title: Math Neurosurgery: Isolating Language Models' Math Reasoning Abilities
    Using Only Forward Passes
summary: 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.
paper_authors._id: 6718d37c5d7e17ad0d5cd5a2
paper_authors.name: Bryan R. Christ
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-10-23T15:06:48.048Z
paper_authors._id: 64832043cb811166c6a2f4e3
paper_authors.avatarUrl: /avatars/44889baaaa6b86468ff6635791b14959.svg
paper_authors.fullname: Bryan Christ
paper_authors.type: user
paper_authors.user: bryanchrist
paper_authors._id: 6718d37c5d7e17ad0d5cd5a3
paper_authors.name: Zack Gottesman
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-10-24T08:37:56.718Z
paper_authors._id: 644135e7bd0c97265297098e
paper_authors.avatarUrl: /avatars/585c8cdc3136e22a0713fae9f6babb1d.svg
paper_authors.fullname: Zack Gottesman
paper_authors.type: user
paper_authors.user: zsg
paper_authors._id: 6718d37c5d7e17ad0d5cd5a4
paper_authors.name: Jonathan Kropko
paper_authors._id: 6718d37c5d7e17ad0d5cd5a5
paper_authors.name: Thomas Hartvigsen
paper_title: Math Neurosurgery: Isolating Language Models' Math Reasoning Abilities
    Using Only Forward Passes
paper_summary: 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.
paper_ai_summary: MathNeurosurgery identifies and manipulates math-specific parameters in LLMs to improve math reasoning without affecting language skills.
paper_ai_keywords: LLM MathNeurosurgery parameter importance weights activations pruning GSM8K data efficiency intervention on math-specific parameters