Predictive relation between feature competition and generalization

Determine whether the ecological picture of competition between features in neural quadratic form dynamics predicts properties of generalization, rather than only optimization behavior.

Background

Under the neural quadratic form reduction, the mode dynamics take the form of generalized Lotka–Volterra equations, allowing learned features to be interpreted as competing or cooperating species. The paper uses this analogy to explain feature acquisition and optimization-time scaling laws.

The analysis does not establish whether this competition picture has implications for test performance or generalization. The authors explicitly identify this as an unresolved question for future investigation.

References

Whether the mapping survives beyond quadratic order, and whether the ecological picture of competition between features predicts anything about generalization rather than optimization, are the questions we regard as most worth pursuing.

— Neural Quadratic Forms: A Unified Minimal Model for Sudden Learning and Scaling Laws  (2608.13335 - Ziyin et al., 13 Aug 2026) in Section 6, Discussion, paragraph “Outlook”

An important open question is what properties of a learning problem determine whether this competition produces overregularization.

— The Dynamics of Quasiregular Neural Learning  (2609.26018 - Sabatelli, 22 Sep 2026) in Discussion and Conclusion, Section 4