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  "body_markdown": "Table Of Contents\n5.\nMultilayer Perceptrons\n¶\nIn this chapter, we will introduce your first truly\ndeep\nnetwork. The\nsimplest deep networks are called\nmultilayer perceptrons\n, and they\nconsist of multiple layers of neurons each fully connected to those in\nthe layer below (from which they receive input) and those above (which\nthey, in turn, influence). Although automatic differentiation\nsignificantly simplifies the implementation of deep learning algorithms,\nwe will dive deep into how these gradients are calculated in deep\nnetworks. Then we will be ready to discuss issues relating to numerical\nstability and parameter initialization that are key to successfully\ntraining deep networks. When we train such high-capacity models we run\nthe risk of overfitting. Thus, we will revisit regularization and\ngeneralization for deep networks. Throughout, we aim to give you a firm\ngrasp not just of the concepts but also of the practice of using deep\nnetworks. At the end of this chapter, we apply what we have introduced\nso far to a real case: house price prediction. We punt matters relating\nto the computational performance, scalability, and efficiency of our\nmodels to subsequent chapters.\n5.1. Multilayer Perceptrons\n5.1.1. Hidden Layers\n5.1.2. Activation Functions\n5.1.3. Summary and Discussion\n5.1.4. Exercises\n5.2. Implementation of Multilayer Perceptrons\n5.2.1. Implementation from Scratch\n5.2.2. Concise Implementation\n5.2.3. Summary\n5.2.4. Exercises\n5.3. Forward Propagation, Backward Propagation, and Computational Graphs\n5.3.1. Forward Propagation\n5.3.2. Computational Graph of Forward Propagation\n5.3.3. Backpropagation\n5.3.4. Training Neural Networks\n5.3.5. Summary\n5.3.6. Exercises\n5.4. Numerical Stability and Initialization\n5.4.1. Vanishing and Exploding Gradients\n5.4.2. Parameter Initialization\n5.4.3. Summary\n5.4.4. Exercises\n5.5. Generalization in Deep Learning\n5.5.1. Revisiting Overfitting and Regularization\n5.5.2. Inspiration from Nonparametrics\n5.5.3. Early Stopping\n5.5.4. Classical Regularization Methods for Deep Networks\n5.5.5. Summary\n5.5.6. Exercises\n5.6. Dropout\n5.6.1. Dropout in Practice\n5.6.2. Implementation from Scratch\n5.6.3. Concise Implementation\n5.6.4. Summary\n5.6.5. Exercises\n5.7. Predicting House Prices on Kaggle\n5.7.1. Downloading Data\n5.7.2. Kaggle\n5.7.3. Accessing and Reading the Dataset\n5.7.4. Data Preprocessing\n5.7.5. Error Measure\n5.7.6.\n\\(K\\)\n-Fold Cross-Validation\n5.7.7. Model Selection\n5.7.8. Submitting Predictions on Kaggle\n5.7.9. Summary and Discussion\n5.7.10. Exercises\nPrevious\n4.7. Environment and Distribution Shift\nNext\n5.1. Multilayer Perceptrons",
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