Time Will Give You the Answer: Controllable Factorial Permutations in Spiking Neural Networks

The brain works through spiking neural networks. In this paper, we investigate the relative order of the first spikes across neurons. The relative order of first spikes across neurons creates a rapidly growing discrete state space. The full first-spike order of $M$ neurons can represent $M!$ discrete states. For $M=10$, this gives 3.6 million possible orders, and the number grows factorially with $M$. We show the ordering space is controllable and trainable. By updating input current or through intrinsic parameters alone—membrane time constant, firing threshold, and membrane resistance—we can reach all permutations. We also design an optimizer that moves the neurons into any target order by updating each neuron's membrane time constant. We picked a 30-class dataset. In a 6-spiking-neuron system, we assign each dataset class an ordered pair of neurons. For example, $(A,B)$ means we want neuron A to fire first and neuron B to fire second; neurons firing after the second are ignored. We reach an accuracy of 27.7% $\pm$ 1.03 across 5 different seeds, compared to 3.33% random chance.