D1Core building blocks

This is where deep learning starts: the small set of differentiable parts that every architecture in the rest of the pillar reuses. A network is just affine maps interleaved with nonlinearities, trained by pushing gradients backward through the computation that produced the loss. Get these mechanics right and everything downstream is variations on a theme; get them wrong and training quietly stalls.

By the end you can trace a forward pass through an MLP, derive backpropagation as reverse-mode differentiation, and even hand-roll a tiny autodiff engine that records its own graph. You will know why Cybenko's theorem promises expressiveness, how to pick activations and avoid dead ReLUs, how Xavier and He initialization keep variance from collapsing, where BatchNorm, LayerNorm, and RMSNorm belong, and how dropout, weight decay, and the Adam family of optimizers actually shape training.

These building blocks recur in every CNN, Transformer, and diffusion model later in the pillar, so the time spent here pays off in every track that follows.