The success of connectome mapping now shifts the challenge of understanding the nervous system to the interpretation of neural circuits. Here, we devise a new automated method, LLantia (LLM automated neural circuit inference and analysis), to systematically infer neural circuit function and the role of its component neural cell types. Our approach distills descriptions of cell type function from the literature and, in combination with the connectome, then infers the function for all other cell types, which serves as a basis for subsequent neural circuit function inference. Results are structured hierarchically, with different possible circuit functions organised under multiple possible behavioural and physiological contexts, and each circuit function composed of subcircuit descriptions alongside relevant cell types to facilitate both backtracking to known, published information and support further experimental research. We illustrate our method by inferring cell type function for all cell types of the adult fruit fly brain and for select broader circuits within, and validate our findings, including by cross-checking with literature published after the release date of our analysis.
We recast predictive coding as continuous-time proximal gradient descent applied to a regularized maximum-a-posteriori (MAP) objective. We study first a single-level problem and then a multi-level hierarchy. For the single-level problem, we show that proximal gradient descent is precisely a leaky firing-rate network: the membrane leak, the effective recurrent matrix, the local synaptic drive, and the static nonlinearity all follow from one optimization principle, and the resulting circuit is the one proposed by Rao and Ballard. The prior selects the nonlinearity through its proximal operator, and the likelihood precision sets the gain on the observation. For the hierarchy, we show that a classical variable-splitting relaxation of the deep MAP problem yields hierarchical predictive coding as the interconnection of local and distributed solvers. In probabilistic modeling terms, this relaxation replaces the directed generative chain by an undirected Markov random field whose node potentials are the level-wise priors. Each level then applies its own activation function, namely the proximal operator of its prior.