DALM: A Domain-Algebraic Language Model via Three-Phase Structured Generation

TL;DR

DALM introduces a structured, three-phase generation framework for language models that enforces algebraic constraints to improve domain-specific knowledge handling and prevent cross-domain contamination.

Contribution

It proposes a novel three-phase generation process using algebraic structures, replacing traditional token-based decoding for better domain knowledge management.

Findings

DALM confines generation within domain fibers, preventing cross-domain contamination.

The framework enables multi-perspective answers within a domain-indexed space.

DALM is instantiated with CDC knowledge system for crystal library evaluation.

Abstract

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.