2026

• When the Jacobian Is Dense but the Program Is Not¹¹ Or why you should never form ${𝐿}^{-1}$
• Which Way Is Down? First-Order Optimizers as a Choice of Norm
• The Polar Express Algorithm
• Batched Backpropagation as a Linear Solve
• Backpropagation as a Linear Solve²² Maybe more natural than the adjoint method.
• Dual Numbers for Automatic Differentiation
• The Boundary Element Method
• The Finite Element Method
• Conic Optimization - Introduction and Implementation Details³³ The math used to solve these problems.

2025

• Backpropagation is the Adjoint Method⁴⁴ I really think more people should know.
• Associative Scan (and its relation to state-space models)
• Structured Masked Attention (and its relation to semiseparable matrices)