Large Language Model Evaluation via Matrix Nuclear-Norm
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.
670e8861559ae9c01f9282cc
Yahan Li
670e8861559ae9c01f9282cd
Tingyu Xia
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2024-10-16T09:44:15.176Z
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xiatingyu
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xiatingyu
670e8861559ae9c01f9282ce
Yi Chang
670e8861559ae9c01f9282cf
Yuan Wu
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2024-10-17T11:26:54.978Z
670e57b3391f1a7021182bff
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Yuan Wu
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WhiteCatY
Large Language Model Evaluation via Matrix Nuclear-Norm
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.
The Matrix Nuclear-Norm is introduced as an efficient and scalable metric for evaluating large language models by approximating matrix rank, reducing computational complexity and improving performance assessment.
Matrix Nuclear-Norm matrix rank computational complexity Singular Value Decomposition (SVD) \(L_{1 2}\text{-norm}\) predictive discriminability diversity information compression CEREBRAS-GPT Pythia