Approximating a smooth multidimensional function using Keras to an error of 1e-4

Question

I am trying to approximate a function that smoothly maps five inputs to a single probability using Keras, but seem to have hit a limit. A similar problem was posed here (Keras Regression to approximate function (goal: loss < 1e-7)) for a ten-dimensional function and I have found that the architecture proposed there, namely:

model = Sequential()

model.add(Dense(128,input_shape=(5,), activation='tanh'))

model.add(Dense(64,activation='tanh'))

model.add(Dense(1,activation='sigmoid'))

model.compile(optimizer='adam', loss='mae')

gives me my best results, converging to a best loss of around 7e-4 on my validation data when the batch size is 1000. Adding or removing more neurons or layers seems to reduce the accuracy. Dropout regularisation also reduces accuracy. I am currently using 1e7 training samples, which took two days to generate (hence the desire to approximate this function). I would like to reduce the mae by another order of magnitude, does anyone have any suggestions how to do this?

Answer 1

I recommend use utilize the keras callbacks ReduceLROnPlateau, documentation is here and ModelCheckpoint, documentation is here.. For the first, set it to monitory validation loss and it will reduce the learning rate by a factor(factor) if the loss fails to reduce after a fixed number (patience) of consecutive epochs. For the second also monitor validation loss and save the weights for the model with the lowest validation loss to a directory. After training load the weights and use them to evaluate or predict on the test set. My code implementation is shown below.

checkpoint=tf.keras.callbacks.ModelCheckpoint(filepath=save_loc, monitor='val_loss', verbose=1, save_best_only=True,
        save_weights_only=True, mode='auto', save_freq='epoch', options=None)
lr_adjust=tf.keras.callbacks.ReduceLROnPlateau( monitor="val_loss", factor=0.5, patience=1, verbose=1, mode="auto",
        min_delta=0.00001,  cooldown=0,  min_lr=0)
callbacks=[checkpoint, lr_adjust]
history = model.fit_generator( train_generator, epochs=EPOCHS,
          steps_per_epoch=STEPS_PER_EPOCH,validation_data=validation_generator,
          validation_steps=VALIDATION_STEPS, callbacks=callbacks)
model.load_weights(save_loc) # load the saved weights
# after this use the model to evaluate or predict on the test set.
# if you are satisfied with the results you can then save the entire model with
model.save(save_loc)