Bridging the Gap between Continuous and Informative Discrete Representations by Random Product Quantization

Self-supervised learning (SSL) has become a core technique in speech processing, but the high dimensionality of its representations makes discretization essential for improving efficiency. However, existing discretization methods still suffer from significant information loss, resulting in a notable performance gap compared to continuous representations. To overcome these limitations, we propose two quantization-based discretization methods: Product Quantization (PQ) and Random Product Quantization (RPQ). PQ partitions the original feature space into multiple subspaces and independently quantizes each sub-vector, producing a fused set of discrete units that retain diverse information from different subspaces, thereby mitigating the loss associated with single-cluster quantization. RPQ further enhances representation diversity by randomly sampling a fixed proportion of feature dimensions multiple times to construct sub-vectors, thereby better capturing the variability in the data distribution. Theoretical analysis shows that RPQ reduces the correlation coefficient rho (where 0 <= rho <= 1) between sub-quantizers. Its quantization error is lower-bounded by the product of rho and epsilon-kms, where epsilon-kms denotes the quantization error of a single K-means quantizer. Experimental results on a combined dataset built from LibriSpeech and ML-SUPERB show that PQ and RPQ outperform standard K-means discretization, achieving relative improvements of 21.8 percent and 20.0 percent in WER on LibriSpeech, and 24.1 percent and 19.6 percent in CER on ML-SUPERB, respectively. Moreover, their performance is competitive with, and in some cases even surpasses, that of continuous SSL representations.