From Objectives to What Models Learn: A Landau Theory of Invariant Learning
Invariant-learning objectives pursue similar goals yet produce qualitatively different regularization paths, leaving unclear when shortcuts can be suppressed without damaging stable modes. Our starting point is simple: in the desired shortcut-suppressed regime, shortcut loading is small, so the objective's low-order expansion governs local stability and residual amplitude. This brings the problem into the domain of Landau phase-transition theory. We establish a mathematical isomorphism between the near-critical normal form of predictive-mode learning and Landau theory, identifying the learning objective as an effective free energy and critical-mode amplitude as an order parameter. The res...
| Authors | Pinli Wang, Yue He, Peng Cui |
|---|---|
| Primary category | cs.LG |
| Published | 10 August 2026 |
| Last updated at source | 28 September 2026 |
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