SoftWater: Class-Aware Rate Allocation for Softmax Quantization
Post-training quantization pipelines routinely leave the softmax output layer in high precision. Yet in small LLMs with modern vocabularies, the head holds 15--30\% of all parameters, so a nominal ``2-bit'' model with an fp16 head can store several times as many bits per weight. We pose softmax-layer quantization as a rate-distortion problem under the KL divergence between the original and quantized output distributions. A second-order analysis reveals a class-aware geometry: quantization error is weighted jointly by feature covariance and class-specific softmax curvature. A separability approximation replaces the $Kn\times Kn$ Cholesky with one $n\times n$ factorization rescaled per clas...
| Authors | Joao V. Cavalcanti, Ashia C. Wilson |
|---|---|
| Primary category | cs.LG |
| Published | 12 August 2026 |
| Last updated at source | 12 August 2026 |
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