The Generalization Ridge: Information Flow in Natural Language Generation

Abstract: Transformer-based LLMs have achieved state-of-the-art performance in natural language generation (NLG) tasks, yet their internal mechanisms for synthesizing task-relevant information remain insufficiently understood. While prior studies suggest that intermediate layers often yield more generalizable representations than final layers, how this generalization ability emerges and propagates across layers during training remains unclear. To address this gap, we propose InfoRidge, an information-theoretic framework, to characterize how predictive information-the mutual information between hidden representations and target outputs-varies across depth. Estimating this quantity enables us to trace the flow of task-relevant information throughout the model during training. Our experiments across various models and datasets reveal a consistent non-monotonic trend: predictive information peaks in upper-middle layers-forming a generalization ridge-before declining in final layers, reflecting a transition between generalization and memorization. To further investigate this phenomenon, we introduce residual scaling coefficients-trainable scalar parameters applied to each residual block-which serve as functional probes for assessing the relative importance of individual transformer layers. These coefficients reveal that, under distribution shift, models downweight final layers and increasingly rely on ridge layers, highlighting their role in generalization. Together, these findings offer new insights into the internal mechanisms of transformers and underscore the critical role of intermediate layers in supporting generalization.