Clarification on Sensory and Motor Neurons in LTC Layers

[RzaRamezanii]

I have a question regarding the implementation of the Liquid Time-Constant (LTC) network in the ncps package. Specifically, I am trying to understand the roles of sensory and motor neurons in the context of an LTC model.
Here is a sample model that I'm working with:

from ncps.tf import LTC

def build_ltc_model(input_shape):
    model = Sequential()
    model.add(LTC(units=10, return_sequences=True, input_shape=input_shape))
    model.add(LTC(units=5, return_sequences=False))
    model.add(Dense(1))
    model.compile(loss=MeanSquaredError(), optimizer=Adam(learning_rate=learning_rate), metrics=[RootMeanSquaredError()])
    model.summary()
    return model

Question

In the above model, the LTC layers are defined with integer values for units (10 and 5, respectively). I would like to know:

1. What constitutes the sensory neurons at each LTC layer?
2. What constitutes the motor neurons at each LTC layer?

In my understanding, sensory neurons are those that map the input features to the internal state, while motor neurons are those that map the internal state to the output. However, I am unclear on how this applies when specifying units as an integer without custom wiring. In other words, I cannot make any connection between these two parameters and my model:

• input_mapping – Mapping applied to the sensory neurons. Possible values None, "linear", "affine" (default "affine").
• output_mapping – Mapping applied to the motor neurons. Possible values None, "linear", "affine" (default "affine").

Any clarification or examples would be greatly appreciated. Thank you in advance!

Best regards,
Reza

@raminmh
@mlech26l

[MoniFarsang]

Sensory neurons: These are the inputs to the LTC layers.
Motor neurons: Since you're not defining a custom wiring architecture, the units specified in each LTC layer correspond directly to the motor neurons.

So, conceptually, in each of your layers, there is a flow like this:
input → input mapping → LTC equation → output mapping → output

More specifically, in your case:

1st LTC layer:

• Sensory neurons: The input to the network, which will be mapped by the input_mapping before being passed to the LTC equations.
• Motor neurons: 10 units (same as your hidden state), which will be mapped by the output_mapping after the LTC equations.

2nd LTC layer:

• Sensory neurons: The output from the previous layer (size 10), which will be mapped by the input_mapping.
• Motor neurons: 5 units (again, same as your hidden state), which will be mapped by the output_mapping after the LTC equations. The output of this will then be passed to your final Dense layer.

I hope this helps.