Spatially-embedded, field-generating recurrent neural networks for multiscale neural computation

Contemporary models of neural computation are largely influenced by the neuron doctrine, treating brain function as arising from pairwise synaptic interactions at the neuronal level while neglecting macroscopic, higher-order variables generated by coordinated neural populations. This reductionist bias leaves the role of endogenous electric fields and other emergent collective dynamics insufficiently understood, preventing a closed account of cross-scale circular causation in neural systems. Evidence from multiple levels of analysis suggests that neural computation is better captured by higher-order structure than by single-unit activity. Whereas neurons exhibit substantial trial-to-trial variability, recurrent neural networks trained on cognitive tasks converge to low-dimensional population manifolds despite heterogeneous connectivity. In parallel, neural electric fields display structural invariances consistent with equivalence across microscopic configurations (i.e., multiple realizability within a degenerate design space), suggesting that higher-order variables such as population dynamics and electric fields may constitute stable computational substrates underlying robust behavior and cognition. Here, we introduce Field-Generating Recurrent Neural Networks (FG-RNNs), spatially embedded, end-to-end differentiable recurrent networks in which neural activity generates a macroscopic electric field that in turn modulates neuronal dynamics, forming a closed-loop, trainable multiscale system. We investigate the extent to which this field-mediated coupling introduces additional computational degrees of freedom that support coordinated dynamics for information encoding, transmission, and retrieval, as well as more complex functions such as compositional representation and long-horizon prediction. To this end, we train FG-RNNs on standard cognitive tasks and analyze how closing the neural-field loop induces emergent spatiotemporal structure, including traveling waves and signatures of cross-frequency coupling. Using information-theoretic and geometric analyses, we quantify when field dynamics carry task-relevant information beyond neural activity alone, providing a framework to assess whether endogenous electric fields constitute functional computational entities in their own right within the neural systems that generate them.