Matrices & Layer Width (Linear Algebra Part 2)
Scale single neurons to parallel layer matrices, computing simultaneous decision factors and mapping input vectors into wider coordinate spaces.
Lessons in this Topic
Matrix Dimensions and Parallel Vectors
Stack individual neuron weight vectors into two-dimensional matrices to evaluate multiple outcomes on the same input vector at once.
Matrix-Vector Multiplication
Matrix-vector multiplication executed as parallel row dot products to transform input feature coordinates into multi-output decision vectors.
Layer Width and Parallel Decisions
Define layer width by the count of parallel neurons evaluating a shared input vector, and establish independent decision hurdles with bias vectors.
The Affine Layer Transformation Math
Affine transformations and coordinate-wise activations that assemble matrix products and bias vectors into the complete forward pass of a dense layer.
Matrices and Layer Width In Practice
Master matrix-vector multiplication, layer width scaling, affine layer transformations, and parallel multi-output evaluation through manual calculation.