Critical dynamics in homeostatic memory networks
Authors: Dasgupta Sakyasingha , Herrmann J. Michael 
Published: January 2023

Critical behavior in neural networks characterized by scale-free event distributions and brought about by self-regulatory mechanisms such as short-term synaptic dynamics or homeostatic plasticity, is believed to optimize sensitivity to input and information transfer in the system. Although theoretical predictions of the spike distributions have been confirmed by in-vitro experiments, in-vivo data yield a more complex picture which might be due to the in-homogeneity of the network structure, leakage in currents or massive driving inputs which has so far not been comprehensively covered by analytical or numerical studies.We address these questions by the study of a neural model of memory that allows for storage and retrieval of patterns and for recombining such patterns as needed for search in problem solving. The model features critical dynamics in the neural assembly as a result of the interplay of synaptic depression and facilitation (Levina e.a 2007, 2009). Model simulations show that the prolonged consolidation of memory patterns induces a bias towards the memories which affects the scale-free spike-frequency distribution. However, selective modification of neuronal circuitry in the form of controlled homeostatic regulation in the form of recalibration of the synaptic weights towards the critical value preserved criticality although characterized by fluctuations between learned random patterns, as observed by the dynamics of stored pattern retrieval quality. The resulting spike statistics depends on the assumed coding scheme, but even sparse or orthogonal memory patterns introduce a typical event size which is incompatible with critical dynamics below the maximal memory capacity. Specifically results obtained for de-correlated patterns show an immediate jump from the sub-critical regime to a state of super-criticality in contrast to a more structured wave-like formation in the avalanche dynamics obtained from a general set of random patterns, pointing towards an eventual evolution of the network connectivity and the optimization of the critical regime. Specifically results obtained for de-correlated patterns show an immediate jump from the sub-critical regime to a state of super-criticality in contrast to a more structured wave-like formation in the avalanche dynamics obtained from a general set of random patterns, pointing towards an eventual evolution of the network connectivity and the optimization of the critical regime (Pearlmutter and Houghton, 2009).The combination of memory and ongoing dynamics in the model was chosen for its implications in the context of cognitive aging. Following the paradigm of aging as a multi-criteria optimization process, we posit aging effects as a result of an increasing incompatibility of learning goals. In aging, a shift from fluid intelligence (flexibility to recombine memory content) towards crystalline intelligence (optimal memory organization) appears as a lifelong trend against the general decrease of resources. We show that in young age memory and criticality can be maintained simultaneously by a homeostatic leveling of the synaptic conductances. This balance is lost in the aging brain where the memory attractors cannot be kept sufficiently shallow due to neural and synaptic loss, a reduction of activity while experiencing a growth in memories. The value of the memory organization is therefore protected on the cost of the partial loss of the capability of recombining memory patterns in a task-dependent way.