What the meaning of loss < 0 - tensorflow

Question

I am comparing two model the one uses binary_crossentropy(Model A) as optimizer, another uses mean_squared_error(Model B)
Model A)
self.seq_len = 2
in_out_neurons = 50
n_hidden = 500
model = Sequential()
model.add(LSTM(n_hidden, batch_input_shape=(None, self.seq_len, in_out_neurons), return_sequences=True))
model.add(Dense(in_out_neurons, activation="relu"))
optimizer = Adam(learning_rate=0.001)
#model.compile(loss="mean_squared_error", optimizer=optimizer)
model.compile(loss='binary_crossentropy', optimizer=optimizer)
Epoch 1/10
718/718 [==============================] - 32s 42ms/step - loss: -0.0633 - val_loss: -0.0649
Epoch 2/10
718/718 [==============================] - 33s 46ms/step - loss: -0.0632 - val_loss: -0.0572
Epoch 3/10
718/718 [==============================] - 43s 60ms/step - loss: -0.0592 - val_loss: -0.0570
Epoch 4/10
718/718 [==============================] - 51s 71ms/step - loss: -0.0522 - val_loss: -0.0431
Epoch 5/10
718/718 [==============================] - 50s 69ms/step - loss: -0.0566 - val_loss: -0.0535
Epoch 6/10
718/718 [==============================] - 49s 68ms/step - loss: -0.0567 - val_loss: -0.0537
Epoch 7/10
718/718 [==============================] - 48s 67ms/step - loss: -0.0627 - val_loss: -0.0499
Epoch 8/10
718/718 [==============================] - 51s 71ms/step - loss: -0.0621 - val_loss: -0.0614
Epoch 9/10
718/718 [==============================] - 47s 65ms/step - loss: -0.0645 - val_loss: -0.0653
Epoch 10/10
718/718 [==============================] - 43s 60ms/step - loss: -0.0661 - val_loss: -0.0622
Model B)
self.seq_len = 2
in_out_neurons = 50
n_hidden = 500
model = Sequential()
model.add(LSTM(n_hidden, batch_input_shape=(None, self.seq_len, in_out_neurons), return_sequences=True))
model.add(Dense(in_out_neurons, activation="relu"))
optimizer = Adam(learning_rate=0.001)
model.compile(loss="mean_squared_error", optimizer=optimizer)
#model.compile(loss='binary_crossentropy', optimizer=optimizer)
Epoch 1/10
718/718 [==============================] - 36s 48ms/step - loss: 0.0189 - val_loss: 0.0190
Epoch 2/10
718/718 [==============================] - 46s 64ms/step - loss: 0.0188 - val_loss: 0.0189
Epoch 3/10
718/718 [==============================] - 48s 67ms/step - loss: 0.0187 - val_loss: 0.0189
Epoch 4/10
718/718 [==============================] - 58s 81ms/step - loss: 0.0187 - val_loss: 0.0188
Epoch 5/10
718/718 [==============================] - 62s 87ms/step - loss: 0.0186 - val_loss: 0.0188
Epoch 6/10
718/718 [==============================] - 72s 100ms/step - loss: 0.0186 - val_loss: 0.0188
Epoch 7/10
718/718 [==============================] - 73s 102ms/step - loss: 0.0185 - val_loss: 0.0187
Epoch 8/10
718/718 [==============================] - 60s 84ms/step - loss: 0.0185 - val_loss: 0.0187
Epoch 9/10
718/718 [==============================] - 64s 89ms/step - loss: 0.0185 - val_loss: 0.0187
Epoch 10/10
718/718 [==============================] - 64s 89ms/step - loss: 0.0185 - val_loss: 0.0187
Model B's loss is more than 0 , so it could be understood.
However,Model A's loss is less than 0, what does it mean??

Answer 1

Cross entropy is calculated as minus expected value of logarithm of the result. Usually it is used after sigmoid or softmax activation, where all values <= 1, their logarithms <= 0, and thus the result is >= 0. But you use it after relu activation that can give values > 1, that's why you obtain the result < 0. The moral is that the output layer activation and the loss should correspond to each other and must make sense from the point of view of the task you are trying to solve. Otherwise you may obtain senseless results.