{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.7.6","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"none","dataSources":[{"sourceType":"competition","sourceId":3004,"databundleVersionId":861823}],"dockerImageVersionId":30035,"isInternetEnabled":false,"language":"python","sourceType":"notebook","isGpuEnabled":false}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"import numpy as np\nimport pandas as pd\nfrom matplotlib import pyplot as plt\n\ndata = pd.read_csv('/kaggle/input/digit-recognizer/train.csv')","metadata":{"_uuid":"8f2839f25d086af736a60e9eeb907d3b93b6e0e5","_cell_guid":"b1076dfc-b9ad-4769-8c92-a6c4dae69d19","trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:55:18.130330Z","iopub.execute_input":"2026-04-19T09:55:18.130691Z","iopub.status.idle":"2026-04-19T09:55:20.718026Z","shell.execute_reply.started":"2026-04-19T09:55:18.130662Z","shell.execute_reply":"2026-04-19T09:55:20.716548Z"}},"outputs":[],"execution_count":null},{"cell_type":"code","source":"data = np.array(data)\nm, n = data.shape\nnp.random.shuffle(data) # shuffle before splitting into dev and training sets\n\ndata_dev = data[0:1000].T\nY_dev = data_dev[0]\nX_dev = data_dev[1:n]\nX_dev = X_dev / 255.\n\ndata_train = data[1000:m].T\nY_train = data_train[0]\nX_train = data_train[1:n]\nX_train = X_train / 255.\n_,m_train = X_train.shape","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:55:20.720462Z","iopub.execute_input":"2026-04-19T09:55:20.720811Z","iopub.status.idle":"2026-04-19T09:55:21.541644Z","shell.execute_reply.started":"2026-04-19T09:55:20.720780Z","shell.execute_reply":"2026-04-19T09:55:21.540538Z"}},"outputs":[],"execution_count":null},{"cell_type":"code","source":"Y_train","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:55:21.543340Z","iopub.execute_input":"2026-04-19T09:55:21.543682Z","iopub.status.idle":"2026-04-19T09:55:21.550529Z","shell.execute_reply.started":"2026-04-19T09:55:21.543651Z","shell.execute_reply":"2026-04-19T09:55:21.549268Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"Our NN will have a simple two-layer architecture. Input layer $a^{[0]}$ will have 784 units corresponding to the 784 pixels in each 28x28 input image. A hidden layer $a^{[1]}$ will have 10 units with ReLU activation, and finally our output layer $a^{[2]}$ will have 10 units corresponding to the ten digit classes with softmax activation.\n\n**Forward propagation**\n\n$$Z^{[1]} = W^{[1]} X + b^{[1]}$$\n$$A^{[1]} = g_{\\text{ReLU}}(Z^{[1]}))$$\n$$Z^{[2]} = W^{[2]} A^{[1]} + b^{[2]}$$\n$$A^{[2]} = g_{\\text{softmax}}(Z^{[2]})$$\n\n**Backward propagation**\n\n$$dZ^{[2]} = A^{[2]} - Y$$\n$$dW^{[2]} = \\frac{1}{m} dZ^{[2]} A^{[1]T}$$\n$$dB^{[2]} = \\frac{1}{m} \\Sigma {dZ^{[2]}}$$\n$$dZ^{[1]} = W^{[2]T} dZ^{[2]} .* g^{[1]\\prime} (z^{[1]})$$\n$$dW^{[1]} = \\frac{1}{m} dZ^{[1]} A^{[0]T}$$\n$$dB^{[1]} = \\frac{1}{m} \\Sigma {dZ^{[1]}}$$\n\n**Parameter updates**\n\n$$W^{[2]} := W^{[2]} - \\alpha dW^{[2]}$$\n$$b^{[2]} := b^{[2]} - \\alpha db^{[2]}$$\n$$W^{[1]} := W^{[1]} - \\alpha dW^{[1]}$$\n$$b^{[1]} := b^{[1]} - \\alpha db^{[1]}$$\n\n**Vars and shapes**\n\nForward prop\n\n- $A^{[0]} = X$: 784 x m\n- $Z^{[1]} \\sim A^{[1]}$: 10 x m\n- $W^{[1]}$: 10 x 784 (as $W^{[1]} A^{[0]} \\sim Z^{[1]}$)\n- $B^{[1]}$: 10 x 1\n- $Z^{[2]} \\sim A^{[2]}$: 10 x m\n- $W^{[1]}$: 10 x 10 (as $W^{[2]} A^{[1]} \\sim Z^{[2]}$)\n- $B^{[2]}$: 10 x 1\n\nBackprop\n\n- $dZ^{[2]}$: 10 x m ($~A^{[2]}$)\n- $dW^{[2]}$: 10 x 10\n- $dB^{[2]}$: 10 x 1\n- $dZ^{[1]}$: 10 x m ($~A^{[1]}$)\n- $dW^{[1]}$: 10 x 10\n- $dB^{[1]}$: 10 x 1","metadata":{}},{"cell_type":"code","source":"def init_params():\n    W1 = np.random.rand(10, 784) - 0.5\n    b1 = np.random.rand(10, 1) - 0.5\n    W2 = np.random.rand(10, 10) - 0.5\n    b2 = np.random.rand(10, 1) - 0.5\n    return W1, b1, W2, b2\n\ndef ReLU(Z):\n    return np.maximum(Z, 0)\n\ndef softmax(Z):\n    A = np.exp(Z) / sum(np.exp(Z))\n    return A\n    \ndef forward_prop(W1, b1, W2, b2, X):\n    Z1 = W1.dot(X) + b1\n    A1 = ReLU(Z1)\n    Z2 = W2.dot(A1) + b2\n    A2 = softmax(Z2)\n    return Z1, A1, Z2, A2\n\ndef ReLU_deriv(Z):\n    return Z > 0\n\ndef one_hot(Y):\n    one_hot_Y = np.zeros((Y.size, Y.max() + 1))\n    one_hot_Y[np.arange(Y.size), Y] = 1\n    one_hot_Y = one_hot_Y.T\n    return one_hot_Y\n\ndef backward_prop(Z1, A1, Z2, A2, W1, W2, X, Y):\n    one_hot_Y = one_hot(Y)\n    dZ2 = A2 - one_hot_Y\n    dW2 = 1 / m * dZ2.dot(A1.T)\n    db2 = 1 / m * np.sum(dZ2)\n    dZ1 = W2.T.dot(dZ2) * ReLU_deriv(Z1)\n    dW1 = 1 / m * dZ1.dot(X.T)\n    db1 = 1 / m * np.sum(dZ1)\n    return dW1, db1, dW2, db2\n\ndef update_params(W1, b1, W2, b2, dW1, db1, dW2, db2, alpha):\n    W1 = W1 - alpha * dW1\n    b1 = b1 - alpha * db1    \n    W2 = W2 - alpha * dW2  \n    b2 = b2 - alpha * db2    \n    return W1, b1, W2, b2","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:55:21.552382Z","iopub.execute_input":"2026-04-19T09:55:21.552689Z","iopub.status.idle":"2026-04-19T09:55:21.578591Z","shell.execute_reply.started":"2026-04-19T09:55:21.552660Z","shell.execute_reply":"2026-04-19T09:55:21.577406Z"}},"outputs":[],"execution_count":null},{"cell_type":"code","source":"def get_predictions(A2):\n    return np.argmax(A2, 0)\n\ndef get_accuracy(predictions, Y):\n    print(predictions, Y)\n    return np.sum(predictions == Y) / Y.size\n\ndef gradient_descent(X, Y, alpha, iterations):\n    W1, b1, W2, b2 = init_params()\n    for i in range(iterations):\n        Z1, A1, Z2, A2 = forward_prop(W1, b1, W2, b2, X)\n        dW1, db1, dW2, db2 = backward_prop(Z1, A1, Z2, A2, W1, W2, X, Y)\n        W1, b1, W2, b2 = update_params(W1, b1, W2, b2, dW1, db1, dW2, db2, alpha)\n        if i % 10 == 0:\n            print(\"Iteration: \", i)\n            predictions = get_predictions(A2)\n            print(get_accuracy(predictions, Y))\n    return W1, b1, W2, b2","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:55:21.581620Z","iopub.execute_input":"2026-04-19T09:55:21.582315Z","iopub.status.idle":"2026-04-19T09:55:21.597636Z","shell.execute_reply.started":"2026-04-19T09:55:21.582234Z","shell.execute_reply":"2026-04-19T09:55:21.596005Z"}},"outputs":[],"execution_count":null},{"cell_type":"code","source":"W1, b1, W2, b2 = gradient_descent(X_train, Y_train, 0.10, 500)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:55:21.599486Z","iopub.execute_input":"2026-04-19T09:55:21.599847Z","iopub.status.idle":"2026-04-19T09:56:07.540462Z","shell.execute_reply.started":"2026-04-19T09:55:21.599817Z","shell.execute_reply":"2026-04-19T09:56:07.539288Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"~85% accuracy on training set.","metadata":{}},{"cell_type":"code","source":"def make_predictions(X, W1, b1, W2, b2):\n    _, _, _, A2 = forward_prop(W1, b1, W2, b2, X)\n    predictions = get_predictions(A2)\n    return predictions\n\ndef test_prediction(index, W1, b1, W2, b2):\n    current_image = X_train[:, index, None]\n    prediction = make_predictions(X_train[:, index, None], W1, b1, W2, b2)\n    label = Y_train[index]\n    print(\"Prediction: \", prediction)\n    print(\"Label: \", label)\n    \n    current_image = current_image.reshape((28, 28)) * 255\n    plt.gray()\n    plt.imshow(current_image, interpolation='nearest')\n    plt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:56:07.542199Z","iopub.execute_input":"2026-04-19T09:56:07.542653Z","iopub.status.idle":"2026-04-19T09:56:07.552130Z","shell.execute_reply.started":"2026-04-19T09:56:07.542607Z","shell.execute_reply":"2026-04-19T09:56:07.550848Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"Let's look at a couple of examples:","metadata":{}},{"cell_type":"code","source":"test_prediction(0, W1, b1, W2, b2)\ntest_prediction(1, W1, b1, W2, b2)\ntest_prediction(2, W1, b1, W2, b2)\ntest_prediction(3, W1, b1, W2, b2)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:56:07.553908Z","iopub.execute_input":"2026-04-19T09:56:07.554273Z","iopub.status.idle":"2026-04-19T09:56:08.149442Z","shell.execute_reply.started":"2026-04-19T09:56:07.554206Z","shell.execute_reply":"2026-04-19T09:56:08.148197Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"Finally, let's find the accuracy on the dev set:","metadata":{}},{"cell_type":"code","source":"dev_predictions = make_predictions(X_dev, W1, b1, W2, b2)\nget_accuracy(dev_predictions, Y_dev)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2026-04-19T09:56:08.150852Z","iopub.execute_input":"2026-04-19T09:56:08.151332Z","iopub.status.idle":"2026-04-19T09:56:08.167711Z","shell.execute_reply.started":"2026-04-19T09:56:08.151235Z","shell.execute_reply":"2026-04-19T09:56:08.166677Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"Still 84% accuracy, so our model generalized from the training data pretty well.","metadata":{}}]}