Making Neural Networks Fast with Vectorization (DL 10) | Highlights and Annotations by Gistr.

Neural network computations, initially understood via individual neuron interactions, are far more efficiently performed using vectorized operations. Activations and deltas are represented as vectors and matrices, enabling matrix multiplications and element-wise operations (Hadamard product) to replace nested loops. Batch processing further optimizes calculations by using matrix-matrix operations, significantly speeding up training and leveraging hardware acceleration (e.g., GPUs). This segment explains how to represent a layer's activations and deltas as vectors, significantly improving efficiency by collecting activations and deltas for each node in a layer into a single vector. This simplifies calculations and lays the groundwork for matrix operations. This segment details how a node's weighted sum of inputs can be calculated as a dot product between the previous layer's activation vector and the weight vector for that node. It then shows how to extend this to calculate the entire vector of inputs to a layer at once using matrix multiplication.This segment introduces the concept of a weight matrix, which combines the weight vectors for all nodes in a layer, enabling the calculation of all inputs to a layer using a single matrix-vector multiplication and vector addition, replacing nested loops for increased efficiency. This segment demonstrates how to vectorize the backward pass (computing deltas) using matrix multiplication and the Hadamard product (element-wise multiplication). It shows how to efficiently calculate all deltas for a layer using matrix operations, mirroring the vectorization of the forward pass.