On the Limits of Hierarchically Embedded Logic in Classical Neural Networks

• URL: http://arxiv.org/abs/2507.20960v1
• Date: Mon, 28 Jul 2025 16:13:41 GMT
• Title: On the Limits of Hierarchically Embedded Logic in Classical Neural Networks
• Authors: Bill Cochran,
• Abstract summary: We show that each layer can encode at most one additional level of logical reasoning.<n>We prove that a neural network of depth a particular depth cannot faithfully represent predicates in a one higher order logic.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a formal model of reasoning limitations in large neural net models for language, grounded in the depth of their neural architecture. By treating neural networks as linear operators over logic predicate space we show that each layer can encode at most one additional level of logical reasoning. We prove that a neural network of depth a particular depth cannot faithfully represent predicates in a one higher order logic, such as simple counting over complex predicates, implying a strict upper bound on logical expressiveness. This structure induces a nontrivial null space during tokenization and embedding, excluding higher-order predicates from representability. Our framework offers a natural explanation for phenomena such as hallucination, repetition, and limited planning, while also providing a foundation for understanding how approximations to higher-order logic may emerge. These results motivate architectural extensions and interpretability strategies in future development of language models.

Related papers

• Neural Networks as Universal Finite-State Machines: A Constructive Deterministic Finite Automaton Theory [0.0]
  We establish feedforward neural networks as universal finite-state machines (N-FSMs)<n>Our results prove that finite-depth ReLU and threshold networks can exactly simulate deterministic finite automata (DFAs)<n>We formalize the expressivity boundary: fixed-depth feedforward networks cannot recognize non-regular languages requiring memory.
  arXiv  Detail & Related papers  (2025-05-16T21:01:34Z)
• Standard Neural Computation Alone Is Insufficient for Logical Intelligence [3.230778132936486]
  We argue that standard neural layers must be fundamentally rethought to integrate logical reasoning.<n>We advocate for Logical Neural Units (LNUs)-modular components that embed differentiable approximations of logical operations.
  arXiv  Detail & Related papers  (2025-02-04T09:07:45Z)
• LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning [73.98142349171552]
  LOGICSEG is a holistic visual semantic that integrates neural inductive learning and logic reasoning with both rich data and symbolic knowledge. During fuzzy logic-based continuous relaxation, logical formulae are grounded onto data and neural computational graphs, hence enabling logic-induced network training. These designs together make LOGICSEG a general and compact neural-logic machine that is readily integrated into existing segmentation models.
  arXiv  Detail & Related papers  (2023-09-24T05:43:19Z)
• Modeling Hierarchical Reasoning Chains by Linking Discourse Units and Key Phrases for Reading Comprehension [80.99865844249106]
  We propose a holistic graph network (HGN) which deals with context at both discourse level and word level, as the basis for logical reasoning. Specifically, node-level and type-level relations, which can be interpreted as bridges in the reasoning process, are modeled by a hierarchical interaction mechanism.
  arXiv  Detail & Related papers  (2023-06-21T07:34:27Z)
• Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations [62.65877150123775]
  Causal abstraction is a promising theoretical framework for explainable artificial intelligence. Existing causal abstraction methods require a brute-force search over alignments between the high-level model and the low-level one. We present distributed alignment search (DAS), which overcomes these limitations.
  arXiv  Detail & Related papers  (2023-03-05T00:57:49Z)
• Extensions to Generalized Annotated Logic and an Equivalent Neural Architecture [4.855957436171202]
  We propose a list of desirable criteria for neuro symbolic systems and examine how some of the existing approaches address these criteria. We then propose an extension to annotated generalized logic that allows for the creation of an equivalent neural architecture. Unlike previous approaches that rely on continuous optimization for the training process, our framework is designed as a binarized neural network that uses discrete optimization.
  arXiv  Detail & Related papers  (2023-02-23T17:39:46Z)
• Join-Chain Network: A Logical Reasoning View of the Multi-head Attention in Transformer [59.73454783958702]
  We propose a symbolic reasoning architecture that chains many join operators together to model output logical expressions. In particular, we demonstrate that such an ensemble of join-chains can express a broad subset of ''tree-structured'' first-order logical expressions, named FOET. We find that the widely used multi-head self-attention module in transformer can be understood as a special neural operator that implements the union bound of the join operator in probabilistic predicate space.
  arXiv  Detail & Related papers  (2022-10-06T07:39:58Z)
• Discourse-Aware Graph Networks for Textual Logical Reasoning [142.0097357999134]
  Passage-level logical relations represent entailment or contradiction between propositional units (e.g., a concluding sentence) We propose logic structural-constraint modeling to solve the logical reasoning QA and introduce discourse-aware graph networks (DAGNs) The networks first construct logic graphs leveraging in-line discourse connectives and generic logic theories, then learn logic representations by end-to-end evolving the logic relations with an edge-reasoning mechanism and updating the graph features.
  arXiv  Detail & Related papers  (2022-07-04T14:38:49Z)
• Logical Neural Networks [51.46602187496816]
  We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning) Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omni rather than focused on predefined target variables, and corresponds to logical reasoning.
  arXiv  Detail & Related papers  (2020-06-23T16:55:45Z)

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.