ExTernD: Expanded-Rank Ternary Decomposition Ternary LLM PTQ with Accuracy Approaching Any Quantization Level

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. We prove the residual decreases monotonically in $k$ and can be driven below any $\varepsilon > 0$: ExTernD approaches bf16 accuracy arbitrarily closely, which no ternary scheme with a fixed plane count can do. ...

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