Analog dual classifier via a time-modulated neuromorphic metasurface

TL;DR

This work addresses the limitation of wave-based physical computing systems that are typically restricted to a single task by introducing a dual-classifier time-modulated neuromorphic metasurface. The system uses two time-modulated metasurface layers to generate multiple frequency channels via harmonics $\omega^-,\omega,\omega^+$ from carrier excitations, enabling two independent neural-network-like classification tasks to run in parallel with readouts at separate label segments. An analytical framework based on transfer and scattering matrices for time-modulated unit cells and waveguides underpins the design, with training that identifies layer parameters $m$, $k_0$, $\phi_m$ and $m'$, $k'_0$, $\phi'_m$ to realize the two tasks. Demonstrations on gesture (four-class) and MNIST digit recognition show accuracies of $93\%$ and $87\%$, highlighting significant potential for compact, energy-efficient, wave-based multifunctional neuromorphic systems. The approach is scalable to more channels and broadly applicable across elastic, acoustic, and optical domains, offering a path to reduced footprint and fabrication complexity in physical intelligent systems.

Abstract

A neuromorphic metasurface embodies mechanical intelligence by realizing physical neural architectures. It exploits guided wave scattering to conduct computations in an analog manner. Through multiple tuned waveguides, the neuromorphic system recognizes the features of an input signal and self-identifies its classification label. The computational input is introduced to the system through mechanical excitations at one edge, generating elastic waves that traverse multiple layers of resonant metasurfaces. These metasurfaces possess a tunable phase akin to trainable parameters in deep learning algorithms. While early efforts have been promising, the well-established constraints on wave propagation in finite media limit such systems to single-task realizations. In this work, we devise a dual classifier neuromorphic metasurface and demonstrate its effectiveness in carrying out two completely independent classification problems that are concurrently carried out in parallel, thus addressing a major bottleneck in physical computing systems. Parallelization is achieved through smart multiplexing of the carrier computational frequency, enabled by prescribed temporal modulations of the embedded waveguides. The presented theory and results pave the way for new paradigms in wave-based computing systems, which have been elusive thus far.

Figures (6)

• Figure 1: (a) Popular classification problems. Binary classifiers distinguish between two classes: multiclass classifiers categorize inputs into one of several classes; and multilabel classifiers, which can assign multiple labels to a single input. (b) A schematic of the proposed dual classifier neuromorphic metasurface. The left panel shows a system consisting of two time-modulated metasurfaces, capable of independently classifying samples from three distinct datasets. The right panel illustrates the system's ability to function as three separate multiclass classifiers, while being structurally a single neuromorphic metasurface system.
• Figure 2: (a) A single-task neuromorphic metasurface with two metasurface layers comprising waveguides of unmodulated unit cells, each with a lumped mass $m$ and a constant time-invariant stiffness $k_0$. (b) A multi-task neuromorphic metasurface with two metasurface layers comprising waveguides of time-modulated unit cells, each with a lumped mass $m$ and a time-varying stiffness $k(t) = k_{0} (1+\delta_m \cos{(\omega_m t + \phi_m)})$. The left side of the system is excited with two sets of features at distinct frequencies, while the right side acts as a detection plane, indicating the outcomes of the different computations carried out via wave energy focusing at different frequencies corresponding to the different tasks.
• Figure 3: Examples of solid elastoacoustic unit cells, which can be represented by a generalizable spring-mass model lee2018masslee2023modezuo2017mathematicalli2015metascreen. The corresponding unit cell's effective inertial and elastic indicators $R_m$ and $R_k$ can be derived directly from the unit cell’s constitutive parameters, as illustrated in the bottom-right example, where the unit cell shown at the bottom left is expanded into an array of six unit cells, and the equivalent lumped model is utilized to generate $R_m$ and $R_k$moghaddaszadeh2024mechanical. Once the pertinent dynamics are mapped from the geometric features of the solid cells, the framework derived in Sec. \ref{['time_modulated_neuromorphic_metasurface']} can be applied to any of the above configurations.
• Figure 4: Multifrequency transmission of time-modulated waveguides. (a) General design of a unit cell, the building block of the metasurface, where ${\hat{u}_i^{[\omega + \alpha \omega_m]}}$ and ${\hat{f}_i^{[\omega + \alpha \omega_m]}}$ represent displacement and forcing at a frequency $\omega + \alpha \omega_m$. (b) Frequency stability analysis of a select time-modulated unit cell performed at various modulation amplitudes (top) and modulation frequencies (bottom), showing that a careful selection of the operating and modulation frequencies is required to ensure the stability of the harmonics and avoid spectral leakage to neighboring frequencies. Here, FFT denotes fast Fourier transform. (c) A single waveguide made of an array of $n$ unit cells, where ${A_{1,2}^{[\omega + \alpha \omega_m]}}$ and ${B_{1,2}^{[\omega + \alpha \omega_m]}}$ denote the amplitudes of forward and backward propagating waves on either side of the waveguide for the frequency channel $\omega+\alpha \omega_m$. $a$ is the lattice constant and $\alpha$ can be $-1$, $0$, or $1$. (d) Transmission amplitude $|\bar{T}|$ and phase $\phi$ of a waveguide made of $n=6$ unmodulated cells with stiffness $k(t) = k_0$ for an incident wave with a frequency $\omega=150$ kHz. Here, $R_m$ and $R_k$ are the effective mass and stiffness ratios as defined in the text. (e) Transmission amplitude $|\bar{T}|$ and phase $\phi$ for the three transmitted harmonics from a waveguide made of $n=6$ time-modulated cells with the following modulation parameters: $\delta = 0.15$, $\omega_m = 7$ kHz, $\phi_m = -\pi/2$ and $\pi/2$, and stiffness $k(t) = k_{0} (1+\delta_m \cos{(\omega_m t + \phi_m)})$, generated from an incident wave with frequency $\omega=150$ kHz. Bordered regions highlight the design space where ${0.8<\bar{T}^{[\omega]}<1}$ and ${0.1<|\bar{T}^{[\omega^{\pm}]}|<0.3}$, ensuring acceptable transmission while maintaining $2\pi$ phase tunability.
• Figure 5: (a) The proposed time-modulated neuromorphic metasurface is composed of an input layer (axis $1$), two time-modulated metasurface layers (spanning axes $2 \rightarrow 3$ and $4 \rightarrow 5$) , and a detection plane (axis $6$). Each two consecutive layers are displaced by a distance $d$. The metasurface layers are comprised of the waveguides illustrated in Fig. \ref{['Fig4']}c. The frequency components propagating in each segment, including the excitation frequency and all harmonics generated by the time-modulated metasurfaces, are listed. (b) Parallel classification logic diagrams. The first neural network channel corresponding to the frequency path $\omega_1 \rightarrow \omega_1 \rightarrow \omega_1 + \omega^{\prime}_m$ is shown on the left with ${\phi^{[\omega_1]}_{2\rightarrow3,j}}$ and ${\phi^{[\omega_1 + \omega^{\prime}_m]}_{4\rightarrow5,h}}$ as trainable parameters, while the second neural network channel corresponding to the frequency path $\omega_2 \rightarrow \omega_2 + \omega_m \rightarrow \omega_2 + \omega_m$ is shown on the right with ${\phi^{[\omega_2 + \omega_m]}_{2\rightarrow3,j}}$ and ${\phi^{[\omega_2 + \omega_m]}_{4\rightarrow5,h}}$ as trainable parameters.