Tracing and Manipulating Intermediate Values in Neural Math Problem Solvers

TL;DR

This paper investigates how Transformer models process intermediate values in multi-step arithmetic problems, using PCA and causal interventions to understand and manipulate their internal representations for better interpretability.

Contribution

It introduces a novel method combining PCA and causal interventions to trace and manipulate intermediate value representations in neural math problem solvers.

Findings

Intermediate values are encoded in specific model activations.

Manipulating identified weights causally affects model predictions.

The model exhibits locality in processing intermediate values.

Abstract

How language models process complex input that requires multiple steps of inference is not well understood. Previous research has shown that information about intermediate values of these inputs can be extracted from the activations of the models, but it is unclear where that information is encoded and whether that information is indeed used during inference. We introduce a method for analyzing how a Transformer model processes these inputs by focusing on simple arithmetic problems and their intermediate values. To trace where information about intermediate values is encoded, we measure the correlation between intermediate values and the activations of the model using principal component analysis (PCA). Then, we perform a causal intervention by manipulating model weights. This intervention shows that the weights identified via tracing are not merely correlated with intermediate values, but causally related to model predictions. Our findings show that the model has a locality to certain intermediate values, and this is useful for enhancing the interpretability of the models.