Topic: edge of chaos

The synaptic connection strengths in the brain largely follow a heavy-tailed distribution, whereas most theoretical frameworks assume a Gaussian distribution due to the mathematical complexity involved. Understanding how these heavy-tailed distributions influence neural dynamics is crucial for developing more biologically realistic models and theories that better capture the brain's properties. To bridge this gap, we provide both theoretical and computational insights into the dynamics shaped by heavy-tailed synaptic weights through mathematical derivations and case studies in recurrent neural

Grid cells, which were first discovered in the entorhinal cortex of mammals, are normatively thought of as instrumental in spatial navigation because of their periodic firing characteristics as the animal traverses its surroundings. In recent years, converging bodies of evidence from etiological and teleological investigations of grid cells indicate that they arise under efficient coding schemes, with metabolic, sparsity, and nonnegativity constraints supporting the formation of regular lattices that approximate what has been observed in animal experiments. Here we import the notion of local a

The power of deep neural networks for pattern recognition tasks lies in their universal approximation abilities, and their theoretical expressivity is well-studied. Practical expressivity, however, is known to lag behind theoretical expressivity. Network performance achieved in practice is determined by a set of inductive biases such as architectural constraints (e.g. residual connections). In this work, we introduce weakly coupled residual recurrent networks (WCRNNs) in which the residual connections result in well-defined Lyapunov exponents. This allows for studying properties of their dynam