📑 arXiv 3d ago
Stability and Generalization in Looped Transformers
Fixed-point framework analyzes looped transformers for test-time compute scaling along reachability, input-dependence, and geometric stability axes. Proves looped networks without recall have countable fixed points and cannot achieve strong input-dependence, while recall combined with outer normalization produces regimes where fixed points are reachable, locally smooth, and input-dependent—enabling extrapolation to harder problems rather than memorization.