title: Large Language Model Evaluation via Matrix Nuclear-Norm
summary: As large language models (LLMs) continue to evolve, efficient evaluation
  metrics are vital for assessing their ability to compress information and
  reduce redundancy. While traditional metrics like Matrix Entropy offer valuable
  insights, they are computationally intensive for large-scale models due to
  their \( O(n^3) \) time complexity with Singular Value Decomposition (SVD). To
  mitigate this issue, we introduce the Matrix Nuclear-Norm, which not only
  serves as a metric to quantify the data compression proficiency of LLM but also
  provides a convex approximation of matrix rank to capture both predictive
  discriminability and diversity. By employing the \( L_{1,2}-norm \) to
  further approximate the nuclear norm, we can effectively assess the model's
  information compression capabilities. This approach reduces the time complexity
  to \( O(n^2) \) and eliminates the need for SVD computation. Consequently, the
  Matrix Nuclear-Norm achieves speeds 8 to 24 times faster than Matrix Entropy
  for the CEREBRAS-GPT model as sizes increase from 111M to 6.7B. This
  performance gap becomes more pronounced with larger models, as validated in
  tests with other models like Pythia. Additionally, evaluations on benchmarks
  and model responses confirm that our proposed Matrix Nuclear-Norm is a
  reliable, scalable, and efficient tool for assessing LLMs' performance,
  striking a balance between accuracy and computational efficiency. The code is
  available at https://github.com/MLGroupJLU/MatrixNuclearNorm.
paper_authors._id: 670e8861559ae9c01f9282cc
paper_authors.name: Yahan Li
paper_authors._id: 670e8861559ae9c01f9282cd
paper_authors.name: Tingyu Xia
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-10-16T09:44:15.176Z
paper_authors._id: 653b5cb0d994e992e2831539
paper_authors.avatarUrl: /avatars/e6b917cb263f10a6d9c72ec539276428.svg
paper_authors.fullname: xiatingyu
paper_authors.type: user
paper_authors.user: xiatingyu
paper_authors._id: 670e8861559ae9c01f9282ce
paper_authors.name: Yi Chang
paper_authors._id: 670e8861559ae9c01f9282cf
paper_authors.name: Yuan Wu
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-10-17T11:26:54.978Z
paper_authors._id: 670e57b3391f1a7021182bff
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/no-auth/N0tuHZVz8KFPCv8G1qUX2.png
paper_authors.fullname: Yuan Wu
paper_authors.type: user
paper_authors.user: WhiteCatY
paper_title: Large Language Model Evaluation via Matrix Nuclear-Norm
paper_summary: As large language models (LLMs) continue to evolve, efficient evaluation
  metrics are vital for assessing their ability to compress information and
  reduce redundancy. While traditional metrics like Matrix Entropy offer valuable
  insights, they are computationally intensive for large-scale models due to
  their \( O(n^3) \) time complexity with Singular Value Decomposition (SVD). To
  mitigate this issue, we introduce the Matrix Nuclear-Norm, which not only
  serves as a metric to quantify the data compression proficiency of LLM but also
  provides a convex approximation of matrix rank to capture both predictive
  discriminability and diversity. By employing the \( L_{1,2}-norm \) to
  further approximate the nuclear norm, we can effectively assess the model's
  information compression capabilities. This approach reduces the time complexity
  to \( O(n^2) \) and eliminates the need for SVD computation. Consequently, the
  Matrix Nuclear-Norm achieves speeds 8 to 24 times faster than Matrix Entropy
  for the CEREBRAS-GPT model as sizes increase from 111M to 6.7B. This
  performance gap becomes more pronounced with larger models, as validated in
  tests with other models like Pythia. Additionally, evaluations on benchmarks
  and model responses confirm that our proposed Matrix Nuclear-Norm is a
  reliable, scalable, and efficient tool for assessing LLMs' performance,
  striking a balance between accuracy and computational efficiency. The code is
  available at https://github.com/MLGroupJLU/MatrixNuclearNorm.
paper_ai_keywords: Large language models (LLMs) Matrix Entropy Singular Value Decomposition (SVD) Matrix Nuclear-Norm predictive discriminability diversity \( L_{1,2}\text{-norm} \)