Abstract
Nonlinear activation is a crucial building block of most machine-learning systems. However, unlike in the digital electrical domain, applying a saturating nonlinear function in a neural network in the analog optical domain is not as easy, especially in integrated systems. In this paper, we first investigate in detail the photodetector nonlinearity in two main readout schemes: electrical readout and optical readout. On a 3-bit-delayed XOR task, we show that optical readout trained with backpropagation gives the best performance. Furthermore, we propose an additional saturating nonlinearity coming from a deliberately non-ideal voltage amplifier after the detector. Compared to an all-optical nonlinearity, these two kinds of nonlinearities are extremely easy to obtain at no additional cost, since photodiodes and voltage amplifiers are present in any system. Moreover, not having to design ideal linear amplifiers could relax their design requirements. We show through simulation that for long-distance nonlinear fiber distortion compensation, using only the photodiode nonlinearity in an optical readout delivers BER improvements over three orders of magnitude. Combined with the amplifier saturation nonlinearity, we obtain another three orders of magnitude improvement of the BER.
Highlights
Nonlinear activation is a crucial building block of most machine-learning systems
We propose to use another accessible nonlinearity, namely that of a deliberately non-ideal voltage amplifier that is part of the transimpedance amplifier (TIA) module present in any readout system
In “Reservoir computing architecture” section, we introduce the reservoir computing system we used for the simulations in the paper
Summary
The optical input to the readout system can be the output of the final layer of any photonic neuromorphic architecture, as long as that signal is coherent. In a so-called electrical readout scheme (Fig. 2 left), optical detection is first performed for each individual input node This is followed by weighting in the (analog or digital). X is the matrix containing the input time traces for each node, Yis the desired target signal, and Wout are the output weights that need to be found so as to minimise the difference between Wout X and Y This can be achieved in one step using the Moore-Penrose generalized matrix inverse[24], where a regularization parameter can be taken into consideration: Wout = (XT X + I)−1XT Y. The eye diagram of the optical readout system trained with backpropagation is more open both in the vertical and the horizontal direction (Fig. 5c), with a BER of 10−10 This again proves that the optical readout system can utilize the nonlinearity in the photodetector better and provide enough computational capability to compensate for the nonlinear distortion. This analog optical dispersion compensation has the potential to reduce the requirements on the DSP after the detection
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