# Beyond Spectral Decomposition: Bayesian Contrastive Learning and its Non-negative Formulation via Factor Analysis

arXiv: https://arxiv.org/abs/2407.21740 · HTML: https://mlsanity.com/paper/2407.21740/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 46 references that are in the map.
- First posted on arXiv 31 Jul 2024.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Unsupervised Embedding Learning via Invariant and Spreading Instance Feature](https://mlsanity.com/paper/1904.03436/) (2019)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Probabilistic Embeddings for Cross-Modal Retrieval](https://mlsanity.com/paper/2101.05068/) (2021)
- [Evaluating Bayesian Deep Learning Methods for Semantic Segmentation](https://mlsanity.com/paper/1811.12709/) (2018)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [Theory and Evaluation Metrics for Learning Disentangled Representations](https://mlsanity.com/paper/1908.09961/) (2019)
- [Contrastive estimation reveals topic posterior information to linear models](https://mlsanity.com/paper/2003.02234/) (2020)
- [Modeling Uncertainty with Hedged Instance Embedding](https://mlsanity.com/paper/1810.00319/) (2018)
- [Bayesian Attention Modules](https://mlsanity.com/paper/2010.10604/) (2020)
- [Probabilistic Representations for Video Contrastive Learning](https://mlsanity.com/paper/2204.03946/) (2022)
- [WHAI: Weibull Hybrid Autoencoding Inference for Deep Topic Modeling](https://mlsanity.com/paper/1803.01328/) (2018)
- [Probabilistic Contrastive Learning Recovers the Correct Aleatoric Uncertainty of Ambiguous Inputs](https://mlsanity.com/paper/2302.02865/) (2023)
- [Representation Uncertainty in Self-Supervised Learning as Variational Inference](https://mlsanity.com/paper/2203.11437/) (2022)
- [Gamma Belief Networks](https://mlsanity.com/paper/1512.03081/) (2015)
- [Non-negative Contrastive Learning](https://mlsanity.com/paper/2403.12459/) (2024)
- [InfoNCE is variational inference in a recognition parameterised model](https://mlsanity.com/paper/2107.02495/) (2021)

## Built on by (most cited first, 2 of 2)

- [Beyond Matryoshka: Revisiting Sparse Coding for Adaptive Representation](https://mlsanity.com/paper/2503.01776/) (2025)
- [CSRv2: Unlocking Ultra-Sparse Embeddings](https://mlsanity.com/paper/2602.05735/) (2026)

## Abstract (arXiv)

Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis is receiving less and less attention due to their limited expressive ability. On the contrary, contrastive learning has emerged as a potent technique with demonstrated efficacy in unsupervised representational learning. While the two methods are different paradigms, recent theoretical analysis has revealed the mathematical equivalence between contrastive learning and matrix factorization, providing a potential possibility for factor analysis combined with contrastive learning. Motivated by the interconnectedness of contrastive learning, matrix factorization, and factor analysis, this paper introduces a novel Contrastive Factor Analysis framework, aiming to leverage factor analysis's advantageous properties within the realm of contrastive learning. To further leverage the interpretability properties of non-negative factor analysis, which can learn disentangled representations, contrastive factor analysis is extended to a non-negative version. Finally, extensive experimental validation showcases the efficacy of the proposed contrastive (non-negative) factor analysis methodology across multiple key properties, including expressiveness, robustness, interpretability, and accurate uncertainty estimation.