Quantitative convergence certification for AFOR

Establish a quantitative convergence certificate for the reported AFOR training runs without relying solely on the conditional gradient-drift requirement and worst-case constants used in the current stability analysis.

Background

The paper develops AFOR, a tensor-wise adaptive forgetting optimizer for cross-subject EEG decoding, and provides a conditional finite-time stationarity bound in Section VI. That analysis assumes a gradient-drift tracking condition and uses worst-case constants, yielding a qualitative stability result rather than a run-specific quantitative guarantee.

The authors explicitly identify the gap between this conditional theoretical result and a quantitative certificate for the empirical experiments as an unresolved issue. Resolving it would connect the convergence analysis more directly to the reported AFOR training runs.

References

While AFOR addresses the fixed second-moment memory limitation, two aspects remain open for future investigation. First, the guarantee in Section~VI is conditional on the gradient-drift requirement and rests on worst-case constants, so it is qualitative rather than a quantitative certificate for the reported runs.

— Adaptive Forgetting for Nonstationary Optimization: Towards Robust EEG Decoding  (2609.24233 - Zhu et al., 21 Sep 2026) in Section VI, CONCLUSION

A formal bound on the streaming-CG tracking error in terms of per-event drift and CG contraction is open.

— OnTrack: Real-Time Monitoring and Intervention in LLM Agent Trajectories via Streaming Structure-Aware Optimal Transport  (2610.12375 - Barazandeh et al., 8 Oct 2026) in Section 6, “Limitations and Future Work,” paragraph “Theory”