Tutorial 4: CANN Parameter Effects

Note

Reading Time: 30-35 minutes

Difficulty: Intermediate

Prerequisites: Tutorial 1-3

This tutorial systematically explores how different CANN1D parameters affect model dynamics.

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1. Parameter Overview

CANN1D has the following main parameters:

Parameter	Default	Physical Meaning
num	256	Number of neurons (network resolution)
tau	1.0	Time constant (dynamics speed)
k	8.1	Global inhibition strength
a	0.5	Connection width (local excitation range)
A	10	External input amplitude
J0	4.0	Synaptic connection strength
tau_v	50.0	SFA [9, 10] time constant (CANN1D_SFA only)

We’ll use SmoothTracking1D task and energy_landscape_1d_animation visualization to observe each parameter’s effect.

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2. Experimental Setup

2.1 Base Code Framework

import brainpy.math as bm  # :cite:p:`wang2023brainpy`
from canns.models.basic import CANN1D, CANN1D_SFA
from canns.task.tracking import SmoothTracking1D
from canns.analyzer.visualization import (
    PlotConfigs,
    energy_landscape_1d_animation
)

# Setup environment
bm.set_dt(0.1)

def run_experiment(model, title="", save_path=None):
    """Run standard experiment and visualize results"""

    # Create smooth tracking task
    task = SmoothTracking1D(
        cann_instance=model,
        Iext=[0.0, 3.0, 2.0, 3.0],
        duration=[20.0, 20.0, 10.0],
        time_step=0.1,
    )

    # Get task data
    task.get_data()

    def run_step(t, inp):
        model.update(inp)
        return model.u.value, model.r.value, model.inp.value

    u_history, r_history, input_history = bm.for_loop(run_step, operands=(task.run_steps, task.data), progress_bar=10)

    # Configure and create visualization
    config = PlotConfigs.energy_landscape_1d_animation(
        time_steps_per_second=100,
        fps=20,
        title=title,
        xlabel='Position',
        ylabel='Firing Rate',
        repeat=True,
        show=True,
        save_path=save_path
    )

    energy_landscape_1d_animation(
        data_sets={'u': (model.x, u_history), 'stimulus': (model.x, input_history)},
        config=config
    )

    return r_history

2.2 Default Parameter Baseline

First, establish a baseline with default parameters:

# Default parameters
model_default = CANN1D(
    num=256, tau=1.0, k=8.1, a=0.5, A=10, J0=4.0
)
r_default = run_experiment(
    model_default,
    title="Default Parameters",
    save_path=None  # Set to 'default.gif' to save
)

<SmoothTracking1D> Generating Task data: 500it [00:00, 997.94it/s]

What to observe: The bump should smoothly track the stimulus from left to right with a stable, well-defined shape.

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3. Parameter Exploration

For each parameter, we’ll create side-by-side comparisons using multiple experiments. This approach allows you to directly compare different parameter values.

3.1 Number of Neurons num

num controls network resolution. More neurons mean finer feature representation but higher computational cost.

# Test different neuron counts
for num_val in [64, 256, 512]:
    model = CANN1D(num=num_val, tau=1.0, k=8.1, a=0.5, A=10, J0=4.0)
    run_experiment(
        model,
        title=f"Number of Neurons: {num_val}",
        save_path=None
    )

<SmoothTracking1D> Generating Task data: 500it [00:00, 1007.50it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 7830.98it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 1487.74it/s]

Observations: - num=64: Lower resolution, coarser bump representation - num=256: Balanced resolution, standard choice - num=512: Finer resolution, smoother bump, but increased computation

Key Insight: Resolution affects bump smoothness but not fundamental dynamics. Use higher num when precise spatial representation matters.

3.2 Time Constant tau

tau controls the dynamics timescale. Larger tau means slower response to inputs.

# Test different time constants
for tau_val in [0.5, 1.0, 2.0]:
    model = CANN1D(num=256, tau=tau_val, k=8.1, a=0.5, A=10, J0=4.0)
    run_experiment(
        model,
        title=f"Time Constant: tau={tau_val}",
        save_path=None
    )

<SmoothTracking1D> Generating Task data: 500it [00:00, 6681.74it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 7698.46it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 1703.66it/s]

Observations: - tau=0.5: Fast response, bump tightly follows stimulus with minimal lag - tau=1.0: Standard response, balanced tracking speed - tau=2.0: Slow response, bump lags behind moving stimulus

Key Insight: tau controls the network’s temporal filtering. Smaller tau means faster adaptation to changing inputs—larger tau means smoother, slower dynamics.

3.3 Global Inhibition k

k controls global inhibition strength—critical for maintaining single-bump attractor state.

# Test different inhibition strengths
for k_val in [4.0, 8.1, 16.0]:
    model = CANN1D(num=256, tau=1.0, k=k_val, a=0.5, A=10, J0=4.0)
    run_experiment(
        model,
        title=f"Global Inhibition: k={k_val}",
        save_path=None
    )

<SmoothTracking1D> Generating Task data: 500it [00:00, 7221.90it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 4806.87it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 5538.20it/s]

Observations: - k=4.0: Weak inhibition, bump may be unstable, wider, or split into multiple bumps - k=8.1: Balanced inhibition, stable single bump - k=16.0: Strong inhibition, sharper, narrower bump

Key Insight: k balances excitation and inhibition. Too weak: instability or multiple bumps. Too strong: bump may fail to form or be overly narrow.

3.4 Connection Width a

a controls the spatial range of local excitatory connections—directly affecting bump width.

# Test different connection widths
for a_val in [0.3, 0.5, 0.8]:
    model = CANN1D(num=256, tau=1.0, k=8.1, a=a_val, A=10, J0=4.0)
    run_experiment(
        model,
        title=f"Connection Width: a={a_val}",
        save_path=None
    )

<SmoothTracking1D> Generating Task data: 500it [00:00, 4087.94it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 2955.45it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 7412.03it/s]

Observations: - a=0.3: Narrow connections, produces narrower bump with sharper peak - a=0.5: Standard width, balanced bump shape - a=0.8: Wide connections, produces wider, more distributed bump

Key Insight: a directly controls the spatial receptive field size. Match a to your application’s required spatial precision.

3.5 External Input Amplitude A

A controls the amplitude of external stimulus input.

# Test different input amplitudes
for A_val in [5, 10, 20]:
    model = CANN1D(num=256, tau=1.0, k=8.1, a=0.5, A=A_val, J0=4.0)
    run_experiment(
        model,
        title=f"Input Amplitude: A={A_val}",
        save_path=None
    )

<SmoothTracking1D> Generating Task data: 500it [00:00, 3244.44it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 4569.55it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 634.16it/s]

Observations: - A=5: Weaker input, bump has lower peak firing rate - A=10: Standard amplitude, balanced response - A=20: Stronger input, bump has higher peak firing rate and potentially wider spread

Key Insight: A controls how strongly external inputs drive the network. Higher A makes the bump more responsive to external stimuli versus internal recurrent dynamics.

3.6 Synaptic Connection Strength J0

J0 controls the maximum strength of recurrent synaptic connections.

# Test different connection strengths
for J0_val in [2.0, 4.0, 8.0]:
    model = CANN1D(num=256, tau=1.0, k=8.1, a=0.5, A=10, J0=J0_val)
    run_experiment(
        model,
        title=f"Synaptic Strength: J0={J0_val}",
        save_path=None
    )

<SmoothTracking1D> Generating Task data: 500it [00:00, 4871.12it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 5754.28it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 590.77it/s]

Observations: - J0=2.0: Weak recurrent connections, bump may not maintain stability without input - J0=4.0: Standard connections, stable bump maintenance - J0=8.0: Strong recurrent connections, very stable bump that may become too rigid

Key Insight: J0 determines the strength of the attractor. Higher J0 means stronger self-sustaining dynamics and better memory maintenance, but may reduce responsiveness to changing inputs.

3.7 SFA Time Constant tau_v

For CANN1D_SFA, tau_v controls the Spike Frequency Adaptation timescale. SFA creates an adaptation current that can cause the bump to drift even without external velocity input.

# Test different SFA time constants
for tau_v_val in [20.0, 50.0, 100.0]:
    model = CANN1D_SFA(
        num=256,
        tau=1.0,
        tau_v=tau_v_val,
        k=8.1,
        a=0.3,
        A=0.2,
        J0=1.0,
        m=0.3
    )
    run_experiment(
        model,
        title=f"SFA Time Constant: tau_v={tau_v_val}",
        save_path=None
    )

<SmoothTracking1D> Generating Task data: 500it [00:00, 987.72it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 7448.12it/s]

<SmoothTracking1D> Generating Task data: 500it [00:00, 1604.13it/s]

Observations: - tau_v=20.0: Fast adaptation, bump may drift faster or lead the stimulus - tau_v=50.0: Standard adaptation, moderate drift behavior - tau_v=100.0: Slow adaptation, weaker drift effect

Key Insight: SFA [9, 10] introduces anticipatory dynamics. The adaptation current creates an asymmetry that can make the bump “predict” motion direction. This is useful for path integration [4, 28] models.

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4. Next Steps

Congratulations on completing all foundation tutorials! You now understand:

• All major CANN parameters and their physical meanings

• Each parameter’s effect on bump dynamics

• How to conduct systematic parameter sweep experiments

• The trade-offs involved in parameter selection

Parameter Selection Guidelines

When configuring CANN models for your applications:

1. Start with defaults—The default parameters provide stable, well-behaved dynamics

2. Match resolution to needs—Higher num for precise spatial coding, lower for efficiency

3. Tune temporal dynamics—Adjust tau based on required response speed

4. Balance stability and flexibility—J0 and k control attractor strength

5. Match spatial scale—Set a based on required bump width

Continue Learning

From here, choose advanced application tutorials:

• Tutorial 5: Grid Cell Velocity-Based Path Integration—Learn velocity-based grid cells and high-accuracy path integration

• Tutorial 6: Hierarchical Path Integration Network—Learn hierarchical path integration with multiple spatial scales

• Tutorial 7: Theta Sweep System Model—Learn Theta Sweep [11, 14] systems combining head direction and grid cells

• Tutorial 8: Theta Sweep Place Cell Network—Learn place cell networks and spatial memory

Or explore other scenarios:

• Scenario 2: Data Analysis—Analyze experimental neural data with CANNs

• Scenario 3: Brain-Inspired Learning—Brain-inspired training methods for CANNs

• Scenario 4: End-to-End Pipeline—Complete research workflow from data to publication

Key Takeaways

1. Parameters are interconnected—Changing one parameter may require adjusting others to maintain stability

2. Visualize to understand—Always use energy landscape visualizations when exploring parameters

3. Start simple—Begin with basic CANN1D before moving to SFA or 2D variants

4. Document your choices—Keep notes on why you selected specific parameter values for reproducibility