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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.15593 |
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| _version_ | 1866910138481246208 |
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| author | Li, Chao |
| author_facet | Li, Chao |
| contents | Large language models compress heterogeneous knowledge into a single parameter space, allowing facts from different domains to interfere during generation. We propose DALM, a Domain-Algebraic Language Model that replaces unconstrained token generation with structured denoising over a domain lattice. DALM follows a three-phase generation path: it first resolves domain uncertainty, then relation uncertainty, and finally concept uncertainty, so each stage operates under explicit algebraic constraints. The framework requires only three ingredients: a lattice of domains with computable meet, join, and implication; a typing function over relations that controls inheritance across domains; and a fiber partition that localizes knowledge to domain-specific subsets. Given these ingredients, DALM yields a three-phase encoder-decoder architecture in which generation is confined to a domain fiber, cross-domain contamination is structurally prevented in closed-vocabulary mode and auditably bounded in open-vocabulary mode, and a single query can produce a domain-indexed multi-perspective answer space. We instantiate the framework with the CDC knowledge representation system and outline training and evaluation on validated domain-annotated crystal libraries. DALM reframes language generation as algebraically constrained structured denoising rather than unconstrained decoding over a flat token space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15593 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | DALM: A Domain-Algebraic Language Model via Three-Phase Structured Generation Li, Chao Computation and Language Artificial Intelligence Large language models compress heterogeneous knowledge into a single parameter space, allowing facts from different domains to interfere during generation. We propose DALM, a Domain-Algebraic Language Model that replaces unconstrained token generation with structured denoising over a domain lattice. DALM follows a three-phase generation path: it first resolves domain uncertainty, then relation uncertainty, and finally concept uncertainty, so each stage operates under explicit algebraic constraints. The framework requires only three ingredients: a lattice of domains with computable meet, join, and implication; a typing function over relations that controls inheritance across domains; and a fiber partition that localizes knowledge to domain-specific subsets. Given these ingredients, DALM yields a three-phase encoder-decoder architecture in which generation is confined to a domain fiber, cross-domain contamination is structurally prevented in closed-vocabulary mode and auditably bounded in open-vocabulary mode, and a single query can produce a domain-indexed multi-perspective answer space. We instantiate the framework with the CDC knowledge representation system and outline training and evaluation on validated domain-annotated crystal libraries. DALM reframes language generation as algebraically constrained structured denoising rather than unconstrained decoding over a flat token space. |
| title | DALM: A Domain-Algebraic Language Model via Three-Phase Structured Generation |
| topic | Computation and Language Artificial Intelligence |
| url | https://arxiv.org/abs/2604.15593 |