文章探讨了技术进步，特别是人工智能领域，通常遵循指数增长模式的理论。作者认为，投入的增加（如资金、计算资源、研究人员）与产出（如AI能力的提升、解决问题的效率）之间存在一种幂律关系。这意味着，随着时间的推移，指数级的投入会带来时间跨度上的平滑指数级增长。这种模式在历史上的技术发展中屡见不鲜，并且有理论基础支持，例如，随着新想法的获取难度增加，需要指数级投入才能维持“持续”的进步。文章还指出，AI领域的投入（如资本、研究人员数量）似乎也在呈指数级增长，部分原因是外部因素（如计算成本的下降）和AI进步本身驱动的炒作效应。尽管如此，作者也提醒，随着现有计算资源的规模化应用接近极限，AI的进步速度可能在2030年后放缓，但仍将保持较快的发展态势。

💡 **指数增长是技术进步的常态**：文章的核心观点是，大多数技术进步，特别是AI领域，表现为指数增长。这意味着进步的速度会随着时间的推移而加速，而不是线性的。作者通过观察历史上的技术发展趋势，如成本曲线效应、GDP增长以及AI领域的效率提升，来支持这一论点。

⚖️ **投入与产出的幂律关系**：作者提出，技术进步的“输入”和“输出”之间存在一种幂律关系。这意味着，随着投入（如计算能力、研发资金、研究人员数量）的指数级增长，解决问题的能力或技术能力的提升也会呈现出指数级的增长。这种关系是理解技术加速发展的原因之一。

🚀 **AI领域投入的指数级增长**：文章指出，AI领域的研究投入、计算资源使用量以及研究人员数量似乎都在呈指数级增长。这种增长部分源于外部因素，如计算成本的下降（受摩尔定律等影响），以及AI自身发展带来的“炒作”效应，吸引了更多的投资和人才。

⏳ **未来进展的预测与挑战**：尽管AI的进步速度可能很快，但作者也提出了一个重要的时间限制。作者认为，当前由大规模训练驱动的计算能力快速扩张可能在2030年左右达到瓶颈，届时AI的进步速度可能会放缓，尽管仍将保持相当快的速度。这意味着，AI在解决复杂、模糊任务方面的时间跨度将比解决清晰、可验证任务的时间跨度更长。

Published on September 29, 2025 4:13 PM GMT

Following in the tradition of @Algon, which linkposted an important thread from Daniel Eth about how AI companies are starting to seriously lobby, and have gotten early successes, I'll linkpost another thread from Daniel Eth, this time about how exponential increases are the default form of increase, assuming something's increasing at all.

In essence, I'm providing the theory for this post Almost all growth is exponential growth.

My sense is there’s generally a power law between “inputs” and “outputs” to technological progress. In this context, that manifests as “exponential increases in inputs over time yields smooth exponential increase in time horizons over time” (ie straight line on semi-log plot)

Why should there be a power law? We actually see this sort of dynamic come up all the time in technological progress - from experience curve effects (think declining PV prices) to GDP growth to efficiency improvements in various AI domains over time to AI scaling laws

And there are theoretical reasons to expect a power law, too. If ideas get harder to find over time, exponential inputs are needed for “consistent” progress. If each idea provides some proportionate improvement, then “consistent” progress cashes out as exponential growth.

I go into some detail defending a view along these lines in the appendix of my report w/ @TomDavidsonX on a software intelligence explosion. The point there was justifying the formulation of ‘r’, but it also may explain the METR Evals result

Will AI R&D Automation Cause a Software Intelligence Explosion?

So then if there’s a power law, the question becomes “is there exponential growth in inputs, and if so, why?” This seems more clearly true (approximately) - considering investment capital, to compute, to researchers in the field, etc

Okay, but why? Couple reasons. There’s exponential growth in some underlying inputs from the outside world (eg Moore for compute costs) - incidentally, I’d argue a similar power law explains that! Second, AI improvement drives hype which drives more researchers & investment

Now, this second reason is a bit fuzzier, since hype could drive non-exponential growth. Empirically, investment & number of researchers do seem to be growing ~exponentially. Same with decisions of scaling up large training runs by multiples of previous runs.

BTW, this is why I'm predicting the messier tasks faced by AI, where they currently struggle will be on the same curve, it's just that their time horizons currently are much shorter.

So AI will conquer the messy tasks similarly to how they've essentially conquered the clean, verifiable tasks, it will just take somewhat longer.

One caveat is that while Moore's law will still continue for the next 2 decades at least, the very fast compute scale-up driven by allocating more compute that we currently have to AI will not extend past 2030, and it's very plausible that it already slows down by 2028, so conditional on us not reaching TAI in 2030, progress in AI will be slower than in the 2020s (though still decently fast).

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