Geodesic Inference

Responsible: Ben Goertzel

Papers: Hyperon for AGI⇒ASI Whitepaper (2025), §5.2–5.4

Status: Proposed. Theoretical framework for PLN inference control described in the 2025 whitepaper. The mathematical foundations draw on Schrödinger bridge geometry and fluid dynamics. Implementation is a research goal.

Geodesic inference proposes eliminating inefficiency in traditional inference by maintaining both forward and backward chaining simultaneously and choosing steps that advance both — following minimum-effort paths through inference space.

Core Concept

Geodesic control frames inference as navigation along shortest paths through information space, where "shortest" means minimum representational effort as defined by weakness theory. At each step, the system would maintain two factors:

• Forward factor (f): reachability from current evidence
• Backward factor (g): usefulness toward current goals

The control rule: choose actions that maximize the change in log(f × g) per unit cost. The whitepaper proposes this f·g product structure as a unifying control principle across inference, evolutionary search, transfer learning, and motivational decisions.

Mathematical Foundation

The approach is grounded in Schrödinger bridge geometry, defining an action functional that combines transport effort with prior regularization. In practice, the factors would be approximated through factor-graph messages (PLN), Monte Carlo estimates, or amortized neural predictors. The whitepaper (§5.3–5.4) also extends this into an incompressible fluid dynamics model for attention routing, where evidence flows as a conserved fluid through the knowledge graph — connecting geodesic inference to ECAN's attention allocation.

Evidence Conservation

The whitepaper describes a proposed safety property: conservation of evidence, ensuring that evidence neither spontaneously appears nor disappears during inference. This would emerge from incompressibility constraints in the fluid model, acting as a Noether invariant that enforces strict budget conservation.

Intended Role in PRIMUS

Geodesic control is designed as one of two architecture-wide formal controls (alongside weakness theory), providing the selection rule for PLN inference, MOSES/GEO-EVO evolutionary search, planning, self-modification evaluation, and Schrödinger bridge curriculum design.

Key References

• Goertzel, B. (2025). Hyperon for AGI⇒ASI Whitepaper, §5.2–5.4: Geodesic Inference, Fluid Dynamics for Attention, Incompressible-Fluid Networks