Hardware-aware training often optimizes FPGA resources, latency, or bit operations, but folding changes what compression saves: shared arithmetic decouples precision, weight storage, and scheduled work. We derive training objectives from the measured costs of a folded streaming speech-enhancement accelerator. Mixed-precision weights reduce on-chip storage; structured channel sparsity removes entire operations from the engine schedule. We deploy a bit-exact implementation on the Kria KV260. The best sparse model eliminates 47.3% of convolution MACs, cutting frame time by 45% (1.86 to 1.03 ms) and dynamic energy by 60% (83 to 33 $μ$J/frame) against a storage-priced model measured in the same session, with higher speech quality. Relative to the most efficient dense build measured separately, frame time falls by 42% and energy by 48%. Reducing weight width from 8 to 6 bits lowers dynamic power by 27% but changes frame time by less than 5%. Plain channel group-lasso removes more work than cycle-cost-weighted lasso. Thus, folded-accelerator training should price storage and removable work separately, rather than rely on a single bit-operation metric.

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