Fig. 6.

Olfactory circuit augmented with a genetically specified pathway. (A) Schematic of the two-pathway model. For the top part of the circuit, the weights ${\mathbf{J}}_p$ and ${\mathit{w}}_p$ are hard wired; for the bottom part, the weights ${\mathbf{J}}_s$ are randomly connected and ${\mathit{w}}_s$ are learned with adaptive SGD. (B–D) Optimal layer size of the projection neurons-to-Kenyon cells pathway ${\mathit{w}}_s·g({\mathbf{J}}_s\mathit{x})$ under different model settings. (B) Low-bit synapses were achieved by adding Gaussian noise to ${\mathbf{J}}_p$ and ${\mathit{w}}_p$. (C) Low-bit synapses were achieved by discretizing ${\mathbf{J}}_p$ and ${\mathit{w}}_p$. (D) Low-bit synapses were achieved by adding noise to ${\mathbf{J}}_p$ and ${\mathit{w}}_p$ as in B, but ${\mathit{w}}_p$ was additionally learned from training samples using SGD (SI Appendix, Eq. S145). In B–D, the teacher network had a hidden-layer size of 500 and a ReLU nonlinearity, and we used ${\sigma }_t^2=0.01$ and $N=10L_x^2$ trials. For s_b = 2 bits we used $G=2,000$, while for s_b = 4 bits we used $G=4,000$. For s_b = 0 bits, we simply removed the hard-wired pathway. The width of the hard-wired intermediate layer, L_p, was found from Eq. 18: $L_p=G/s_b(L_x+1)$, rounded up to an integer. See SI Appendix, sections 6 and 7.5 for details.