src.canns.models.basic

Submodules

• src.canns.models.basic.cann
• src.canns.models.basic.hierarchical_model
• src.canns.models.basic.theta_sweep_model

Classes

CANN1D	A standard 1D Continuous Attractor Neural Network (CANN) model.
CANN1D_SFA	A 1D CANN model that incorporates Spike-Frequency Adaptation (SFA).
CANN2D	A 2D Continuous Attractor Neural Network (CANN) model.
CANN2D_SFA	A 2D Continuous Attractor Neural Network (CANN) model with a specific
HierarchicalNetwork	A full hierarchical network composed of multiple grid modules.

Package Contents

class src.canns.models.basic.CANN1D(num, tau=1.0, k=8.1, a=0.5, A=10, J0=4.0, z_min=-u.math.pi, z_max=u.math.pi, **kwargs)

Bases: BaseCANN1D

A standard 1D Continuous Attractor Neural Network (CANN) model. This model implements the core dynamics where a localized “bump” of activity can be sustained and moved by external inputs.

Reference:

Wu, S., Hamaguchi, K., & Amari, S. I. (2008). Dynamics and computation of continuous attractors. Neural computation, 20(4), 994-1025.

Initializes the base 1D CANN model.

Parameters:

• num (int) – The number of neurons in the network.

• tau (float) – The synaptic time constant, controlling how quickly the membrane potential changes.

• k (float) – A parameter controlling the strength of the global inhibition.

• a (float) – The half-width of the excitatory connection range. It defines the “spread” of local connections.

• A (float) – The magnitude (amplitude) of the external stimulus.

• J0 (float) – The maximum connection strength between neurons.

• z_min (float) – The minimum value of the feature space (e.g., -pi for an angle).

• z_max (float) – The maximum value of the feature space (e.g., +pi for an angle).

• **kwargs – Additional keyword arguments passed to the parent BasicModel.

init_state(*args, **kwargs)

Initializes the state variables of the model.

update(inp)

The main update function, defining the dynamics of the network for one time step.

Parameters:

inp (Array) – The external input for the current time step.

class src.canns.models.basic.CANN1D_SFA(num, tau=1.0, tau_v=50.0, k=8.1, a=0.3, A=0.2, J0=1.0, z_min=-u.math.pi, z_max=u.math.pi, m=0.3, **kwargs)

Bases: BaseCANN1D

A 1D CANN model that incorporates Spike-Frequency Adaptation (SFA). SFA is a slow negative feedback mechanism that causes neurons to fire less over time for a sustained input, which can induce anticipative tracking behavior.

Reference:

Mi, Y., Fung, C. C., Wong, K. Y., & Wu, S. (2014). Spike frequency adaptation implements anticipative tracking in continuous attractor neural networks. Advances in neural information processing systems, 27.

Initializes the 1D CANN model with SFA.

Parameters:

• tau_v (float) – The time constant for the adaptation variable ‘v’. A larger value means slower adaptation.

• m (float) – The strength of the adaptation, coupling the membrane potential ‘u’ to the adaptation variable ‘v’.

• BaseCANN1D) ((Other parameters are inherited from)

init_state(*args, **kwargs)

Initializes the state variables of the model, including the adaptation variable.

update(inp)

The main update function for the SFA model. It includes dynamics for both the membrane potential and the adaptation variable.

Parameters:

inp (Array) – The external input for the current time step.

m = 0.3

tau_v = 50.0

class src.canns.models.basic.CANN2D(length, tau=1.0, k=8.1, a=0.5, A=10, J0=4.0, z_min=-u.math.pi, z_max=u.math.pi, **kwargs)

Bases: BaseCANN2D

A 2D Continuous Attractor Neural Network (CANN) model. This model extends the base CANN2D class to include specific dynamics and properties for a 2D neural network.

Reference:

Wu, S., Hamaguchi, K., & Amari, S. I. (2008). Dynamics and computation of continuous attractors. Neural computation, 20(4), 994-1025.

Initializes the base 2D CANN model.

Parameters:

• length (int) – The number of neurons in one dimension of the network (the network is square).

• tau (float) – The synaptic time constant, controlling how quickly the membrane potential changes.

• k (float) – A parameter controlling the strength of the global inhibition.

• a (float) – The half-width of the excitatory connection range. It defines the “spread” of local connections.

• A (float) – The magnitude (amplitude) of the external stimulus.

• J0 (float) – The maximum connection strength between neurons.

• z_min (float) – The minimum value of the feature space (e.g., -pi for an angle).

• z_max (float) – The maximum value of the feature space (e.g., +pi for an angle).

• **kwargs – Additional keyword arguments passed to the parent BasicModel.

init_state(*args, **kwargs)

Initializes the state variables of the model.

update(inp)

The main update function, defining the dynamics of the network for one time step.

Parameters:

inp (Array) – The external input to the network, which can be a stimulus or other driving force.

class src.canns.models.basic.CANN2D_SFA(length, tau=1.0, tau_v=50.0, k=8.1, a=0.3, A=0.2, J0=1.0, z_min=-u.math.pi, z_max=u.math.pi, m=0.3, **kwargs)

Bases: BaseCANN2D

A 2D Continuous Attractor Neural Network (CANN) model with a specific implementation of the Synaptic Firing Activity (SFA) dynamics. This model extends the base CANN2D class to include SFA-specific dynamics.

Initializes the 2D CANN model with SFA dynamics.

init_state(*args, **kwargs)

Initializes the state variables of the model, including the adaptation variable.

update(inp)

The main update function for the SFA model. It includes dynamics for both the membrane potential and the adaptation variable.

Parameters:

inp (Array) – The external input for the current time step.

m = 0.3

tau_v = 50.0

class src.canns.models.basic.HierarchicalNetwork(num_module, num_place, spacing_min=2.0, spacing_max=5.0, module_angle=0.0, band_size=180, band_noise=0.0, band_w_L2S=0.2, band_w_S2L=1.0, band_gain=0.2, grid_num=20, grid_tau=0.1, grid_tau_v=10.0, grid_k=0.005, grid_a=u.math.pi / 9, grid_A=1.0, grid_J0=1.0, grid_mbar=1.0, gauss_tau=1.0, gauss_J0=1.1, gauss_k=0.0005, gauss_a=2 / 9 * u.math.pi, nonrec_tau=0.1)

Bases: src.canns.models.basic._base.BasicModelGroup

A full hierarchical network composed of multiple grid modules.

This class creates and manages a collection of HierarchicalPathIntegrationModel modules, each with a different grid spacing. By combining the outputs of these modules, the network can represent position unambiguously over a large area. The final output is a population of place cells whose activities are used to decode the animal’s estimated position.

num_module

The number of grid modules in the network.

Type:

int

num_place

The number of place cells in the output layer.

Type:

int

place_center

The center locations of the place cells.

Type:

brainunit.math.ndarray

MEC_model_list

A list containing all the HierarchicalPathIntegrationModel instances.

Type:

list

grid_fr

The firing rates of the grid cell population.

Type:

brainstate.HiddenState

band_x_fr

The firing rates of the x-oriented band cell population.

Type:

brainstate.HiddenState

band_y_fr

The firing rates of the y-oriented band cell population.

Type:

brainstate.HiddenState

place_fr

The firing rates of the place cell population.

Type:

brainstate.HiddenState

decoded_pos

The final decoded 2D position.

Type:

brainstate.State

References

Anonymous Author(s) “Unfolding the Black Box of Recurrent Neural Networks for Path Integration” (under review).

Initializes the HierarchicalNetwork.

Parameters:

• num_module (int) – The number of grid modules to create.

• num_place (int) – The number of place cells along one dimension of a square grid.

• spacing_min (float, optional) – Minimum spacing for grid modules. Defaults to 2.0.

• spacing_max (float, optional) – Maximum spacing for grid modules. Defaults to 5.0.

• module_angle (float, optional) – Base orientation angle for all modules. Defaults to 0.0.

• band_size (int, optional) – Number of neurons in each BandCell group. Defaults to 180.

• band_noise (float, optional) – Noise level for BandCells. Defaults to 0.0.

• band_w_L2S (float, optional) – Weight from band cells to shifter units. Defaults to 0.2.

• band_w_S2L (float, optional) – Weight from shifter units to band cells. Defaults to 1.0.

• band_gain (float, optional) – Gain factor for velocity signal in BandCells. Defaults to 0.2.

• grid_num (int, optional) – Number of neurons per dimension for GridCell. Defaults to 20.

• grid_tau (float, optional) – Synaptic time constant for GridCell. Defaults to 0.1.

• grid_tau_v (float, optional) – Adaptation time constant for GridCell. Defaults to 10.0.

• grid_k (float, optional) – Global inhibition strength for GridCell. Defaults to 5e-3.

• grid_a (float, optional) – Connection width for GridCell. Defaults to pi/9.

• grid_A (float, optional) – External input magnitude for GridCell. Defaults to 1.0.

• grid_J0 (float, optional) – Maximum connection strength for GridCell. Defaults to 1.0.

• grid_mbar (float, optional) – Base adaptation strength for GridCell. Defaults to 1.0.

• gauss_tau (float, optional) – Time constant for GaussRecUnits in BandCells. Defaults to 1.0.

• gauss_J0 (float, optional) – Connection strength scaling for GaussRecUnits. Defaults to 1.1.

• gauss_k (float, optional) – Global inhibition for GaussRecUnits. Defaults to 5e-4.

• gauss_a (float, optional) – Connection width for GaussRecUnits. Defaults to 2/9*pi.

• nonrec_tau (float, optional) – Time constant for NonRecUnits in BandCells. Defaults to 0.1.

init_state(*args, **kwargs)

update(velocity, loc, loc_input_stre=0.0)

MEC_model_list = []

num_module

num_place

place_center