Variational Autoreasoners: Recursive Reasoning by Amortizing the Other Half of EM

Recursive reasoning models share a set of design choices-a persistent state, a shared transformation, a prediction at every iteration, and local supervision with truncated gradients-whose computational role remains unclear. We interpret them through variational EM. Existing amortized inference amortizes only the E-step: it refines a posterior that conditions on the target, with no way to carry the result forward or to continue without the target. We introduce an instance-level M-step that adapts a per-problem memory conditioning the prior while shared weights stay fixed; the resulting inference-adaptation process inherits the monotone likelihood ascent of EM and anneals the prior toward the best explanations of the target. Variational Autoreasoners amortize this process with local variational objectives and run without the target through a recursive reasoning prior. The divergence between posterior-driven and prior-driven execution decomposes into the KL terms of the local objectives, and each design choice of recursive reasoners acquires a computational role.