Recent studies have highlighted an intriguing phenomenon in transformer models trained on algorithmic tasks. Traditionally, these models demonstrated a delayed transition from training accuracy to a sudden leap in generalization, known as “grokking.” The research focuses on deciphering the nature of this delay, emphasizing that it stems not from the inability to learn underlying structures but from limited access to these representations during their training.
The investigation centered on one-step Collatz prediction revealed that basic structures, such as parity and residue, are established early in training. Despite this early organization, the model’s accuracy remained stagnant for tens of thousands of steps, hovering at near chance levels. To further explore this bottleneck, researchers employed causal interventions, unveiling how the various components of the model interact with the learned structures.
One remarkable finding was that transferring an encoder from a trained model to a new one could accelerate the grokking process by 2.75 times. Conversely, reusing a trained decoder proved counterproductive. When researchers froze the encoder and retrained the decoder alone, it eliminated the accuracy plateau, achieving an impressive 97.6%, compared to just 86.1% with joint retraining.
The study also uncovered the critical role of numeral representation in influencing the decoder’s efficiency. Notably, representations that align with the Collatz map’s arithmetic substantially enhanced accuracy, while binary representations struggled, failing to recover as needed. This indicates that the choice of base serves as an inductive bias, significantly impacting the learnability of the same task, underscoring the nuanced dynamics between model architecture and training strategies.