Grokking is the phenomenon whereby, unlike the training performance, which peaks early in the training process, the test/generalization performance of a model stagnates over arbitrarily many epochs and then suddenly jumps to usually close to perfect levels. In practice, it is desirable to reduce the length of such plateaus, that is to make the learning process "grok" faster. In this work, we provide new insights into grokking. First, we show both empirically and theoretically that grokking can be induced by asymmetric speeds of (stochastic) gradient descent, along different principal (i.e singular directions) of the gradients. We then propose a simple modification that normalizes the gradients so that dynamics along all the principal directions evolves at exactly the same speed. Then, we establish that this modified method, which we call egalitarian gradient descent (EGD) and can be seen as a carefully modified form of natural gradient descent, groks much faster. In fact, in some cases the stagnation is completely removed. Finally, we empirically show that on classical arithmetic problems such as modular addition and sparse parity problem which this stagnation has been widely observed and intensively studied, that our proposed method eliminates the plateaus.

The Wizard of Oz (WoZ) method is a widely adopted research approach where a human Wizard "role-plays" a not readily available technology and interacts with participants to elicit user behaviors and probe the design space. With the growing ability for modern large language models (LLMs) to role-play, one can apply LLMs as Wizards in WoZ experiments with better scalability and lower cost than the traditional approach. However, methodological guidance on responsibly applying LLMs in WoZ experiments and a systematic evaluation of LLMs' role-playing ability are lacking. Through two LLM-powered WoZ studies, we take the first step towards identifying an experiment lifecycle for researchers to safely integrate Figure 1: An overview of our proposed experiment lifecycle LLMs into WoZ experiments and interpret data generated compared to traditional Wizard of Oz experiments. We ask from settings that involve Wizards role-played by LLMs. We also GPT-4 empowered agents to play the role of "Wizards" in contribute a heuristic-based evaluation framework that allows the conversation-based Wizard of Oz experiments. The agents estimation of LLMs' role-playing ability in WoZ experiments and talk to either Simulacrums powered by GPT-4 (in Study 1) or reveals LLMs' behavior patterns at scale.