Neural Circuit Policies Enabling Auditable Autonomy

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Neural Circuit Policies (NCPs) are designed sparse recurrent neural networks based on the LTC neuron and synapse model loosely inspired by the nervous system of the organism C. elegans. This page is a description of the Keras (TensorFlow 2 package) reference implementation of NCPs. For reproducibility materials of the paper see the corresponding subpage.

Installation

Requirements:

• Python 3.6
• TensorFlow 2.4
• (Optional) PyTorch 1.7

pip install keras-ncp

Update January 2021: Experimental PyTorch support added

With keras-ncp version 2.0 experimental PyTorch support is added. There is an example on how to use the PyTorch binding in the examples folder and a Colab notebook linked below. Note that the support is currently experimental, which means that it currently misses some functionality (e.g., no plotting, no irregularly sampled time-series,etc. ) and might be subject to breaking API changes in future updates.

Breaking API changes between 1.x and 2.x

The TensorFlow bindings have been moved to the tf submodule. Thus the only breaking change regarding the TensorFlow/Keras bindings concern the import

# Import shared modules for wirings, datasets,...
import kerasncp as kncp
# Import framework-specific binding
from kerasncp.tf import LTCCell      # Use TensorFlow binding
(from kerasncp.torch import LTCCell  # Use PyTorch binding)

Colab notebooks

We have created a few Google Colab notebooks for an interactive introduction to the package

• Google Colab: Basic usage
• Google Colab: Stacking NCPs with other layers
• NEW: Google Colab: Pytorch binding

Usage: the basics

The package is composed of two main parts:

• The LTC model as a tf.keras.layers.Layer or torch.nn.Module RNN cell
• An wiring architecture for the LTC cell above

The wiring could be fully-connected (all-to-all) or sparsely designed using the NCP principles introduced in the paper. As the LTC model is expressed in the form of a system of ordinary differential equations in time, any instance of it is inherently a recurrent neural network (RNN).

Let's create a LTC network consisting of 8 fully-connected neurons that receive a time-series of 2 input features as input. Moreover, we define that 1 of the 8 neurons acts as the output (=motor neuron):

from tensorflow import keras
import kerasncp as kncp
from kerasncp.tf import LTCCell

wiring = kncp.wirings.FullyConnected(8, 1)  # 8 units, 1 motor neuron
ltc_cell = LTCCell(wiring) # Create LTC model

model = keras.Sequential(
    [
        keras.layers.InputLayer(input_shape=(None, 2)), # 2 input features
        keras.layers.RNN(ltc_cell, return_sequences=True),
    ]
)
model.compile(
    optimizer=keras.optimizers.Adam(0.01), loss='mean_squared_error'
)

We can then fit this model to a generated sine wave, as outlined in the tutorials (open in Google Colab).

More complex architectures

We can also create some more complex NCP wiring architecture. Simply put, an NCP is a 4-layer design vaguely inspired by the wiring of the C. elegans worm. The four layers are sensory, inter, command, and motor layer, which are sparsely connected in a feed-forward fashion. On top of that, the command layer realizes some recurrent connections. As their names already indicate, the sensory represents the input and the motor layer the output of the network.

We can also customize some of the parameter initialization ranges, although the default values should work fine for most cases.

ncp_wiring = kncp.wirings.NCP(
    inter_neurons=20,  # Number of inter neurons
    command_neurons=10,  # Number of command neurons
    motor_neurons=5,  # Number of motor neurons
    sensory_fanout=4,  # How many outgoing synapses has each sensory neuron
    inter_fanout=5,  # How many outgoing synapses has each inter neuron
    recurrent_command_synapses=6,  # Now many recurrent synapses are in the
    # command neuron layer
    motor_fanin=4,  # How many incoming synapses has each motor neuron
)
ncp_cell = LTCCell(
    ncp_wiring,
    initialization_ranges={
        # Overwrite some of the initialization ranges
        "w": (0.2, 2.0),
    },
)

We can then combine the NCP cell with arbitrary keras.layers, for instance to build a powerful image sequence classifier:

height, width, channels = (78, 200, 3)

model = keras.models.Sequential(
    [
        keras.layers.InputLayer(input_shape=(None, height, width, channels)),
        keras.layers.TimeDistributed(
            keras.layers.Conv2D(32, (5, 5), activation="relu")
        ),
        keras.layers.TimeDistributed(keras.layers.MaxPool2D()),
        keras.layers.TimeDistributed(
            keras.layers.Conv2D(64, (5, 5), activation="relu")
        ),
        keras.layers.TimeDistributed(keras.layers.MaxPool2D()),
        keras.layers.TimeDistributed(keras.layers.Flatten()),
        keras.layers.TimeDistributed(keras.layers.Dense(32, activation="relu")),
        keras.layers.RNN(ncp_cell, return_sequences=True),
        keras.layers.TimeDistributed(keras.layers.Activation("softmax")),
    ]
)
model.compile(
    optimizer=keras.optimizers.Adam(0.01),
    loss='sparse_categorical_crossentropy',
)

@article{lechner2020neural,
  title={Neural circuit policies enabling auditable autonomy},
  author={Lechner, Mathias and Hasani, Ramin and Amini, Alexander and Henzinger, Thomas A and Rus, Daniela and Grosu, Radu},
  journal={Nature Machine Intelligence},
  volume={2},
  number={10},
  pages={642--652},
  year={2020},
  publisher={Nature Publishing Group}
}