mlsanityData to 7 Oct 2026

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

arXiv 2604.15593 ↗First posted 17 Apr 2026cs.CL cs.AIcited by 0

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Abstract (arXiv)

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.

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References · 17

  1. 2020Retrieval-Augmented Generation for Knowledge-Intensive NLP Taskscited by 9,160
  2. 2020REALM: Retrieval-Augmented Language Model Pre-Trainingcited by 2,126
  3. 2013Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computationcited by 2,031
  4. 2022Atlas: Few-shot Learning with Retrieval Augmented Language Modelscited by 940
  5. 2025Large Language Diffusion Modelscited by 872
  6. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  7. 2025Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decodingcited by 404
  8. 2017Lexically Constrained Decoding for Sequence Generation Using Grid Beam Searchcited by 234
  9. 2021Constrained Language Models Yield Few-Shot Semantic Parserscited by 162
  10. 2024A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Datacited by 88
  11. 2023How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Modelcited by 70
  12. 2026Attention Residualscited by 57
5 more
  1. 2024Probing the Latent Hierarchical Structure of Data via Diffusion Modelscited by 25
  2. 2026dLLM: Simple Diffusion Language Modelingcited by 12
  3. 2026Domain-constrained knowledge representation: A modal frameworkcited by 2
  4. 2026Domain-Contextualized Inference: A Computable Graph Architecture for Explicit-Domain Reasoningcited by 2
  5. 2026Reasoning as Data: Representation-Computation Unity and Its Implementation in a Domain-Algebraic Inference Enginecited by 1

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