Cornell University and NTT Research Introduce Physical Neural Networks (PNNs): A Universal Framework that Leverages a Backpropagation Algorithm for Arbitrary Physical Systems


DNNs (Deep neural networks) have proven to be of great use in solving various complex problems in image and speech recognition and NLP. DDNs are now making their way into the actual physical world. The similarities between DNNs and physical processes, such as hierarchy, approximation symmetries, redundancy, and nonlinearity, suggest that DNNs could be used to process data from the physical environment.

Researchers at Cornell University and NTT Research in their recent paper suggest that controlled evolutions of physical systems are highly suitable for realizing deep learning (DL) models. Therefore, they introduce Physical Neural Networks (PNN), a novel framework that uses a backpropagation algorithm to train arbitrary, real physical systems to execute DNNs.

Backpropagation algorithms work on the premise of modeling mathematical operations by adjusting the weights of input signals to produce a predicted output signal. Computing the gradient descent allows you to determine the best parameter changes and so enhance model performance.


The Physics-Aware Training (PAT) methodology enables the proposed PNN framework. PAT is based on a novel hybrid physical-digital algorithm that can effectively and reliably perform the backpropagation algorithm on a sequence of physical input-output transformations. In essence, this means that a problem is handled by using backpropagation algorithms to train sequences of real physical operations to accomplish the required physical tasks.

Introduction to Physics-Aware Training.

There are five steps in the PAT training procedure.:

  • The physical system receives training input data as well as parameters as inputs.
  • The physical system applies its transformation to give an output in a forward pass.
  • To calculate the error, the physical output is compared to the anticipated output.
  • The gradient of the loss is determined with respect to the controllable parameters using a differentiable digital model for estimating the gradients of the physical system.
  • The parameters are then updated based on the gradient inferred.

During training, the process is performed iteratively over training examples until the error is decreased to a pre-defined threshold. The researchers used three different physical systems to test the generality of PNNs: optical, mechanical, and electrical.

In one of the experiments, the team tested a PNN that uses broadband optical second harmonic generation (SHG) with shaped femtosecond pulses. The PNN was aimed to learn to predict spoken vowels from 12-dimensional input data vectors of formant frequencies collected from audio recordings and then classify the spoken vowels based on their formant frequencies. 


The results demonstrated that the suggested SHG-PNN could correctly classify vowels with a 93 percent accuracy rate. The trainable SHG transformations improve the accuracy of digital operations from around 90 percent to 97 percent on the MNIST handwritten digit classification task.

It is now believed that PNNs serve as a foundation for co-designing hardware, physics, and software in machine learning. They can develop new machine learning hardware with higher energy efficiency and faster than conventional electronic processors.



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