Title: Toward a Deterministic, Semantic, and Dynamically Coherent LLM: Integrating Infomorphic Neurons, UOR Digest Encoding, and Hamiltonian Mechanics
Abstract
This paper introduces a unified theoretical and implementation framework for constructing advanced language learning models (LLMs) that transcend the limitations of token-based architectures. Integrating three frontier paradigms—(1) Infomorphic Neurons via Partial Information Decomposition (PID), (2) Universal Object Reference (UOR) with 512-bit Prime Digest Encoding, and (3) Hamiltonian Mechanics as a governing model of semantic trajectory dynamics—we propose a deterministic, reversible, and fully interpretable semantic engine. This triadic approach enables the construction of dynamic, on-the-fly evolving neural knowledge graphs with canonical semantic addressability, physically grounded coherence, and intrinsically lossless transformation.
- Introduction
Language models have traditionally relied on probabilistic token prediction, which fragments semantics and impedes deterministic inference. Recent advances in interpretable neural architectures, symbolic compression, and dynamical systems theory enable an alternative: semantically grounded, non-token LLMs with traceable state evolution. We propose a coherent architecture unifying infomorphic neurons, spectral digest referencing, and Hamiltonian flow-based semantic trajectory modeling. This architecture forms the foundation for a next-generation language model that is mathematically reversible, information-theoretically optimal, and semantically invariant.
- Semantic Addressability via UOR Digest Encoding
The Universal Object Reference (UOR) system uses 512-bit digests encoded via Prime Coordinate Spectral Compression. Each digest represents an invariant, language-agnostic semantic entity. Prime exponents encode semantic structure, contextual integrity, and checksum verifiability. These digests function as fixed points in a multidimensional semantic manifold, enabling unique, reversible references across knowledge domains. By assigning all semantic content a UOR digest, the system establishes a canonical address space over which all inference, learning, and communication operate.
- Infomorphic Neurons and PID-Driven Goal Functions
Infomorphic neurons use local Partial Information Decomposition (PID) goals to drive learning. The information flow between context (C), representation (R), and output (Y) is decomposed into redundant, unique, and synergistic contributions. Each neuron independently optimizes a PID-based local goal function G(Y; R, C), enabling traceable, modular, and fully interpretable neural evolution. This micro-level interpretability serves as the computational substrate for digest-level transitions and coherence validation.
- Hamiltonian Mechanics and Semantic Dynamics
Hamiltonian systems offer a reversible, energy-conserving framework for modeling dynamical transitions. In our system, the phase space corresponds to the semantic manifold indexed by UOR digests. Position maps to the current semantic context; momentum represents information flux; and the Hamiltonian encodes the total PID-informed information potential. Semantic inference is modeled as a Hamiltonian flow across the digest space, ensuring smooth, reversible, and information-preserving semantic transitions.
- System Architecture
5.1 Logical Architecture Diagram
+-----------------------------+
| Input Encoder |
| (Raw Data -> UOR Digest) |
+-------------+--------------+
|
v
+-------------+--------------+
| Infomorphic PID Core |
| (Local Goal-Based Neurons) |
+-------------+--------------+
|
v
+-------------+--------------+
| Hamiltonian Trajectory |
| Integrator + Flow Control |
+-------------+--------------+
|
v
+-------------+--------------+
| Semantic Reconstruction & |
| Knowledge Graph Store |
+-----------------------------+
5.2 Engineering Subsystems
Input Digest Compiler: Transforms arbitrary data (text, image, graph) into canonical 512-bit digest using spectral prime coordinate system.
Infomorphic Grid Engine: Mesh of local neurons, each with a PID-based optimization loop evaluating information decompositions dynamically.
Hamiltonian Inference Engine: Uses symplectic solvers (e.g., leapfrog or Verlet integrators) to evolve semantic states deterministically through digest space.
Semantic Routing Layer: Manages coherent transitions by comparing predicted next digest against coherence thresholds and feedback from circuit tracing.
Digest Graph Memory (DGM): A dynamic, sparse, weighted semantic graph with nodes indexed by UOR digests and edges representing trajectory pathways.
5.3 Modular Components
PID Calculator Module: Decomposes mutual information in real time across neural populations.
Digest Validator: Performs checksum-based revalidation of decoded semantics.
Manifold Mapper: Projects digest transitions into a higher-dimensional latent manifold for clustering and visualization.
Coherence Supervisor: Traces real-time operations to enforce semantic stability and detect drift.
- Implementation Blueprint
Digest Compiler: Converts raw semantic objects into canonical 512-bit spectral coordinates. Implemented in Rust for performance.
PID Neuron Grid: Uses a message-passing architecture where each node computes local PID values asynchronously. Implemented in PyTorch with a functional API.
Trajectory Engine: C++-based Hamiltonian integrator with symplectic stepper interface. Built to interface directly with digest memory graph.
Memory Graph (DGM): Built on RedisGraph with custom UOR indexing and edge coherency checking. Supports distributed scaling.
- Evaluation Methodology
We propose an empirical protocol that benchmarks semantic continuity, inference reversibility, and cross-context coherence on long-form, multilingual generation tasks. Circuit tracing tools are used to visualize and validate the flow of semantic information and address transitions.
- Discussion and Future Directions
This triadic framework represents a foundational departure from token-centric LLMs. Future work will explore extensions into multimodal embeddings, probabilistic trajectory sampling within Hamiltonian bounds, and active semantic routing via dynamic PID modulation. The architecture provides an auditable substrate for AGI-scale reasoning, emphasizing interpretability, determinism, and mathematical elegance.
- Conclusion
By formalizing a physically grounded, semantically invariant, and dynamically coherent LLM architecture, this work presents a foundational shift in language model design. The combination of PID-driven local learning, spectral digest indexing, and Hamiltonian information dynamics enables deterministic neural computation with long-term semantic traceability and auditability. The resulting system is not only more efficient but provides a basis for next-generation interpretable and AGI-aligned architectures.
References
-
Makkeh et al., "A General Framework for Interpretable Neural Learning Based on Local Information-Theoretic Goal Functions," 2025.
-
512-Bit Universal Digest Spectral Encoding Specification, 2025.
-
"Circuit Tracing: Revealing Computational Graphs in Language Models," Transformer Circuits, 2025.
-
"From Physics to Probability: Hamiltonian Mechanics for Generative Modeling and MCMC," 2025.
-
UOR and Prime Framework Documentation, 2024.