Math Neurosurgery: Isolating Language Models' Math Reasoning Abilities
  Using Only Forward Passes
Authors: name: Bryan R. Christ, name: Zack Gottesman, name: Jonathan Kropko, name: Thomas Hartvigsen

Math reasoning is a highly active area of Large Language Model (LLM) research
because it is a hallmark of artificial intelligence. However, few works have
explored how math reasoning is encoded within LLM parameters and if it is a
skill that can be isolated within a model. Doing so could allow targeted
intervention to improve math performance without altering non-math behavior and
foster understanding of how models encode math reasoning. We introduce Math
Neurosurgery (MathNeuro), a method for isolating math-specific parameters in
LLMs using only forward passes. MathNeuro builds on existing work by using
weights and activations to calculate parameter importance, but isolates
math-specific parameters by removing those important for general language
tasks. Pruning parameters MathNeuro identifies deletes a LLM's math reasoning
ability without destroying its general language ability. Scaling these
parameters by a small constant improves a pretrained or instruction-tuned LLM's
performance by 4-17% on GSM8K while leaving non-math behavior unaltered.
MathNeuro is also data efficient: most of its effectiveness holds when
identifying math-specific parameters using a single sample. MathNeuro
highlights the potential for future work to intervene on math-specific
parameters.