# I-Con: A Unifying Framework for Representation Learning

Source: [I-Con: A Unifying Framework for Representation Learning](<https://www.sota2.com/research/paper/68fa5d4d1e209131ce9d8daf>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T05:38:12.809Z

Authors: Shaden Alshammari, John Hershey, Axel Feldmann, William T. Freeman, Mark Hamilton

Published: 2025-04-23T17:59:01.000Z

## Abstract

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [In-distribution Retrieval on CIFAR-100](<https://www.sota2.com/research/sota/in-distribution-retrieval-on-cifar-100.md>): In-distribution Retrieval; CIFAR-100; LP@1: 99.9.

- [In-distribution Retrieval on ImageNet 1K](<https://www.sota2.com/research/sota/in-distribution-retrieval-on-imagenet-1k.md>): In-distribution Retrieval; ImageNet-1K; LP@1: 38.6.

- [Out-of-Distribution Retrieval on ImageNet-1K OOD (test)](<https://www.sota2.com/research/sota/out-of-distribution-retrieval-on-imagenet-1k-ood-test.md>): Out-of-Distribution Retrieval; ImageNet-1K OOD (test); AR@1: 84.9.

- [Out-of-Distribution Retrieval on FGVC-Aircraft OOD (test)](<https://www.sota2.com/research/sota/out-of-distribution-retrieval-on-fgvc-aircraft-ood-test.md>): Out-of-Distribution Retrieval; FGVC-Aircraft OOD (test); AR@1: 85.3.

- [Out-of-Distribution Retrieval on CIFAR-10 OOD (test)](<https://www.sota2.com/research/sota/out-of-distribution-retrieval-on-cifar-10-ood-test.md>): Out-of-Distribution Retrieval; CIFAR-10 OOD (test); AR@1: 79.7.

- [Out-of-Distribution Retrieval on Food-101 (test)](<https://www.sota2.com/research/sota/out-of-distribution-retrieval-on-food-101-test.md>): Out-of-Distribution Retrieval; Food-101 OOD (test); AR@1: 82.1.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2504.16929>)

[PDF](<https://arxiv.org/pdf/2504.16929.pdf>)