import numpy as np
from nengo.builder import Builder, Operator, Signal
from nengo.builder.operator import Copy, Reset
from nengo.connection import LearningRule
from nengo.ensemble import Ensemble
from nengo.exceptions import BuildError
from nengo.learning_rules import BCM, Oja, PES, Voja
from nengo.node import Node
[docs]class SimPES(Operator):
r"""Calculate connection weight change according to the PES rule.
Implements the PES learning rule of the form
.. math:: \Delta \omega_{ij} = \frac{\kappa}{n} e_j a_i
where
* :math:`\kappa` is a scalar learning rate,
* :math:`n` is the number of presynaptic neurons
* :math:`e_j` is the error for the jth output dimension, and
* :math:`a_i` is the activity of a presynaptic neuron.
.. versionadded:: 3.0.0
Parameters
----------
pre_filtered : Signal
The presynaptic activity, :math:`a_i`.
error : Signal
The error signal, :math:`e_j`.
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
learning_rate : float
The scalar learning rate, :math:`\kappa`.
encoders : Signal, optional
If not None, multiply the error signal by these post-synaptic
encoders (in the case that we want to learn a neuron-to-neuron
weight matrix instead of decoder weights).
tag : str, optional
A label associated with the operator, for debugging purposes.
Attributes
----------
pre_filtered : Signal
The presynaptic activity, :math:`a_i`.
error : Signal
The error signal, :math:`e_j`.
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
learning_rate : float
The scalar learning rate, :math:`\kappa`.
encoders : Signal, optional
If not None, multiply the error signal by these post-synaptic
encoders (in the case that we want to learn a neuron-to-neuron
weight matrix instead of decoder weights).
tag : str, optional
A label associated with the operator, for debugging purposes.
Notes
-----
1. sets ``[]``
2. incs ``[]``
3. reads ``[pre_filtered, error, encoders]``
4. updates ``[delta]``
"""
def __init__(
self, pre_filtered, error, delta, learning_rate, encoders=None, tag=None
):
super(SimPES, self).__init__(tag=tag)
self.learning_rate = learning_rate
self.sets = []
self.incs = []
self.reads = [pre_filtered, error] + ([] if encoders is None else [encoders])
self.updates = [delta]
@property
def delta(self):
return self.updates[0]
@property
def encoders(self):
return None if len(self.reads) < 3 else self.reads[2]
@property
def error(self):
return self.reads[1]
@property
def pre_filtered(self):
return self.reads[0]
def _descstr(self):
return "pre=%s, error=%s -> %s" % (self.pre_filtered, self.error, self.delta)
[docs] def make_step(self, signals, dt, rng):
pre_filtered = signals[self.pre_filtered]
error = signals[self.error]
delta = signals[self.delta]
n_neurons = pre_filtered.shape[0]
alpha = -self.learning_rate * dt / n_neurons
if self.encoders is None:
def step_simpes():
np.outer(alpha * error, pre_filtered, out=delta)
else:
encoders = signals[self.encoders]
def step_simpes():
np.outer(alpha * np.dot(encoders, error), pre_filtered, out=delta)
return step_simpes
[docs]class SimBCM(Operator):
r"""Calculate connection weight change according to the BCM rule.
Implements the Bienenstock-Cooper-Munroe learning rule of the form
.. math:: \Delta \omega_{ij} = \kappa a_j (a_j - \theta_j) a_i
where
* :math:`\kappa` is a scalar learning rate,
* :math:`a_j` is the activity of a postsynaptic neuron,
* :math:`\theta_j` is an estimate of the average :math:`a_j`, and
* :math:`a_i` is the activity of a presynaptic neuron.
Parameters
----------
pre_filtered : Signal
The presynaptic activity, :math:`a_i`.
post_filtered : Signal
The postsynaptic activity, :math:`a_j`.
theta : Signal
The modification threshold, :math:`\theta_j`.
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
learning_rate : float
The scalar learning rate, :math:`\kappa`.
tag : str, optional
A label associated with the operator, for debugging purposes.
Attributes
----------
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
learning_rate : float
The scalar learning rate, :math:`\kappa`.
post_filtered : Signal
The postsynaptic activity, :math:`a_j`.
pre_filtered : Signal
The presynaptic activity, :math:`a_i`.
tag : str or None
A label associated with the operator, for debugging purposes.
theta : Signal
The modification threshold, :math:`\theta_j`.
Notes
-----
1. sets ``[]``
2. incs ``[]``
3. reads ``[pre_filtered, post_filtered, theta]``
4. updates ``[delta]``
"""
def __init__(
self, pre_filtered, post_filtered, theta, delta, learning_rate, tag=None
):
super().__init__(tag=tag)
self.learning_rate = learning_rate
self.sets = []
self.incs = []
self.reads = [pre_filtered, post_filtered, theta]
self.updates = [delta]
@property
def delta(self):
return self.updates[0]
@property
def pre_filtered(self):
return self.reads[0]
@property
def post_filtered(self):
return self.reads[1]
@property
def theta(self):
return self.reads[2]
def _descstr(self):
return "pre=%s, post=%s -> %s" % (
self.pre_filtered,
self.post_filtered,
self.delta,
)
[docs] def make_step(self, signals, dt, rng):
pre_filtered = signals[self.pre_filtered]
post_filtered = signals[self.post_filtered]
theta = signals[self.theta]
delta = signals[self.delta]
alpha = self.learning_rate * dt
def step_simbcm():
delta[...] = np.outer(
alpha * post_filtered * (post_filtered - theta), pre_filtered
)
return step_simbcm
[docs]class SimOja(Operator):
r"""Calculate connection weight change according to the Oja rule.
Implements the Oja learning rule of the form
.. math:: \Delta \omega_{ij} = \kappa (a_i a_j - \beta a_j^2 \omega_{ij})
where
* :math:`\kappa` is a scalar learning rate,
* :math:`a_i` is the activity of a presynaptic neuron,
* :math:`a_j` is the activity of a postsynaptic neuron,
* :math:`\beta` is a scalar forgetting rate, and
* :math:`\omega_{ij}` is the connection weight between the two neurons.
Parameters
----------
pre_filtered : Signal
The presynaptic activity, :math:`a_i`.
post_filtered : Signal
The postsynaptic activity, :math:`a_j`.
weights : Signal
The connection weight matrix, :math:`\omega_{ij}`.
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
learning_rate : float
The scalar learning rate, :math:`\kappa`.
beta : float
The scalar forgetting rate, :math:`\beta`.
tag : str, optional
A label associated with the operator, for debugging purposes.
Attributes
----------
beta : float
The scalar forgetting rate, :math:`\beta`.
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
learning_rate : float
The scalar learning rate, :math:`\kappa`.
post_filtered : Signal
The postsynaptic activity, :math:`a_j`.
pre_filtered : Signal
The presynaptic activity, :math:`a_i`.
tag : str or None
A label associated with the operator, for debugging purposes.
weights : Signal
The connection weight matrix, :math:`\omega_{ij}`.
Notes
-----
1. sets ``[]``
2. incs ``[]``
3. reads ``[pre_filtered, post_filtered, weights]``
4. updates ``[delta]``
"""
def __init__(
self, pre_filtered, post_filtered, weights, delta, learning_rate, beta, tag=None
):
super().__init__(tag=tag)
self.learning_rate = learning_rate
self.beta = beta
self.sets = []
self.incs = []
self.reads = [pre_filtered, post_filtered, weights]
self.updates = [delta]
@property
def delta(self):
return self.updates[0]
@property
def pre_filtered(self):
return self.reads[0]
@property
def post_filtered(self):
return self.reads[1]
@property
def weights(self):
return self.reads[2]
def _descstr(self):
return "pre=%s, post=%s -> %s" % (
self.pre_filtered,
self.post_filtered,
self.delta,
)
[docs] def make_step(self, signals, dt, rng):
weights = signals[self.weights]
pre_filtered = signals[self.pre_filtered]
post_filtered = signals[self.post_filtered]
delta = signals[self.delta]
alpha = self.learning_rate * dt
beta = self.beta
def step_simoja():
# perform forgetting
post_squared = alpha * post_filtered * post_filtered
delta[...] = -beta * weights * post_squared[:, None]
# perform update
delta[...] += np.outer(alpha * post_filtered, pre_filtered)
return step_simoja
[docs]class SimVoja(Operator):
r"""Simulates a simplified version of Oja's rule in the vector space.
See :doc:`examples/learning/learn-associations` for details.
Parameters
----------
pre_decoded : Signal
Decoded activity from presynaptic ensemble, :math:`a_i`.
post_filtered : Signal
Filtered postsynaptic activity signal.
scaled_encoders : Signal
2d array of encoders, multiplied by ``scale``.
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
scale : ndarray
The length of each encoder.
learning_signal : Signal
Scalar signal to be multiplied by ``learning_rate``. Expected to be
either 0 or 1 to turn learning off or on, respectively.
learning_rate : float
The scalar learning rate.
tag : str, optional
A label associated with the operator, for debugging purposes.
Attributes
----------
delta : Signal
The synaptic weight change to be applied, :math:`\Delta \omega_{ij}`.
learning_rate : float
The scalar learning rate.
learning_signal : Signal
Scalar signal to be multiplied by ``learning_rate``. Expected to be
either 0 or 1 to turn learning off or on, respectively.
post_filtered : Signal
Filtered postsynaptic activity signal.
pre_decoded : Signal
Decoded activity from presynaptic ensemble, :math:`a_i`.
scale : ndarray
The length of each encoder.
scaled_encoders : Signal
2d array of encoders, multiplied by ``scale``.
tag : str or None
A label associated with the operator, for debugging purposes.
Notes
-----
1. sets ``[]``
2. incs ``[]``
3. reads ``[pre_decoded, post_filtered, scaled_encoders, learning_signal]``
4. updates ``[delta]``
"""
def __init__(
self,
pre_decoded,
post_filtered,
scaled_encoders,
delta,
scale,
learning_signal,
learning_rate,
tag=None,
):
super().__init__(tag=tag)
self.scale = scale
self.learning_rate = learning_rate
self.sets = []
self.incs = []
self.reads = [pre_decoded, post_filtered, scaled_encoders, learning_signal]
self.updates = [delta]
@property
def delta(self):
return self.updates[0]
@property
def learning_signal(self):
return self.reads[3]
@property
def pre_decoded(self):
return self.reads[0]
@property
def post_filtered(self):
return self.reads[1]
@property
def scaled_encoders(self):
return self.reads[2]
@property
def weights(self):
return self.reads[2]
def _descstr(self):
return "pre=%s, post=%s -> %s" % (
self.pre_decoded,
self.post_filtered,
self.delta,
)
[docs] def make_step(self, signals, dt, rng):
pre_decoded = signals[self.pre_decoded]
post_filtered = signals[self.post_filtered]
scaled_encoders = signals[self.scaled_encoders]
delta = signals[self.delta]
learning_signal = signals[self.learning_signal]
alpha = self.learning_rate * dt
scale = self.scale[:, np.newaxis]
def step_simvoja():
delta[...] = (
alpha
* learning_signal
* (
scale * np.outer(post_filtered, pre_decoded)
- post_filtered[:, np.newaxis] * scaled_encoders
)
)
return step_simvoja
[docs]def get_pre_ens(conn):
"""Get the input `.Ensemble` for connection."""
return conn.pre_obj if isinstance(conn.pre_obj, Ensemble) else conn.pre_obj.ensemble
[docs]def get_post_ens(conn):
"""Get the output `.Ensemble` for connection."""
return (
conn.post_obj
if isinstance(conn.post_obj, (Ensemble, Node))
else conn.post_obj.ensemble
)
[docs]def build_or_passthrough(model, obj, signal):
"""Builds the obj on signal, or returns the signal if obj is None."""
return signal if obj is None else model.build(obj, signal)
[docs]@Builder.register(LearningRule)
def build_learning_rule(model, rule):
"""Builds a `.LearningRule` object into a model.
A brief summary of what happens in the learning rule build process,
in order:
1. Create a delta signal for the weight change.
2. Add an operator to increment the weights by delta.
3. Call build function for the learning rule type.
The learning rule system is designed to work with multiple learning rules
on the same connection. If only one learning rule was to be applied to the
connection, then we could directly modify the weights, rather than
calculating the delta here and applying it in `.build_connection`.
However, with multiple learning rules, we must isolate each delta signal
in case calculating the delta depends on the weights themselves,
making the calculation depend on the order of the learning rule
evaluations.
Parameters
----------
model : Model
The model to build into.
rule : LearningRule
The learning rule to build.
Notes
-----
Sets ``model.params[rule]`` to ``None``.
"""
conn = rule.connection
# --- Set up delta signal
if rule.modifies == "encoders":
if not conn.is_decoded:
ValueError(
"The connection must be decoded in order to use encoder learning."
)
post = get_post_ens(conn)
target = model.sig[post]["encoders"]
tag = "encoders += delta"
elif rule.modifies in ("decoders", "weights"):
target = model.sig[conn]["weights"]
tag = "weights += delta"
else:
raise BuildError("Unknown target %r" % rule.modifies)
delta = Signal(shape=target.shape, name="Delta")
model.add_op(Copy(delta, target, inc=True, tag=tag))
model.sig[rule]["delta"] = delta
model.params[rule] = None # by default, no build-time info to return
model.build(rule.learning_rule_type, rule) # updates delta
[docs]@Builder.register(BCM)
def build_bcm(model, bcm, rule):
"""Builds a `.BCM` object into a model.
Calls synapse build functions to filter the pre and post activities,
and adds a `.SimBCM` operator to the model to calculate the delta.
Parameters
----------
model : Model
The model to build into.
bcm : BCM
Learning rule type to build.
rule : LearningRule
The learning rule object corresponding to the neuron type.
Notes
-----
Does not modify ``model.params[]`` and can therefore be called
more than once with the same `.BCM` instance.
"""
conn = rule.connection
pre_activities = model.sig[get_pre_ens(conn).neurons]["out"]
post_activities = model.sig[get_post_ens(conn).neurons]["out"]
pre_filtered = build_or_passthrough(model, bcm.pre_synapse, pre_activities)
post_filtered = build_or_passthrough(model, bcm.post_synapse, post_activities)
theta = build_or_passthrough(model, bcm.theta_synapse, post_activities)
model.add_op(
SimBCM(
pre_filtered,
post_filtered,
theta,
model.sig[rule]["delta"],
learning_rate=bcm.learning_rate,
)
)
# expose these for probes
model.sig[rule]["theta"] = theta
model.sig[rule]["pre_filtered"] = pre_filtered
model.sig[rule]["post_filtered"] = post_filtered
[docs]@Builder.register(Oja)
def build_oja(model, oja, rule):
"""Builds a `.BCM` object into a model.
Calls synapse build functions to filter the pre and post activities,
and adds a `.SimOja` operator to the model to calculate the delta.
Parameters
----------
model : Model
The model to build into.
oja : Oja
Learning rule type to build.
rule : LearningRule
The learning rule object corresponding to the neuron type.
Notes
-----
Does not modify ``model.params[]`` and can therefore be called
more than once with the same `.Oja` instance.
"""
conn = rule.connection
pre_activities = model.sig[get_pre_ens(conn).neurons]["out"]
post_activities = model.sig[get_post_ens(conn).neurons]["out"]
pre_filtered = build_or_passthrough(model, oja.pre_synapse, pre_activities)
post_filtered = build_or_passthrough(model, oja.post_synapse, post_activities)
model.add_op(
SimOja(
pre_filtered,
post_filtered,
model.sig[conn]["weights"],
model.sig[rule]["delta"],
learning_rate=oja.learning_rate,
beta=oja.beta,
)
)
# expose these for probes
model.sig[rule]["pre_filtered"] = pre_filtered
model.sig[rule]["post_filtered"] = post_filtered
[docs]@Builder.register(Voja)
def build_voja(model, voja, rule):
"""Builds a `.Voja` object into a model.
Calls synapse build functions to filter the post activities,
and adds a `.SimVoja` operator to the model to calculate the delta.
Parameters
----------
model : Model
The model to build into.
voja : Voja
Learning rule type to build.
rule : LearningRule
The learning rule object corresponding to the neuron type.
Notes
-----
Does not modify ``model.params[]`` and can therefore be called
more than once with the same `.Voja` instance.
"""
conn = rule.connection
# Filtered post activity
post = conn.post_obj
post_filtered = build_or_passthrough(
model, voja.post_synapse, model.sig[post]["out"]
)
# Learning signal, defaults to 1 in case no connection is made
# and multiplied by the learning_rate * dt
learning = Signal(shape=rule.size_in, name="Voja:learning")
assert rule.size_in == 1
model.add_op(Reset(learning, value=1.0))
model.sig[rule]["in"] = learning # optional connection will attach here
scaled_encoders = model.sig[post]["encoders"]
# The gain and radius are folded into the encoders during the ensemble
# build process, so we need to make sure that the deltas are proportional
# to this scaling factor
encoder_scale = model.params[post].gain / post.radius
assert post_filtered.shape == encoder_scale.shape
model.add_op(
SimVoja(
pre_decoded=model.sig[conn]["out"],
post_filtered=post_filtered,
scaled_encoders=scaled_encoders,
delta=model.sig[rule]["delta"],
scale=encoder_scale,
learning_signal=learning,
learning_rate=voja.learning_rate,
)
)
model.sig[rule]["scaled_encoders"] = scaled_encoders
model.sig[rule]["post_filtered"] = post_filtered
[docs]@Builder.register(PES)
def build_pes(model, pes, rule):
"""Builds a `.PES` object into a model.
Calls synapse build functions to filter the pre activities,
and adds a `.SimPES` operator to the model to calculate the delta.
Parameters
----------
model : Model
The model to build into.
pes : PES
Learning rule type to build.
rule : LearningRule
The learning rule object corresponding to the neuron type.
Notes
-----
Does not modify ``model.params[]`` and can therefore be called
more than once with the same `.PES` instance.
"""
conn = rule.connection
# Create input error signal
error = Signal(shape=rule.size_in, name="PES:error")
model.add_op(Reset(error))
model.sig[rule]["in"] = error # error connection will attach here
# Filter pre-synaptic activities with pre_synapse
acts = build_or_passthrough(model, pes.pre_synapse, model.sig[conn.pre_obj]["out"])
if conn.is_decoded:
encoders = None
else:
post = get_post_ens(conn)
encoders = model.sig[post]["encoders"][:, conn.post_slice]
model.add_op(
SimPES(
acts, error, model.sig[rule]["delta"], pes.learning_rate, encoders=encoders
)
)
# expose these for probes
model.sig[rule]["error"] = error
model.sig[rule]["activities"] = acts
