  Compactness in deep learning can be critical to a model's viability in
low-resource applications, and a common approach to extreme model compression
is quantization. We consider Iterative Product Quantization (iPQ) with
Quant-Noise to be state-of-the-art in this area, but this quantization
framework suffers from preventable inference quality degradation due to
prevalent empty clusters. In this paper, we propose several novel enhancements
aiming to improve the accuracy of iPQ with Quant-Noise by focusing on resolving
empty clusters. Our contribution, which we call Partitioning-Guided k-means (PG
k-means), is a heavily augmented k-means implementation composed of three main
components. First, we propose a partitioning-based pre-assignment strategy that
ensures no initial empty clusters and encourages an even weight-to-cluster
distribution. Second, we propose an empirically superior empty cluster
resolution heuristic executed via cautious partitioning of large clusters.
Finally, we construct an optional optimization step that consolidates
intuitively dense clusters of weights to ensure shared representation. The
proposed approach consistently reduces the number of empty clusters in iPQ with
Quant-Noise by 100x on average, uses 8x fewer iterations during empty cluster
resolution, and improves overall model accuracy by up to 12%, when applied to
RoBERTa on a variety of tasks in the GLUE benchmark.
