We introduce ExTernD (Expanded-rank Ternary Decomposition), a post-training factorization of each LLM weight matrix $A \in \mathbb{R}^{m \times n}$ into $A \approx B \mathrm{diag}(D) C$ with ternary factors $B \in \{-1,0,+1\}^{m \times k}$, $C \in \{-1,0,+1\}^{k \times n}$ and a real scale vector $D \in \mathbb{R}^k$. The inner rank $k = μ\min(m,n)$ is deliberately expanded beyond full rank ($μ> 1$), so that components past full rank correct the quantization error of earlier ones.
ShamAN-Q is a sub‑1‑bit post‑training quantization technique that builds on NanoQuant by replacing its diagonal reconstruction geometry with a dense curvature metric inspired by the Shampoo optimizer. For each linear weight, it fits a Kronecker product to the empirical Fisher information matrix of a small calibration set via Kullback–Leibler minimization, yielding a Mahalanobis reconstruction loss. The method updates continuous ADMM steps to Sylvester equations while keeping the discrete projection and deployment format unchanged, and it redistributes uniform rank across layers, achieving lower perplexity on Qwen3‑Base at roughly 1 bpw and matching or improving zero‑shot accuracy on the Eleuther LM Evaluation Harness.
By Jonathan Mei, Sang Hyub Kim, Oliver Knitter, Chi Chen, Martin Roetteler
arXiv:2609.00224v1 Announce Type: cross
Abstract: Weight-only post-training quantization (PTQ) can alleviate the computational burden of serving large language models (LLMs) at scale. However, existi...
By Yipin Guo, Arun M George, Jie Fu, Tareq Mahmoud, Sixue Xing, Siddharth Joshi
arXiv:2608.28150v2 Announce Type: replace
Abstract: How much matrix rank is required to preserve every bounded value output of normalized softmax attention? We study the unrestricted maximum-row-\(\e...
By Yuhe Sui, Jianing Zhang, Yingzhi Tang
arXiv:2605.11222v2 Announce Type: replace
Abstract: Quantization is an effective strategy to reduce the storage and computation footprint of large language models (LLMs). Post-training quantization (...
By Ryan Lucas, Mehdi Makni, Xiang Meng, Adam Deng, Rahul Mazumder
The paper introduces a ternary multiplicative adaptation technique that enables fine‑tuning of ternary transformers without dequantization. By representing discrete weight updates as a low‑rank Kronecker factorization of two small ternary matrices applied element‑wise, the method preserves the ternary domain and allows direct merging of adaptation weights. Experiments on six language and vision models, including ternarized LLaMA‑3 and ViT‑B/16, show that the approach recovers most of the performance lost to quantization and outperforms existing low‑bit and ternary baselines.
By Alexandru-Dragos Manolache, Yunqiang Li, Jan van Gemert