Math: Bifurcations

Machine-learning ideas tagged Bifurcations in the Math taxonomy of the Math2NN corpus.

2 ideas found

Solves: Inference speedup Math: Bifurcations Clear all

✗ Failed on benchmark 2026

Spectral-gap adaptive halting

Use the local Jacobian of a looped transformer to estimate its remaining relaxation time and stop the recurrent computation when the predicted residual reduction is sufficient. Near a saddle-node fold, the paper's asymptotic relation converts an estimated dominant eigenvalue into a compute forecast, allowing dynamic iteration budgets instead of a conservative fixed maximum.

Useful8/10

Difficulty5/10

Novelty6/10

Dynamics Inference speedup Stability Transformer

Paper: Dynamical phase selection controls compute scaling in looped transformers arXiv:2608.26556

Unverified 2026

Phase-controlled Jacobian training

Add a local Jacobian spectral regularizer and an initialization sweep to steer a looped transformer away from uncontrolled near-unit dynamics. The goal is to prevent examples from entering a fold-critical regime with very long relaxation times, or alternatively to deliberately target a controlled critical regime when adaptive test-time compute is useful.

Useful6/10

Difficulty6/10

Novelty5/10

Regularization Stability Inference speedup Generalization

Paper: Dynamical phase selection controls compute scaling in looped transformers arXiv:2608.26556