10. Neural Networks / Deep Learning
Happy Halloween (Neural Networks Are Not Scary)
The term Neural Network might sound really fancy and complicated but what a Neural Network does is fit a squiggle or a bent shape to data.
Tensors for Neural Networks, Clearly Explained!!! Part 1
The video begins by defining tensors as multi-dimensional arrays that can hold numerical data. The presenter explains that tensors are the fundamental data structure used in deep learning and neural networks. The video goes on to explain the different types of tensors, including scalar (0-dimensional), vector (1-dimensional), matrix (2-dimensional), and higher-dimensional tensors. The presenter also explains the concept of tensor rank, which refers to the number of dimensions in a tensor. The presenter then demonstrates how tensors are used in neural networks, showing how input data is represented as tensors and how the weights and biases in a neural network are also represented as tensors. The video also explains how tensor operations are used to compute the outputs of neural network layers. Finally, the presenter provides some practical tips for working with tensors, such as using libraries like NumPy and TensorFlow to manipulate tensors and understanding how to reshape tensors to match the input requirements of different neural network layers.
Neural Networks Part 6: Cross Entropy
The video begins by explaining that a loss function is a measure of how well a neural network is performing on a given task. The cross-entropy loss function is commonly used in classification tasks, where the goal is to predict the correct class label for a given input. The video then discusses the mathematical formula for the cross-entropy loss function, which is based on the concept of information entropy from information theory. The presenter provides a clear and intuitive explanation of how the cross-entropy loss function works, and how it penalizes the network for making incorrect predictions. The video also discusses some practical considerations for implementing the cross-entropy loss function in neural networks, such as the need to ensure that the predicted probabilities sum to one, and the use of regularization techniques to prevent overfitting.
Neural Networks Part 5: ArgMax and SoftMax
The video begins by explaining that the ArgMax function is a mathematical function that returns the index of the largest value in an array or vector. The ArgMax function is commonly used in neural networks to make predictions, by identifying the class with the highest probability given the input data. The video then discusses the SoftMax function, which is a mathematical function that transforms a vector of values into a vector of probabilities that sum to one. The SoftMax function is commonly used in neural networks to generate a probability distribution over the possible classes given the input data. The video provides a detailed example of how the SoftMax function can be used in a neural network to predict the probability of a customer making a purchase based on their demographic information and previous purchase history. The presenter shows how the SoftMax function is used to convert the output of the network into a probability distribution over the possible outcomes. The video also discusses some of the limitations of the SoftMax function, such as the fact that it can be sensitive to outliers and can generate overconfident predictions when the data is noisy. The presenter suggests some modifications to the SoftMax function, such as adding a temperature parameter, to address these issues.
Neural Networks Pt. 3: ReLU in Action!!!
The video begins by explaining that the ReLU function is a simple mathematical function that sets negative input values to zero, and leaves positive values unchanged. The ReLU function is commonly used as an activation function in neural networks because it is computationally efficient, and has been shown to work well in practice. ReLU (Rectified Linear Unit) — the ReLU activation function outputs whichever value is larger, 0 or the input value Technical Detail Alert: "Some of you may have noticed that the ReLU activation function is bent and not curved. This means that the derivative is not defined where the function is bent. And that's a problem because Gradient Descent, which we use to estimate the Weights and Biases, requires a derivative for all points. However, it's not a big problem because we can get around this by simply defining the derivative at the bent part to be 0 or 1, it doesn't really matter.
Long Short-Term Memory (LSTM), Clearly Explained
The video begins by explaining the limitations of traditional RNNs for handling long-term dependencies, such as the problem of vanishing gradients. LSTMs address these limitations by using a memory cell and three gates - the input gate, the forget gate, and the output gate - to selectively store or forget information at each time step. The video then discusses the structure of an LSTM, providing a clear and intuitive explanation of how the memory cell and gates work together to update the hidden state at each time step. The presenter also provides visualizations to help viewers understand the flow of information through the network. The video also discusses some practical considerations for using LSTMs, such as the use of dropout to prevent overfitting and the use of bidirectional LSTMs to incorporate information from both past and future time steps.
Word Embedding and Word2Vec, Clearly Explained Part 1: Embedding
The video begins by explaining the limitations of traditional approaches to representing words in natural language processing tasks, such as one-hot encoding. Word embeddings address these limitations by representing each word as a dense vector in a continuous space, where words with similar meanings are located closer together. The presenter then introduces the Word2Vec algorithm, which uses a neural network to learn word embeddings from a large corpus of text. The algorithm has two main variants: continuous bag-of-words (CBOW), which predicts a target word based on the context words surrounding it, and skip-gram, which predicts the context words based on a target word. The video goes on to explain how the Word2Vec algorithm trains the neural network to generate high-quality word embeddings, using techniques such as negative sampling and subsampling. The presenter also provides some practical tips for using Word2Vec, such as selecting the appropriate size for the embedding vector and using pre-trained embeddings when training data is limited.
Neural Networks Part 8: Image Classification with Convolutional Neural Networks (CNNs)
The video begins by explaining the limitations of traditional neural networks for image classification, such as the inability to handle spatial information and the large number of parameters required. CNNs address these limitations by using convolutional layers that can detect features in the input image and reduce the number of parameters needed. The video then discusses the structure of a typical CNN, which consists of convolutional layers followed by pooling layers and fully connected layers. The presenter provides a clear and intuitive explanation of how each of these layers works, and how they combine to form the overall CNN architecture. The video also discusses some practical considerations for training CNNs, such as the use of data augmentation to increase the size of the training set and prevent overfitting.
Recurrent Neural Networks (RNNs), Clearly Explained
The video begins by explaining the limitations of traditional neural networks for sequential data analysis, such as the inability to handle variable-length input and the lack of memory between time steps. RNNs address these limitations by using recurrent connections that allow information to be passed from one time step to the next. The video then discusses the structure of a typical RNN, which consists of a recurrent layer that applies the same weights and biases at each time step, and a hidden state that represents the memory of the network. The presenter provides a clear and intuitive explanation of how the hidden state is updated at each time step, using the current input and the previous hidden state. The video also discusses some practical considerations for training RNNs, such as the use of gradient clipping to prevent exploding gradients and the use of long short-term memory (LSTM) and gated recurrent unit (GRU) cells to address the problem of vanishing gradients.
Neural Networks Pt. 4: Multiple Inputs and Outputs
The video begins by reviewing the basic structure of a neural network with one input layer, one hidden layer, and one output layer. The presenter then demonstrates how this architecture can be extended to accommodate multiple input and output layers, by adding additional neurons to each layer and adjusting the weights of the connections between them. The video provides a detailed example of a neural network with three input layers and two output layers, which is used to predict the probability of a customer making a purchase based on their demographic information and previous purchase history. The presenter shows how the input data is fed into the network and how the output probabilities are computed using a softmax function. The video also discusses some of the challenges that arise when working with neural networks with multiple input and output layers, such as the need for careful preprocessing of the input data to ensure that it is properly normalized, and the need to carefully tune the network architecture and hyperparameters to avoid overfitting.
Neural Networks Pt 2: Backpropagation Main Ideas
The video begins by reviewing the basic structure of a neural network, which consists of an input layer, one or more hidden layers, and an output layer. During training, the network is presented with input data, and the weights of the connections between the neurons are adjusted so that the network produces the correct output for that input. The backpropagation algorithm is used to calculate the gradient of the loss function with respect to each weight in the network, which is necessary for updating the weights in a way that minimizes the loss. The video explains that the algorithm works by propagating the error from the output layer back through the network to the input layer, and using the chain rule of calculus to calculate the gradient of the loss with respect to each weight. The presenter then breaks down the backpropagation algorithm into several steps, starting with the forward pass, in which the input data is fed through the network to produce an output. The error between the output and the desired output is then calculated, and the algorithm proceeds to the backward pass, in which the error is propagated back through the network to calculate the gradient of the loss with respect to each weight. The video also covers some important details of the backpropagation algorithm, such as the use of the sigmoid function to introduce nonlinearity into the network, and the regularization techniques that are used to prevent overfitting.
Neural Networks Part 7: Cross Entropy Derivatives and Backpropagation
The video begins by reviewing the concept of the cross-entropy loss function, which is commonly used in classification tasks. The cross-entropy loss function measures the difference between the predicted probabilities and the true probabilities of the target classes. The video then explains how the derivative of the cross-entropy loss function is used in the backpropagation algorithm to update the weights and biases of the neural network. The presenter provides a step-by-step derivation of the derivative, using calculus and the chain rule. The video also discusses some practical considerations for implementing the cross-entropy derivative in code, such as using vectorization to improve efficiency and handling the case where the target class is a one-hot encoded vector.
Neural Networks Pt. 1: Inside the Black Box
The video starts with an analogy that compares neural networks to a game of hot and cold, where the goal is to find a hidden object in a room by listening to the feedback of someone giving you hints. The hints get warmer as you get closer to the object, and colder as you move farther away. Similarly, in a neural network, the input data is passed through layers of neurons that progressively extract more complex features from the data, and the feedback from each layer helps to guide the network towards the correct output. The video then goes on to explain the basic structure of a neural network, which consists of an input layer, one or more hidden layers, and an output layer. Each layer contains multiple neurons, which are connected to the neurons in the adjacent layers by weighted connections. During training, the weights are adjusted so that the network learns to produce the correct output for a given input. The presenter also covers some key concepts related to neural network training, such as the loss function, which measures the difference between the network's output and the desired output, and the backpropagation algorithm, which uses the chain rule of calculus to calculate the gradient of the loss with respect to each weight in the network. The gradient is then used to update the weights in a way that minimizes the loss.
