The Information Bottleneck’s Ordinary Differential Equation
  • Information Bottleneck
  • bifurcations
  • ordinary differential equation
  • numerical approximation
Video Introduction

This video is adapted from 10.3390/e25101370

The Information Bottleneck (IB) is a method of lossy compression of relevant information. Its rate-distortion (RD) curve describes the fundamental tradeoff between input compression and the preservation of relevant information embedded in the input. However, it conceals the underlying dynamics of optimal input encodings. Researchers argue that these typically follow a piecewise smooth trajectory when input information is being compressed, as recently shown in RD. These smooth dynamics are interrupted when an optimal encoding changes qualitatively, at a bifurcation.

By leveraging the IB's intimate relations with RD, researchers provide substantial insights into its solution structure, highlighting caveats in its finite-dimensional treatments. Sub-optimal solutions are seen to collide or exchange optimality at their bifurcations.

Despite the acceptance of the IB and its applications, there are surprisingly few techniques to solve it numerically, even for finite problems whose distribution is known.

Researchers derive anew the IB's first-order Ordinary Differential Equation, which describes the dynamics underlying its optimal tradeoff curve.

To exploit these dynamics, researchers not only detect IB bifurcations but also identify their type to handle them accordingly.

Rather than approaching the IB's optimal tradeoff curve from sub-optimal directions, the latter allows us to follow a solution's trajectory along the optimal curve under mild assumptions.

Researchers thereby translate an understanding of IB bifurcations into a surprisingly accurate numerical algorithm.

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Agmon, S. The Information Bottleneck’s Ordinary Differential Equation. Encyclopedia. Available online: (accessed on 23 April 2024).
Agmon S. The Information Bottleneck’s Ordinary Differential Equation. Encyclopedia. Available at: Accessed April 23, 2024.
Agmon, Shlomi. "The Information Bottleneck’s Ordinary Differential Equation" Encyclopedia, (accessed April 23, 2024).
Agmon, S. (2024, February 25). The Information Bottleneck’s Ordinary Differential Equation. In Encyclopedia.
Agmon, Shlomi. "The Information Bottleneck’s Ordinary Differential Equation." Encyclopedia. Web. 25 February, 2024.