Clockless Computation

Biological neural systems operate asynchronously and lack a global clock. Their components are relatively slow, noisy, and imprecise. Yet, despite these limitations, such systems exhibit remarkable memory capacity and coordinate complex behaviors with high temporal precision. A central challenge for autonomous networks, which is critical for sustained memory and continuous information generation, arises from the absence of an external regulatory drive. In the absence of a global clock, local timing perturbations can accumulate and compound, ultimately disrupting the integrity of information within the network dynamics. This thesis demonstrates that network dynamics can be made robust against such degradation without reliance on a global clock. Extensive numerical simulations indicate that, within appropriate parameter ranges, virtually any random target spike train (or firing score) can be robustly memorized and autonomously reproduced across the network. Upon proper initialization, the network preserves precise relative timing of (almost) all spikes across all neurons, even with significant perturbations, acting globally as an error-correcting system. Empirical results further indicate that the maximum duration of memorizable content scales linearly with the number of inputs per neuron, provided these inputs are sufficiently diverse. When parallel connections exist between the same pair of neurons, this diversity can be achieved entirely through heterogeneous transmission delays. Consequently, even a single-neuron network with delayed self-connections can autonomously memorize and reproduce a complex spike train. In all experiments, synaptic weights are computed offline by solving an ensemble of convex optimization problems that enforce geometric constraints on each neuron's internal state. Specifically, the optimization ensures that the neuron's potential remains well below the firing threshold during silent periods and intersects the threshold with a steep slop