Per-Group Codebook

The PerGroupCodebook codec models the per-group nibble distribution of quantized MXFP4 VALUE planes.

Theory

In microscaled formats like MXFP4, weights are grouped into blocks (typically 32 elements). The value distributions across different blocks can vary significantly.

This codec extracts a histogram of nibble occurrences for every group in the plane. It then runs a multi-seed, deterministic k-means clustering algorithm to find a set of K representative PMFs (the codebook centroids).

Each group is assigned to its nearest centroid. The codec range-codes the nibbles in each group using the assigned centroid's PMF, heavily compressing groups that have highly skewed local distributions.

Usage

This codec exclusively accepts nibble-packed Value planes with a Nibble element width.

References

• Robert M. Gray, "Vector Quantization", IEEE ASSP Magazine (1984). Link