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lmu

A Legendre Memory Unit in Nengo, demonstrated learning a fixed delay.

model advanced NengoGUI-ready lmu memory recurrent learning pes

lmu

A Legendre Memory Unit in Nengo, demonstrated learning a fixed delay.

Description

Legendre Memory Units (LMUs), described in Voelker, Kajić, and Eliasmith (NeurIPS 2019), are a recurrent neural-network architecture. Broadly: an LMU optimally represents a sliding window of a continuous-time signal using a basis of Legendre polynomials, giving the network access to a compressed but information-dense history of its input.

This submission wires an LMU layer into a Nengo network and trains a downstream spiking ensemble (with PES learning) to compute a fixed time delay of a white-noise input. Learning is on for the first 80 % of the run and off for the last 20 % so generalization can be assessed.

This is a GUI-first submission: open lmu.py in NengoGUI to watch the network learn the delay live. The full notebook walkthrough is in lmu.ipynb and the long-form training-and-plotting script is in examples/run_training.py.

Run it

In NengoGUI:

pip install -r requirements.txt nengo-gui
nengo lmu.py

Long-form training run (~100 simulated seconds; takes a couple of minutes wall-clock and produces plots):

python examples/run_training.py

Tutorial walkthrough — open lmu.ipynb in Jupyter for a step-by-step explanation of the math (A/B matrix derivation, the IdealDelay synapse, the PES training loop).

Citation

@inproceedings{voelker2019lmu,
  author    = {Voelker, Aaron R. and Kajić, Ivana and Eliasmith, Chris},
  title     = {Legendre Memory Units: Continuous-time representation in recurrent neural networks},
  booktitle = {Advances in Neural Information Processing Systems 32 (NeurIPS 2019)},
  year      = {2019}
}

License

GPLv2 (see LICENSE).