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Cross-platform frequency-domain physical neural networks with identical models and parameters

Zichen Xi, Jun Ji, Liyang Jin, Hsuan-Hao Lu, Wenjie Xiong, Linbo Shao

arXiv:2610.01059v1physics.opticseess.SPphysics.app-ph

TL;DR

Existing frequency-domain PNN implementations often depend on hardware-specific models or training, limiting direct transfer of pretrained networks across physical platforms. This paper demonstrates a shared second-order spectral-convolution PNN using identical pretrained parameters across optical, electronic, and phononic systems. The three implementations achieve 97.6%, 98.4%, and 98.2% inference accuracy on a unified four-class task.

  • Problem

    Frequency-domain PNN implementations often incorporate hardware-specific physical responses in their models or training, so transferring pretrained networks across platforms can require retraining or parameter fine-tuning.

    Source: Introduction · p. 2

  • Method

    The authors implement a two-layer frequency-domain PNN using a common second-order spectral-convolution model and identical pretrained parameters across optical, electronic, and phononic platforms.

    Source: Introduction · p. 2, Frequency-domain neural network… · pp. 2–3

  • Results

    97.6% optical, 98.4% electronic, and 98.2% phononic inference accuracies were achieved on the four-class Fashion-MNIST task.

    Source: Introduction · p. 2

  • Takeaways & Limitations

    The results establish a basis for deploying pretrained neural networks across different analogue physical systems without platform-specific fine-tuning.

    Source: Conclusion and outlook · p. 9

    Frequency encoding requires the assigned frequency bands to be separated sufficiently to avoid overlap between encoded input bins and second-order generated bins.

    Source: Encoding and decoding methods of… · p. 14

Abstract

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Frequency-domain physical neural networks (PNNs) have emerged as a promising analog computing paradigm, achieving a reduced number of devices, enhanced robustness, and high inference accuracy. However, existing demonstrations across various physical domains, such as optics, acoustics, and electronics, are mostly specific to the target devices or platforms, usually requiring hardware-dependent models and post-fabrication parameter tuning. Here, we demonstrate cross-platform implementations of frequency-domain PNN across different wave-based computing platforms using identical, pre-trained parameters. By exploiting shared second-order nonlinear processes, the PNN model is implemented on optical, microwave, and acoustic-wave platforms without the need of fine tuning the parameters. Evaluated on a unified four-class classification task, the frequency-domain PNN achieves high inference accuracies of 97.6% in optics, 98.4% in electronics, and 98.2% in mechanics. Further, we systematically compare related performance metrics across these three distinct physical domains, paving the way to a universal neural network across different physical platforms.

Introduction

Frequency-domain PNNs offer reconfigurable wave-based computing, but platform-specific physical responses and training often prevent direct deployment of pretrained networks across hardware. The paper presents a second-order spectral-convolution framework that reuses identical pretrained parameters across optical, electronic, and phononic implementations.

Introduction

  • Frequency-domain PNNs provide reconfigurability through spectral programming, while single-device phononic computation alleviates device-to-device variation.The passage contrasts this approach with programmable device arrays, whose scaling typically requires additional computing units and control channels.Source: Introduction · p. 1
  • 97.6% optical, 98.4% electronic, and 98.2% phononic experimental inference accuracies were achieved on the same four-class Fashion-MNIST task using identical pretrained parameters.The implementations use a common two-layer architecture and require no retraining or parameter fine-tuning.Source: Introduction · p. 2
  • Existing implementations often incorporate hardware-specific responses in their models or training, so transferring pretrained networks across physical domains can require retraining or parameter fine-tuning.The authors identify this as a barrier to direct deployment across platforms with different operating characteristics.Source: Introduction · p. 2
  • The framework uses a common mathematical model of second-order spectral convolution across optical, electronic, and phononic systems with distinct physical mechanisms.The paper compares their nonlinear conversion bandwidths, efficiencies, and computing accuracies.Source: Introduction · p. 2

Frequency-domain neural network architecture

The frequency-domain PNN uses a nonlinear convolution layer followed by a fully connected linear mapping layer. Both layers encode input features and pretrained parameters into frequency bins, and second-order nonlinear systems generate the spectra from which class scores are read.

Frequency-domain neural network architecture

  • The two-layer network combines a nonlinear convolution layer with a fully connected linear mapping layer, encoding data and pretrained parameters in frequency bins.The elements are vectorized and concurrently encoded in the frequency spectrum.Source: Frequency-domain neural network… · p. 2
  • Layer 1 convolves a 28 × 28 image with its parameters using 2,000 input bins and produces 3,999 second-order bins, of which 2,783 image-related outputs are retained.The other 1,216 output bins, contributed solely by parameter self-convolution, are discarded.Source: Frequency-domain neural network… · p. 2
  • Layer 2 maps the 2,783 Layer-1 outputs against four sets of 2,783 pretrained parameters, and four designated output-bin amplitudes give the class scores.The class with the highest score is the predicted class.Source: Frequency-domain neural network… · p. 3
  • Optical PPLN, an RF mixer, and a surface-acoustic-wave device implement the same spectral-convolution framework through second-order nonlinear responses.The platforms operate from MHz to THz frequency regimes.Source: Frequency-domain neural network… · p. 3, Figure 1 · p. 3

Optical implementation based on a periodically poled lithium niobate module

The optical implementation encodes image features and pretrained parameters into a modulated laser signal, then uses PPLN second-harmonic generation to perform the nonlinear operation. Experiments achieve 97.6% accuracy, while modulation nonlinearity creates a layer-dependent accuracy trade-off with signal-to-noise ratio.

Optical implementation based on a periodically poled lithium niobate module

  • Increasing Layer-1 modulation depth from 0.1π to 1.9π reduced calculated accuracy from 98.4% to 55.4%, whereas the same Layer-2 change reduced it to 96.2%.The authors report different layer tolerances to electro-optic modulator nonlinearity.Source: Optical implementation based on a… · p. 6
  • The experiment set modulation depths to 0.72π in Layer 1 and 1.45π in Layer 2 to trade off modulation linearity against spectral signal-to-noise ratio.Reducing the applied voltage improves modulation linearity but lowers measured spectral signal-to-noise ratio.Source: Optical implementation based on a… · p. 6

Electronic implementation based on an RF mixer

An RF mixer implements the electronic PNN by multiplying two copies of an encoded waveform, physically producing the spectral self-convolution used by the two-layer model. The electronic implementation reaches 98.4% experimental accuracy, with complete agreement between numerical and experimental predictions.

Electronic implementation based on an RF mixer

  • 98.4% inference accuracy was achieved in both numerical calculations and analogue electronic experiments, with 100% agreement between their predictions.The analogue experiments slightly exceeded the optical implementation's reported accuracies.Source: Electronic implementation based on an… · p. 6
  • The RF mixer multiplies two copies of the encoded waveform, producing an output proportional to its square and implementing spectral self-convolution.The AWG synthesizes the encoded waveform, and an oscilloscope records the mixer output.Source: Electronic implementation based on an… · p. 6
  • The electronic implementation uses the same pretrained parameters and encoding and decoding procedures as the optical implementation, but assigns different frequency bins.The authors state that the architecture accommodates frequency assignments tailored to different platforms.Source: Electronic implementation based on an… · p. 6

Platform performance comparison

The three platforms reproduce the common numerical model’s inferences with high fidelity despite differing physical performance. Their comparison spans conversion bandwidth, nonlinear conversion efficiency, and calculation accuracy.

Platform performance comparison

Conclusion and outlook

The frequency-domain PNN uses the same pre-trained parameters across distinct physical platforms without platform-specific fine-tuning. The authors propose extending this framework to other platforms with controllable second-order nonlinear interactions and selecting hardware to suit application requirements.

Conclusion and outlook

  • The same pre-trained neural-network parameters work across substantially different physical platforms without platform-specific fine-tuning.Source: Conclusion and outlook · p. 9
  • Platform independence does not require identical carrier or encoding frequencies, nonlinear conversion efficiency, physical interfaces, or driving conditions.Source: Conclusion and outlook · p. 9
  • Other platforms with controllable second-order nonlinear interactions could implement the framework, with hardware chosen according to application requirements.Source: Conclusion and outlook · pp. 9–10

Conflict of interests

The authors disclose no conflicts of interest.

Conflict of interests

Encoding and decoding methods of frequency-domain PNN framework

The framework encodes input and parameter vectors as frequency bins, then uses second-order spectral products to compute Layer 1 outputs and Layer 2 class scores.

Encoding

  • Input pixels and Layer 1 parameters are vectorized and assigned to frequency bins, with frequency spacing chosen to prevent overlap between encoded and generated bins.The input vector contains scaled pixel grayscale values, while the parameter vector contains scaled pre-trained weights.Source: Encoding and decoding methods of… · p. 14
  • AWG waveforms preserve relative spectral amplitudes while their overall voltage scale is set by peak-to-peak voltage.The encoded spectra are synthesized as time-domain waveforms; the frequency-grid conditions separate cross-convolution terms and avoid overlap with second-order bins.Source: Encoding and decoding methods of… · p. 14

Layer 1 decoding

  • Layer 1 discards bins containing only parameter self-interactions, then squares the amplitudes of the remaining decoded bins to form the Layer 2 input vector.The decoded frequencies span 2M+N−1 bins.Source: Encoding and decoding methods of… · p. 15

Layer 2 decoding

  • Layer 2 partitions its parameter vector into class-weight blocks, aligning each block’s products with Layer 1 outputs into one readout bin per class.For each class, corresponding products accumulate at the same frequency, whose amplitude is proportional to the absolute inner product of that class’s weights and the Layer 1 output.Source: Encoding and decoding methods of… · p. 15
  • The largest of the four readout-bin scores determines the predicted class.The readout frequencies are set by the frequency assignments, and the nonlinear conversion coefficient depends on the second-order system.Source: Encoding and decoding methods of… · p. 15
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