Quantization of large models with weight outliers and sparsity

Post-training quantization (PTQ) reduces the memory burden of large model deployment by casting the high precision trained weights to fewer bits. While this promotes memory-efficient inference, it also incurs quantization error that impairs model performance. To compensate for quantization error, the present contribution decomposes the original trained weights into a quantized matrix, a low-rank component, and a sparse matrix that accounts for outlier rows in the weights. Due to analytical intractability and the discrete structure of the decomposition, a simulated annealing search is employed to explore candidate decompositions while avoiding poor local minima. Numerical tests demonstrate the effectiveness of this approach across a broad suite of large language models, including Llama 3.2 1B, Llama 3.2 3B, Llama 3.1 8B, and Qwen2.5 7B, evaluated on natural language generation benchmarks using 4-bit NF4 and FP4 quantizers. The novel method can markedly outperform direct quantization while incurring minimal memory overhead.