Contraction of the Future Horizon by Memory: A Minimal Information Law and an Interventional Proof Instrument

Introduction Modern deep neural networks exhibit a well-known transition during training: an initial generalization phase followed by progressive memorization of the training data. While this phenomenon is widely observed, detecting the precise transition point remains difficult in practice and typically requires validation heuristics, retraining procedures, or architecture-dependent monitoring. In this work, we introduce a lightweight log-only monitoring approach capable of detecting the memorization flip directly from standard training logs, without access to gradients, internal model states, or retraining. The proposed method relies exclusively on the temporal relationship between training loss improvement and validation accuracy evolution. The memorization flip is identified when loss continues decreasing while generalization performance stabilizes or ceases to improve. We evaluate this approach across models of increasing capacity, ranging from small convolutional networks trained on MNIST to Wide Residual Networks on CIFAR-10 and Vision Transformers trained from scratch. Results reveal a consistent scaling behavior of flip timing with model capacity, with transformer attention mechanisms introducing an additional delay while sharpening the transition. These findings suggest that memorization onset follows a measurable and architecture-dependent dynamic, opening the possibility of universal training efficiency monitoring using only publicly available training logs.