stdp_nn_restr_synapse

class brainpy.state.stdp_nn_restr_synapse(weight=1.0, delay=Quantity(1., 'ms'), receptor_type=0, tau_plus=Quantity(20., 'ms'), tau_minus=Quantity(20., 'ms'), lambda_=0.01, alpha=1.0, mu_plus=1.0, mu_minus=1.0, Wmax=100.0, post=None, name=None)

NEST-compatible stdp_nn_restr_synapse connection model.

Short description

Synapse type for spike-timing dependent plasticity with restricted symmetric nearest-neighbour spike pairing.

Description

stdp_nn_restr_synapse mirrors NEST models/stdp_nn_restr_synapse.h and implements the restricted nearest-neighbor pairing scheme from Morrison et al. (2008, fig. 7C):

• On a presynaptic spike, depression uses the nearest preceding postsynaptic spike only if that postsynaptic spike occurred after the previous presynaptic spike,

• On postsynaptic spikes, facilitation pairs only with the nearest preceding presynaptic spike that has not already been used for facilitation.

A spike therefore participates in at most one depression pair and at most one facilitation pair.

Compared with stdp_synapse, this model changes two core STDP mechanisms:

• No running presynaptic Kplus trace is used,

• Depression is nearest-neighbor and restricted to intervals where at least one postsynaptic spike occurred since the last presynaptic spike.

1. Mathematical Formulation

With normalized weight \(\hat w = w/W_{max}\):

\[\hat w \leftarrow \hat w + \lambda (1-\hat w)^{\mu_+} k_+\]

\[\hat w \leftarrow \hat w - \alpha \lambda \hat w^{\mu_-} k_-\]

with clipping to [0, Wmax] in normalized coordinates, as in NEST.

The potentiation trace factor for the restricted rule is:

\[k_+ = \exp\left(\frac{t_{\mathrm{last}} - (t_{post} + d)}{\tau_+}\right)\]

where \(t_{\mathrm{last}}\) is the previous presynaptic spike time, \(t_{post}\) is the first postsynaptic spike time in the readout window, and \(d\) is the dendritic delay.

The depression trace factor is:

\[k_- = \exp\left(\frac{t_{post}^{\mathrm{nn}} - (t_{pre} - d)}{\tau_-}\right)\]

where \(t_{post}^{\mathrm{nn}}\) is the nearest postsynaptic spike strictly before \(t_{pre} - d\).

2. Update Order (NEST Source Equivalent)

For a presynaptic spike at \(t_{pre}\) with dendritic delay \(d\), NEST stdp_nn_restr_synapse::send performs:

1. Read postsynaptic history in \((t_{\mathrm{last}}-d,\, t_{pre}-d]\).

2. If history is non-empty, facilitate once using the first postsynaptic spike in that interval: \(\exp((t_{\mathrm{last}}-(t_{post}+d))/\tau_+)\).

3. If history is non-empty, depress once using nearest-neighbor postsynaptic trace at \(t_{pre}-d\): \(\exp((t_{post}^{\mathrm{nn}}-(t_{pre}-d))/\tau_-)\).

4. Send event with updated weight.

5. Set t_lastspike = t_pre.

This implementation preserves that exact ordering.

3. Coincidence Semantics

Pairs with exact coincidence are discarded by strict time comparisons (NEST stdp_eps behavior). If presynaptic_spike == postsynaptic_spike + dendritic_delay, \(\Delta t = 0\) is not used; the nearest strictly earlier valid post-spike is used instead.

4. Restricted Pairing Constraint

The “restricted” property ensures that a postsynaptic spike contributes to plasticity only if it occurred in the inter-spike interval between two consecutive presynaptic spikes. This prevents accumulation of plasticity from postsynaptic spikes that precede the synapse’s activation history.

Parameters:

• weight (ArrayLike, optional) – Initial synaptic weight (scalar, float). Must have same sign as Wmax. Default: 1.0.

• delay (ArrayLike, optional) – Synaptic delay (scalar, saiunit time). Dendritic delay for spike transmission. Default: 1.0 * u.ms.

• receptor_type (int, optional) – Receiver port/receptor id (non-negative integer). Identifies which input channel of the postsynaptic neuron this synapse targets. Default: 0.

• tau_plus (ArrayLike, optional) – Potentiation time constant (scalar, saiunit time, positive). Controls the temporal window for LTP. Default: 20.0 * u.ms.

• tau_minus (ArrayLike, optional) – Depression trace time constant (scalar, saiunit time, positive). Controls the temporal window for LTD. In NEST this belongs to the postsynaptic archiving neuron; here it is stored on the synapse for standalone compatibility. Default: 20.0 * u.ms.

• lambda (ArrayLike, optional) – Learning-rate parameter (scalar, float, positive). Global scaling factor for weight updates. Default: 0.01.

• alpha (ArrayLike, optional) – Depression scaling parameter (scalar, float, positive). Relative strength of LTD versus LTP. Default: 1.0.

• mu_plus (ArrayLike, optional) – Potentiation exponent (scalar, float, non-negative). Controls the weight-dependence of LTP. mu_plus=0 gives additive LTP, mu_plus=1 gives multiplicative LTP. Default: 1.0.

• mu_minus (ArrayLike, optional) – Depression exponent (scalar, float, non-negative). Controls the weight-dependence of LTD. mu_minus=0 gives additive LTD, mu_minus=1 gives multiplicative LTD. Default: 1.0.

• Wmax (ArrayLike, optional) – Maximum weight bound (scalar, float). Must have same sign as weight. Weights are clipped to the range [0, Wmax] or [Wmax, 0] depending on sign. Default: 100.0.

• post (object, optional) – Default receiver object. Must implement postsynaptic input methods. If None, must be specified in send() calls. Default: None.

• name (str, optional) – Object name for identification. Default: None.

Parameter Mapping

The following table maps NEST parameter names to their brainpy.state equivalents:

NEST Parameter	brainpy.state	Notes
weight	weight	Synaptic efficacy
delay	delay	Dendritic delay (ms)
receptor_type	receptor_type	Target receptor port
tau_plus	tau_plus	LTP time constant (ms)
tau_minus	tau_minus	LTD time constant (ms)
lambda	lambda_	Learning rate
alpha	alpha	LTD scaling factor
mu_plus	mu_plus	LTP weight-dependence exponent
mu_minus	mu_minus	LTD weight-dependence exponent
Wmax	Wmax	Maximum weight bound
t_lastspike	t_lastspike	Previous presynaptic spike time

Notes

• In NEST, tau_minus is a postsynaptic-neuron parameter.

• As in NEST, STDP updates are based on on-grid spike stamps and ignore sub-step precise offsets.

• Kplus is not a parameter of this model (unlike stdp_synapse).

• The restriction mechanism ensures each spike participates in at most one pair of each type (facilitation and depression).

Examples

Create a restricted nearest-neighbor STDP synapse:

>>> import brainpy.state as bst
>>> import saiunit as u
>>> syn = bst.nn.stdp_nn_restr_synapse(
...     weight=0.5,
...     delay=1.5 * u.ms,
...     tau_plus=20.0 * u.ms,
...     tau_minus=20.0 * u.ms,
...     lambda_=0.01,
...     alpha=1.0,
...     mu_plus=1.0,
...     mu_minus=1.0,
...     Wmax=100.0
... )

Configure asymmetric learning rates:

>>> syn = bst.nn.stdp_nn_restr_synapse(
...     weight=1.0,
...     lambda_=0.005,
...     alpha=1.05,  # Slightly stronger depression
...     mu_plus=0.0,  # Additive LTP
...     mu_minus=1.0  # Multiplicative LTD
... )

References

[1]

NEST source: models/stdp_nn_restr_synapse.h and models/stdp_nn_restr_synapse.cpp.

[2]

Morrison A, Diesmann M, Gerstner W (2008). Phenomenological models of synaptic plasticity based on spike timing. Biological Cybernetics, 98:459-478. DOI: 10.1007/s00422-008-0233-1

get()

Return current public parameters and mutable state.

Returns the NEST-compatible parameter dictionary for this synapse, excluding Kplus (which is not used in this model).

Returns:

Dictionary containing all public parameters and mutable state: weight, delay, receptor_type, tau_plus, tau_minus, lambda, alpha, mu_plus, mu_minus, Wmax, t_lastspike, and synapse_model.

Return type:

dict

Notes

• The returned dictionary has synapse_model='stdp_nn_restr_synapse' for NEST compatibility.

• Kplus is removed from the parent class’s output since it is not part of the restricted nearest-neighbor pairing scheme.

send(multiplicity=1.0, *, post=None, receptor_type=None)

Schedule one outgoing event with NEST stdp_nn_restr_synapse dynamics.

Implements the restricted nearest-neighbor STDP pairing rule. On each presynaptic spike:

1. Reads postsynaptic spike history in the interval \((t_{\mathrm{last}}-d,\, t_{pre}-d]\).

2. If the history is non-empty:

   • Applies facilitation (LTP) using the first postsynaptic spike in the interval.

   • Applies depression (LTD) using the nearest-neighbor postsynaptic trace.

3. Schedules the spike event with updated weight for delivery after the dendritic delay.

4. Updates t_lastspike to the current spike time.

Parameters:

• multiplicity (ArrayLike, optional) – Scalar event weight multiplier (e.g., spike count). If zero or very small, no event is sent. Default: 1.0.

• post (object, optional) – Target receiver object. If None, uses the default receiver set during initialization. Must implement postsynaptic input methods.

• receptor_type (ArrayLike, optional) – Target receptor port (non-negative integer). If None, uses self.receptor_type. Default: None.

Returns:

True if an event was scheduled, False if multiplicity was zero and no event was sent.

Return type:

bool

Notes

• Restricted pairing: Both LTP and LTD are applied only if at least one postsynaptic spike occurred between the previous and current presynaptic spikes.

• Facilitation: Uses the first postsynaptic spike in the readout window with trace factor \(\exp((t_{\mathrm{last}} - (t_{post} + d))/\tau_+)\).

• Depression: Uses the nearest-neighbor postsynaptic trace at \(t_{pre} - d\).

• Event timing: Uses on-grid spike stamps (ignores sub-step precise offsets).

• Weight bounds: Updated weight is clipped to [0, Wmax] or [Wmax, 0] depending on sign.

Examples

Send a presynaptic spike with default multiplicity:

>>> sent = syn.send()

Send with custom multiplicity and receptor type:

>>> sent = syn.send(multiplicity=2.0, receptor_type=1)

set(**kwargs)

Set NEST-style public parameters and mutable state.

Accepts keyword arguments matching NEST parameter names for this synapse model. Raises an error if Kplus is provided (not used in this model).

Parameters:

**kwargs – Keyword arguments for parameters to update. Valid keys: weight, delay, receptor_type, tau_plus, tau_minus, lambda, alpha, mu_plus, mu_minus, Wmax, t_lastspike.

Raises:

• ValueError – If Kplus is provided (not a valid parameter for this model).

• ValueError – If any provided value fails validation (e.g., negative time constant, incompatible weight/Wmax signs).

Notes

• Setting weight or Wmax will re-validate the sign consistency constraint (both must have the same sign).