'80 Percent Sparse, 5x Faster' and a Distillation Plan: Evaluate the Claims

A vendor demo shows a transformer pruned to 80 percent unstructured sparsity with accuracy within 0.3 points and claims "5x faster inference on your GPUs". Separately, your team wants to distill a 7B assistant into a 1B student for cost, using the 7B's logits. The 7B uses a 128k-token vocabulary; the 1B you have in mind uses a 32k vocabulary from another family.

1. Explain why the 5x claim is probably not true on a standard GPU inference stack, what questions you ask the vendor, and which forms of sparsity do translate to speedups.
2. Give the byte arithmetic that shows when sparse storage even saves memory, using a 4096 x 4096 fp32 matrix.
3. Explain the distillation loss with temperature, why the T^2 factor is there, and what the vocabulary mismatch breaks. Propose two workable alternatives.
4. In a toy experiment, teacher soft targets on the labeled data helped only slightly, while teacher labels on lots of extra unlabeled data helped a lot. What does that tell you about where the gain comes from and how it shapes your data plan?