Topological analysis of sharp-wave ripple waveforms reveals input mechanisms behind feature variations.

The reactivation of experience-based neural activity patterns in the hippocampus is crucial for learning and memory. These reactivation patterns and their associated sharp-wave ripples (SWRs) are highly variable. However, this variability is missed by commonly used spectral methods. Here, we use topological and dimensionality reduction techniques to analyze the waveform of ripples recorded at the pyramidal layer of CA1. We show that SWR waveforms distribute along a continuum in a low-dimensional space, which conveys information about the underlying layer-specific synaptic inputs. A decoder trained in this space successfully links individual ripples with their expected sinks and sources, demonstrating how physiological mechanisms shape SWR variability. Furthermore, we found that SWR waveforms segregated differently during wakefulness and sleep before and after a series of cognitive tasks, with striking effects of novelty and learning. Our results thus highlight how the topological analysis of ripple waveforms enables a deeper physiological understanding of SWRs.