Add simple neural network (#6452)

* feat: add simple foward propagation implementation

* fix: add PR requested changes

* feat: add code example

* fix: solve pre-commit failure

* feat: add doctest inside code execution

* fix: PR requested changes

* fix: pr requested changes

Co-authored-by: Caio Cordeiro <ccordeirodemorae@apple.com>

neural_network/simple_neural_network.py

@@ -0,0 +1,63 @@
+"""
+Forward propagation explanation:
+https://towardsdatascience.com/forward-propagation-in-neural-networks-simplified-math-and-code-version-bbcfef6f9250
+"""
+
+import math
+import random
+
+
+# Sigmoid
+def sigmoid_function(value: float, deriv: bool = False) -> float:
+    """Return the sigmoid function of a float.
+
+    >>> sigmoid_function(3.5)
+    0.9706877692486436
+    >>> sigmoid_function(3.5, True)
+    -8.75
+    """
+    if deriv:
+        return value * (1 - value)
+    return 1 / (1 + math.exp(-value))
+
+
+# Initial Value
+INITIAL_VALUE = 0.02
+
+
+def forward_propagation(expected: int, number_propagations: int) -> float:
+    """Return the value found after the forward propagation training.
+
+    >>> res = forward_propagation(32, 10000000)
+    >>> res > 31 and res < 33
+    True
+
+    >>> res = forward_propagation(32, 1000)
+    >>> res > 31 and res < 33
+    False
+    """
+
+    # Random weight
+    weight = float(2 * (random.randint(1, 100)) - 1)
+
+    for _ in range(number_propagations):
+        # Forward propagation
+        layer_1 = sigmoid_function(INITIAL_VALUE * weight)
+        # How much did we miss?
+        layer_1_error = (expected / 100) - layer_1
+        # Error delta
+        layer_1_delta = layer_1_error * sigmoid_function(layer_1, True)
+        # Update weight
+        weight += INITIAL_VALUE * layer_1_delta
+
+    return layer_1 * 100
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    expected = int(input("Expected value: "))
+    number_propagations = int(input("Number of propagations: "))
+    print(forward_propagation(expected, number_propagations))