Diagnostic tools to measure implicit EM dynamics

Develop diagnostic methods to empirically measure implicit expectation-maximization in trained neural networks by extracting responsibilities from gradients, tracking component specialization over training, and detecting failure or degeneration of responsibility-weighted updates.

Background

The paper’s core claim is that responsibilities are gradients under log-sum-exp distance-based objectives, implying that training implements inference. Practical verification and monitoring of these dynamics would help bridge theory and practice.

Diagnostic tools that quantify responsibilities, specialization, and failure modes would turn the framework into an instrumented methodology researchers can apply to confirm and debug implicit EM behavior in real models.

References

Several directions remain open. Finally, diagnostic tools are needed. If trained networks perform implicit EM, it should be possible to measure this: to extract responsibilities from gradients, to track specialization over training, to detect when the mechanism fails or degenerates.

— Gradient Descent as Implicit EM in Distance-Based Neural Models (2512.24780 - Oursland, 31 Dec 2025) in Discussion, Open Directions (Section 7, Open Directions)