如何构建 CANN 模型？¶

目标：完成本指南后，您将能够创建并运行一个基础的 CANN 模型。

预计阅读时间：10 分钟

介绍¶

在本库中，我们以经典的 Wu-Amari-Wong (WAW) 连续吸引子神经网络 (CANNs) [5, 6, 7, 8] 作为标准实现。得益于与 BrainPy [18]——一个基于 JAX 构建的强大脑动力学编程框架——的无缝集成，构建这一数学上严谨的模型变得非常简单。本指南将向您展示如何：

设置 BrainPy 环境
创建 CANN1D 模型实例
初始化模型状态
运行简单的前向传播

基础知识：BrainPy 框架¶

CANN 模型使用 BrainPy 构建，它提供：

统一的时间步管理，通过 brainpy.math 实现
状态容器 (bm.Variable)，用于管理神经动力学
JIT 编译，通过 bm.for_loop 实现高性能
自动微分 支持，用于基于梯度的分析

所有 CANN 模型都继承自 bp.DynamicalSystem，这意味着它们在库中遵循一致的接口。

逐步指南：创建您的第一个 CANN¶

1. 设置时间步¶

在创建任何模型之前，您必须设置模拟时间步：

[1]:

import brainpy.math as bm

# Set time step to 0.1 ms (or your preferred value)
bm.set_dt(0.1)

为什么这很重要：时间步 dt 控制您模拟的粒度。您会话中的所有模型都将使用此值进行动力学更新。

2. 导入并创建模型¶

[2]:

from canns.models.basic import CANN1D

# Create a 1D CANN with 512 neurons
cann = CANN1D(num=512)

这里发生了什么： - num=512 指定网络中的神经元数量 - 该模型自动设置连接权重、神经元位置和动力学参数 - 使用默认参数（例如连接强度 k、时间常数 tau），除非您指定其他参数

3. 运行前向传播¶

现在您可以调用模型来更新其状态：

[3]:

import jax.numpy as jnp

# Create a simple external input (stimulus at position 0)
external_input = jnp.zeros(512)

# Run one time step
cann(external_input)

# Access the model's current state
print("Synaptic input:", cann.u.value)
print("Neural activity:", cann.r.value)

Synaptic input: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0.]
Neural activity: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0.]

发生了什么：

模型接收外部输入并更新其内部动力学
cann.u 存储突触输入（膜电位）
cann.r 存储神经放电速率（活动）
每次调用 cann(...) 将模型推进一个时间步（dt）

完整的工作示例¶

这是一个将所有内容整合在一起的最小可运行示例：

[4]:

import brainpy.math as bm  # :cite:p:`wang2023brainpy`
import jax.numpy as jnp
from canns.models.basic import CANN1D

# Step 1: Set time step
bm.set_dt(0.1)

# Step 2: Create model
cann = CANN1D(num=512)

# Step 3: Create a Gaussian bump stimulus centered at position 0
positions = cann.x  # Neuron positions from -pi to pi
stimulus = jnp.exp(-0.5 * (positions - 0.0)**2 / 0.25**2)

# Step 4: Run several forward pass
cann(stimulus)
cann(stimulus)
cann(stimulus)

# Step 5: Check the output
print(f"Activity shape: {cann.r.value.shape}")
print(f"Max activity: {jnp.max(cann.r.value)}")

Activity shape: (512,)
Max activity: 0.002971156034618616

[ ]:

cann = CANN1D(
    num=512,           # Number of neurons
    k=1.0,             # Global connection strength
    tau=1.0,           # Time constant (ms)
    a=0.5,             # Width of excitatory connections
    A=10.0,            # Amplitude of excitatory connections
    J0=1.0,            # External input strength
)

关键参数：

num: 神经元数量（数值越高 = 空间分辨率越精细，但速度越慢）
k: 控制整体连接强度（数值越高 = 自组织能力越强）
tau: 动力学的时间常数（数值越高 = 变化越慢）
a: 连接核的宽度（控制波包宽度）
A: 连接的幅度（影响稳定性）

对于大多数应用，默认参数表现良好。我们将在核心概念部分探索参数调整。

运行多个时间步¶

在实践中，您将在循环中运行许多时间步。BrainPy 为此提供了优化的工具：

[5]:

def step_function(t, stimulus):
    """Run one time step of the model."""
    cann(stimulus)
    return cann.r.value  # Return activity for each step

# Create stimuli for 100 time steps (here, constant stimulus)
stimuli = jnp.tile(stimulus, (100, 1))

# Run optimized loop with progress bar
activities = bm.for_loop(
    step_function,
    operands=(jnp.arange(0, 100), stimuli),  # Number of steps and input data
    progress_bar=10  # Show progress (updates every 10%)
)

print(f"Recorded activities shape: {activities.shape}")  # (100, 512)

Recorded activities shape: (100, 512)

发生了什么：

bm.for_loop 对循环进行 JIT 编译以提高速度
进度条显示模拟进度（每 10% 更新一次）
结果是所有已记录活动的 JAX 数组

常见错误及如何避免¶

❌ 错误 1：错误的输入维度¶

[6]:

cann = CANN1D(num=512)
try:
    cann(jnp.zeros(256))  # ERROR! Input size doesn't match num neurons
except Exception as e:
    print(f"Caught error as expected: {e}")

Caught error as expected: The shape of the original data is (512,), while we got (256,) with batch_axis=None.

✅ 解决方案：输入必须与 num 的大小相同：

[7]:

cann = CANN1D(num=512)
cann(jnp.zeros(512))  # Correct size

❌ 错误 2: 没有设置时间步¶

[8]:

from canns.models.basic import CANN1D
cann = CANN1D(num=512)  # Uses whatever dt was set before (or default)

✅ 解决方案: 在脚本开始时显式设置 dt：

[ ]:

import brainpy.math as bm  # :cite:p:`wang2023brainpy`
bm.set_dt(0.1)  # Set dt first
cann = CANN1D(num=512)

关于 2D CANN？¶

相同的原理也适用于 2D 模型：

[9]:

from canns.models.basic import CANN2D

bm.set_dt(0.1)

# Create 2D CANN with 32x32 neurons
cann2d = CANN2D(32)

# Input must be (32, 32) shaped
stimulus_2d = jnp.zeros((32, 32))
cann2d(stimulus_2d)

print(f"2D activity shape: {cann2d.r.value.shape}")  # (32, 32)

2D activity shape: (32, 32)

API 几乎相同——只需调整您的输入维度！

后续步骤¶

现在您知道如何创建和运行 CANN 模型，您已准备好：

生成任务数据 - 学习如何创建平滑跟踪输入、导航任务等
探索模型集合 - 发现其他模型变体（SFA-CANN、分层网络、脑启发模型）
学习 BrainPy 基础 - 如果您想构建自定义模型或深入理解该框架

有疑问? 打开 GitHub Discussion.