rate_connection_delayed

class brainpy.state.rate_connection_delayed(*args, **kwargs)

NEST-compatible rate_connection_delayed connection spec.

Carries the NEST-facing parameters and status of a delayed rate connection: a scalar weight and an integer delay_steps (>= 1). It mirrors NEST’s GetStatus / SetStatus surface (weight, delay / delay_steps aliases, has_delay, supports_wfr) so connection parameters round-trip identically to the C++ model.

The delayed rate coupling itself is realized by the Simulator’s continuous-rate (seam-(H)) emission path: a presynaptic rate neuron emits its graded rate each step, and the connection routes weight · rate through an input delay line of delay_steps steps (delay_steps · dt of latency) into the postsynaptic neuron’s delta input channel, which the post reads via sum_delta_inputs. This spec object carries the parameters; the Simulator builds the delay line from them.

Unlike rate_connection_instantaneous, this model enforces a minimum delay of one simulation step.

Parameters:

• weight (float or array-like, optional) – Connection gain/strength applied to transmitted rate signals. Must be scalar. Default: 1.0.

• delay_steps (int or array-like, optional) – Transmission delay in discrete simulation steps. Must be integer-valued and >= 1. Default: 1.

• name (str or None, optional) – Optional name identifier for this connection instance. Default: None.

weight

Connection gain (validated scalar).

Type:

float

delay_steps

Delay in simulation steps (validated >= 1).

Type:

int

name

Instance name.

Type:

str or None

HAS_DELAY

Class attribute, always True (this model enforces delay).

Type:

bool

SUPPORTS_WFR

Class attribute, always False (waveform relaxation not supported).

Type:

bool

Parameter Mapping

The following table maps NEST parameters to this implementation:

NEST Parameter	brainpy.state	Notes
weight	weight	Connection gain (scalar float)
delay	delay_steps	Delay in steps (integer >= 1)
has_delay	HAS_DELAY	Always True (class attribute)
supports_wfr	SUPPORTS_WFR	Always False (class attribute)

Mathematical Description

A delayed connection transmits a rate signal \(r_\text{pre}\) to the postsynaptic neuron with delay \(d\) and weight \(w\):

\[r_\text{post}(t) = w \cdot r_\text{pre}(t - d)\]

In discrete-time simulation with step size \(\Delta t\), the delay is quantized to an integer number of steps \(d_\text{steps} \geq 1\), and on the JAX substrate is realized by an input delay line of length \(d_\text{steps}\):

\[d_\text{steps} = \left\lceil \frac{d}{\Delta t} \right\rceil, \quad d_\text{steps} \geq 1\]

The presynaptic rate captured at step \(k\) is therefore deposited into the postsynaptic input at step \(k + d_\text{steps}\), matching NEST’s delayed rate delivery.

Implementation Notes

Delay Validation

This model enforces delay_steps >= 1 to comply with NEST semantics. Attempting to set delay_steps = 0 raises a ValueError. For instantaneous (zero-delay) connections, use rate_connection_instantaneous instead.

Unit Handling

All parameters accept brainunit.Quantity objects or plain numeric values. If a Quantity is provided, its mantissa is extracted. Internally, values are stored as dimensionless floats or integers.

Compatibility with NEST

• NEST stores delays in time units (ms), while this implementation uses discrete steps to match BrainPy’s event system.

• The set_status method accepts both delay and delay_steps as aliases (if both are provided, they must be identical).

Raises:

• ValueError – If weight or delay_steps is not scalar, or if delay_steps < 1.

• ValueError – If delay and delay_steps are both provided in set_status with conflicting values.

See also

rate_connection_instantaneous

Zero-delay rate connection model (NEST equivalent)

rate_neuron_ipn

Input rate neuron (delayed rate receiver)

rate_neuron_opn

Output rate neuron (delayed rate receiver)

References

[1]

Hahne, J., et al. (2015). “A unified framework for spiking and rate-based neural networks.” Frontiers in Neuroinformatics, 9, 22.

[2]

NEST Simulator documentation: Rate neuron models. https://nest-simulator.readthedocs.io/en/stable/models/rate_connection_delayed.html

[3]

NEST source: models/rate_connection_delayed.{h,cpp}.

[4]

NEST delayed-rate receiver handling: models/rate_neuron_ipn_impl.h and models/rate_neuron_opn_impl.h.

Examples

Basic Usage

Create a delayed connection with weight 2.0 and 3-step delay:

>>> from brainpy import state as bst
>>> conn = bst.rate_connection_delayed(weight=2.0, delay_steps=3)
>>> conn.get_status()
{'weight': 2.0, 'delay_steps': 3, 'delay': 3, 'has_delay': True, 'supports_wfr': False}

Dynamic Parameter Updates

Update connection parameters at runtime:

>>> conn.set_status(weight=1.5, delay_steps=5)
>>> conn.get('weight')
1.5
>>> conn.get('delay_steps')
5

Delay Validation

Zero or sub-step delays are rejected:

>>> conn.set_delay_steps(0)
Traceback (most recent call last):
    ...
ValueError: delay_steps must be >= 1.

Using with Rate Neurons

Typical usage in a rate-based network — the Simulator builds the delay line from the connection’s delay_steps:

>>> import brainunit as u
>>> from brainpy import state as bst
>>> sim = bst.Simulator(dt=0.1 * u.ms)
>>> pre = sim.create(bst.lin_rate_ipn, 10, params=dict(tau=10.0 * u.ms))
>>> post = sim.create(bst.lin_rate_ipn, 5, params=dict(tau=10.0 * u.ms))
>>> proj = sim.connect(pre, post, weight=0.5, delay=0.3 * u.ms, comm='dense')

get(key='status')

Retrieve a specific parameter or full status dictionary.

Parameters:

key (str, optional) – Parameter name to retrieve. Special value 'status' returns full status dictionary. Supported keys: 'status', 'weight', 'delay', 'delay_steps', 'has_delay', 'supports_wfr'. Default: 'status'.

Returns:

If key == 'status', returns full status dictionary. Otherwise, returns the requested parameter value.

Return type:

dict or scalar

Raises:

KeyError – If key is not a recognized parameter name.

Examples

>>> conn = rate_connection_delayed(weight=2.0, delay_steps=3)
>>> conn.get('weight')
2.0
>>> conn.get('delay_steps')
3
>>> conn.get('status')
{'weight': 2.0, 'delay_steps': 3, ...}

get_status()

Retrieve all connection parameters as a dictionary.

Follows NEST’s GetStatus API convention.

Returns:

Dictionary with keys:

• 'weight' (float): Connection gain.

• 'delay_steps' (int): Delay in simulation steps.

• 'delay' (int): Alias for delay_steps (NEST compatibility).

• 'has_delay' (bool): Always True.

• 'supports_wfr' (bool): Always False.

Return type:

dict

Examples

>>> conn = rate_connection_delayed(weight=1.5, delay_steps=2)
>>> status = conn.get_status()
>>> status['weight']
1.5
>>> status['delay']
2

property properties

Return connection model properties.

Returns:

Dictionary with keys:

• 'has_delay' (bool): Always True for this model.

• 'supports_wfr' (bool): Always False (waveform relaxation not supported).

Return type:

dict

set_delay(delay)

Update the connection delay (alias for set_delay_steps).

Parameters:

delay (int or array-like) – New delay in simulation steps. Must be integer-valued scalar >= 1. Accepts brainunit.Quantity (mantissa will be extracted).

Raises:

ValueError – If delay is not scalar, not integer-valued, or < 1.

Examples

>>> conn = rate_connection_delayed()
>>> conn.set_delay(5)
>>> conn.get('delay_steps')
5

set_delay_steps(delay_steps)

Update the connection delay in simulation steps.

Parameters:

delay_steps (int or array-like) – New delay in simulation steps. Must be integer-valued scalar >= 1. Accepts brainunit.Quantity (mantissa will be extracted).

Raises:

ValueError – If delay_steps is not scalar, not integer-valued, or < 1.

Examples

>>> conn = rate_connection_delayed()
>>> conn.set_delay_steps(3)
>>> conn.get('delay_steps')
3

set_status(status=None, **kwargs)

Update connection parameters from a dictionary or keyword arguments.

Follows NEST’s SetStatus API convention. Accepts both delay and delay_steps as aliases (if both provided, they must match).

Parameters:

• status (dict or None, optional) – Dictionary of parameters to update. Keys: 'weight', 'delay', 'delay_steps'.

• **kwargs – Alternative parameter specification as keyword arguments. Merged with status (keyword args take precedence).

Raises:

• ValueError – If delay and delay_steps are both provided with conflicting values.

• ValueError – If any parameter fails validation (e.g., non-scalar, delay < 1).

Examples

>>> conn = rate_connection_delayed(weight=1.0, delay_steps=1)
>>> conn.set_status({'weight': 2.5, 'delay_steps': 4})
>>> conn.get('weight')
2.5
>>> conn.set_status(weight=3.0)  # Keyword argument style
>>> conn.get('weight')
3.0

set_weight(weight)

Update the connection weight.

Parameters:

weight (float or array-like) – New connection gain. Must be scalar. Accepts brainunit.Quantity (mantissa will be extracted).

Raises:

ValueError – If weight is not scalar.

Examples

>>> conn = rate_connection_delayed()
>>> conn.set_weight(2.5)
>>> conn.get('weight')
2.5