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6 changes: 5 additions & 1 deletion DESIGN.md
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# Quaternary Quantization: Design

> **Related documents:** [PREDICTIONS.md](PREDICTIONS.md) · [TESTING.md](TESTING.md)
> **Related documents:** [PREDICTIONS.md](PREDICTIONS.md) · [TESTING.md](TESTING.md) · [RELATED_WORK.md](RELATED_WORK.md)

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This is **reconstruction quantization**: the objective is to minimize $\|W - \hat{W}\|_F^2$, approximating the original signal as closely as possible. **Structural quantization** (the subject of this document) has a different objective: preserve relational and topological structure — distances, trajectories, and complement relationships — rather than pointwise values. The two objectives share the quaternary alphabet but differ in metric, distribution, and purpose.

A survey of overlapping work — including BQQ (NeurIPS 2025), QUAD, QuES, BitNet, and domain-specific applications — is in [RELATED_WORK.md](RELATED_WORK.md).

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### 2.5 Quaternary quantization
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- Hammons, A. R., Kumar, P. V., Calderbank, A. R., Sloane, N. J. A., & Solé, P. (1994). The $\mathbb{Z}_4$-linearity of Kerdock, Preparata, Goethals, and related codes. *IEEE Trans. Inform. Theory* 40:2, 301–319.
- Wildberger, N. J. & Rubine, D. (2025). A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode. *Amer. Math. Monthly* 132:5, 383–402. DOI: 10.1080/00029890.2025.2460966

For references to overlapping work in the ML literature (BQQ, QUAD, QuES, BitNet, and related methods), see [RELATED_WORK.md](RELATED_WORK.md).

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[^1]: The $1/n_s$ variance normalisation ensures the dot product of two random unit
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