training error
时间: 2023-10-07 20:12:30 浏览: 121
训练误差(Training Error)指的是在训练过程中,神经网络在训练数据上的预测结果与真实标签之间的差异。它是衡量神经网络在训练集上的性能的指标。
训练误差通常通过计算损失函数(如均方误差、交叉熵等)来衡量。损失函数衡量了神经网络的预测结果与真实标签之间的差异,而训练误差则是对这些差异的总体度量。
在训练过程中,神经网络的目标是通过反向传播和梯度下降等优化算法来最小化训练误差。通过不断调整网络参数(如权重和偏置),神经网络会逐渐学习到输入数据中的模式和特征,使得训练误差逐渐减小。
然而,仅仅关注训练误差可能会导致过拟合问题。因此,在评估神经网络性能时,还需要考虑测试误差(Test Error)或验证误差(Validation Error),以确保网络能够良好地泛化到新数据上。
相关问题
在下图中,我们可以观察到误差出现了许多小的“涨落”。这种情况我们应该担心吗?() Training error 03 Validation error 0.2 01. 10000 20000 Epochs A:需要,这也许意味着神经网络的学习速率存在问题 B:不需要,只要在训练集和交叉验证集上有累积的下降就可以了 C:不确定
如果在训练误差和验证误差曲线中出现了许多小的“涨落”,我们不必太过担心。这种情况表明神经网络可能正在学习更复杂的特征,但它们可能不会立即改善模型的性能。只要训练误差和验证误差在一段时间内保持稳定或下降,即可认为神经网络正在有效地学习。因此,选项B“不需要,只要在训练集和交叉验证集上有累积的下降就可以了”是正确答案。
完善以下程序:clear all X = [ 0 0 1; 0 1 1; 1 0 1; 1 1 1; ]; D = [ 0 0 1 1 ]; E1 = zeros(1000, 1); E2 = zeros(1000, 1); W11 = 2*rand(4, 3) - 1; % Cross entropy W12 = 2*rand(1, 4) - 1; % W21 = W11; % Sum of squared error W22 = W12; % for epoch = 1:1000 [W11 W12] = BackpropCE(W11, W12, X, D); [W21 W22] = BackpropXOR(W21, W22, X, D); es1 = 0; es2 = 0; N = 4; for k = 1:N x = X(k, :)'; d = D(k); v1 = W11*x; y1 = Sigmoid(v1); v = W12*y1; y = Sigmoid(v); % 填空:es1=? v1 = W21*x; y1 = Sigmoid(v1); v = W22*y1; y = Sigmoid(v); % 填空:es2=? end E1(epoch) = es1 / N; E2(epoch) = es2 / N; end plot(E1, 'r') hold on plot(E2, 'b:') xlabel('Epoch') ylabel('Average of Training error') legend('Cross Entropy', 'Sum of Squared Error')
clear all
X = [ 0 0 1;
0 1 1;
1 0 1;
1 1 1;
];
D = [ 0
0
1
1
];
E1 = zeros(1000, 1);
E2 = zeros(1000, 1);
W11 = 2*rand(4, 3) - 1; % Cross entropy
W12 = 2*rand(1, 4) - 1; %
W21 = W11; % Sum of squared error
W22 = W12; %
for epoch = 1:1000
[W11, W12, es1] = BackpropCE(W11, W12, X, D);
[W21, W22, es2] = BackpropXOR(W21, W22, X, D);
es1 = 0;
es2 = 0;
N = 4;
for k = 1:N
x = X(k, :)';
d = D(k);
v1 = W11*x;
y1 = Sigmoid(v1);
v = W12*y1;
y = Sigmoid(v);
es1 = es1 + CrossEntropy(d, y); % 填空:es1=?
v1 = W21*x;
y1 = Sigmoid(v1);
v = W22*y1;
y = Sigmoid(v);
es2 = es2 + SSE(d, y); % 填空:es2=?
end
E1(epoch) = es1 / N;
E2(epoch) = es2 / N;
end
plot(E1, 'r')
hold on
plot(E2, 'b:')
xlabel('Epoch')
ylabel('Average of Training error')
legend('Cross Entropy', 'Sum of Squared Error')
% 交叉熵损失函数
function [loss] = CrossEntropy(d, y)
loss = -1 * (d * log(y) + (1 - d) * log(1 - y));
end
% 平方误差损失函数
function [loss] = SSE(d, y)
loss = (d - y) ^ 2;
end
% Sigmoid激活函数
function [y] = Sigmoid(x)
y = 1 ./ (1 + exp(-x));
end
% 反向传播算法(Cross Entropy版本)
function [W1, W2, e] = BackpropCE(W1, W2, X, D)
alpha = 0.9;
N = 4;
e = 0;
for k = 1:N
x = X(k, :)';
d = D(k);
v1 = W1 * x;
y1 = Sigmoid(v1);
v = W2 * y1;
y = Sigmoid(v);
e = e + CrossEntropy(d, y);
delta = d - y;
delta1 = y1 .* (1 - y1) .* (W2' * delta);
dW2 = alpha * delta * y1';
dW1 = alpha * delta1 * x';
W2 = W2 + dW2;
W1 = W1 + dW1;
end
end
% 反向传播算法(Sum of Squared Error版本)
function [W1, W2, e] = BackpropXOR(W1, W2, X, D)
alpha = 0.9;
N = 4;
e = 0;
for k = 1:N
x = X(k, :)';
d = D(k);
v1 = W1 * x;
y1 = Sigmoid(v1);
v = W2 * y1;
y = Sigmoid(v);
e = e + SSE(d, y);
delta = (d - y) .* y .* (1 - y);
delta1 = y1 .* (1 - y1) .* (W2' * delta);
dW2 = alpha * delta * y1';
dW1 = alpha * delta1 * x';
W2 = W2 + dW2;
W1 = W1 + dW1;
end
end