Exploring Structural Nonlinearity in Binary Polariton-Based Neuromorphic Architectures

TL;DR

It is demonstrated that structural nonlinearity, derived from the network's layout, plays a crucial role in facilitating complex computational tasks, effectively reducing the reliance on the inherent nonlinearity of individual neurons.

Abstract

This study investigates the performance of a binarized neuromorphic network leveraging polariton dyads, optically excited pairs of interfering polariton condensates within a microcavity to function as binary logic gate neurons. Employing numerical simulations, we explore various neuron configurations, both linear (NAND, NOR) and nonlinear (XNOR), to assess their effectiveness in image classification tasks. We demonstrate that structural nonlinearity, derived from the network's layout, plays a crucial role in facilitating complex computational tasks, effectively reducing the reliance on the inherent nonlinearity of individual neurons. Our findings suggest that the network's configuration and the interaction among its elements can emulate the benefits of nonlinearity, thus potentially simplifying the design and manufacturing of neuromorphic systems and enhancing their scalability. This shift in focus from individual neuron properties to network architecture could lead to significant advancements in the efficiency and applicability of neuromorphic computing.

Figures (6)

• Figure 1: (a) Schematic of the excitation and control of a polariton dyad within an optical microcavity, using localized non-resonant laser pumping. Orange cones represent the laser pump for excitation of the condensates, while blue cones indicate the control signals. (b,c) Schematic density distribution of polaritons within the dyad in the absence (b) and presence (c) of the control signals. The positions of the excitation and control laser beams are indicated by gray solid and blue dashed circles, respectively. (d) Example of the effective potential geometry, along with pump and control signal beams for exciting a lattice of polariton dyads.
• Figure 2: (a) Schematic representation of an assembly of four binary polariton neurons displaying various input signal combinations, from top to bottom: '1 and 1', '0 and 1', '0 and 0' and '1 and 0'. The primary color scheme illustrates the profiles of non-resonant optical pumping of condensates within the dyads. The potential trap profile, isolating individual polaritonic dyads, is depicted in white. Control laser beams, acting as input signals, are shown in blue. Panels (b), (c), and (d) show spatial distribution of polaritons in the presence of control signals within neurons configured to function based on NOR, NAND, and XNOR gates, respectively. White dashed boxes serve as guides for the eye to outline the area of individual polariton neurons. The output value for each neuron, reflects whether there is a signal present in the neuron's center (1) or not (0). A white bar at the bottom of the panels corresponds to a scale of $10\, \mu\text{m}$.
• Figure 3: (a) The XOR problem in the input space: the two classes of outputs, 0 (blue) and 1 (red), cannot be separated by a single straight line. (b,c) Schematics of two simple neural networks with a hidden layer composed of three neurons, considered for solving the XOR problem. (d,e) Schematics of the hidden layer with configurations of input signals as per (b) and (c), respectively. The input signals $X_1$ and $X_2$ are denoted in maroon and green, respectively. (f,g) The XOR problem in the feature space of the hidden layers composed of three neurons functioning as NOR and NAND gates, respectively. The solution in (f) is effective for both configurations as in (b) and (c), while (g) works solely for the configuration in (b). The green plane separates the classes 0 and 1. Dashed lines serve as guides for the eye.
• Figure 4: (a--d) Schematic depiction of a binary neural network configured with a lattice of pairwise coupled polariton condensates. A binarized $28\times28$ pixel image from the MNIST dataset (a) is mapped onto a transformation lattice of dimensions $n_{\text{in}} \times n_{\text{in}}$ (b). This lattice serves as the template for the input optical signal. Neurons within the hidden layer are activated by this input (c), generating the output signal. This output is subsequently processed through a linear classifier LC (d). As an example, neurons in the diagram are shown functioning as XNOR gates. (e) Schematic representation of the operation of artificial neuronal assemblies composed of NAND, NOR and XNOR gates is illustrated in Fig. \ref{['FIG_Gates']}(b--d).
• Figure 5: Dependence of the accuracy of MNIST handwritten digit recognition on the size of the input lattice $n_{\text{in}}$ (lower scale) or the number of neurons $N_{\text{d}}$ (upper scale), for neurons in the hidden layer functioning as XNOR (blue), NAND (red), and NOR (green) gates. Each data point is the average outcome of ten numerical experiments, each employing distinct randomization masks. The shaded area indicates the range of accuracy variation observed across these numerical experiments. Vertical magenta lines mark specific conditions: dash-dotted line where the size of the polariton lattice corresponds to that of the initial images, and dashed line where the number of neurons matches the number of pixels in the initial image. Horizontal dashed lines represent the accuracy levels of various established classification approaches: linear software classification for the grayscale (92.5%) and the binarized (91.9%) MNIST dataset, a binarized polariton network utilizing XOR gates NanoLett213715, and a nonlinear polariton network trained with software-based backpropagation PhysRevApplied18024028.