Computation Graphs (DL 25) | Highlights and Annotations by Gistr.

Computational graphs visualize data flow and computation sequences, especially useful for understanding forward and backward propagation in neural networks. They explicitly represent all computational steps (e.g., multiplications, summations, activations). Each node in the graph represents a variable, and edges show dependencies. The graph's granularity can be adjusted; finer granularity allows for more detailed derivative calculations. Forward propagation calculates the network's output by traversing the graph topologically, computing each node's value based on its inputs. Backward propagation (backpropagation) calculates partial derivatives of the loss function concerning network parameters (weights) using the chain rule. The derivative of each node is multiplied by the derivative from the preceding node. Nodes with multiple outputs sum the derivatives from each output. Vectorized computations (using matrices and vectors) can be represented in computational graphs, simplifying calculations for entire layers at once. This is particularly advantageous for complex layer structures. The computational graph facilitates gradient calculation for gradient descent optimization. It provides a structured way to compute the gradient of the loss function with respect to each weight, guiding the weight updates during training. This segment introduces the concept of computational graphs as a visual representation of neural network computations, highlighting the implicit operations like weight multiplication, summation, activation function computation, and loss calculation. It emphasizes the need for making these implicit steps explicit for better understanding.This segment details the explicit representation of a neural network slice as a computational graph, showing how nodes represent variables (activations and weights) and edges represent dependencies between them. It illustrates the flow of computations from input nodes to output nodes, including multiplication, summation, and activation function application. Computational graphs visualize data flow in programs, especially neural networks' forward and backward propagation. Nodes represent variables, edges show dependencies. Forward propagation computes outputs; backward propagation (using the chain rule) calculates partial derivatives for gradient descent, optimizing network parameters. Vectorized representations efficiently handle matrix/vector operations in neural networks. This segment explains the core structure of a computational graph, where each variable is a node and dependencies are edges. It emphasizes the importance of knowing how to take the derivative of any node to enable both forward and backward propagation, crucial for gradient descent in neural networks.This segment describes how a computational graph can be used for both forward and backward propagation. It explains the process of topological sorting to compute outputs during forward propagation and the use of partial derivatives to propagate errors backward during backpropagation, focusing on the calculation of partial derivatives of the loss with respect to weights. This segment demonstrates the application of the chain rule during backpropagation. It shows how partial derivatives are calculated and propagated backward through the network, step-by-step, using a specific example and highlighting the role of multiplication and summation in the process. This segment focuses on handling nodes with multiple outputs during backpropagation. It explains how to sum the derivatives coming from each output to obtain the overall derivative with respect to the node's output, illustrating the process with a specific example and emphasizing the importance of summing derivatives for nodes with multiple outputs.