 30 of 39)

- [Generate What You Prefer: Reshaping Sequential Recommendation via Guided Diffusion](https://mlsanity.com/paper/2310.20453/) (2023)
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- [Adap-τ: Adaptively Modulating Embedding Magnitude for Recommendation](https://mlsanity.com/paper/2302.04775/) (2023)
- [Language Representations Can be What Recommenders Need: Findings and Potentials](https://mlsanity.com/paper/2407.05441/) (2024)
- [Neighborhood-Enhanced Supervised Contrastive Learning for Collaborative Filtering](https://mlsanity.com/paper/2402.11523/) (2024)
- [Que2Engage: Embedding-based Retrieval for Relevant and Engaging Products at Facebook Marketplace](https://mlsanity.com/paper/2302.11052/) (2023)
- [Scaling Session-Based Transformer Recommendations using Optimized Negative Sampling and Loss Functions](https://mlsanity.com/paper/2307.14906/) (2023)
- [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)
- [Toward a Better Understanding of Loss Functions for Collaborative Filtering](https://mlsanity.com/paper/2308.06091/) (2023)
- [Continuous-Time User Preference Modelling for Temporal Sets Prediction](https://mlsanity.com/paper/2204.05490/) (2022)
- [Scaling Sequential Recommendation Models with Transformers](https://mlsanity.com/paper/2412.07585/) (2024)
- [BSL: Understanding and Improving Softmax Loss for Recommendation](https://mlsanity.com/paper/2312.12882/) (2023)
- [Test Time Embedding Normalization for Popularity Bias Mitigation](https://mlsanity.com/paper/2308.11288/) (2023)
- [Pareto Front Approximation for Multi-Objective Session-Based Recommender Systems](https://mlsanity.com/paper/2407.16828/) (2024)
- [eSASRec: Enhancing Transformer-based Recommendations in a Modular Fashion](https://mlsanity.com/paper/2508.06450/) (2025)
- [Invariant Graph Learning Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2408.01697/) (2024)
- [Learning Cascade Ranking as One Network](https://mlsanity.com/paper/2503.09492/) (2025)
- [On the Role of Weight Decay in Collaborative Filtering: A Popularity Perspective](https://mlsanity.com/paper/2505.11318/) (2025)
- [Advancing Loss Functions in Recommender Systems: A Comparative Study with a R'enyi Divergence-Based Solution](https://mlsanity.com/paper/2506.15120/) (2025)
- [Understanding and Scaling Collaborative Filtering Optimization from the Perspective of Matrix Rank](https://mlsanity.com/paper/2410.23300/) (2024)
- [Rejuvenating Cross-Entropy Loss in Knowledge Distillation for Recommender Systems](https://mlsanity.com/paper/2509.20989/) (2025)
- [Autoregressive Ranking: Bridging the Gap Between Dual and Cross Encoders](https://mlsanity.com/paper/2601.05588/) (2026)
- [BEAR: Towards Beam-Search-Aware Optimization for Recommendation with Large Language Models](https://mlsanity.com/paper/2601.22925/) (2026)
- [UIPC-MF: User-Item Prototype Connection Matrix Factorization for Explainable Collaborative Filtering](https://mlsanity.com/paper/2308.07048/) (2023)
- [Multi-Margin Cosine Loss: Proposal and Application in Recommender Systems](https://mlsanity.com/paper/2405.04614/) (2024)
- [Negative Feedback for Music Personalization](https://mlsanity.com/paper/2406.04488/) (2024)

## Abstract (arXiv)

The learning objective plays a fundamental role to build a recommender system. Most methods routinely adopt either pointwise or pairwise loss to train the model parameters, while rarely pay attention to softmax loss due to its computational complexity when scaling up to large datasets or intractability for streaming data. The sampled softmax (SSM) loss emerges as an efficient substitute for softmax loss. Its special case, InfoNCE loss, has been widely used in self-supervised learning and exhibited remarkable performance for contrastive learning. Nonetheless, limited recommendation work uses the SSM loss as the learning objective. Worse still, none of them explores its properties thoroughly and answers ``Does SSM loss suit for item recommendation?'' and ``What are the conceptual advantages of SSM loss, as compared with the prevalent losses?'', to the best of our knowledge. In this work, we aim to offer a better understanding of SSM for item recommendation. Specifically, we first theoretically reveal three model-agnostic advantages: (1) mitigating popularity bias; (2) mining hard negative samples; and (3) maximizing the ranking metric. However, based on our empirical studies, we recognize that the default choice of cosine similarity function in SSM limits its ability in learning the magnitudes of representation vectors. As such, the combinations of SSM with the models that also fall short in adjusting magnitudes may result in poor representations. One step further, we provide mathematical proof that message passing schemes in graph convolution networks can adjust representation magnitude according to node degree, which naturally compensates for the shortcoming of SSM. Extensive experiments on four benchmark datasets justify our analyses, demonstrating the superiority of SSM for item recommendation. Our implementations are available in both TensorFlow and PyTorch.