This repository contains PyTorch implementations of the following papers:

• Legendre Memory Units: Continuous-Time Representation in Recurrent Neural Networks, by Voelker AR, Kajić I, and Eliasmith C
• Parallelizing Legendre Memory Unit Training, by Chilkuri N and Eliasmith C

Performance on the psMNIST dataset is demonstrated in examples/.

torch, numpy, and scipy are the only requirements.
src/lmu.py contains the implementations of LMUCell, LMU and LMUFFT.

Examples:

• LMU

  import torch
  from lmu import LMU
  
  model = LMU(
      input_size = 1,
      hidden_size = 212,
      memory_size = 256,
      theta = 784
  )
  
  x = torch.rand(100, 784, 1) # [batch_size, seq_len, input_size]
  output, (h_n, m_n) = model(x)

• LMUFFT

  import torch
  from lmu import LMUFFT
  
  model = LMUFFT(
      input_size = 1,
      hidden_size = 346,
      memory_size = 468, 
      seq_len = 784, 
      theta = 784
  )
  
  x = torch.rand(100, 784, 1) # [batch_size, seq_len, input_size]
  output, h_n = model(x)

• Clone this repository and open:

  • examples/lmu_psmnist.ipynb, for training and evaluating an LMU model on the psMNIST dataset
  • examples/lmu_fft_psmnist.ipynb, for training and evaluating an LMUFFT model on the psMNIST dataset

  Running in Google Colab is preferred

• examples/permutation.pt contains the permutation tensor used while creating the psMNIST data; it's included for reproducibility. Alternatively, torch.randperm(784) can be used to test with a new permutation.

• Voelker, Aaron R., Ivana Kajić, and Chris Eliasmith. "Legendre memory units: Continuous-time representation in recurrent neural networks." (2019).
• Chilkuri, Narsimha, and Chris Eliasmith. "Parallelizing Legendre Memory Unit Training." (2021)
• Official Keras implementation of LMU and LMUFFT: nengo/keras-lmu
• Legendre Memory Units in NengoDL