AI systems material often splits into separate subjects: model math, GPU kernels, runtimes, and production serving. That makes each topic easier to name and harder to connect.
Trace a Tensor uses one workload as the thread. The first week starts with data representation and backpropagation. The point is to explain what a tensor contains, how its shape affects a computation, and what work a forward pass creates for the backward pass.
The second week follows the same data through the compute, memory, and storage hierarchy. Before changing a kernel, the learner has to profile the runtime and identify where time or bandwidth is actually going. That prevents an interesting optimization from becoming a substitute for diagnosis.
The third week changes the work. Flash Attention and quantization are studied as different ways to reduce movement or numerical cost. Both come with a quality or correctness boundary, so the exercise is not complete when the faster path runs. It must preserve the behavior the system needs.
The final week moves into engines, continuous batching, and serving economics. Latency, throughput, utilization, quality, and cost now sit in the same decision. The capstone asks for a reproducible workload or performance model, a measured bottleneck, a before-and-after comparison, and a defended optimization.
That shape is more useful than memorizing a stack diagram. It gives every abstraction a place in one causal chain: values become tensors, tensors create work, the machine schedules that work, and the serving system pays for the result.
The complete roadmap is at https://learn.significanthobbies.com/curriculum/roadmaps/trace-a-tensor.
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