Classical Amdahl's Law quantifies the limit of speedup under a fixed serial-parallel decomposition and homogeneous replication. Modern systems instead allocate constrained resources across heterogeneous hardware while the workload itself changes: some stages become effectively bounded, whereas others continue to absorb additional compute because more compute still creates value. This paper reformulates Amdahl's Law around that shift. We replace processor count with an allocation variable, replace the classical parallel fraction with a value-scalable fraction, and model specialization by a relative efficiency ratio between dedicated and programmable compute. The resulting objective yields a finite collapse threshold. For a specialized efficiency ratio R, there is a critical scalable fraction S_c = 1 - 1/R beyond which the optimal allocation to specialization becomes zero. Equivalently, for a given scalable fraction S, the minimum efficiency ratio required to justify specialization is R_c = 1/(1-S). Thus, as value-scalable workload grows, specialization faces a rising bar. The point is not that programmable hardware is always superior, but that specialization must keep re-earning its place against a moving programmable substrate. The model helps explain increasing GPU programmability, the migration of value-producing work toward learned late-stage computation, and why AI domain-specific accelerators do not simply displace the GPU.

翻译：经典阿姆达尔定律量化了在固定串行-并行分解与同构复制下的加速比极限。现代系统则倾向异构硬件间分配约束资源，同时工作负载本身也在发生变化：某些阶段变得有效受限，而其他阶段因更多计算仍能创造价值而持续吸收额外算力。本文围绕这一转变重新构建阿姆达尔定律。我们用分配变量替代处理器数量，用价值可扩展比例替代经典并行比例，并通过专用计算与可编程计算间的相对效率比来建模专业化。由此得到的目标函数产生有限饱和阈值：对于专业效率比R，存在临界可扩展比例S_c = 1 - 1/R，当实际比例超过该值时，专业化的最优分配将归零。等价地，给定可扩展比例S，证明专业化合理所需的最小效率比为R_c = 1/(1-S)。因此，随着价值可扩展工作负载增长，专业化面临日益升高的门槛。关键并非可编程硬件始终更优，而是专业化必须不断在演进中的可编程基座上重新证明自身价值。该模型有助于解释：为何GPU可编程性持续增强，为何价值创造型工作向学习型后期计算迁移，以及AI领域专用加速器为何不会简单取代GPU。