deep learning

Where you put the LayerNorm changes whether gradients survive a hundred layers. Pre-norm keeps a clean residual highway and well-scaled gradients so deep models train without warmup heroics; post-norm normalizes the output but fights vanishing gradients at depth.

Attention is bottlenecked by moving the N x N score matrix to and from HBM, not by FLOPs. FlashAttention tiles the computation in fast on-chip SRAM and fuses softmax with an online running statistic, so it computes the exact same output while never materializing the full matrix.

Without a KV cache, generating token N re-attends over all N-1 prior tokens from scratch every step, turning decoding quadratic. The cache stores each layer's past keys and values so each new token costs one forward step, and its size is what caps your batch and context.

Backprop is just the chain rule run efficiently in reverse, but the question that separates levels is why a hundred-layer network trains when a naive one wouldn't. The credit-assignment intuition plus the three tricks that keep gradients alive.

The honest version: deep learning learns its own features but is hungry for data and compute, and on a customer's 50,000-row tabular dataset a gradient-boosted tree wins on accuracy, cost, and time-to-ship. The dividing line and the conditions that flip it.