# Two-factor synaptic consolidation reconciles robustness with pruning and homeostatic scaling

## TL;DR

This paper introduces a new model explaining how memories are preserved in the brain by combining synaptic pruning and homeostatic scaling during sleep.

## Contribution

A novel two-factor synaptic model that unifies memory consolidation mechanisms with robustness to noise and experimental observations.

## Key findings

- The model reproduces experimental signs of synaptic pruning and memory formation.
- It predicts sublinear scaling of synaptic noise with synaptic strength, supported by data.
- The model outperforms previous ones in replicating developmental trends in neural connectivity.

## Abstract

While most experiences are forgotten after only a few days, some memories can last an entire lifetime. The neurophysiological mechanisms that enable such memory preservation are poorly understood but are believed to be active during sleep, when neurons replay past events, prune their synapses, and regulate their firing. We provide a unified mathematical explanation for these processes in the form of an algorithm that stores memories in neural networks with maximal noise robustness. By representing each synapse as a product of two factors, our model automatically removes and tunes appropriate connections, while homeostatically scaling each neuron’s input. Our model reproduces experimental signs of activity-dependent rewiring and long-term memory formation in synaptic, cortical, and psychological data, and offers testable predictions.

Memory consolidation refers to a process of engram reorganization and stabilization that is thought to occur primarily during sleep through a combination of neural replay, homeostatic plasticity, synaptic maturation, and pruning. From a computational perspective, however, this process remains puzzling, as it is unclear how to incorporate the underlying mechanisms into a common mathematical model of learning and memory. Here, we propose a solution by deriving a self-supervised consolidation model that uses replay and two-factor synapses to encode memories in neural networks in a way that maximizes the robustness of cued recall with respect to intrinsic synaptic noise. We show that the dynamics of this optimization make the connectivity sparse and offer a unified account of several experimentally observed signs of consolidation, such as multiplicative homeostatic scaling, task-driven synaptic pruning, increased neural stimulus selectivity, and preferential strengthening of weak memories. The model also reproduces developmental trends in connectivity and stimulus selectivity better than previous models. Finally, it predicts that intrinsic synaptic noise fluctuations should scale sublinearly with synaptic strength; we find support for this in a meta-analysis of published synaptic imaging datasets.