Splitting a long prefill across multiple iterations keeps decode requests from stalling, with no extra FLOPs and negligible IO overhead.

How iteration-level scheduling eliminates GPU idle time by inserting new requests the moment a slot opens, and the math behind mixing prefill and decode in a single forward pass.

How vLLM borrows the OS paging idea to eliminate KV cache memory fragmentation, pushing GPU utilization from ~30% to ~96%.

how online softmax extends the fused kernel to handle rows that exceed sram capacity, using a numerically stable 2-pass tiling algorithm.

why the key-value cache avoids redundant computation in autoregressive decoding, and the memory/compute tradeoffs it introduces.

how to write a fused softmax kernel in triton that eliminates redundant memory accesses and outperforms pytorch's native implementation.

understand batch gradient descent, stochastic gradient descent, and mini-batch gradient descent.

understand how backward propagation works in gradient descent.