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# Towards an Understanding of Stepwise Inference in Transformers: A Synthetic Graph Navigation Model

*Proceedings of the 41st International Conference on Machine Learning*, PMLR 235:23758-23780, 2024.

#### Abstract

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. To unravel the underlying mechanisms of stepwise inference we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. We find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy trade-off in model generations as sampling temperature varies; (iii) a simplicity bias in the model’s output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.