Adaptrode synapse
An Adaptrode synapse driven by a train of input pulses that stops after a while.
- Name:
adaptrode - Field:
biology/neuroscience - Formalism: discrete map
- References: Mobus 1994; Mobus 2022
Factory
@register_model(
field='biology/neuroscience',
tags=('synapse', 'learning', 'memory', 'discrete map'),
references=('Mobus 1994', 'Mobus 2022'),
defaults={'until': 400, 'dt': 1},
)
def adaptrode(
*,
alpha0: float = 0.25,
alpha1: float = 0.05,
alpha2: float = 0.01,
delta0: float = 0.1,
delta1: float = 0.02,
delta2: float = 0.002,
period: float = 10.0,
stop: float = 150.0,
) -> System:
"""Return an Adaptrode synapse driven by a train of input pulses that stops after a while.
While the pulses arrive the fast weight follows each pulse, the medium weight builds up, and the slow weight
builds up further. After the input stops the fast weight falls back quickly to the medium one, which keeps a
trace of the activity far longer, while the slow weight retains a long-term memory.
Args:
alpha0:
The learning rate of the fast weight.
alpha1:
The learning rate of the medium weight.
alpha2:
The learning rate of the slow weight.
delta0:
The decay rate of the fast weight.
delta1:
The decay rate of the medium weight.
delta2:
The decay rate of the slow weight.
period:
The number of steps between the starts of two pulses.
stop:
The step after which the input stays off.
Returns:
system:
The model, with the weights `synapse.w0`, `synapse.w1`, and `synapse.w2`.
Examples:
>>> from skcomplex.models.biology.neuroscience import adaptrode
>>> adaptrode(stop=50.0).elements[0].stop
50.0
"""
synapse = AdaptrodeElement(
'synapse',
alpha0=alpha0,
alpha1=alpha1,
alpha2=alpha2,
delta0=delta0,
delta1=delta1,
delta2=delta2,
period=period,
stop=stop,
)
levels = [
MapInteraction(
'fast_level',
target='synapse',
state='w0',
function=lambda s: s.target.w0
+ s.target.alpha0 * _input(s) * (s.target.w_max - s.target.w0)
- s.target.delta0 * (s.target.w0 - s.target.w1),
),
MapInteraction(
'medium_level',
target='synapse',
state='w1',
function=lambda s: s.target.w1
+ s.target.alpha1 * (s.target.w0 - s.target.w1)
- s.target.delta1 * (s.target.w1 - s.target.w2),
),
MapInteraction(
'slow_level',
target='synapse',
state='w2',
function=lambda s: s.target.w2
+ s.target.alpha2 * (s.target.w1 - s.target.w2)
- s.target.delta2 * s.target.w2,
),
]
return System(elements=[synapse], interactions=levels)
Components
class AdaptrodeElement(Element):
"""Adaptrode of Mobus, a synaptic weight with three levels of memory that learn on increasing time scales.
At every step the fast weight `w0` rises toward `w_max` in proportion to the input `x` and decays toward the
slower weight `w1`, which rises toward `w0` and decays toward the slowest weight `w2`, which rises toward `w1` and
decays toward zero. The input is a train of pulses of height `amplitude`, `width` steps long, every `period`
steps, until the step `stop`, so the weights record recent, medium-term, and long-term activity. The element holds
the states and parameters and has no laws of its own: the maps of `adaptrode`, one per level, read its parameters.
Args:
label:
The label of the synapse.
visual:
How the element is drawn, or `None` for `default_visual_`.
w0:
The initial fast weight.
w1:
The initial medium weight.
w2:
The initial slow weight.
w_max:
The largest weight.
alpha0:
The learning rate of the fast weight.
alpha1:
The learning rate of the medium weight.
alpha2:
The learning rate of the slow weight.
delta0:
The decay rate of the fast weight.
delta1:
The decay rate of the medium weight.
delta2:
The decay rate of the slow weight.
amplitude:
The height of the input pulses.
period:
The number of steps between the starts of two pulses.
width:
The number of steps of each pulse.
stop:
The step after which the input stays off.
Examples:
>>> from skcomplex.models.biology.neuroscience import AdaptrodeElement
>>> AdaptrodeElement('synapse').w_max
1.0
"""
def __init__(
self,
label: str,
visual: VisualSpec | None = None,
*,
w0: Annotated[float, StateSpec(domain=RealSet.closed_open(0, oo))] = 0.0,
w1: Annotated[float, StateSpec(domain=RealSet.closed_open(0, oo))] = 0.0,
w2: Annotated[float, StateSpec(domain=RealSet.closed_open(0, oo))] = 0.0,
w_max: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 1.0,
alpha0: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.25,
alpha1: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.05,
alpha2: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.01,
delta0: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.1,
delta1: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.02,
delta2: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 0.002,
amplitude: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
period: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 10.0,
width: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 3.0,
stop: Annotated[float, ParameterSpec()] = 150.0,
) -> None:
super().__init__(label, visual=visual)
self.w0 = w0
self.w1 = w1
self.w2 = w2
self.w_max = w_max
self.alpha0 = alpha0
self.alpha1 = alpha1
self.alpha2 = alpha2
self.delta0 = delta0
self.delta1 = delta1
self.delta2 = delta2
self.amplitude = amplitude
self.period = period
self.width = width
self.stop = stop
class MapInteraction(Interaction):
"""Map of a state of discrete time, whose next value is a function, or the state plus it.
In the mode `'replace'` the next value of the state is `f`, and in the mode `'increment'` it is the state plus `f`.
Under the `'synchronous'` schedule every member of a bound group updates at once, from the states at the start of
the step. Under the `'sequential'` schedule the members update one after the other, in their order, and under the
`'random-sequential'` schedule in a new random order every step, each member reading the values the members before
it set. Under the `'member'` schedule of the agent form, every member updates in its own activation, together with
the rules of its element and the other member interactions, in the order the system lists them.
In the `'symbolic'` form, `function(namespace)` returns a symbolic expression, or a vector of them for a vector
state, where `namespace.target` holds the states and parameters of the target, `namespace.sources` the namespaces
of the sources, and `namespace.t` the time, and may hold draws such as `normal('noise')`. In the `'agent'` form,
the target is an agent group and `function(agent, model)` returns the value as a number, or as an array of the
shape of a vector state, so it can read the agent, its neighbours, and the history and storage of the model view.
Args:
label:
The label of the interaction, unique among the parts of its system.
target:
The path of the element or group whose state the map sets.
state:
The name of the state of the target.
function:
The function `f(namespace)` in the symbolic form, or `f(agent, model)` in the agent form.
sources:
The paths of the elements, or members of groups such as `cells[0]`, that the function reads.
mode:
`'replace'` or `'increment'`.
schedule:
`'synchronous'`, `'sequential'`, `'random-sequential'`, or `'member'` for the agent form.
form:
`'symbolic'` for update laws of the states of the target, or `'agent'` for a rule over an agent group.
phase:
The phase of the step the agent form runs in, or `None` for the default phase.
Raises:
ValidationError:
The mode, the schedule, or the form is unknown, the symbolic form has the schedule `'member'`, the
function is not callable, or the agent form returns a value that does not match the state, raised by
`run` of the simulation.
Examples:
>>> from skcomplex.core.elements import Element
>>> from skcomplex.core.interactions import MapInteraction
>>> from skcomplex.core.spaces import DiscreteTime
>>> from skcomplex.core.system import System
>>> from skcomplex.engine.runtime import Simulation
>>> from skcomplex.specs import StateSpec
>>> from typing import Annotated, SupportsFloat
>>> class ValueElement(Element):
... def __init__(self, label, x: Annotated[float, StateSpec()] = 0.5):
... super().__init__(label)
... self.x = x
>>> logistic = MapInteraction(
... 'map', target='value', state='x', function=lambda s: 3 * s.target.x * (1 - s.target.x)
... )
>>> system = System(elements=[ValueElement('value')], interactions=[logistic], time=DiscreteTime())
>>> Simulation(system).check().prepare().run(until=2).trajectory_.values('value.x').tolist()
[0.5, 0.75, 0.5625]
>>> agents = MapInteraction('map', target='walkers', state='x', function=lambda a, m: a.x + 1, form='agent')
>>> type(agents.check().prepare().run(SimpleNamespace()).laws_[0]).__name__
'RuleLaw'
>>> from skcomplex.core.elements import GroupElement
>>> class WeightsElement(Element):
... def __init__(self, label, visual=None, *, w: Annotated[object, StateSpec(vector=True)] = 0.0):
... super().__init__(label, visual=visual)
... self.w = w
>>> group = GroupElement('weights', element=WeightsElement, size=1, values={'w': [1.0, 2.0]})
>>> doubling = MapInteraction(
... 'double', target='weights', state='w', function=lambda a, m: [2 * x for x in a.w], form='agent'
... )
>>> trajectory = Simulation(System(elements=[group], interactions=[doubling])).check().prepare().run(until=2)
>>> trajectory.trajectory_.agents('weights', 2).values['w'].tolist()
[[4.0, 8.0]]
"""
def __init__(
self,
label: str,
*,
target: Annotated[str, RoleSpec()],
state: str,
function: Callable[..., object],
sources: Annotated[Sequence[str], RoleSpec(variadic=True)] = (),
mode: str = 'replace',
schedule: str = 'synchronous',
form: str = 'symbolic',
phase: str | None = None,
) -> None:
super().__init__(label)
self.target = target
self.state = state
self.function = function
self.sources = sources
self.mode = mode
self.schedule = schedule
self.form = form
self.phase = phase
def _check(self) -> None:
"""Raise an error for an unknown mode, schedule, or form, or a function that cannot be called.
Raises:
ValidationError:
The mode, the schedule, or the form is unknown, the symbolic form has the schedule `'member'`, or the
function is not callable.
"""
super()._check()
self._check_variant('mode', self.mode, MODES, (BaseSpec,))
for name, value, variants in (
('schedule', self.schedule, SCHEDULES),
('form', self.form, FORMS),
):
if value not in variants:
error_msg = f'The {name} of map {self.label!r} is {value!r}. Use one of {", ".join(variants)}.'
raise ValidationError(error_msg)
if self.schedule == 'member' and self.form != 'agent':
error_msg = (
f'The map {self.label!r} updates every member in its activation, which only the agent form does.'
)
raise ValidationError(error_msg)
if not callable(self.function):
error_msg = f'The function of map {self.label!r} must be callable, but it is {self.function!r}.'
raise ValidationError(error_msg)
def _apply_mode(self, current: Value, value: Value) -> Value:
"""Return the next value of a state from its current value and the value of the function, by the mode."""
if self.mode == 'increment':
return current + value
if self.mode == 'replace':
return value
raise self._get_variant_error(self.mode, 'mode', '_apply_mode')
def _get_vector(self, agent: AgentViewProtocol, model: ModelViewProtocol) -> Value:
"""Return the next value of a vector state of an agent."""
current = np.asarray(getattr(agent, self.state), dtype=np.float64)
value = np.asarray(self.function(agent, model), dtype=np.float64)
if value.shape != current.shape:
error_msg = (
f'The function of map {self.label!r} returns the shape {value.shape} for the state {self.state!r} of '
f'the shape {current.shape}. Return an array of the shape of the state.'
)
raise ValidationError(error_msg)
return self._apply_mode(current, value)
def _get_value(self, agent: AgentViewProtocol, model: ModelViewProtocol) -> Value:
"""Return the next value of the state of an agent, a number or the array of a vector state."""
if np.ndim(getattr(agent, self.state)) > 0:
return self._get_vector(agent, model)
found = self.function(agent, model)
if not isinstance(found, SupportsFloat):
error_msg = f'The function of map {self.label!r} returns {found!r} for an agent. Return a number.'
raise ValidationError(error_msg)
value = float(found)
return self._apply_mode(float(getattr(agent, self.state)), value)
def _set_value(self, agent: AgentViewProtocol, value: Value) -> None:
"""Set the state of an agent to its next value."""
setattr(agent, self.state, value)
def _update_member(self, agent: AgentViewProtocol, model: ModelViewProtocol) -> None:
"""Set the state of one member to its next value."""
if agent.alive:
self._set_value(agent, self._get_value(agent, model))
def update(self, model: ModelViewProtocol) -> None:
"""Set the state of every agent of the target to its next value, by the schedule.
Args:
model:
The model view of the interaction.
"""
self._update_agents(model, self.schedule, self._get_value, self._set_value)
def _get_order(self) -> object:
"""Return the order of the members of the symbolic form: none, their own order, or a uniform draw."""
if self.schedule == 'synchronous':
return None
if self.schedule == 'sequential':
return SR(0)
return uniform(re.sub(r'\W', '_', f'order_{self.label}'))
def _get_laws(self, namespace: SimpleNamespace) -> list[BasePart]:
"""Return the update of the state to its next value, or the rule of the agent form.
Args:
namespace:
The namespace of the symbols the laws can use, with `namespace.target` and `namespace.sources`.
Returns:
laws:
The update law of the state, or the rule that runs the map of the agents.
"""
if self.form == 'agent' and self.schedule == 'member':
return [RuleLaw(self._update_member, phase=self.phase, members=self._get_role('target'))]
if self.form == 'agent':
return [RuleLaw(self.update, phase=self.phase)]
value = getattr(self._get_member(namespace, 'target'), self.state)
mapped = cast(Value, self.function(namespace))
next_value = self._apply_mode(value, mapped)
return [UpdateLaw(value, next_value, increment=self.mode == 'increment', order=self._get_order())]
Equations
synapse.w0: w0_synapse(t + 1) == alpha0_synapse*(w_max_synapse - w0_synapse(t))*where(mod(t, period_synapse) < width_synapse, where(t < stop_synapse, amplitude_synapse, 0), 0) - delta0_synapse*(w0_synapse(t) - w1_synapse(t)) + w0_synapse(t)
synapse.w1: w1_synapse(t + 1) == alpha1_synapse*(w0_synapse(t) - w1_synapse(t)) - delta1_synapse*(w1_synapse(t) - w2_synapse(t)) + w1_synapse(t)
synapse.w2: w2_synapse(t + 1) == alpha2_synapse*(w1_synapse(t) - w2_synapse(t)) - delta2_synapse*w2_synapse(t) + w2_synapse(t)