Language models can learn implicit multi-hop reasoning, but only if they have lots of training data

Implicit reasoning is the ability of a language model to solve multi-hop reasoning tasks in a single forward pass, without chain of thought. We investigate this capability using GPT2-style language models trained from scratch on controlled k-hop reasoning datasets (k = 2, 3, 4). We show that while such models can indeed learn implicit k-hop reasoning, the required training data grows exponentially in k, and the required number of transformer layers grows linearly in k. We offer a theoretical explanation for why this depth growth is necessary. We further find that the data requirement can be mitigated, but not eliminated, through curriculum learning.