Sharp Threshold for Softmax Stability in Logit Systems
A groundbreaking theorem has been proposed that refines the stability threshold for affine logit systems in finite dimensions, moving beyond previous overly cautious methods. The new criterion specifies a stability limit encapsulated by the formula β‖ΠWΠ‖_{T→T} < 2, pinpointing where significant system changes occur. Earlier approaches inaccurately assumed softmax as a baseline, limiting their findings to random conditions without acknowledging stability in all contexts. This advancement has important applications in fields such as entropy-regularized reinforcement learning, logit game analysis, population modeling, and mean-field variational approaches. The study is available on arXiv under identifier 2605.15651.
Key facts
- The sharp threshold is β‖ΠWΠ‖_{T→T} < 2.
- Classical condition certified stability only in over-regularized regime.
- Theorem fills previously missing pre-bifurcation analysis.
- Applies to softmax feedback systems in multiple fields.
- Published on arXiv:2605.15651.
- Dimension-free Euclidean threshold.
- Corrects conservative classical theory.
- Identifies true point of qualitative change.
Entities
Institutions
- arXiv