expand_less
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.
FluidDynamics Foundation
The whitepaper (§5.3–5.4) also extends this frameworkinto through an incompressible fluid dynamics model calledfor In-Fluid-Net, where attention androuting, where evidence flowflows as a conserved fluid through the knowledge graph.graph This— approachconnecting usesgeodesic Hamilton-Jacobi-Bellmaninference (HJB) gradient descent for optimal control and Helmholtz-Hodge projection to decomposeECAN's flow into irrotational (gradient-driven) and solenoidal (circulation) components. The solenoidal drift component enables attention toallocation. circulate through the graph even in the absence of direct gradient signals — proposed as a mechanism for exploratory reasoning in the ambient cognitive loop.
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 fromthe incompressibility constraintconstraints (∇·u = 0) in the fluid model, acting as a Noether invariant that enforces strict budget conservationconservation. of attention and evidential mass.
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
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.
Fluid
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
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