expand_less Responsible: Ben Goertzel

Traditional inference systems waste effort oscillating between forward chaining (from facts toward goals) and backward chaining (from goals toward facts). Geodesic inference eliminatesproposes eliminating this inefficiency by maintaining both directions simultaneously and choosing steps that advance both — following minimum-effort paths through inference space.

Status: Proposed. Geodesic inference is described in the 2025 whitepaper (§5.2) as a theoretical framework for PLN inference control. The mathematical foundations draw on Schrödinger bridge geometry. Implementation within the Hyperon stack is a research goal.

Core Concept

Geodesic control implementsframes 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 maintainswould maintain two factors:


Forward factor (f): reachability from current evidence — what can we derive from what we know?
Backward factor (g): usefulness toward current goals — what would help us reach our objectives?


The control rulerule: is straightforward: choose actions that maximize the change in log(f × g) per unit cost, while maintaining approximately constant effort per step. This f·g product structure appearsis proposed to appear throughout PRIMUS — in inference, evolutionary search, transfer learning, Schrödinger bridge interpolation, and even motivational decisions.

Mathematical Foundation

The approach is grounded in Schrödinger bridge geometry, defining an action functional that combines transport effort with prior regularization. The optimal solution has anthe elegantproperty property:that at each point, the probability density is proportional to the product of forward and backward factors.

In practice, the factors arewould be approximated through:

Factor-graph messages for logical inference (PLN)
Monte Carlo estimates for meet probabilities
Amortized neural predictors for complex domains


Evidence Conservation

Geodesic control enforcesis adesigned criticalto safetyenforce property: conservation of evidence. Just— asensuring physical systems conserve energy, the inference system ensures that evidence neither spontaneously appears nor disappears —during inference, preventing both hallucination and information loss.

This emergeswould emerge from a quantale-valued "generalized energy" thatacting acts as a Noether invariantinvariant,. Implementationimplemented usesvia local evidence capsules (similar to CRDTs),CRDTs) overlap-safe merge operations, and content-addressed messagesmessages. in the scheduler.

Intended Role in PRIMUS

Geodesic control is designed as one of two architecture-wide formal controls (alongside weakness theory).theory), Itproviding provides the selection rule for:

PLN inference step selection
MOSES/GEO-EVO evolutionary search direction
Planning and action selection
Self-modification proposal evaluation
Schrödinger bridge curriculum design


The approach is particularly elegant within PLN, where it unifies forward and backward chaining into a single bidirectional process guided by principled cost metrics.

Key References

Goertzel, B. (2025). Hyperon for AGI⇒ASI Whitepaper, §5.2: Geodesic Inference and Control