How do I define/change the accuracy for a non-classification convolutional neural network?

Question

I'm using Keras to make a prediction model. It takes in two time series and outputs a number between 0 and 1. Currently, I am getting very low accuracy as the model is only considered "correct" if it gets the exact number. For example, the correct number is 0.34, it would be considered incorrect if it predicted 0.35. I want to be able to consider all numbers within a range to be correct, for example: within 0.05 of the true value. Another option may be to round, but I have the problem of it outputting 6 decimal places.

1. How can I consider all numbers within a range to be "correct" for the accuracy?
2. How can I round the output of the CNN?

Here is my CNN code:

def networkModel():
    model = tf.keras.Sequential([

tf.keras.layers.Conv2D(filters = 16, kernel_size=(2, 2), activation='relu',padding='same'),
tf.keras.layers.Conv2D(filters = 9, kernel_size=(2, 2), activation='relu',padding='same'),
tf.keras.layers.MaxPooling2D(pool_size=(2, 2)),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(256, activation='relu'),
tf.keras.layers.Dense(1, activation='sigmoid')

])

    model.compile(optimizer='adam',
            loss = tf.keras.losses.BinaryCrossentropy(),
            metrics=['accuracy'])

    return model

Answer 1

For this specific case, you can define a custom accuracy function as a metric and define a Callback for your Keras model.

Custom Accuracy Metric:

import keras.backend as K

def custom_accuracy(y_true, y_pred, tolerance=0.05):
    absolute_difference = K.abs(y_true - y_pred)
    correct_predictions = K.cast(absolute_difference <= tolerance, dtype='float32')
    return K.mean(correct_predictions)

model.compile(optimizer='adam', loss='mse', metrics=[custom_accuracy])

Custom Callback:

from keras.callbacks import Callback
import numpy as np

class CustomAccuracyCallback(Callback):
    def __init__(self, validation_data, tolerance=0.05):
        super(CustomAccuracyCallback, self).__init__()
        self.validation_data = validation_data
        self.tolerance = tolerance

    def on_epoch_end(self, epoch, logs={}):
        x_val, y_val = self.validation_data
        y_pred = self.model.predict(x_val)
        accuracy = np.mean(np.abs(y_val - y_pred) <= self.tolerance)
        print(f"\nEpoch {epoch + 1}: Custom Accuracy: {accuracy:.4f}")
        logs['custom_accuracy'] = accuracy

custom_callback = CustomAccuracyCallback((x_val, y_val))
model.fit(x_train, y_train, validation_data=(x_val, y_val), callbacks=[custom_callback])