# Rethinking the Information Bottleneck: Structured Decomposition under Label-Induced Partitions

arXiv: https://arxiv.org/abs/2610.01175 · HTML: https://mlsanity.com/paper/2610.01175/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Emergence of Invariance and Disentanglement in Deep Representations](https://mlsanity.com/paper/1706.01350/) (2017)
- [Gland Segmentation in Colon Histology Images: The GlaS Challenge Contest](https://mlsanity.com/paper/1603.00275/) (2016)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [Robust Classification with Convolutional Prototype Learning](https://mlsanity.com/paper/1805.03438/) (2018)
- [How Does Information Bottleneck Help Deep Learning?](https://mlsanity.com/paper/2305.18887/) (2023)
- [Learning Representations for Neural Network-Based Classification Using the Information Bottleneck Principle](https://mlsanity.com/paper/1802.09766/) (2018)
- [Compressive Visual Representations](https://mlsanity.com/paper/2109.12909/) (2021)
- [An Information-theoretic Approach to Distribution Shifts](https://mlsanity.com/paper/2106.03783/) (2021)
- [Transfer Entropy Bottleneck: Learning Sequence to Sequence Information Transfer](https://mlsanity.com/paper/2211.16607/) (2022)

## Abstract (arXiv)

Standard information bottleneck (IB) regularization constrains representations via a single scalar I(Z;X), implicitlytreating all information as homogeneous. However, a single global compression control couples label-relevant structurewith residual within-condition variation, rather than regulating their allocation independently, allowing nuisanceinformation to persist in learned representations. For example, in medical imaging applications, residual variation oftenstems from acquisition conditions, background factors, or subject-specific appearance. This issue becomes particularlypronounced in data-limited settings, where models tend to overfit such variation, hindering generalization. While existingregularization methods can stabilize training, control capacity, or shape representation geometry, they do not explicitlyseparate nuisance-like variation from task-supporting structure. To address this limitation, we revisit IB from a structuredperspective based on a label-induced partition, where condition-level structure and within-condition information playdistinct roles. This leads to a dual-bottleneck formulation: a standard KL term controls global information capacity, while aconditional KL term targets within-condition information. We show that the conditional KL admits an exact decompositioninto a within-condition information term and a prior-mismatch term, explaining its alignment with the design objective.With a simplex-structured conditional prior, the method provides controllable latent geometry and integrates seamlesslyinto existing pipelines. Experiments on classification and segmentation show the clearest gains in low-data classificationand consistent improvements across dense prediction benchmarks.