Equation 3 · Part 8 · Model Systems in 2035: Four Scenarios, Their Signals, and What Would Falsify Them
=
=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
Write F(t) for peak arithmetic throughput and B(t) for memory bandwidth. The quantity that matters for a serving system is their ratio, because it sets the arithmetic intensity — operations per byte moved — at which a machine becomes compute-bound rather than bandwidth-bound: . with and the annual growth factors. When > , 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
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
Open the illustrated equality: what the equals sign claims guide →
Sources cited in the article section
- [6] Compute Trends Across Three Eras of Machine Learning ↗
- [2] Key Trends and Figures in Machine Learning ↗
- [3] Scaling Laws for Neural Language Models ↗
- [4] Training Compute-Optimal Large Language Models ↗
- [5] Will We Run Out of Data? Limits of LLM Scaling Based on Human-Generated Data ↗
These citations provide research context; check each source for the exact claim it supports.