Computing threshold functions using dendrites
This work addresses a bottleneck in neural modeling for computational neuroscience and neuromorphic engineering, offering a potential pathway for networks with binary synapses.
The paper tackles the problem of computing threshold functions with high-precision synaptic weights by introducing a non-linear threshold unit (nLTU) that models dendritic saturation. It shows that nLTU can compute all threshold functions with smaller weight precision and more functions with single synapses compared to linear threshold units.
Neurons, modeled as linear threshold unit (LTU), can in theory compute all thresh- old functions. In practice, however, some of these functions require synaptic weights of arbitrary large precision. We show here that dendrites can alleviate this requirement. We introduce here the non-Linear Threshold Unit (nLTU) that integrates synaptic input sub-linearly within distinct subunits to take into account local saturation in dendrites. We systematically search parameter space of the nTLU and TLU to compare them. Firstly, this shows that the nLTU can compute all threshold functions with smaller precision weights than the LTU. Secondly, we show that a nLTU can compute significantly more functions than a LTU when an input can only make a single synapse. This work paves the way for a new generation of network made of nLTU with binary synapses.