Pushing Toward the Simplex Vertices: A Simple Remedy for Code Collapse in Smoothed Vector Quantization

Vector quantization, which discretizes a continuous vector space into a finite set of representative vectors (a *codebook*), has been widely adopted in modern machine learning. Despite its effectiveness, vector quantization poses a fundamental challenge: the non-differentiable quantization step blocks gradient backpropagation. *Smoothed* vector quantization addresses this issue by relaxing the hard assignment of a codebook vector into a weighted combination of codebook entries, represented as the matrix product of a simplex vector and the codebook. Effective smoothing requires two properties: 1. smoothed code-selection vectors should remain close to a onehot vector, ensuring tight approximation, and 2. all codebook entries should be utilized, preventing *code collapse*. Existing methods typically address these desiderata separately. By contrast, the present study introduces a simple and intuitive regularization that promotes both simultaneously by minimizing the distance between each simplex vertex and its $K$-nearest smoothed code-selectors. Representative benchmarks on image encoding demonstrate that the proposed method achieves more effective codebook utilization and improves performance over prior approaches.