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Your vertex buffer should hold indices for which bones influence the position of each vertex and by what fraction. Each vertex could, for example, have 4 indices and 4 floats to indicate these values, and these only need to be uploaded to the gpu once.

The transformation matrices are interpolated for each rendered frame using the hierarchial animation data and the computed matrices are uploaded to the gpu in a buffer. The matrices are accessed in the vertex shader by indexing into the matrix buffer to calculate the vertex position.