Neuromorphic Computing via Fission-based Broadband Frequency Generation

Abstract

The performance limitations of traditional computer architectures have led to the rise of brain-inspired hardware, with optical solutions gaining popularity due to the energy efficiency, high speed, and scalability of linear operations. However, the use of optics to emulate the synaptic activity of neurons has remained a challenge since the integration of nonlinear nodes is power-hungry and, thus, hard to scale. Neuromorphic wave computing offers a new paradigm for energy-efficient information processing, building upon transient and passively nonlinear interactions between optical modes in a waveguide. Here, an implementation of this concept is presented using broadband frequency conversion by coherent higher-order soliton fission in a single-mode fiber. It is shown that phase encoding on femtosecond pulses at the input, alongside frequency selection and weighting at the system output, makes transient spectro-temporal system states interpretable and allows for the energy-efficient emulation of various digital neural networks. The experiments in a compact, fully fiber-integrated setup substantiate an anticipated enhancement in computational performance with increasing system nonlinearity. The findings suggest that broadband frequency generation, accessible on-chip and in-fiber with off-the-shelf components, may challenge the traditional approach to node-based brain-inspired hardware design, ultimately leading to energy-efficient, scalable, and dependable computing with minimal optical hardware requirements.

Keywords: artificial neural networks; higher-order soliton fissions; neuromorphic computing; nonlinear fiber optics; optics and photonics.

Figure 1

Operational principle of neuromorphic frequency‐domain wave computing. A) Example of a feed‐forward neural network architecture. Each hidden layer can be decomposed into a linear sublayer (green) performing node‐wise linear weighting and summation and a nonlinear activation layer (orange). B) Illustration of the heuristic resemblance between neural networks and fiber‐based neuromorphic wave computing. Information is encoded in the spectral phase of a femtosecond pulse before being launched into a highly nonlinear optical fiber. Nonlinear pulse propagation can be modeled as a concatenation of linear dispersive shifts $\mathcal{D}$ and third‐order optical nonlinear transformations $\mathcal{N}$ (i.e., the Kerr effect), leading to the mixing and generation of optical frequencies. The broadband system output is then measured and weighted to provide a task‐specific computational result. C) System state representation illustrating the information flow in a transient optical network while propagating in the spectro‐temporal space. An input field is represented as a finite distribution of weights on specific transient nodes, i.e., transform‐limited field entities in time and frequency. Continuously alternating linear dispersion and nonlinearity will cause energy redistribution along time and frequency, respectively, creating highly input‐specific information trajectories. In the visualization, the field amplitudes per node are coded in both the size and color of the shape for better visibility. D) Schematic setup of our experimental realization (see Figure S1, Supporting Information for more details). The system is trained offline by frequency selection and weighting at the system read‐out.

Figure 2

Coherent soliton fission as a computing resource. A–C) System sensitivity analysis. A) A single‐phase window (called bit; in blue) is shifted through the spectrum of a pulse input to a nonlinear fiber (in gray). B,C) Output spectra of a 100 m long nonlinear fiber measured for 72 different spectral bit‐positions. The variations in the spectrum demonstrate the phase sensitivity of the nonlinear broadening process for B) low phase magnitude (π/10) and C) high phase magnitude (π) (see also Figure S3, Supporting Information). The purple and blue lines indicate the maximum and minimum values per spectral read‐out (called bin), respectively. D) Schematics for encoding the nonlinear 2‐bit parity (XOR) problem in the spectral phase of a femtosecond pulse. E–G) Simulated spectral evolutions of the femtosecond pulse over 50 m of commercial highly nonlinear fiber for each input encoding in (D). H) Intensity spectra measured at the fiber output for each input in (D). The unique information trajectories in (E–G) yield easily separable intensity features in the output spectra. This allows the XOR problem to be solved by measuring the power in a single wavelength band (see table inset) indicated by the grey area in (H).

Figure 3

System training and solving the n‐bit parity problem. A) Flowchart of the digital processing layers to interpret the system readout. The training is performed offline using bin selection and linear regression. A simple search algorithm iterates through different frequency bin combinations (see Experimental Section). For each combination, linear regression is used to predict the label (or value) of an inference task. The prediction error was estimated through cross‐validation of subsets of the training data. The best‐performing combination of bins (i.e., lowest loss) defines an inference‐ready system configuration. B) Experimentally measured operation fidelity associated with the n‐bit parity problem for increasing bit length and system nonlinearity. The latter is given in units of soliton number N (Experimental Section). The best performance is achieved at higher system nonlinearity. C) Experimentally measured operation fidelity for a 5‐bit parity problem versus increasing the number of readout bins for low (left panel) and high (right panel) system nonlinearity. Higher system nonlinearity requires fewer readout bins for optimal performance since a higher degree of frequency mixing leads to a larger set of possible data projections. For instance, 52 bins are required at low nonlinearity to achieve 85% inference accuracy (see red line in C), while only 10 bins are needed at high nonlinearity.

Figure 4

Task‐dependent benchmarks commonly used to evaluate neural networks. A–D) Digital artificial neural network primitives for the A) IRIS, B) WINE, C) Abalone, and D) MNIST tasks, featuring equal performance as our experimental fiber‐based processor. E–H) Operation accuracy of experimentally obtained data for the encoded test sets. The system was operated under the same conditions for all sets. I–L) Spectral position (in nanometers) of the readout bins that yield the best operational performance at 0.5 nm bin width.

Figure 5

COVID‐19 diagnosis from digital speech audio recordings. A) Simplified scheme for feature extraction based on principle component analysis of processed audio signals. The same selected features have been used as input to both digital and optical classifiers for direct comparison. B) The test results for the digital support vector machine (UAR = 0.631) and C) The test results of the experimental fiber‐based ELM implementation (UAR = 0.7133) show a notable performance increase of our approach compared to a digital state‐of‐the‐art technique.