Contextual fear conditioning is an experimental framework widely used to investigate how aversive experiences affect the valence an animal associates with an environment. While the initial formation of associative context-fear memories is well studied - dependent on plasticity in hippocampus and amygdala - the neural mechanisms underlying their subsequent consolidation remain less understood. Recent evidence suggests that the recall of contextual fear memories shifts from hippocampal-amygdalar to amygdalo-cortical networks as they age. This transition is thought to rely on sleep. In particular, neural replay during hippocampal sharp-wave ripple events seems crucial, though open questions regarding the involved neural interactions remain. Here, we propose a biologically informed neural network model of context-fear learning. It expands the scope of previous models through the addition of a sleep phase. Hippocampal representations of context, formed during wakefulness, are replayed in conjunction with cortical and amygdalar activity patterns to establish long-term fear memories. In addition, valence-coding synapses within the amygdala are subject to homeostatic plasticity overnight, which stabilizes fear associations and regulates the fear circuitry's synaptic density. The model reproduces experimentally observed phenomena, including context-dependent fear renewal and time-dependent increases in fear generalisation. Our model integrates mechanisms of fear learning, systems consolidation and synaptic homeostasis to provide a unified account of how contextual fear memories form and evolve over time. Our framework yields testable predictions about how disruptions in synaptic homeostasis may promote a persistent, fear-sensitized state. Accounting for neural mechanisms that reshape fear memories after their formation is a step towards bridging computational models of fear learning and the mechanisms behind trauma and anxiety disorders.

Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In parallel, machine learning has seen a surge of interest in understanding how dynamical systems perform computations on time-varying input data. Yet, the link between computation-through-dynamics and representational geometry remains poorly understood. Here, we hypothesise that recurrent neural networks (RNNs) perform computations by dynamically warping their representations of task variables. To test this hypothesis, we develop a Riemannian geometric framework that enables the derivation of the manifold topology and geometry of a dynamical system from the manifold of its inputs. By characterising the time-varying geometry of RNNs, we show that dynamic warping is a fundamental feature of their computations.

Learning relies on coordinated synaptic changes in recurrently connected populations of neurons. Therefore, understanding the collective evolution of synaptic connectivity over learning is a key challenge in neuroscience and machine learning. In particular, recent work has shown that the weight matrices of task-trained RNNs are typically low rank, but how this low rank structure unfolds over learning is unknown. To address this, we investigate the rank of the 3-tensor formed by the weight matrices throughout learning. By fitting RNNs of varying rank to large-scale neural recordings during a motor learning task, we find that the inferred weights are low-tensor-rank and therefore evolve over a fixed low-dimensional subspace throughout the entire course of learning. We next validate the observation of low-tensor-rank learning on an RNN trained to solve the same task. Finally, we present a set of mathematical results bounding the matrix and tensor ranks of gradient descent learning dynamics which show that low-tensor-rank weights emerge naturally in RNNs trained to solve low-dimensional tasks. Taken together, our findings provide insight on the evolution of population connectivity over learning in both biological and artificial neural networks, and enable reverse engineering of learning-induced changes in recurrent dynamics from large-scale neural recordings.