fix(hw_acceleration): merge math-anchored multiplier into single span

$10^2$$\times$ produced two adjacent math spans rendering with a
visible seam at print scale. Per book-prose.md $2 (math-anchored
multiplier exception, added 2026-05-05), include \times inside the
same span as the power: $10^2\times$.
This commit is contained in:
Vijay Janapa Reddi
2026-05-05 08:21:57 -04:00
parent 9da65edf51
commit 1448133cb7

View File

@@ -749,7 +749,7 @@ Machine learning constitutes a computational domain with unique characteristics
Machine learning computational requirements reveal limitations in traditional processors. CPUs reach only `{python} CpuMlInefficiency.cpu_utilization_min_str``{python} CpuMlInefficiency.cpu_utilization_max_str` percent utilization on neural network workloads, delivering approximately `{python} CpuMlInefficiency.cpu_gflops_str` GFLOPS (billions of floating-point operations per second) while consuming hundreds of watts. This inefficiency results from architectural mismatches: CPUs optimize for single-thread performance and irregular memory access, while neural networks require massive parallelism and predictable data streams. The memory bandwidth constraint compounds the problem: a single neural network layer may require accessing gigabytes of parameters, overwhelming CPU cache hierarchies designed for kilobyte-scale working sets.
\index{Energy!data movement cost}
The energy economics of data movement influence accelerator design. Accessing data from DRAM can consume on the order of $10^2$$\times$ more energy than a multiply-accumulate operation (exact values vary by technology node and design), making minimizing data movement a primary optimization target. This disparity helps explain the progression from repurposed graphics processors to purpose-built neural network accelerators. TPUs and other custom accelerators can sustain high utilization on dense kernels by implementing systolic arrays and other architectures that maximize data reuse while minimizing movement.
The energy economics of data movement influence accelerator design. Accessing data from DRAM can consume on the order of $10^2\times$ more energy than a multiply-accumulate operation (exact values vary by technology node and design), making minimizing data movement a primary optimization target. This disparity helps explain the progression from repurposed graphics processors to purpose-built neural network accelerators. TPUs and other custom accelerators can sustain high utilization on dense kernels by implementing systolic arrays and other architectures that maximize data reuse while minimizing movement.
\index{Training vs. Inference!accelerator design}
Training and inference present distinct computational profiles that influence accelerator design. Training requires high-precision arithmetic (FP32 or FP16) [@ieee_754_2019]\index{FP16!training precision}\index{FP32!gradient computation} for gradient computation and weight updates, bidirectional data flow for backpropagation\index{Backpropagation!memory requirements} (see @sec-model-training for activation memory analysis), and large memory capacity for storing activations. Inference can exploit reduced precision (INT8 or INT4), requires only forward computation, and prioritizes latency over throughput[^fn-latency-throughput-hw]. These differences drive specialized architectures: training accelerators maximize FLOPS and memory bandwidth, while inference accelerators optimize for energy efficiency and deterministic latency.