expand_less Responsible: Ben Goertzel

Traditional
Papers: Hyperon for AGI⇒ASI Whitepaper (2025), §5.2
Status: Proposed. Theoretical framework for PLN inference systemscontrol wastedescribed effortin oscillatingthe between2025 forwardwhitepaper. chainingThe (frommathematical factsfoundations towarddraw goals)on andSchrödinger backwardbridge chaininggeometry. (fromImplementation goalsis towarda facts).research goal.

Geodesic inference proposes eliminating this inefficiency in traditional inference by maintaining both directionsforward and backward chaining 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 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 — what can we derive from what we know?
Backward factor (g): usefulness toward current goals — what would help us reach our objectives?


The control rule: choose actions that maximize the change in log(f × g) per unit cost,cost. whileThe maintainingwhitepaper approximatelyproposes constantthis effort per step. This f·g product structure isas proposeda tounifying appearcontrol throughoutprinciple PRIMUSacross — in inference, evolutionary search, transfer learning, Schrödinger bridge interpolation, and 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 the property that at each point, the probability density is proportional to the product of forward and backward factors.

In practice, the factors would be approximated through:through

Factor-graph factor-graph messages for(PLN), logical inference (PLN)
Monte Carlo estimatesestimates, foror meetamortized probabilities
Amortized neural predictorspredictors. for complex domains


Evidence Conservation

GeodesicThe controlwhitepaper isdescribes designeda toproposed enforcesafety property: conservation of evidence, — ensuring that evidence neither spontaneously appears nor disappears during inference,inference. preventing both hallucination and information loss. This would emerge from a quantale-valued "generalized energy" acting as a Noether invariant,invariant. implemented via local evidence capsules (similar to CRDTs) and content-addressed messages.

Intended Role in PRIMUS

Geodesic control is designed as one of two architecture-wide formal controls (alongside weakness theory), providing the selection rule for:
for
PLN inferenceinference, step selection
MOSES/GEO-EVO evolutionary searchsearch, directionplanning,
Planning andself-modification actionevaluation, selectionand
Self-modification proposal evaluation
Schrödinger bridge curriculum designdesign.


Key References

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