Fig. 2: Multilayer physical neural networks with complex nodes.
From: Neuromorphic overparameterisation and few-shot learning in multilayer physical neural networks
Schematics of a parallel (+) networks, b series (→) networks and c physical neural networks (PNN). Network nodes are recurrent, non-linear nanomagnetic reservoirs with high output dimensionality. In parallel networks, input is fed to multiple nodes independently. In series, the output of one node is virtually fed as input to the next. PNN networks combine series networks in parallel. All interconnections are made virtually, as opposed to physical interconnection. The response of every node is combined offline to create the output of a network. d WM FMR amplitudes at maximum (dark blue) and minimum (light blue) input fields. e Frequency-channel signal correlation (Corr) to previous time steps and nonlinearity (NL). These metrics are used to guide which frequency channel is used as input for the next node in a series network. f Relationship between first reservoir node output metrics, correlation (Corrin) and nonlinearity (NLin), used for interconnections and measured second reservoir metrics, memory-capacity (MCR2) and nonlinearity (NLR2), when the second reservoir (R2) is WM. Lines represent linear fits. Higher metric scores are correlated with higher-scoring reservoir output channels. g Memory capacity (MC) and nonlinearity (NL) of selected single (circles), parallel (triangles) and series networks (squares for series length 2, diamonds for series length 3). Networks have a broad enhancement of metrics versus single arrays. PNN's can take any metric combination. MSE profiles for h Mackey-Glass future prediction, i NARMA transformation and j future prediction of NARMA-7 processed Mackey-Glass for the best single (WM), parallel (MS+WM+PW), 2 series (MS→WM), 3 series (MS→WM→PW) and PNN. Also shown is the performance of a software echo-state network with 100 nodes. MSE profiles are significantly flattened for the PNN. Shading is the standard deviation of the prediction of 10 feature selection trials or 10 echo-state networks. k, l Example predictions for t+9 of the NARMA—7 processed Mackey-Glass signal. Shading represents the residual of the prediction.
