Optimizing a NengoDL model

Optimizing Nengo models via deep learning training methods is one of the important features of NengoDL. This functionality is accessed via the Simulator.train() method. For example:

with nengo.Network() as net:
    <construct the model>

with nengo_dl.Simulator(net, ...) as sim:
    sim.train(<inputs>, <targets>, <optimizer>, n_epochs=10,
              objective=<objective>)

When the Simulator is first constructed, all the parameters in the model (e.g., encoders, decoders, connection weights, biases) are initialized based on the functions/distributions specified during model construction (see the Nengo documentation for more detail on how that works). What the Simulator.train() method does is then further optimize those parameters based on some inputs and desired outputs. We’ll go through each of those components in more detail below.

Simulator.train arguments

Inputs

The first argument to the Simulator.train() function is the input data. We can think of a model as computing a function \(y = f(x, \theta)\), where \(f\) is the model, mapping inputs \(x\) to outputs \(y\) with parameters \(\theta\). This argument is specifying the values for \(x\).

In practice what that means is specifying values for the input Nodes in the model. A Node is a Nengo object that inserts values into a Network, usually used to define external inputs. Simulator.train() will override the normal Node values with the training data that is provided. This is specified as a dictionary {<node>: <array>, ...}, where <node> is the input node for which training data is being defined, and <array> is a numpy array containing the training values. This training array should have shape (n_inputs, n_steps, node.size_out), where n_inputs is the number of training examples, n_steps is the number of simulation steps to train across, and node.size_out is the dimensionality of the Node.

When training a NengoDL model the user must specify the minibatch_size to use during training, via the Simulator(..., minibatch_size=n) argument. This defines how many inputs (out of the total n_inputs defined above) will be used for each optimization step.

Here is an example illustrating how to define the input values for two input nodes:

with nengo.Network() as net:
    a = nengo.Node([0])
    b = nengo.Node([1, 2, 3])
    ...

n_inputs = 1000
minibatch_size = 20
n_steps = 10

with nengo_dl.Simulator(net, minibatch_size=minibatch_size) as sim:
    sim.train(inputs={a: np.random.randn(n_inputs, n_steps, 1),
                      b: np.random.randn(n_inputs, n_steps, 3)},
              ...)

Input values must be provided for at least one Node, but beyond that can be defined for as many Nodes as desired. Any Nodes that don’t have data provided will take on the values specified during model construction. Also note that inputs can only be defined for Nodes with no incoming connections (i.e., Nodes with size_in == 0).

Targets

Returning to the network equation \(y = f(x, \theta)\), the goal in optimization is to find a set of parameter values such that given inputs \(x\) the actual network outputs \(y\) are as close as possible to some target values \(t\). This argument is specifying those desired outputs \(t\).

This works very similarly to defining inputs, except instead of assigning input values to Nodes it assigns target values to Probes. The structure of the argument is similar – a dictionary of {<probe>: <array>, ...}, where <array> has shape (n_inputs, n_steps, probe.size_in). Each entry in the target array defines the desired output for the corresponding entry in the input array.

For example:

with nengo.Network() as net:
    ...
    ens = nengo.Ensemble(10, 2)
    p = nengo.Probe(ens)

n_inputs = 1000
minibatch_size = 20
n_steps = 10

with nengo_dl.Simulator(net, minibatch_size=minibatch_size) as sim:
    sim.train(targets={p: np.random.randn(n_inputs, n_steps, 2)},
              ...)

Note that these examples use random inputs/targets, for the sake of simplicity. In practice we would do something like targets={p: my_func(inputs)}, where my_func is a function specifying what the ideal outputs are for the given inputs.

Optimizer

The optimizer is the algorithm that defines how to update the network parameters during training. Any of the optimization methods implemented in TensorFlow can be used in NengoDL; more information can be found in the TensorFlow documentation.

An instance of the desired TensorFlow optimizer is created (specifying any arguments required by that optimizer), and that instance is then passed to Simulator.train(). For example:

import tensorflow as tf

with nengo_dl.Simulator(net, ...) as sim:
    sim.train(optimizer=tf.train.MomentumOptimizer(
        learning_rate=1e-2, momentum=0.9, use_nesterov=True), ...)

Objective

The goal in optimization is to minimize the error between the network’s actual outputs \(y\) and the targets \(t\). The objective is the function \(e = o(y, t)\) that computes an error value \(e\), given \(y\) and \(t\).

The default objective in NengoDL is the standard mean squared error. This will be used if the user doesn’t specify an objective.

Users can specify a custom objective by creating a function and passing that to the objective argument in Simulator.train(). Note that the objective is defined using TensorFlow operators. It should accept Tensors representing outputs and targets as input (each with shape (minibatch_size, n_steps, probe.size_in)) and return a scalar Tensor representing the error. This example manually computes mean squared error, rather than using the default:

import tensorflow as tf

def my_objective(outputs, targets):
    return tf.reduce_mean((targets - outputs) ** 2)

with nengo_dl.Simulator(net, ...) as sim:
    sim.train(objective=my_objective, ...)

If there are multiple output Probes defined in targets then the error will be computed for each output individually (using the specified objective). Then the error will be averaged across outputs to produce an overall error value.

Note that Simulator.loss() can be used to check the loss (error) value for a given objective.

Other parameters

  • n_epochs (int): run training for this many passes through the input data
  • shuffle (bool): if True (default), randomly assign data to different minibatches each epoch
  • profile (bool or str): collect profiling information (as in Simulator.run)

Choosing which elements to optimize

By default, NengoDL will optimize the following elements in a model:

  1. Connection weights (neuron–neuron weight matrices or decoders)
  2. Ensemble encoders
  3. Neuron biases

These elements will not be optimized if they are targeted by an online learning rule. For example, nengo:nengo.PES modifies connection weights as a model is running. If we also tried to optimize those weights with some offline training method then those two processes would conflict with each other, likely resulting in unintended effects. So NengoDL will assume that those elements should not be optimized.

Any of these default behaviours can be overriden using Nengo’s config system. Specifically, setting the trainable config attribute for an object will control whether or not it will be optimized.

configure_settings() is a utility function that can be used to add a configurable trainable attribute to the objects in a network. Setting trainable=None will use the defaults described above, or True/False can be passed to override the default for all objects in a model.

For example, suppose we only want to optimize one connection in our network, while leaving everything else unchanged. This could be achieved via

with nengo.Network() as net:
    # this adds the `trainable` attribute to all the trainable objects
    # in the network, and initializes it to `False`
    nengo_dl.configure_settings(trainable=False)

    a = nengo.Node([0])
    b = nengo.Ensemble(10, 1)
    c = nengo.Node(size_in=1)

    nengo.Connection(a, b)

    # make this specific connection trainable
    conn = nengo.Connection(b, c)
    net.config[conn].trainable = True

Or if we wanted to disable training for some subnetwork:

with nengo.Network() as net:
    nengo_dl.configure_settings(trainable=None)
    ...
    with nengo.Network() as subnet:
        net.config[subnet].trainable = False
        ...

Note that config[nengo.Ensemble].trainable controls both encoders and biases, as both are properties of an Ensemble. However, it is possible to separately control the biases via config[nengo.ensemble.Neurons].trainable or config[my_ensemble.neurons].trainable.

There are two important caveats to keep in mind when configuring trainable, which differ from the standard config behaviour:

  1. trainable applies to all objects in a network, regardless of whether they were created before or after trainable is set. For example,

    with nengo.Network() as net:
    ...
    net.config[nengo.Ensemble].trainable = False
    a = nengo.Ensemble(10, 1)
    ...

    is the same as

    with nengo.Network() as net:
    ...
    a = nengo.Ensemble(10, 1)
    net.config[nengo.Ensemble].trainable = False
    ...

  2. trainable can only be set on the config of the top-level network. For example,

    with nengo.Network() as net:
    nengo_dl.configure_settings(trainable=None)

    with nengo.Network() as subnet:
        my_ens = nengo.Ensemble(...)

        # incorrect
        subnet.config[my_ens].trainable = False

        # correct
        net.config[my_ens].trainable = False