Linear algebra is the backbone of deep learning. Tensors (N-dimensional arrays) represent data, weights, and gradients. Scalars (single numbers), vectors (1D), matrices (2D), and higher-dimensional tensors enable operations like element-wise addition, matrix multiplication, and broadcasting. For example, matrix multiplication (e.g., `A @ B`) combines layers in neural networks, while broadcasting automates dimension alignment (e.g., adding a scalar to a matrix). Special matrices like identity matrices (`torch.eye(3)`) and transposes (`A.T`) are crucial for transformations and gradient calculations. Reshaping tensors (`A.view(2, 3)`) adapts data for model inputs.
A practical example: linear regression using PyTorch. Data (house sizes vs. prices) is modeled as `y_pred = X @ W + b`, with mean squared error (MSE) loss. Autograd computes gradients (`loss.backward()`) for weight (`W`) and bias (`b`) updates via gradient descent. Over epochs, `W` converges to 2.0 and `b` to 0.0, learning the true relationship `y = 2X`. Key steps include forward passes, loss calculation, backward passes for gradients, and parameter updates with gradient zeroing.
#LinearAlgebra#DeepLearning#Tensors#MatrixMultiplication#PyTorch#Autograd#GradientDescent#MachineLearning#DataScience#NeuralNetworks#Broadcasting#Reshaping#LinearRegression#MSE#ParameterOptimization
Hassan Jalloh
Linear algebra is the backbone of deep learning. Tensors (N-dimensional arrays) represent data, weights, and gradients. Scalars (single numbers), vectors (1D), matrices (2D), and higher-dimensional tensors enable operations like element-wise addition, matrix multiplication, and broadcasting. For example, matrix multiplication (e.g., `A @ B`) combines layers in neural networks, while broadcasting automates dimension alignment (e.g., adding a scalar to a matrix). Special matrices like identity matrices (`torch.eye(3)`) and transposes (`A.T`) are crucial for transformations and gradient calculations. Reshaping tensors (`A.view(2, 3)`) adapts data for model inputs.
A practical example: linear regression using PyTorch. Data (house sizes vs. prices) is modeled as `y_pred = X @ W + b`, with mean squared error (MSE) loss. Autograd computes gradients (`loss.backward()`) for weight (`W`) and bias (`b`) updates via gradient descent. Over epochs, `W` converges to 2.0 and `b` to 0.0, learning the true relationship `y = 2X`. Key steps include forward passes, loss calculation, backward passes for gradients, and parameter updates with gradient zeroing.
#LinearAlgebra #DeepLearning #Tensors #MatrixMultiplication #PyTorch #Autograd #GradientDescent #MachineLearning #DataScience #NeuralNetworks #Broadcasting #Reshaping #LinearRegression #MSE #ParameterOptimization
8 months ago | [YT] | 0