Determine how to train the proposal and consistency critic

Determine whether the proposal network and consistency critic in Settling-Based Inference should be trained independently, jointly, or with alternating objectives, and characterize how the choice affects ambiguity resolution.

Background

Settling-Based Inference separates an amortized proposal network, which supplies a context-aligned initialization, from a consistency critic, which defines the validity landscape used during test-time refinement. These components have different inferential roles, and the paper does not commit to a particular training relationship between them.

The paper leaves unresolved whether independent training, joint training, or alternating optimization produces the most useful proposal initialization and consistency landscape for resolving ambiguity. This design question is especially relevant to learned deployments because poor coupling could lead to proposals outside recoverable basins or critics with spurious stable equilibria.