Add backpropagation batching

[handwriting-recognition.git] / train.py

diff --git a/train.py b/train.py
index 8a6dc96f2c1d40281d452fc3c894fffb79a73436..b29effaa799aeb738f932c8e3260facdf6467a86 100755 (executable)
--- a/train.py
+++ b/train.py
@@ -46,7 +46,7 @@ for i in range(1, NUM_LAYERS):
     biases.append(rg.normal(scale=10, size=SIZES[i]))
 
 
-def feed_forward(x, transfer=reLU):
+def feed_forward(x, transfer=sigmoid):
     '''Compute all z and output vectors for given input vector'''
 
     a_s = [x]
@@ -63,6 +63,59 @@ def classify(y):
     return np.argmax(y), np.max(y)
 
 
+def cost_grad(x, target_y, transfer=sigmoid, transfer_prime=sigmoid_prime):
+    '''Return (∂C/∂w, ∂C/∂b) for a particular input and desired output vector'''
+
+    # forward pass, remember all z vectors and activations for every layer
+    z_s, a_s = feed_forward(x, transfer)
+
+    # backward pass
+    deltas = [None] * len(weights)  # delta = dC/dz error for each layer
+    # insert the last layer error
+    deltas[-1] = transfer_prime(z_s[-1]) * 2 * (a_s[-1] - target_y)
+    for i in reversed(range(len(deltas) - 1)):
+        deltas[i] = (weights[i + 1].T @ deltas[i + 1]) * transfer_prime(z_s[i])
+
+    dw = [d @ a_s[i+1] for i, d in enumerate(deltas)]
+    db = deltas
+    return dw, db
+
+
+def label_vector(label):
+    x = np.zeros(10)
+    x[label] = 1.0
+    return x
+
+
+def backpropagate(image_batch, label_batch, eta):
+    '''Update NN with gradient descent and backpropagation to a batch of inputs
+
+    eta is the learning rate.
+    '''
+    global weights, biases
+
+    num_images = image_batch.shape[1]
+    for i in range(num_images):
+        y = label_vector(label_batch[i])
+        dws, dbs = cost_grad(image_batch[:, i], y)
+        weights = [w + eta * dw for w, dw in zip(weights, dws)]
+        biases = [b + eta * db for b, db in zip(biases, dbs)]
+
+
+def train(images, labels, eta, batch_size=100):
+    '''Do backpropagation for smaller batches
+
+    This greatly speeds up the learning process, at the expense of finding a more erratic path to the local minimum.
+    '''
+    num_images = images.shape[1]
+    offset = 0
+    while offset < num_images:
+        images_batch = images[:, offset:offset + batch_size]
+        labels_batch = labels[offset:offset + batch_size]
+        backpropagate(images_batch, labels_batch, eta)
+        offset += batch_size
+
+
 def test():
     """Count percentage of test inputs which are being recognized correctly"""
 
@@ -80,3 +133,9 @@ print(f'output vector of first image: {res[1][-1]}')
 digit, conf = classify(res[1][-1])
 print(f'classification of first image: {digit} with confidence {conf}; real label {test_labels[0]}')
 print(f'correctly recognized images after initialization: {test()}%')
+
+for i in range(1):
+    print(f"round #{i} of learning...")
+    train(test_images, test_labels, 1)
+
+print(f'correctly recognized images: {test()}%')