Polariton lattices as binarized neuromorphic networks

TL;DR

A novel neuromorphic network architecture based on a lattice of exciton-polariton condensates, intricately interconnected and energized through nonresonant optical pumping, which enables parallel processing and demonstrates the potential to outperform existing polaritonic neuromorphic systems.

Abstract

We introduce a novel neuromorphic network architecture based on a lattice of exciton-polariton condensates, intricately interconnected and energized through non-resonant optical pumping. The network employs a binary framework, where each neuron, facilitated by the spatial coherence of pairwise coupled condensates, performs binary operations. This coherence, emerging from the ballistic propagation of polaritons, ensures efficient, network-wide communication. The binary neuron switching mechanism, driven by the nonlinear repulsion through the excitonic component of polaritons, offers computational efficiency and scalability advantages over continuous weight neural networks. Our network enables parallel processing, enhancing computational speed compared to sequential or pulse-coded binary systems. The system's performance was evaluated using diverse datasets, including the MNIST dataset for image recognition and the Speech Commands dataset for voice recognition tasks. In both scenarios, the proposed system demonstrates the potential to outperform existing polaritonic neuromorphic systems. For image recognition, this is evidenced by an impressive predicted classification accuracy of up to 97.5%. In voice recognition, the system achieved a classification accuracy of about 68\% for the ten-class subset, surpassing the performance of conventional benchmark, the Hidden Markov Model with Gaussian Mixture Model.

Figures (5)

• Figure 1: (a) A diagram depicting the possible experimental implementation of a lattice of pairwise coupled polariton condensates with optically controlled connections. Red cones symbolize input signal beams, and red arrows indicate the connections influenced by these beams. The dyads are numbered with Roman numerals to correspond with the numbering in Fig. \ref{['FIG_ManyDyads']}. (b) A streamlined illustration of the envisaged structure, with gray, red, and blue circles denoting condensate lattice nodes, input, and output optical signals, respectively. Empty (filled) circles correspond to the absence (presence) of the signals. (c--e) Illustration of polariton dyad excitation in a planar microcavity, showing (c) profiles of two non-resonant optical pump spots for dyad excitation, (d,e) the condensates in the dyad with even (OFF) and odd (ON) interference patterns. (f-l) Depiction of the excitation of two adjacent dyads in OFF (f,h,k) and ON (g,j,l) states. Each pair of panels shows polariton density distribution (left) and pump intensity profiles, including the potential barrier (right). Switching between OFF and ON states is achieved using a signal optical pump beam equidistant from the four nodes. Panels (f,g) illustrate no separation between the dyads, (h,j) and (k,l) show the dyads separated by real (orange rectangle) and imaginary (blue rectangle) potential barriers, respectively.
• Figure 2: Depiction of excitation of a lattice of dyads of geometry, schematically shown in Figs. \ref{['FIG_Scheme1']}(a) and \ref{['FIG_Scheme1']}(b), in the absence (a) and in the presence (b) of control signals. The panels show time-integrated spatial distribution of the polariton density. Regions with densities higher than the range covered by the color scale are indicated in white. (c) The profiles of the non-resonant pump spots (main color scheme), the trapping potential profile for isolating dyads (white) and the control beam profiles (blue) for toggling dyads between ON and OFF states. The indices (i) to (xii) enumerate neurons in (a) and (b). (d) The dependence of distinguishability, $\Delta \tilde{I}$, of the OFF and ON signals on the intensities of the pump pulses for condensates in dyads, $P_{10}$, and intensities of signal pulses, $P_{20}$. Values of $\Delta \tilde{I}<0$ are colored in black. Pulse durations are taken as $w_{\tau1} = 5$ ps and $w_{\tau2} = 8$ ps, respectively. Definition of the distinguishability, $\Delta \tilde{I}$, is given in the text. Star markers enumerated from 1 to 17 indicate maximal $\Delta \tilde{I}$ at given $P_{10}$. The red star indicates the parameters used for (a) and (b). (e) Variation of the relative intensity of output signals, $\bar{I}$, in each neuron from (i) to (xii) at the pump intensities $(P_{10},P_{20})$ corresponding to points $j=1,2,... 17$ in (d). In (iv), the dependence should be multiplied by 2.5. Each dot corresponds to a separate numerical experiment, in which positions of the pump pulses, that excite condensates in dyads across the lattice, deviate randomly from their owing positions in the range of distances from $-\delta$ to $+\delta$. Dots of different colors correspond to different deviations $\delta$. Gray lines used as references indicate the average of the minimal relative intensity of the neuron in the ON state and the maximal relative intensity of the neuron in the OFF state in the absence of deviations of the pump pulses.
• Figure 3: Conceptual diagram of a binarized neural network based on a lattice of pairwise coupled polariton condensates. The initial signal originates from a grayscale image from the MNIST dataset, which is binarized and projected onto a $n _{\text{in}} \times n _{\text{in}}$ transformation lattice. This lattice serves as a pattern for the input optical signal. This signal then activates neurons within the hidden layer, generating the resultant optical output signal. Subsequently, the output is processed via a linear classifier (LC).
• Figure 4: Evaluation of the MNIST handwritten digit recognition by the polariton neuromorphic network. (a1,a2) Schematic depicting the conversion of a binarized initial signal lattice of size $n_{0} \times n_{0}$ into an input signal lattice of size $n_{\text{in}} \times n_{\text{in}}$, utilizing randomization and expansion, both without (a1) and with (a2) signal densing. (b) The recognition accuracy in dependence on the size of the input signal lattice $n_{\text{in}}$ (lower scale) or the number of neurons (dyads) in the hidden layer $N_{\text{d}}$ (upper scale). Each data point represents an average from ten numerical experiments, each utilizing different randomization masks. The shaded area reflects the variation in accuracy across these numerical experiments. Vertical lines, serving as guides for the eye, indicate the conditions, where the size of the polariton lattice matches that of the initial images (dashed), and when the number of neurons equals the number of pixels in the initial image (dash-dotted). (c) The recognition accuracy in dependence of the densing degree $s$ of the input signal for square polariton lattice systems of different size $d_{\text{in}}$ with different numbers of neurons in the interaction layer: $d_{\text{in}} = 20$ with 220 neurons (blue), $d_{\text{in}} = 28$ with 420 neurons (green), $d_{\text{in}} = 39$ with 800 neurons (red), $d_{\text{in}} = 75$ with 2890 neurons (violet), and $d_{\text{in}} = 160$ with 12960 neurons (brown). Red markers indicate the maxima of the dependencies. Horizontal dashed lines indicate the accuracy levels for alternative established classification approaches (from bottom to top): the linear software classification of the grayscale (92.5%) and binarized (91.9%) MNIST data set, the binarized polariton network based on a layer of XOR gates NanoLett213715 and the nonlinear polariton network with the software backpropagation training PhysRevApplied18024028.
• Figure 5: Evaluation of the Speech Commands warden2018speechcommandsdatasetlimitedvocabularyspeechcommandsv2 recognition (ten commands) by the polariton neuromorphic network. (a) The recognition accuracy in dependence on the size of the input signal lattice $n_{\text{in}}$ (lower scale) or the number of neurons (dyads) in the hidden layer $N_{\text{d}}$ (upper scale). (c) The recognition accuracy in dependence of the overlap degree $s$ of the input signal for square polariton lattice systems of different size $d_{\text{in}}$ with different numbers of neurons in the interaction layer: $d_{\text{in}} = 20$ with 220 neurons (blue), $d_{\text{in}} = 28$ with 420 neurons (green), $d_{\text{in}} = 39$ with 800 neurons (red), and $d_{\text{in}} = 160$ with 12960 neurons (brown). Red markers indicate the maxima of the dependencies. Horizontal dashed lines indicate the accuracy levels for alternative classification approaches (from bottom to top): the linear software classification of the binarized (49.2%) and non-binarized (61%) MFCC feature matrices, and the HMM-GMM-based classification of the MFCC feature matrices (65.8%).