【机器学习】 Flux.jl 求解 XOR 分类问题的神经网络模型

Flux.jl 搭建神经网络基本流程

using Flux, Statistics

# 生成XOR问题的数据
noisy = rand(Float32, 2, 200)  # 2×200的矩阵
truth = [xor(col[1] > 0.5, col[2] > 0.5) for col in eachcol(noisy)]  # 200元素向量
target = Flux.onehotbatch(truth, [true, false])  # 2×200的OneHotMatrix

# 定义模型，一个具有3个隐藏层的多层感知器
model = Chain(
    Dense(2 => 3, tanh),  # 使用tanh激活函数
    BatchNorm(3),         # 批量归一化
    Dense(3 => 2)         # 输出层
)

# 模型输出
out1 = model(noisy)
probs1 = softmax(out1)  # 使用softmax函数获取概率

# 为训练准备目标数据


# 创建数据加载器
loader = Flux.DataLoader((noisy, target), batchsize=64, shuffle=true)

# 设置优化器
optim = Flux.setup(Flux.Adam(0.01), model)  # Adam 策略随机梯度方法

# 训练循环，遍历整个数据集1000次
losses = []
for epoch in 1:1000
    for (x, y) in loader
        loss, grads = Flux.withgradient(model) do m
            y_hat = m(x)
            Flux.logitcrossentropy(y_hat, y)
        end
        Flux.update!(optim, model, grads[1])
        push!(losses, loss)
    end
end

# 训练后的模型输出
out2 = model(noisy)
probs2 = softmax(out2)

# 计算准确率
accuracy = mean((probs2[1,:] .> 0.5) .== truth)
println("Accuracy: $(accuracy * 100)%")

using Plots  # to draw the above figure

p_true = scatter(noisy[1,:], noisy[2,:], zcolor=truth, title="True classification", legend=false)
p_raw =  scatter(noisy[1,:], noisy[2,:], zcolor=probs1[1,:], title="Untrained network", label="", clims=(0,1))
p_done = scatter(noisy[1,:], noisy[2,:], zcolor=probs2[1,:], title="Trained network", legend=false)

plot(p_true, p_raw,layout=(1,3), size=(200,330))

输出分类效果