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Why the loss in this code is not equal to the mean squared error in the training data? It should be equal because I set alpha =0 , therefore there is no regularization.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.neural_network import MLPRegressor
from sklearn.metrics import mean_squared_error


#
i = 1 #difficult index

X_train = np.arange(-2,2,0.1/i).reshape(-1,1)
y_train = 1+ np.sin(i*np.pi*X_train/4)

fig = plt.figure(figsize=(8,8))
ax = fig.add_axes([0,0,1,1])
ax.plot(X_train,y_train,'b*-')
ax.set_xlabel('X_train')
ax.set_ylabel('y_train')
ax.set_title('Function')
nn = MLPRegressor(
    hidden_layer_sizes=(1,),  activation='tanh', solver='sgd', alpha=0.000, batch_size='auto',
    learning_rate='constant', learning_rate_init=0.01, power_t=0.5, max_iter=1000, shuffle=True,
    random_state=0, tol=0.0001, verbose=True, warm_start=False, momentum=0.0, nesterovs_momentum=False,
    early_stopping=False, validation_fraction=0.1, beta_1=0.9, beta_2=0.999, epsilon=1e-08)

nn = nn.fit(X_train, y_train)

predict_train=nn.predict(X_train)



print('MSE training : {:.3f}'.format(mean_squared_error(y_train, predict_train)))

When I ran this code I found loss = 0.02061828 and the MSE in the training (MSE training) = 0.041

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That's because the square loss is defined as 0.5*MSE.

See definition here:

enter image description here

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The log data is forward propagation loss,still have a backward modify. If use model train one time,you will get the data you wanted.

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