A robust low-dimensional manifold organizes neuronal responses to sustained input

Understanding how neurons transform synaptic input into spiking output remains a central challenge in neuroscience. Although neuronal responses are often described in high-dimensional terms, it remains unclear to what extent neuronal input-output transformations are governed by lower-dimensional structure. Here, we examine the geometric organization of neuronal input-output relationships using intracellular current-clamp recordings from mouse visual cortex. By representing neuronal responses in a feature space capturing multiple aspects of spike timing and excitability, we analyze how response variability is distributed across dimensions. We find that neuronal responses are organized within a robust low-dimensional manifold that accounts for the majority of observed variance and emerges despite substantial heterogeneity in neuronal responses and stimulation conditions, indicating a general organizational constraint rather than idiosyncratic properties of individual neurons. Importantly, the identified low-dimensional manifold is not a trivial consequence of feature reduction but delineates a constrained response space within which neuronal input-output transformations are expressed. Together, these results reveal a previously underappreciated regularity in neuronal response organization and delineate geometric constraints shaping neuronal input-output mappings under sustained drive, providing a principled foundation for computational models of neuronal function.