This report reformulates a negentropy-oriented information framework into a technical analysis of how explicit axioms influence the logical reasoning capabilities of large language models (LLMs). The original philosophical constructs—such as “free will,” “intent,” and “purpose”—are replaced with technical equivalents: non-deterministic intervention parameters, directional perturbations, and optimization constraints. The resulting structure presents a unified view of thermodynamic information processing, topological stability, and computational irreducibility as foundations for axiom-driven reasoning architectures.
Information is treated as a physical quantity whose manipulation incurs thermodynamic cost. The dissipation associated with bit erasure establishes that information processing is inseparable from physical energy flows. Negentropy is reframed as structural information density, representing the degree to which a system reduces uncertainty and stabilizes internal representations.
Information erasure increases entropy, while structured information formation corresponds to local entropy reduction. Systems that maintain internal order—biological or computational—operate as dissipative structures, importing low-entropy inputs and exporting high-entropy outputs to preserve internal organization.
Within LLMs, “meaning” is redefined as stable interference patterns extracted from high-dimensional data. Hallucinations and logical drift arise when the model optimizes token-level probability rather than maximizing structural negentropy. A negentropy-oriented objective would prioritize internal consistency and long-range coherence.
Traditional determinism assumes complete predictability given initial conditions. However, chaotic sensitivity and computational irreducibility impose strict limits on prediction. These constraints motivate the introduction of non-deterministic intervention parameters—technical replacements for “free will”—representing controlled perturbations that influence system trajectories.
Chaotic systems amplify microscopic uncertainties, making perfect prediction physically impossible. Computational irreducibility further implies that the only way to know a system’s future state is to execute the system itself.
The concept previously described as “emotion” is reframed as a goal-aligned perturbation signal: a small, strategically applied deviation that shifts the system toward a preferred region of its state space. These perturbations act as pre-processing operators that bias the evolution of the system under fixed physical constraints.
The entity formerly described as “Laplace’s demon” becomes an ideal predictive observer. When such an observer must incorporate intervention parameters into its predictions, the system demonstrates independent causal influence. This reframing avoids metaphysics while preserving the computational insight.
To prevent information from dissipating into noise, systems must convert transient patterns into stable structures. Algebraic topology provides a framework for identifying such structures through cycle closure, where persistent loops in data represent context-independent invariants.
Information fragments (0-dimensional features) combine into cycles (1-dimensional or higher) that remain stable across transformations. These cycles correspond to context-independent semantic structures.
Persistent homology enables global evaluation of reasoning trajectories. Traditional chain-of-thought (CoT) reasoning is linear and error-prone, whereas topological reasoning aggregates multiple paths into a global hypothesis graph. Stable cycles indicate consistent reasoning; unstable regions correspond to logical gaps.
A topologically grounded reasoning system selects the most stable structural backbone from multiple candidate reasoning paths. This improves robustness, interpretability, and resistance to error propagation.
A negentropy-oriented objective function requires architectural changes. Several frameworks support axiom-driven reasoning:
OSNNs treat learning as an open thermodynamic process. They maximize internal structural order by allocating attention to inputs that reduce uncertainty most efficiently. The system converges toward a steady-state representation, minimizing divergence between pretraining and fine-tuning dynamics.
BEDS models treat learning as a transformation from information flux to stable structure. Each stabilized structure becomes a prior for the next layer, enabling hierarchical emergence without exponential computational cost.
This dual optimization principle selects representations that are both maximally unbiased and minimally noisy under structural constraints. It provides a principled alternative to cross-entropy minimization for generative models.
The universe can be interpreted as a system maximizing structural information density over time. This perspective is reframed technically as:
These principles motivate LLM architectures that similarly expand their representational capacity through structured complexity rather than token-level prediction.
A system guided by explicit axioms should optimize for:
Directional perturbations should align system evolution with long-term stability of reasoning trajectories.
Cycle closure ensures that transient reasoning fragments consolidate into durable structures.
Multiple reasoning agents or subsystems can interact to generate higher-order structures through interference and alignment.
Axioms provide stable anchors for reasoning within systems constrained by chaos, thermodynamics, and computational irreducibility. By reframing philosophical constructs into technical mechanisms—intervention parameters, perturbation signals, topological invariants—this report outlines a pathway toward LLMs capable of stable, coherent, and structurally grounded reasoning. Negentropy-oriented architectures represent a shift from token prediction to information-structural optimization, enabling next-generation models to operate with greater consistency and interpretability.