aiqbench analysis
ShamAN-Q advances post-training quantization by integrating the Shampoo optimizer's dense curvature metrics into NanoQuant, enabling more efficient sub-1-bit compression of large language model weights. This method improves perplexity scores across various model sizes while maintaining zero-shot accuracy, offering a significant step forward in reducing the memory footprint of AI models without sacrificing performance.
ShamAN-Q: Shampoo Augmented NanoQuant for Sub-1-bit LLM Weights
arXiv:2609.38521v1 Announce Type: cross Abstract: We introduce ShamAN-Q, a sub-1-bit post-training quantization method that extends NanoQuant by replacing each its diagonal reconstruction geometry with a tractable dense curvature metric, using a general paradigm popularized by the Shampoo optimizer. For each linear weight, ShamAN-Q fits a Kronecker product to the empirical Fisher information matrix of a small calibration set by Kullback--Leibler minimization, forming a Mahalanobis reconstruction loss from the result. The continuous ADMM updates from NanoQuant become solutions to Sylvester equations, while its discrete projection and deployment format remain unchanged. Because the curvature is local to a given set of weights, ShamAN-Q re-measures the input curvature statistic for each layer immediately before layer factorization, periodically refreshing all statistics on the partially quantized model. ShamAN-Q also redistributes the uniform rank from NanoQuant across layers at the same total number of bits. On Qwen3-Base, ShamAN-Q lowers WikiText-2 perplexity at $\approx$1 bpw from 27.56 to 22.96 (0.6B), 19.21 to 16.72 (1.7B), and 14.29 to 13.80 (4B) while matching or improving zero-shot accuracy on the Eleuther LM Evaluation Harness. On 0.6B, ShamAN-Q at $\approx$0.8 bpw matches the published perplexity of NanoQuant at $\approx$1.0 bpw.
Abstract:We introduce ShamAN-Q, a sub-1-bit post-training quantization method that extends NanoQuant by replacing each its diagonal reconstruction geometry with a tractable dense curvature metric, using a general paradigm popularized by the Shampoo optimizer. For each linear weight, ShamAN-Q fits a Kronecker product to the empirical Fisher information matrix of a small calibration set by Kullback--Leibler minimization, forming a Mahalanobis reconstruction loss from the result. The continuous ADMM updates from NanoQuant become solutions to Sylvester equations, while its discrete projection and deployment format remain unchanged. Because the curvature is local to a given set of weights, ShamAN-Q re-measures the input curvature statistic for each layer immediately before layer factorization, periodically refreshing all statistics on the partially quantized model. ShamAN-Q also redistributes the uniform rank from NanoQuant across layers at the same total number of bits. On Qwen3-Base, ShamAN-Q lowers WikiText-2 perplexity at $\approx$1 bpw from 27.56 to 22.96 (0.6B), 19.21 to 16.72 (1.7B), and 14.29 to 13.80 (4B) while matching or improving zero-shot accuracy on the Eleuther LM Evaluation Harness. On 0.6B, ShamAN-Q at $\approx$0.8 bpw matches the published perplexity of NanoQuant at $\approx$1.0 bpw.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
arXiv:2609.38521 [cs.LG]
(or arXiv:2609.38521v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.38521 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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