# Stable and Convexified Information Bottleneck Optimization via Symbolic Continuation and Entropy-Regularized Trajectories

arXiv: https://arxiv.org/abs/2505.09239 · HTML: https://mlsanity.com/paper/2505.09239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 14 May 2025.

## Builds on (most cited first, 4 of 4)

- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Nonlinear Information Bottleneck](https://mlsanity.com/paper/1705.02436/) (2017)
- [The Convex Information Bottleneck Lagrangian](https://mlsanity.com/paper/1911.11000/) (2019)
- [Phase Transitions for the Information Bottleneck in Representation Learning](https://mlsanity.com/paper/2001.01878/) (2020)

## Abstract (arXiv)

The Information Bottleneck (IB) method frequently suffers from unstable optimization, characterized by abrupt representation shifts near critical points of the IB trade-off parameter, beta. In this paper, I introduce a novel approach to achieve stable and convex IB optimization through symbolic continuation and entropy-regularized trajectories. I analytically prove convexity and uniqueness of the IB solution path when an entropy regularization term is included, and demonstrate how this stabilizes representation learning across a wide range of beta values. Additionally, I provide extensive sensitivity analyses around critical points (beta) with statistically robust uncertainty quantification (95% confidence intervals). The open-source implementation, experimental results, and reproducibility framework included in this work offer a clear path for practical deployment and future extension of my proposed method.