Fig. 2: Digit recognition using a scattering neuromorphic system with a layered structure.
From: Fully nonlinear neuromorphic computing with linear wave scattering
a, Scattering network used for digit recognition consisting of two or three fully connected layers with N1 = 128, N3 = 10 and either without a hidden layer or with N2 ∈ {20, 30, 60, 80}. We consider equal decay rates κ, set the intrinsic decay to zero (κ′ = 0) at the probe sites and start from J/κ = 2 with an added random disorder. The input consisting of 64 grey-scale pixel values is encoded in the detuning of the first layer to which we initially add a trainable offset. A vector of pixel values serves as the input. We choose to detune the background to xj = 5κ and make the foreground—the numerals—resonant, that is, xj = 0. The inset illustrates the nonlinear effect of the first layer, showing the real and imaginary parts of \({[{{{{\mathcal{G}}}}}_{1}(0)]}_{j,\;j}\) (equation (13)). The response to a probe signal at the third layer constitutes the output vector. The index ℓ of maximal yℓ = ImSℓ,ℓ constitutes the class. b, Evolution of the test accuracy during training for different architectures (left, early times; right, full training): without the hidden layer or with N2 = {20, 30, 60, 80}. We compare this with a linear classifier, ANN and CNN. During one epoch, each image in the training set is shown to the network once in mini-batches of 200 randomly chosen images; the shown test accuracy is evaluated on the entire test set. Increasing the size of the hidden layer improves both convergence speed and best accuracy. c, Confusion matrix corresponding to the best result with N2 = 80 after 2,922 epochs. d, Convergence and training progress for selected input pictures. One iteration corresponds to one mini-batch. The scattering matrix element with the largest imaginary part indicates the class. In most cases, the training rapidly converges towards the correct classification results. Digits with a similar appearance, however, are frequently mistaken for the other, such as the digits 4 and 9, and only converge relatively late during training.
