Design of optical neural networks with component imprecisions

Abstract

For the benefit of designing scalable, fault resistant optical neural networks (ONNs), we investigate the effects architectural designs have on the ONNs' robustness to imprecise components. We train two ONNs -one with a more tunable design (GridNet) and one with better fault tolerance (FFTNet) -to classify handwritten digits. When simulated without any imperfections, GridNet yields a better accuracy (∼ 98%) than FFTNet (∼ 95%). However, under a small amount of error in their photonic components, the more fault tolerant FFTNet overtakes GridNet. We further provide thorough quantitative and qualitative analyses of ONNs' sensitivity to varying levels and types of imprecisions. Our results offer guidelines for the principled design of fault-tolerant ONNs as well as a foundation for further research.Second, rather than optimization towards a specific matrix, the linear operations learned for the classification task is not, a priori, known. As such, our primary figure of merit is the classification accuracy instead of the fidelity between the target unitary matrix and the one learned.Lastly, the aforementioned studies mainly focused on the optimization of the networks after fabrication. The imprecisions introduced generally reduced the expressivity of the network -how well the network can represent arbitrary transformations. Evaluation of this reduction in tunability and mitigating strategies were provided. However, such post-fabrication optimization requires the characterization of every MZI, the number of which scales with the dimension (N ) of the network as N 2 . Protocols for self configuration of imprecise photonic networks have been demonstrated [17,18]. While measurement of MZIs were not necessary in such protocols, each MZI needed to be configured progressively and sequentially. Thus, the same N 2 scaling problem remained. Furthermore, if multiple ONN devices are fabricated, each device, with unique imperfections, has to be optimized separately. The total computational power required, therefore, scales with the number of devices produced.In contrast, we consider the effects of imprecisions introduced after software training of ONNs (Code 1, Ref.[19]), details of which we present in Sec. 3. This pre-fabrication training is more scalable, both in network size and fabrication volume. An ideal ONN (i.e., one with no imprecisions) is trained in software only once and the parameters are transferred to multiple fabricated instances of the network with imprecise components. No subsequent characterization or tuning of devices are necessary. In addition to the benefit of better scalability, fabrication of static MZIs can be made more precise and cost effective compared to re-configurable ones.We evaluate the degradation of ONNs from their ideal performances with increasing imprecision. To understand how such effects can be minimized, we investigate the role that the architectural designs have on ONNs' sensitivity to imprecisions. The results are presented in Sec. 4.1. Specifically, we study the performance of two ONNs i...

Photonic convolutional neural networks using integrated diffractive optics

“…In addition, there will inevitably be fabrication imperfections of the photonic components (star couplers, waveguides, phase shifters, beamsplitters etc.) which break the correspondence between the trained software model and the hardware implementation [28], [56]. Such additional uncertainty introduced by physical implementation becomes non-negligible especially when scaling to a large number of components, hence it is important to evaluate its effects on the photonic CNN performance.…”

“…Previous studies have considered phase noise of width up to 0.02 rad, which is justified for low index contrast platforms [28], [56]. However, for high index contrast platforms like silicon-on-insulator, the phase errors resulting from imperfections could be up to 2 orders of magnitude greater [57] and hence we considered much larger phase errors.…”

Photonic convolutional neural networks using integrated diffractive optics

“…Comparing with the ideal DFT, the greatest deviation in amplitude and phase response occurs at the waveguides furthest from the center. Adopting the fidelity measure as a distance metric [28], gives F = 0.997 for the star coupler described above, where || • || denotes division by the Frobenius norm. Another useful summary metric is the overall transmission…”

“…In addition, there will inevitably be fabrication imperfections of the photonic components (star couplers, waveguides, phase shifters, beam-splitters etc.) which break the correspondence between the trained software model and the hardware implementation [28], [56]. Such additional uncertainty introduced by physical implementation becomes non-negligible especially when scaling to a large number of components, hence it is important to evaluate its effects on the photonic CNN performance.…”

“…amplitude and phase gaussian noise to the star coupler matrices F k and the complex-valued filter masks A k . We avoided adding noise to the fully-connected layers as this has been studied in previous literature along with several methods to ameliorate its effects being suggested [28], [56]. The added phase noise ∆ϕ is zero mean normally distributed with width 2πσ, whereas the amplitude noise is modeled as an additional loss i.e.…”