In the context of machine learning, how does the concept of matrix multiplication enhance model training?

Matrix multiplication lets a model combine many inputs at once, turning a long list of numbers into a new list that captures all their interactions in a single step. In training, the weight matrix is multiplied by the input vector to produce predictions, and the same operation is used backward to compute gradients for updating weights. Because the multiplication is a single, highly optimized operation, it runs fast on GPUs and allows the model to learn thousands of parameters simultaneously. For example, a 3×3 weight matrix multiplied by a 3‑element input vector gives three output values that can be fed into the next layer or loss function, showing how data flows through the network. Thus, matrix multiplication makes the forward and backward passes efficient and scalable, which speeds up learning and improves accuracy.