Toward Multi-Trit Quantization for Large Language Models: A Theoretical Framework for Balanced N-Trit Weights, Trit-Plane Generalization, and Mixed-Layer Precision
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866902326213607424 |
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| author | Heiden, Jeff McGillis |
| author_facet | Heiden, Jeff McGillis |
| contents | <p>Low-bit quantization for large language models has advanced rapidly through binary, ternary, post-training, and mixed-precision methods, yet the design space remains organized mainly around integer bit-width ladders or special-case ternary schemes. We introduce multi-trit quantization as a theory-first framework that generalizes ternary weight representations into balanced N-trit expansions, significance-ordered trit-plane decompositions, and mixed-layer trit-depth allocation. In the proposed formulation, each quantized weight is represented by a scale parameter multiplied by a significance-ordered sum of signed ternary digits drawn from the set {-1, 0, +1}. We show that this family induces precision operating points at rates equal to N times log base 2 of 3, generates exact representable sets with 3^N values, and supports fixed-scale nested representable families together with a canonical digit-wise decomposition structure. At fixed scale, the scalar representable set coincides with a symmetric uniform grid of 3^N levels; the value of the framework lies not in denying that scalar fact, but in exposing a structured ternary decomposition, canonical digit-wise truncation and bounded remainder relations, and a mixed-layer allocation variable based on radix depth rather than binary bit-width alone. Fixed-depth examples such as T3, T5, and T7 should therefore be read as illustrative operating points or controlled baselines, not as evidence that a single global trit depth is the intended deployment policy. We position prior ternary LLM work, trit-plane coding, non-uniform quantization, and mixed-precision allocation as supporting precedent rather than direct realizations of the full framework. The paper therefore claims not empirical superiority, but the formal definition and positioning of a new research program for LLM quantization and future trit-native architectures.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19880386 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Toward Multi-Trit Quantization for Large Language Models: A Theoretical Framework for Balanced N-Trit Weights, Trit-Plane Generalization, and Mixed-Layer Precision Heiden, Jeff McGillis Machine Learning Large language models Quantization Ternary quantization Model compression Balanced ternary Trit-plane decomposition <p>Low-bit quantization for large language models has advanced rapidly through binary, ternary, post-training, and mixed-precision methods, yet the design space remains organized mainly around integer bit-width ladders or special-case ternary schemes. We introduce multi-trit quantization as a theory-first framework that generalizes ternary weight representations into balanced N-trit expansions, significance-ordered trit-plane decompositions, and mixed-layer trit-depth allocation. In the proposed formulation, each quantized weight is represented by a scale parameter multiplied by a significance-ordered sum of signed ternary digits drawn from the set {-1, 0, +1}. We show that this family induces precision operating points at rates equal to N times log base 2 of 3, generates exact representable sets with 3^N values, and supports fixed-scale nested representable families together with a canonical digit-wise decomposition structure. At fixed scale, the scalar representable set coincides with a symmetric uniform grid of 3^N levels; the value of the framework lies not in denying that scalar fact, but in exposing a structured ternary decomposition, canonical digit-wise truncation and bounded remainder relations, and a mixed-layer allocation variable based on radix depth rather than binary bit-width alone. Fixed-depth examples such as T3, T5, and T7 should therefore be read as illustrative operating points or controlled baselines, not as evidence that a single global trit depth is the intended deployment policy. We position prior ternary LLM work, trit-plane coding, non-uniform quantization, and mixed-precision allocation as supporting precedent rather than direct realizations of the full framework. The paper therefore claims not empirical superiority, but the formal definition and positioning of a new research program for LLM quantization and future trit-native architectures.</p> |
| title | Toward Multi-Trit Quantization for Large Language Models: A Theoretical Framework for Balanced N-Trit Weights, Trit-Plane Generalization, and Mixed-Layer Precision |
| topic | Machine Learning Large language models Quantization Ternary quantization Model compression Balanced ternary Trit-plane decomposition |
| url | https://doi.org/10.5281/zenodo.19880386 |