Semantic Field Theory: Historical Origin, Higher-Order Interaction, and Stabilized Semantic Inference

• URL: http://arxiv.org/abs/2607.20451v1
• Date: Thu, 14 May 2026 13:10:06 GMT
• Title: Semantic Field Theory: Historical Origin, Higher-Order Interaction, and Stabilized Semantic Inference
• Abstract summary: This paper contributes five formal elements to Semantic Field Theory (SFT)<n>First, it defines a semantic field model as a consisting of a semantic space, a lexical field lifting, a contextual deformation map, an interaction complex, and an interpretation functional.<n>Third, it generalizes the three-word problem by using Mobius inversion on the subset lattice to isolate irreducible semantic interactions of arbitrary order.<n>Fourth, it introduces an order spectrum that measures how much field mass is explained at each interaction order.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Semantic Field Theory (SFT) has developed from a philosophical critique of strong anti-formalist readings of language games into a proposed computational model class for lexical semantics, higher order composition, and stabilized interpretation. This paper reconstructs that evolution and gives SFT a sharper mathematical core suitable for independent evaluation in computational linguistics and representation learning. The central proposal is that a tractable level of linguistic organization can be modeled through lexical representations expressed as semantic fields, through contextual deformation of those fields, through interaction terms defined over subsets of tokens, and through stabilization governed by semantic energy dynamics. The paper contributes five formal elements. First, it defines a semantic field model as a tuple consisting of a semantic space, a lexical field lifting, a contextual deformation map, an interaction complex, and an interpretation functional. Second, it proves a Gaussian product closure result showing that multiplicative field interactions have explicit centers, precisions, and compatibility factors. Third, it generalizes the three-word problem by using Mobius inversion on the subset lattice to isolate irreducible semantic interactions of arbitrary order. Fourth, it introduces an order spectrum that measures how much field mass is explained at each interaction order. Fifth, it formulates stabilized interpretation as minimization of an energy functional associated with the sentence and gives existence, descent, and stability conditions. A small worked example shows how a three-word summer day triple can be represented by Gaussian semantic fields, implemented in Python, and summarized by a flow diagram. The result is not a completed theory of natural language meaning and does not replace social, pragmatic, or normative accounts of language.

Related papers

• Does Syntax Matter? A Graph-Augmented Variational Topic Model for Computational Social Sciences [51.56484100374058]
  This paper introduces the Structural Contextual Probabilistic Topic Model ( SCPTM), an architecture that incorporates syntactic dependency relations into topic inference.<n>We evaluate seven topic modeling techniques across four corpora differing in register and discourse structure.<n>Results show that SCPTM's neural architecture yields substantial gains in document-topic alignment over generative baselines.
  arXiv  Detail & Related papers  (2026-09-07T17:39:06Z)
• Aggregative Semantics for Quantitative Bipolar Argumentation Frameworks [2.9722048871879636]
  We introduce a novel family of gradual semantics, called aggregative semantics.<n>In order to deal with situations in which attackers and supporters do not play a symmetric role, we propose to aggregate attackers and supporters separately.<n>This leads to a three-stage computation, which consists in computing a global weight for attackers and another for supporters.
  arXiv  Detail & Related papers  (2026-03-06T09:22:55Z)
• Visual Language Hypothesis [14.062822951292402]
  We study visual representation learning from a structural and topological perspective.<n>We show that approximating the quotient also places structural demands on the model architecture.
  arXiv  Detail & Related papers  (2025-12-29T09:43:10Z)
• Steering Embedding Models with Geometric Rotation: Mapping Semantic Relationships Across Languages and Models [2.3204178451683264]
  We introduce Rotor-Invariant Shift Estimation (RISE), a geometric approach that represents semantic transformations as consistent rotational operations in embedding space.<n>RISE operations have the ability to operate across both languages and models with high transfer of performance.<n>This work provides the first systematic demonstration that discourse-level semantic transformations correspond to consistent geometric operations in multilingual embedding spaces.
  arXiv  Detail & Related papers  (2025-10-10T18:51:32Z)
• A Complexity-Based Theory of Compositionality [53.025566128892066]
  In AI, compositional representations can enable a powerful form of out-of-distribution generalization.<n>Here, we propose a definition, which we call representational compositionality, that accounts for and extends our intuitions about compositionality.<n>We show how it unifies disparate intuitions from across the literature in both AI and cognitive science.
  arXiv  Detail & Related papers  (2024-10-18T18:37:27Z)
• Syntax and Semantics Meet in the "Middle": Probing the Syntax-Semantics Interface of LMs Through Agentivity [68.8204255655161]
  We present the semantic notion of agentivity as a case study for probing such interactions. This suggests LMs may potentially serve as more useful tools for linguistic annotation, theory testing, and discovery.
  arXiv  Detail & Related papers  (2023-05-29T16:24:01Z)
• How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding [56.222097640468306]
  We provide mechanistic understanding of how transformers learn "semantic structure" We show, through a combination of mathematical analysis and experiments on Wikipedia data, that the embedding layer and the self-attention layer encode the topical structure.
  arXiv  Detail & Related papers  (2023-03-07T21:42:17Z)
• Variational Cross-Graph Reasoning and Adaptive Structured Semantics Learning for Compositional Temporal Grounding [143.5927158318524]
  Temporal grounding is the task of locating a specific segment from an untrimmed video according to a query sentence. We introduce a new Compositional Temporal Grounding task and construct two new dataset splits. We argue that the inherent structured semantics inside the videos and language is the crucial factor to achieve compositional generalization.
  arXiv  Detail & Related papers  (2023-01-22T08:02:23Z)
• Plurality and Quantification in Graph Representation of Meaning [4.82512586077023]
  Our graph language covers the essentials of natural language semantics using only monadic second-order variables. We present a unification-based mechanism for constructing semantic graphs at a simple syntax-semantics interface. The present graph formalism is applied to linguistic issues in distributive predication, cross-categorial conjunction, and scope permutation of quantificational expressions.
  arXiv  Detail & Related papers  (2021-12-13T07:04:41Z)
• Decomposing lexical and compositional syntax and semantics with deep language models [82.81964713263483]
  The activations of language transformers like GPT2 have been shown to linearly map onto brain activity during speech comprehension. Here, we propose a taxonomy to factorize the high-dimensional activations of language models into four classes: lexical, compositional, syntactic, and semantic representations. The results highlight two findings. First, compositional representations recruit a more widespread cortical network than lexical ones, and encompass the bilateral temporal, parietal and prefrontal cortices.
  arXiv  Detail & Related papers  (2021-03-02T10:24:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.