Lab Notebooks

Cosine similarity, document vectors, attention-style weighted averages, matrix actions, composition, and affine maps.

Reachable outputs, forgotten directions, rank, null space, and consistency checks for linear systems.

Jacobian matrices, shape checks, local predictions, and nonlinear functions read through linear approximations.

Design matrices, projection, residual orthogonality, normal equations, and least-squares interpretation.

Gradient descent loops, learning-rate behavior, loss functions, and a small fixed-hidden-layer training model.

Singular values, dominant directions, rank-k reconstruction, compression, and low-rank error.

Polynomials as vectors, inner products, projection equations, Taylor approximation, and least squares.

A synthesis lab connecting token embeddings, attention scores, weighted averages, affine layers, nonlinear blocks, gradients, and low-rank updates.