Thermo-Logic Attention Dynamics (TLAD): Differentiable Hard Logic via Disentangled Lagrangian Mechanics Article Swipe
Neuro-symbolic (NeSy) AI faces a long-standing trilemma: no method simultaneously achieves end-to-end differentiability, strict hard constraint satisfaction, and data efficiency. We propose Thermo-Logic Attention Dynamics (TLAD), a framework that reformulates logical reasoning as the dynamic evolution of attention states via a bilevel optimization loop. The outer loop learns logic-aware representations to anchor initial attention, while the inner loop optimizes attention via constraint-derived energy gradients enforced by disentangled Lagrangian mechanics. TLAD resolves the trilemma by encoding hard constraints into gradient forces and eliminating cross-constraint gradient confusion with dedicated attention heads. Extensive experiments on the large-scale Big Kaggle Sudoku benchmark (100k) demonstrate that TLAD transforms a stagnating perceptual baseline (54.1\% accuracy) into a rigorous logical solver (99.2\% accuracy). Analysis of reasoning depth reveals a "phase transition": a single thermodynamic step repairs 90\% of errors (reaching 95.9\%), while deeper dynamics resolve the hardest corner cases. Furthermore, sensitivity analysis confirms the framework's structural robustness across varying capacities and thermodynamic schedules, paving a rigorous pathway toward human-like reasoning in deep networks.
Related Topics
Concepts
Computer science
Differentiable function
Robustness (evolution)
Solver
Constraint (computer-aided design)
Augmented Lagrangian method
Trilemma
Benchmark (surveying)
Reinforcement learning
Sensitivity (control systems)
Complementarity (molecular biology)
Complementarity theory
Mathematics
Algorithm
Lagrangian relaxation
Artificial intelligence
Automated reasoning
Representation (politics)
Constraint satisfaction problem
Perception
Lagrangian
Energy (signal processing)
Formalism (music)
Mathematical optimization
Automatic differentiation
Feature (linguistics)
Deep learning
Dynamics (music)
Metadata
- Type
- preprint
- Landing Page
- https://doi.org/10.5281/zenodo.17793623
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7108337606
All OpenAlex metadata
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https://openalex.org/W7108337606Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17793623Digital Object Identifier
- Title
-
Thermo-Logic Attention Dynamics (TLAD): Differentiable Hard Logic via Disentangled Lagrangian MechanicsWork title
- Type
-
preprintOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-12-02Full publication date if available
- Authors
-
Zhang, ChusongList of authors in order
- Landing page
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https://doi.org/10.5281/zenodo.17793623Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.5281/zenodo.17793623Direct OA link when available
- Concepts
-
Computer science, Differentiable function, Robustness (evolution), Solver, Constraint (computer-aided design), Augmented Lagrangian method, Trilemma, Benchmark (surveying), Reinforcement learning, Sensitivity (control systems), Complementarity (molecular biology), Complementarity theory, Mathematics, Algorithm, Lagrangian relaxation, Artificial intelligence, Automated reasoning, Representation (politics), Constraint satisfaction problem, Perception, Lagrangian, Energy (signal processing), Formalism (music), Mathematical optimization, Automatic differentiation, Feature (linguistics), Deep learning, Dynamics (music)Top concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |