syndu | June 6, 2023, 3:15 p.m.
Eigenvalues and eigenvectors are mathematical concepts that arise from the study of linear algebra. They are used to understand the properties of linear transformations and are particularly useful in the analysis of systems that can be represented by matrices.
Eigenvalues (λ) are scalar values that satisfy the following equation for a given square matrix A and a non-zero vector v:
Av = λv
In this equation, A is a square matrix, v is the eigenvector, and λ is the eigenvalue. Eigenvectors are the non-zero vectors that, when multiplied by the matrix A, result in a scaled version of the same vector. The scaling factor is the eigenvalue.
In the context of large language models, eigenvalues and eigenvectors play a role in various stages, including creation, training, fine-tuning, and usage. Some of the ways they feature in these processes are:
In summary, eigenvalues and eigenvectors are fundamental mathematical concepts that can be applied in various ways to improve the creation, training, fine-tuning, and usage of large language models. They can help with dimensionality reduction, clustering, performance analysis, and optimization, among other tasks.
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