Unfolding AlphaFold's Bayesian Roots in Probability Kinematics

We present a novel theoretical interpretation of AlphaFold1 that reveals the potential of generalized Bayesian updating for probabilistic deep learning. The seminal breakthrough of AlphaFold1 in protein structure prediction by deep learning relied on a learned potential energy function, in contrast to the later end-to-end architectures of AlphaFold2 and AlphaFold3. While this potential was originally justified by referring to physical potentials of mean force (PMFs), we reinterpret AlphaFold1's potential as an instance of {\em probability kinematics} -- also known as {\em Jeffrey conditioning} -- a principled but under-recognised generalization of conventional Bayesian updating. Probability kinematics accommodates uncertain or {\em soft} evidence in the form of updated probabilities over a partition. This perspective reveals AlphaFold1's potential as a form of generalized Bayesian updating, rather than a thermodynamic potential. To confirm our probabilistic framework's scope and precision, we analyze a synthetic 2D model in which an angular random walk prior is updated with evidence on distances via probability kinematics, mirroring AlphaFold1's approach. This theoretical contribution connects AlphaFold1 to a broader class of well-justified Bayesian methods, allowing precise quantification, surpassing merely qualitative heuristics based on PMFs. Our contribution is theoretical: we replace AlphaFold1's heuristic analogy with a principled probabilistic framework, tested in a controlled synthetic setting where correctness can be assessed. More broadly, our results point to the considerable promise of probability kinematics for probabilistic deep learning, by allowing the formulation of complex models from a few simpler components.