REPRESENTATIONAL SIMILARITY IS PRESERVED DURING REPRESENTATIONAL DRIFT IN RANDOM NETWORKS

Neurons in the brain show ongoing changes in their response properties over days, even under stable behavioral conditions - a phenomenon termed representational drift. This drift occurs across multiple brain regions (e.g. Rokni et al., 2007; Ziv et al., 2013; Aschauer et al., 2022). Paradoxically, global neuronal representations remain stable despite ongoing single-neuron variability (Gallego et al., 2020; Noda et al., 2025). Understanding how this stability of representational similarity can coexist with changing neuronal responses is essential for explaining long-term stable perception and behaviour.
We addressed this using binary feedforward network models with random connectivity. Across network instances, population response vectors for each input varied strongly, yet a consistent principle emerged: the similarity between output patterns increases monotonically with input similarity, independent of the particular connectivity. Random networks thus preserve the topological structure of input similarity despite differing population activity patters. The effects of synaptic drift follow directly from this property. We modelled drift by gradually changing the network’s connectivity matrix. Population response vectors changed considerably even for small connectivity perturbations, yet pairwise response similarities remained remarkably stable. This stability is a direct consequence of the topological preservation inherent in random projections.
Together, these results show that random networks provide a general computational framework for understanding how stable representational similarity can coexist with ongoing synaptic and activity-level drift. The preservation of similarity arises inherently from the intrinsic mapping properties of random networks, without requiring fine-tuned connectivity or plasticity mechanisms.