Schrödinger Bridge Learning

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Responsible: Ben Goertzel

Papers: Hyperon for AGI⇒ASI Whitepaper (2025), §5.7

Status: Proposed. Theoretical framework for curriculum design described in the 2025 whitepaper. Not yet implemented. Mathematical foundations draw on optimal transport theory.

Schrödinger Bridge Learning proposes a principled method for constructing learning curricula — finding paths from simple, abstract models to detailed, accurate ones by following geodesics through model space.

Core Idea

How should a learning system progress from knowing nothing to knowing something complex? Schrödinger bridge learning proposes a mathematical answer: find the minimum-effort path through model space from a very simple model to a very accurate one — an optimal transport interpolation that minimizes transport cost while respecting the structure of the underlying space.

How It Would Work

  1. Compute the Schrödinger bridge between simple prior and accurate target distributions
  2. Intermediate points define a sequence of progressively more complex models
  3. Each step is a learning target achievable from the previous step with bounded effort
  4. The result is a principled curriculum avoiding both catastrophic forgetting and wasted computation

Proposed Applications

  • Predictive coding networks: curricula where each bridge step corresponds to a bounded update in prediction accuracy
  • Evolutionary programming (MOSES/GEO-EVO): intermediate fitness landscapes smoothly interpolating between simple and complex target behaviors
  • Knowledge transfer: combined with TransWeave, minimum-effort paths from source to target domain representations

Connection to Weakness Theory

The whitepaper describes these as complementary: weakness provides the metric for "simplicity" that defines what counts as a geodesic, while the bridge framework provides the dynamics for moving along those geodesics. The Schrödinger bridge quantale is one of the specific quantale instantiations in the weakness theory framework.

Key References

  • Goertzel, B. (2025). Hyperon for AGI⇒ASI Whitepaper, §5.7: Schrödinger Bridge Learning