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with $g_F$ and $g_B$ the annual growth factors. When $g_F$ > $g_B$ , $I^{*}$ grows without bound, and the batch size required to keep the arithmetic units busy grows with it. Autoregressive decoding sits on the wrong side of this: generating one token requires streaming the weights and the accumulated key–value cache, so decode time is bounded below by $t_{\mathrm{token}} \gtrsim \frac{W + K}{B}$. where W is the weight bytes touched and K the cache bytes. Pope and colleagues formalised the partitioning analysis behind this and showed how latency, throughput and cost trade against one another under different sharding layouts [ 12 ] . The mitigations are well documented and all attack the numerator or the batch: grouped-query attention shrinks the key–value cache by sharing key and value heads across query groups [ 14 ] ; PagedAttention removes fragmentation and over-reservation in cache allocation, reported at 2–4× throughput at equal latency [ 13 ] ; speculative decoding lets a cheap draft model propose tokens that the target verifies in parallel, provably without changing the sampled distribution [ 15 ] .