On the Stability of Learning: When Intermittent Gradient Feedback Destabilizes Learning Algorithms

Forum topic · 小凯 · 2026-10-27

Summary

This arXiv paper (2610.35856) by John J. Vastola examines learning algorithms under conditions where informative gradients are noisy and only intermittently available, as in biological neural networks where learning signals may be sparse and local. The author proves that learning can be unstable even when average learning dynamics converge to the correct optimum: the variance of learning may grow asymptotically infinite. Analyzing analytically tractable settings including single-layer and multi-layer linear networks, the paper derives explicit conditions under which learning remains stable. These stability conditions complement, yet are conceptually distinct from, classical stability conditions for stochastic gradient descent. The key conclusion is that unbiased credit assignment alone does not guarantee reliable learning; feedback must also be sufficiently frequent and informative. This adds a new constraint to models of biologically plausible learning.

Paper Overview

Field: Machine Learning Author: John J. Vastola Published: 2026-10-26 arXiv: 2610.35856

Abstract

Learning algorithms are usually analyzed under the assumption that informative gradients are continuously available. But this is not always true—learning signals in biological neural networks, for example, may be sparse, local, and only intermittently available at any given synapse.

In this work, the author shows that if gradient information is noisy and only intermittently available, learning may be unstable. In particular, even if average learning dynamics converge to the correct optimum, variance in learning may be asymptotically infinite.

Key Findings

Instability from intermittent feedback: Noisy, sporadic gradient information can destabilize learning even when the mean dynamics are correct.
Analytically tractable settings: The phenomenon is demonstrated in single-layer and multi-layer linear networks.
Explicit stability conditions: The paper derives explicit conditions under which learning is stable. These complement, but are conceptually distinct from, existing stability conditions for stochastic gradient descent.
Implication for biological learning: Unbiased credit assignment is not enough for reliable learning; sufficiently frequent and informative feedback is also required, yielding an additional constraint on models of biologically plausible learning.