QAMNet: Fast and Efficient Optical QAM Neural Networks

TL;DR

This work introduces QAMNet, an optical neural network hardware and architecture with superior energy consumption to existing ONNs, that fully utilizes the complex nature of the amplitude of light with QAM and accelerates complex-valued deep neural networks with accuracies indistinguishable from digital hardware, based on physics-based simulations.

Abstract

The energy consumption of neural network inference has become a topic of paramount importance with the growing success and adoption of deep neural networks. Analog optical neural networks (ONNs) can reduce the energy of matrix-vector multiplication in neural network inference below that of digital electronics. However, realizing this promise remains challenging due to digital-to-analog conversion: even at low bit precisions $b$, encoding the $2^b$ levels of digital weights and inputs into the analog domain requires specialized and power-hungry electronics. Faced with similar challenges, the field of telecommunications has developed the complex-valued Quadrature-Amplitude Modulation (QAM), the workhorse modulation format for decades. QAM maximally exploits the complex amplitude to provide a quadratic $O(N^2) \to O(N)$ energy saving over intensity-only modulation. Inspired by this advantage, this work introduces QAMNet, an optical neural network hardware and architecture with superior energy consumption to existing ONNs, that fully utilizes the complex nature of the amplitude of light with QAM. When implemented with conventional telecommunications equipment, we show that QAMNet accelerates complex-valued deep neural networks with accuracies indistinguishable from digital hardware, based on physics-based simulations. Compared to standard ONNs, we find that QAMNet ONNs: (1) attain higher accuracy above moderate levels of total bit precision, (2) are more accurate above low energy budgets, and (3) are an optimal choice when hardware bit precision is limited.

Figures (7)

• Figure 1: Taxonomy of DNN inference hardware, highlighting the advantages of Quadrature-Amplitude Modulation (QAM) optical neural networks and their relationship to other analog and optical deep neural network accelerator approaches. QAMNet is a QAM-based photoelectric multiplication scheme that provides linear scaling of energy with respect to levels of precision.
• Figure 2: Illustration of QAMNet's algebra, circuit, and hardware. a. Algebra of complex-valued multi-layer perceptron neural network inference. A linear layer $i$ with input dimension $d_i$ and output dimension $d_{i+1}$ is parameterized by weight matrices $W^{(i)}\in\mathbb C^{d_{i+1}\times d_{i}}$ and a nonlinear function $f:\mathbb C^{d_{i+1}}\to\mathbb C^{d_{i+1}}$. Layer $i$ shows detail of the inner products computed during inference. b. Detail of the learnable encoding that maps real-valued data to complex-valued data of the same dimension. c. Detail of the computation of a single layer. Complex-valued weights and inputs represented as symbols in a QAM constellation. d. Detail of the I/Q photoelectric multiplier computing a complex-valued inner product. e. Components of the I/Q photoelectric multiplier that are found in standard QAM demodulators, with the only difference being the replacement of the local oscillator with a I/Q modulator for weights. f. Detail of each I/Q QAM modulator, highlighting how two amplitude modulators (i.e. implemented as Mach-Zehnder modulators) are used off-phase to perform phase and amplitude modulation. g. Detail of the mixer found in standard QAM demodulators, implemented by a beamsplitter (depicted as an evanescent coupler) and balanced photodetectors which collect the difference current on a capacitor.
• Figure 3: Accuracy degradation across hardware Signal to Noise Ratio (SNR) and QAM side (number of quantization levels per QAM axis) for the Deep Signal Network tu2020complex architecture. Outlined region indicates combinations with $\le5\%$ drop in accuracy, where the digitally trained accuracy was 68%.
• Figure 4: Accuracy comparisons between QAMNet and level equivalent, hardware equivalent, and energy equivalent 1D ONNs on the MNIST dataset. Equivalence definitions found in Table \ref{['tab:equivalences']}. The shaded blue region highlights the regimes of advantage of QAMNet over the equivalent 1D ONN, achieving up to $9.7\%$ greater accuracy.
• Figure 5: QAM ONNs vs. Level Equivalent 1D ONNs, for different numbers of total levels (QAM constellation points). For an equivalent number of total levels, the QAM ONN uses quadratically less energy than the 1D ONN.