bernoulli_synapse

class brainpy.state.bernoulli_synapse(weight=1.0, delay=Quantity(1., 'ms'), receptor_type=0, p_transmit=1.0, post=None, event_type='spike', name=None)

NEST-compatible bernoulli_synapse connection model.

Short description

Static synapse with stochastic transmission.

Description

bernoulli_synapse mirrors NEST models/bernoulli_synapse.h. The model is non-plastic and stores fixed parameters:

• synaptic weight weight,

• synaptic delay delay,

• receiver port receptor_type,

• transmission probability p_transmit.

On each outgoing event, one Bernoulli trial is drawn and the event is transmitted only if the trial succeeds:

\[\mathrm{send} \iff U < p_{\mathrm{transmit}}, \quad U \sim \mathrm{Uniform}(0, 1).\]

A failed trial drops the event entirely.

1. Mathematical formulation

Stochastic transmission probability: Each spike arriving at the synapse triggers a Bernoulli trial with success probability \(p_{\mathrm{transmit}}\). The trial outcome determines whether the event is forwarded to the postsynaptic target. Formally:

\[P(\text{transmit spike}) = p_{\mathrm{transmit}}\]

The transmission decision for each spike is independent of previous trials. No state variables are maintained across spikes — the synapse is memoryless.

2. Implementation details

Random number generation uses NumPy’s global RNG state (np.random.random()). The trial outcome is computed by comparing a uniform random variate \(U \sim \mathrm{Uniform}(0, 1)\) to the threshold \(p_{\mathrm{transmit}}\):

\[\begin{split}\text{transmit} = \begin{cases} \text{True}, & U < p_{\mathrm{transmit}} \\ \text{False}, & \text{otherwise} \end{cases}\end{split}\]

If the trial fails, the spike is discarded before scheduling. If successful, the spike is forwarded using the parent static_synapse delivery mechanism with the configured weight and delay.

3. Event send ordering (NEST source equivalent)

NEST models/bernoulli_synapse.h performs:

1. Draw Bernoulli decision from uniform random number and p_transmit.

2. If successful: e.set_weight(weight_)

3. e.set_delay_steps(get_delay_steps())

4. e.set_receiver(*get_target(tid))

5. e.set_rport(get_rport())

6. e() (deliver event)

This implementation preserves the same semantics: stochastic transmission is decided before scheduling; when accepted, inherited static_synapse scheduling applies weight, delay steps, receiver and receptor port in the same effective order.

4. Biological motivation

Synaptic transmission in real neural circuits is stochastic due to finite vesicle release probabilities and quantal failures. This model approximates such unreliable transmission using a simple Bernoulli process, which is computationally efficient and captures the essential statistical properties of transmission failures.

Applications include:

• Sparse networks with probabilistic connectivity (e.g., cortical column models, [2]).

• Networks with strong-sparse and weak-dense connectivity motifs [3].

• Recurrent networks where transmission failures contribute to decorrelation and robustness [4].

5. Computational considerations

• Random number generation introduces non-determinism. For reproducible simulations, seed the NumPy RNG before initializing the network: np.random.seed(42).

• Each spike invokes one call to np.random.random(), adding negligible computational overhead compared to deterministic synapses.

• The model is stateless and suitable for large-scale network simulations where memory footprint per synapse is a constraint.

Parameters:

• weight (ArrayLike, optional) – Fixed synaptic weight (dimensionless or receiver-dependent units such as pA, nS, or mV). Must be scalar. Default: 1.0.

• delay (ArrayLike, optional) – Synaptic delay in ms. Must be scalar. Converted to integer simulation steps using round-to-nearest with midpoint-up (NEST convention). Default: 1.0 * u.ms.

• receptor_type (int, optional) – Receiver port/receptor id. Used to target specific synaptic receptor channels on the postsynaptic neuron. Default: 0.

• p_transmit (ArrayLike, optional) – Spike transmission probability in [0, 1]. Must be scalar. Values outside this range raise ValueError. Default: 1.0.

• post (object, optional) – Default receiver object (postsynaptic neuron or target module). If not provided, a receiver must be passed explicitly to send() when scheduling events.

• event_type (str, optional) – Event transmission type. Inherited from static_synapse. One of 'spike', 'rate', 'current', 'conductance', 'double_data', 'data_logging'. Default: 'spike'.

• name (str, optional) – Object name for debugging and introspection.

Raises:

ValueError – If p_transmit is not scalar or is outside [0, 1].

See also

static_synapse

Parent class implementing deterministic event scheduling.

tsodyks_synapse

Short-term plasticity model with dynamic transmission.

Notes

• This model does not implement plasticity (no weight updates, no state evolution).

• Random draws use NumPy’s global RNG state. Use np.random.seed(...) for reproducible test traces when needed.

• The model is compatible with all event types supported by static_synapse, though biological applications typically use event_type='spike'.

• Transmission failures are independent across spikes and across different synapse instances.

Examples

Create a stochastic synapse with 50% transmission probability:

>>> import brainpy.state as bst
>>> import saiunit as u
>>> post_neuron = bst.LIF(1)
>>> syn = bst.bernoulli_synapse(
...     weight=5.0,
...     delay=2.0 * u.ms,
...     p_transmit=0.5,
...     post=post_neuron,
... )

Simulate stochastic transmission and observe dropped spikes:

>>> import numpy as np
>>> np.random.seed(42)  # for reproducibility
>>> transmitted = [syn.send(multiplicity=1.0) for _ in range(10)]
>>> transmitted
[False, True, False, True, True, False, True, False, False, True]

Query current parameters:

>>> params = syn.get()
>>> params['p_transmit']
0.5

Update transmission probability dynamically:

>>> syn.set(p_transmit=0.8)
>>> syn.p_transmit
0.8

References

[1]

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

[2]

Lefort S, Tomm C, Sarria J-C F, Petersen CCH (2009). The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron, 61(2):301-316. DOI: https://doi.org/10.1016/j.neuron.2008.12.020

[3]

Teramae J, Tsubo Y, Fukai T (2012). Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links. Scientific Reports 2, 485. DOI: https://doi.org/10.1038/srep00485

[4]

Omura Y, Carvalho MM, Inokuchi K, Fukai T (2015). A lognormal recurrent network model for burst generation during hippocampal sharp waves. Journal of Neuroscience, 35(43):14585-14601. DOI: https://doi.org/10.1523/JNEUROSCI.4944-14.2015

get()

Return current public parameters.

Returns:

Dictionary containing all connection parameters:

• 'weight' : float — synaptic weight.

• 'delay' : float — synaptic delay in ms.

• 'receptor_type' : int — receiver port id.

• 'p_transmit' : float — transmission probability in [0, 1].

• 'synapse_model' : str — model identifier ('bernoulli_synapse').

Return type:

dict

Examples

>>> syn = bst.bernoulli_synapse(weight=2.0, p_transmit=0.7)
>>> params = syn.get()
>>> params['p_transmit']
0.7

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

Stochastically schedule one outgoing event.

Performs a Bernoulli trial to decide whether to transmit the event. If the trial succeeds, the event is scheduled for delivery using the inherited static_synapse mechanism. If the trial fails, the event is discarded.

Parameters:

• multiplicity (ArrayLike, optional) – Event payload value (spike count, rate, or current). If zero or negligible (< 1e-12), the event is dropped without drawing a random number. Default: 1.0.

• post (object, optional) – Receiver object (postsynaptic neuron). Overrides the default receiver set in __init__() or set(). If both are None, scheduling will fail.

• receptor_type (int, optional) – Receiver port/receptor id. Overrides the default receptor type.

• event_type (str, optional) – Event transmission type. Overrides the default event type.

Returns:

True if the event was successfully transmitted and scheduled. False if the event was zero, or if the Bernoulli trial failed.

Return type:

bool

Notes

• Zero-valued events (multiplicity < 1e-12) are dropped before the Bernoulli trial to avoid unnecessary random number generation.

• Each call draws one uniform random variate from NumPy’s global RNG.

• The transmission decision is independent of previous calls.

Examples

Simulate stochastic transmission with 50% probability:

>>> import numpy as np
>>> np.random.seed(42)
>>> syn = bst.bernoulli_synapse(p_transmit=0.5, post=post_neuron)
>>> results = [syn.send(multiplicity=1.0) for _ in range(10)]
>>> results
[False, True, False, True, True, False, True, False, False, True]
>>> sum(results)  # approximately 5 out of 10
5

Zero-valued events are dropped without drawing random numbers:

>>> syn.send(multiplicity=0.0)
False

set(*, weight=<object object>, delay=<object object>, receptor_type=<object object>, p_transmit=<object object>, post=<object object>, event_type=<object object>)

Set NEST-style public parameters.

Updates one or more connection parameters. All parameters are optional; unspecified parameters retain their current values.

Parameters:

• weight (ArrayLike, optional) – New synaptic weight. Must be scalar.

• delay (ArrayLike, optional) – New synaptic delay in ms. Must be scalar.

• receptor_type (int, optional) – New receiver port/receptor id.

• p_transmit (ArrayLike, optional) – New transmission probability in [0, 1]. Must be scalar.

• post (object, optional) – New default receiver object.

• event_type (str, optional) – New event transmission type ('spike', 'rate', 'current', 'conductance', 'double_data', 'data_logging').

Raises:

ValueError – If p_transmit is provided and is not scalar or is outside [0, 1].

Examples

>>> syn = bst.bernoulli_synapse(weight=1.0, p_transmit=0.5)
>>> syn.set(p_transmit=0.8, weight=2.0)
>>> syn.p_transmit
0.8