\n\\( Z[1] = W[1]X + b[1] \\)\n
\n\n\n\\( A[1] = g_{\\text{ReLU}}(Z[1]) \\)\n
\n\n\n\\( Z[2] = W[2]A[1] + b[2] \\)\n
\n\n\n\\( A[2] = g_{\\text{softmax}}(Z[2]) \\)\n
\n","metadata":{}},{"cell_type":"code","source":"def 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 ","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:38:08.995977Z","iopub.execute_input":"2024-09-21T20:38:08.996354Z","iopub.status.idle":"2024-09-21T20:38:09.007988Z","shell.execute_reply.started":"2024-09-21T20:38:08.996310Z","shell.execute_reply":"2024-09-21T20:38:09.006932Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"### encode the label","metadata":{}},{"cell_type":"code","source":"def one_hot(Y):\n one_hot_Y = np.zeros((Y.size,Y.max()+1)) #Y.size = m , Y.max + 1 = 9 +1\n one_hot_Y[np.arange(Y.size),Y] = 1\n one_hot_Y = one_hot_Y.T\n return one_hot_Y","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:38:09.009577Z","iopub.execute_input":"2024-09-21T20:38:09.009991Z","iopub.status.idle":"2024-09-21T20:38:09.022854Z","shell.execute_reply.started":"2024-09-21T20:38:09.009948Z","shell.execute_reply":"2024-09-21T20:38:09.021803Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"# Derivative of ReLU Function\n\nThe ReLU (Rectified Linear Unit) activation function is defined as:\n\n\\[\n\\text{ReLU}(x) = \n\\begin{cases} \n0 & \\text{if } x < 0 \\\\\nx & \\text{if } x \\geq 0\n\\end{cases}\n\\]\n\nThe derivative of the ReLU function is:\n\n\\[\n\\text{ReLU}'(x) = \n\\begin{cases} \n0 & \\text{if } x < 0 \\\\\n1 & \\text{if } x \\geq 0\n\\end{cases}\n\\]\n\nBelow is an illustration of the ReLU function's derivative:\n\n","metadata":{},"attachments":{"a1b8513e-b7d7-45ca-bd4c-0f91a53d04f9.png":{"image/png":"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"}}},{"cell_type":"code","source":"def deriv_Relu(Z):\n return Z > 0\n","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:38:09.026929Z","iopub.execute_input":"2024-09-21T20:38:09.027365Z","iopub.status.idle":"2024-09-21T20:38:09.036222Z","shell.execute_reply.started":"2024-09-21T20:38:09.027315Z","shell.execute_reply":"2024-09-21T20:38:09.035153Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## Backward Propagation\n\n\n\\( dZ[2] = A[2] - Y \\)\n
\n\n\n\\( dW[2] = \\frac{1}{m} dZ[2] A[1]^T \\)\n
\n\n\n\\( dB[2] = \\frac{1}{m} \\sum dZ[2] \\)\n
\n\n\n\\( dZ[1] = W[2]^T dZ[2] \\cdot g'[1](Z[1]) \\)\n
\n\n\n\\( dW[1] = \\frac{1}{m} dZ[1] A[0]^T \\)\n
\n\n\n\\( dB[1] = \\frac{1}{m} \\sum dZ[1] \\)\n
\n","metadata":{}},{"cell_type":"code","source":"def back_prop(Z1,A1,Z2,A2,W2,X,Y):\n m =Y.size\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) * deriv_Relu(Z1)\n dw1 = 1 / m * dz1.dot(X.T)\n db1 = 1 / m * np.sum(dz1)\n \n return dw1 , db1 ,dw2,db2","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"def ubdate_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 \n return W1 , b1 ,W2 ,b2\n ","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:38:09.037892Z","iopub.execute_input":"2024-09-21T20:38:09.038269Z","iopub.status.idle":"2024-09-21T20:38:09.054920Z","shell.execute_reply.started":"2024-09-21T20:38:09.038213Z","shell.execute_reply":"2024-09-21T20:38:09.053591Z"},"trusted":true},"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,iteration,alpha):\n W1 , b1 ,W2 ,b2 = init_params()\n for i in range(iteration):\n Z1, A1, Z2, A2 = forward_prop(W1 , b1 ,W2 ,b2,X)\n dw1,db1 ,dw2,db2 = back_prop(Z1, A1, Z2, A2,W2,X,Y)\n W1 , b1 ,W2 ,b2 = ubdate_params(W1 , b1 ,W2 ,b2,dw1,db1 ,dw2,db2,alpha)\n if i % 10 == 0:\n print(\"iteration: \", i)\n print(\"Accuracy: \",get_accuracy(get_predictions(A2),Y))\n return W1 , b1 ,W2 ,b2","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:38:09.056414Z","iopub.execute_input":"2024-09-21T20:38:09.056785Z","iopub.status.idle":"2024-09-21T20:38:09.067757Z","shell.execute_reply.started":"2024-09-21T20:38:09.056745Z","shell.execute_reply":"2024-09-21T20:38:09.066792Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"# Train1 500 epoch 0.1 learning rate ","metadata":{}},{"cell_type":"code","source":"W1, b1, W2, b2 = gradient_descent(X_train, Y_train,500,0.10)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:38:09.069058Z","iopub.execute_input":"2024-09-21T20:38:09.069468Z","iopub.status.idle":"2024-09-21T20:39:09.847729Z","shell.execute_reply.started":"2024-09-21T20:38:09.069428Z","shell.execute_reply":"2024-09-21T20:39:09.846095Z"},"trusted":true},"outputs":[],"execution_count":null},{"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":{"execution":{"iopub.status.busy":"2024-09-21T20:39:09.849726Z","iopub.execute_input":"2024-09-21T20:39:09.850575Z","iopub.status.idle":"2024-09-21T20:39:09.862340Z","shell.execute_reply.started":"2024-09-21T20:39:09.850520Z","shell.execute_reply":"2024-09-21T20:39:09.860822Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(4,W1,b1,W2,b2)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:39:09.864482Z","iopub.execute_input":"2024-09-21T20:39:09.865540Z","iopub.status.idle":"2024-09-21T20:39:10.139971Z","shell.execute_reply.started":"2024-09-21T20:39:09.865485Z","shell.execute_reply":"2024-09-21T20:39:10.138876Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(5,W1,b1,W2,b2)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:39:10.141569Z","iopub.execute_input":"2024-09-21T20:39:10.142010Z","iopub.status.idle":"2024-09-21T20:39:10.386954Z","shell.execute_reply.started":"2024-09-21T20:39:10.141958Z","shell.execute_reply":"2024-09-21T20:39:10.385850Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(1,W1,b1,W2,b2)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:39:10.388660Z","iopub.execute_input":"2024-09-21T20:39:10.389017Z","iopub.status.idle":"2024-09-21T20:39:10.637228Z","shell.execute_reply.started":"2024-09-21T20:39:10.388980Z","shell.execute_reply":"2024-09-21T20:39:10.636071Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(100,W1,b1,W2,b2)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:51:01.002234Z","iopub.execute_input":"2024-09-21T20:51:01.002798Z","iopub.status.idle":"2024-09-21T20:51:01.248139Z","shell.execute_reply.started":"2024-09-21T20:51:01.002749Z","shell.execute_reply":"2024-09-21T20:51:01.247114Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(20,W1,b1,W2,b2)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:51:44.773128Z","iopub.execute_input":"2024-09-21T20:51:44.773586Z","iopub.status.idle":"2024-09-21T20:51:45.017757Z","shell.execute_reply.started":"2024-09-21T20:51:44.773542Z","shell.execute_reply":"2024-09-21T20:51:45.016594Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(200,W1,b1,W2,b2)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:51:13.422858Z","iopub.execute_input":"2024-09-21T20:51:13.423313Z","iopub.status.idle":"2024-09-21T20:51:13.669991Z","shell.execute_reply.started":"2024-09-21T20:51:13.423253Z","shell.execute_reply":"2024-09-21T20:51:13.668910Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## train 1 accuracy 84%","metadata":{}},{"cell_type":"code","source":"dev_predictions = make_predictions(X_dev, W1, b1, W2, b2)\nget_accuracy(dev_predictions, Y_dev)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:43:57.441637Z","iopub.execute_input":"2024-09-21T20:43:57.442073Z","iopub.status.idle":"2024-09-21T20:43:57.484478Z","shell.execute_reply.started":"2024-09-21T20:43:57.442030Z","shell.execute_reply":"2024-09-21T20:43:57.482957Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"# Train 2 learning rate 0.1 epochs 1500","metadata":{}},{"cell_type":"code","source":"W12, b12, W22, b22 = gradient_descent(X_train, Y_train,1500,0.10)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:39:11.384161Z","iopub.execute_input":"2024-09-21T20:39:11.384547Z","iopub.status.idle":"2024-09-21T20:42:11.177507Z","shell.execute_reply.started":"2024-09-21T20:39:11.384500Z","shell.execute_reply":"2024-09-21T20:42:11.175880Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(650,W12,b12,W22,b22)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:51:59.374958Z","iopub.execute_input":"2024-09-21T20:51:59.375835Z","iopub.status.idle":"2024-09-21T20:51:59.561834Z","shell.execute_reply.started":"2024-09-21T20:51:59.375783Z","shell.execute_reply":"2024-09-21T20:51:59.560669Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(200,W12,b12,W22,b22)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:50:40.688963Z","iopub.execute_input":"2024-09-21T20:50:40.689409Z","iopub.status.idle":"2024-09-21T20:50:40.881879Z","shell.execute_reply.started":"2024-09-21T20:50:40.689366Z","shell.execute_reply":"2024-09-21T20:50:40.880575Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## train 2 accuracy 88.7% ","metadata":{}},{"cell_type":"code","source":"dev_predictions = make_predictions(X_dev, W12, b12, W22, b22)\nget_accuracy(dev_predictions, Y_dev)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:43:12.733702Z","iopub.execute_input":"2024-09-21T20:43:12.734156Z","iopub.status.idle":"2024-09-21T20:43:12.771787Z","shell.execute_reply.started":"2024-09-21T20:43:12.734111Z","shell.execute_reply":"2024-09-21T20:43:12.769501Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"# train 3 learning rate 0.4 epochs 600","metadata":{}},{"cell_type":"code","source":"W13, b13, W23, b23 = gradient_descent(X_train, Y_train,600,0.4)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:47:26.938235Z","iopub.execute_input":"2024-09-21T20:47:26.938704Z","iopub.status.idle":"2024-09-21T20:48:38.821234Z","shell.execute_reply.started":"2024-09-21T20:47:26.938662Z","shell.execute_reply":"2024-09-21T20:48:38.819662Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## train 3 accurcy 90.5%","metadata":{}},{"cell_type":"code","source":"dev_predictions = make_predictions(X_dev, W13, b13, W23, b23)\nget_accuracy(dev_predictions, Y_dev)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:49:18.410214Z","iopub.execute_input":"2024-09-21T20:49:18.410792Z","iopub.status.idle":"2024-09-21T20:49:18.458394Z","shell.execute_reply.started":"2024-09-21T20:49:18.410738Z","shell.execute_reply":"2024-09-21T20:49:18.456789Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(5,W13,b13,W23,b23)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:49:58.689785Z","iopub.execute_input":"2024-09-21T20:49:58.690550Z","iopub.status.idle":"2024-09-21T20:49:58.875826Z","shell.execute_reply.started":"2024-09-21T20:49:58.690482Z","shell.execute_reply":"2024-09-21T20:49:58.874551Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"test_prediction(200,W13,b13,W23,b23)","metadata":{"execution":{"iopub.status.busy":"2024-09-21T20:50:24.647319Z","iopub.execute_input":"2024-09-21T20:50:24.647762Z","iopub.status.idle":"2024-09-21T20:50:24.895975Z","shell.execute_reply.started":"2024-09-21T20:50:24.647718Z","shell.execute_reply":"2024-09-21T20:50:24.894831Z"},"trusted":true},"outputs":[],"execution_count":null},{"cell_type":"code","source":"","metadata":{},"outputs":[],"execution_count":null}]}