Intelligence = log(Compute)
There is a peculiar thing about the current AI build-out. Everybody agrees, at least implicitly, that throwing more compute at the problem has diminishing returns. And yet the largest technology companies in the world are doing exactly that, at a scale that is difficult to make intuitive sense of. More chips, more datacenters, more power contracts, more debt, more depreciation.
In February 2025, Sam Altman summarized this tension in one sentence: the intelligence of an AI model roughly equals the logarithm of the resources used to train and run it. These resources are mainly training compute, data, and inference compute. Shortly afterwards, Satya Nadella put the corporate version of the same observation on Dwarkesh Patel's podcast: if intelligence is log of compute, whoever can do lots of compute is a big winner.
At first sight this sounds almost contradictory. A logarithm is not an exciting growth function. It is what you get when every next step costs multiplicatively more than the previous one. If intelligence really grows like
then a fixed improvement in model capability requires a fixed multiplicative increase in resources. We do not add another rack and get another unit of intelligence. We multiply the cluster.
Epoch AI estimates that frontier training compute has been growing by roughly 4-5x per year since 2020. This is exactly what one would expect if the industry is climbing a logarithmic curve: exponential growth in compute is the price paid for roughly linear progress in capability.
This is not a comfortable equation. It says that raw scaling works, but that it works in an expensive way. It also explains why the jumps feel smaller from the outside. GPT-5, when it arrived in 2025, was clearly stronger than previous systems, but many users experienced it as incremental rather than magical. That is what a logarithm feels like in practice. A great deal of additional effort buys a visible but not revolutionary shift.
For those of us coming from optimization, this is a familiar situation. Brute force can be useful, but it usually runs into the geometry of the problem. In combinatorial optimization, for example, an algorithm may work beautifully on moderate instances and then suddenly spend all its time trying to close the last gap. The hard part is not that progress is impossible. The hard part is that the marginal unit of certainty becomes expensive.
So why keep scaling?
Thresholds, not averages
The short answer is that economic value does not usually grow smoothly with capability. Human tasks are full of thresholds.
A coding assistant that can solve ten-minute tasks is useful, but mostly as a convenience. A coding agent that can reliably handle a multi-hour task, keep track of context, run tests, recover from errors, and produce something that can be reviewed rather than babysat is a different object. It crosses from autocomplete to delegation.
METR's time-horizon work is useful here. Their metric asks: what is the length of task, measured by human completion time, for which an AI agent succeeds with a given probability? The striking observation is that this horizon has been growing exponentially, with a doubling time on the order of months. The unit is not benchmark score. The unit is how long you can leave the agent alone.
This is a much more economic measure. A model that can do a five-minute task and a model that can do a five-hour task may differ by a few benchmark points, but they do not differ by a few dollars of value. They differ by workflow. One is a tool. The other starts to look like labor.
The same threshold structure appears elsewhere. A self-driving system that is almost safe is not almost valuable; it is a liability. A forecasting model that is slightly below break-even in trading is not slightly less useful; it loses money. A theorem-proving assistant that gets almost all details right still needs a human to find the one false step. Across many domains, the payoff turns on whether a system clears a minimum bar.
This is the main reason the logarithm does not kill the investment thesis by itself. If value grows roughly exponentially with capability, then the two curves can cancel each other:
Of course this is only a toy equation. We are sweeping all constants, discontinuities, and institutional frictions under the rug. But it captures the basic intuition: logarithmic capability growth can still justify massive compute spending if the value unlocked by the next capability threshold is sufficiently non-linear.
Put differently, the industry is not buying average benchmark points. It is buying threshold crossings.
Compute is not only training compute
There is a second subtlety. When people say "more compute," they often mean bigger pretraining runs. That is only one part of the story.
A major shift since 2024 has been the move toward inference-time compute: spending more computation at query time to search, verify, backtrack, and refine. The old picture was roughly: train a large model once, then ask it for a fast answer. The newer picture is: train a capable model, and then let it think longer when the task is hard.
This matters because it changes where the scaling happens. Instead of baking every bit of capability into the weights, we can allocate compute conditionally. Easy questions get cheap answers. Hard questions get search. For mathematical reasoning, coding, planning, and agentic tasks this is natural. In many settings, finding the answer is hard but checking pieces of the answer is easier. This is the same asymmetry that shows up all over theoretical computer science.
NB. This does not make compute disappear. It just moves it. Reasoning models can burn a large number of internal tokens before emitting a small final answer. So the falling price per token is not the same thing as a falling price per completed task. The right unit is not tokens. The right unit is verified work.
This is also why agent architecture matters. A model coupled to a compiler, a test suite, a theorem prover, a search procedure, or a database is not merely a language model producing text. It is a proposal-and-verification system. For the optimizers in the know, this is the familiar trick: do not try to solve everything in one monolithic step if you can decompose the problem into generation, checking, pruning, and restart.
DeepSeek V4 Pro and moving the curve
This brings us to DeepSeek V4 Pro. It is a useful 2026 datapoint because it is not just another "bigger is better" story.
DeepSeek announced the V4 preview on April 24, 2026. V4 Pro is a mixture-of-experts model with about 1.6 trillion total parameters but only 49 billion active parameters per token. V4 Flash is much smaller, at 284 billion total and 13 billion active parameters. Both support one-million-token context windows. Artificial Analysis placed V4 Pro near the top of the open-weight reasoning models, second only to Kimi K2.6 on its Intelligence Index at release, and reported strong agentic performance on real-world work tasks.
At the same time, V4 Pro is not free magic. It is cheaper than the top closed frontier systems for some workloads, but it is also substantially more expensive than earlier DeepSeek models. Artificial Analysis reported high token usage when running its benchmark suite, which helps explain why low per-token prices do not automatically imply low total task cost. Moreover, V4 Pro's hallucination behavior remains a warning sign: more capability does not automatically mean better calibrated uncertainty.
The right lesson is therefore not "DeepSeek disproves scaling." It is more interesting than that. DeepSeek shifts the curve. Sparse activation, hardware-aware design, long-context efficiency, and better post-training can give more capability per unit compute. They do not repeal the logarithm, but they change the constants, and in practice constants matter enormously.
This is exactly what happened in classical computing. Moore's law was not only smaller transistors. It was architecture, caching, compilers, vectorization, specialization, and a long list of boring engineering improvements that collectively moved the feasible frontier. AI scaling will be similar. There will be brute force, but also algorithmic efficiency, systems engineering, and many little tricks that make the same compute go further.
The depreciation clock
The remaining question is whether the build-out pays in time.
Reported and projected 2026 hyperscaler capex is now in the hundreds of billions of dollars, with a large fraction tied directly to AI infrastructure. Stargate alone is sized around $500 billion and several gigawatts of capacity. At the same time, directly attributable AI-services revenue is still much smaller than the infrastructure spend. Depending on how one allocates revenue, the ratio is not comforting.
This does not mean the AI build-out is necessarily a bubble. Fiber optics looked absurdly overbuilt in the early 2000s and then became the backbone of the internet economy. But it does mean that timing matters. The hardware depreciates. Debt has to be serviced. Customers have to pay. The capability thresholds have to be crossed within the economic life of the assets.
This is where the log formula is helpful. It does not predict doom, and it does not justify everything. It tells us what the race is about. The hyperscalers are trying to buy their way across capability thresholds faster than the depreciation clock runs. The model labs are trying to move the curve down through efficiency. Users are trying to convert token streams into actual workflow improvements. All three have to work.