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

• URL: http://arxiv.org/abs/2505.09239v1
• Date: Wed, 14 May 2025 09:27:09 GMT
• Title: Stable and Convexified Information Bottleneck Optimization via Symbolic Continuation and Entropy-Regularized Trajectories
• Authors: Faruk Alpay,
• Abstract summary: I introduce a novel approach to achieve stable and convex IB optimization.<n>I analytically prove convexity and uniqueness of the IB solution path when an entropy regularization term is included.<n>I provide extensive sensitivity analyses around critical points (beta) with statistically robust uncertainty.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 \b{eta} 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.

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