Anything that can improve itself stops being linear.
Recursive self-improvement is not only a story about AI agents improving AI agents. Anything that lives in a computer, and now anything that lives in language — code, proofs, experiments, entire fields of science — can read its own output and act on it. That feedback is what bends a straight line into a curve.
the curve / 01
One system, one extra term.
interactive
Read y as everything one system has produced so far — theorems proved, experiments closed, code that runs — and t as how long it has been running. The only question is what its rate of production depends on. Three answers, three terms.
ẏ = a + by2 − cy1.5
fixed a = 1 · y(0) = 0
- a
- baseline output
- by2
- self-influence
- cy1.5
- verification drag
With b at zero, only a is left: the system makes a fixed amount per unit time and never looks at what it has already made. y is a straight line, forever. Turn b up and the second term starts feeding output back in — as better tools, better questions, a better search — and the same equation leaves the frame, then leaves the real line altogether, in finite time.
Nothing actually blows up, at least not always. Real loops also carry c: evaluation costs something, verification lags behind generation, compute and data run out. That drag grows more slowly than the feedback does, so it can only win over a middle range of y — but winning there is enough, because y stalls at a ceiling and never reaches the range where feedback would run away.
None of this is a forecast. It is the smallest equation that still contains the argument: whether the feedback term is switched on at all, and whether the drag term can be kept ahead of it.
So the question is quantitative, not apocalyptic: how strong is the feedback, and how far out can the ceiling be pushed?
scope / 02
Where the term switches on.
A loop only closes if something can hand back a verdict. What that verdict costs is the c term, read across domains instead of across time. The difference between these three is not how fast the work goes but what does the judging: left to right the verdict gets cheaper to run, and narrower in what it can see.
01 / science
Experiments that design the next experiment
A result stops being an endpoint and becomes an input. The loop from question to evidence can close without waiting for a person to read the log — but never without waiting for the world, which sets the clock.
02 / models & agents
Systems that rewrite their own tooling
Models and agents that improve the thing producing them. Each pass changes not only the artifact but the capability that made it. The verdict is cheap to run here and easy to overfit, so it has to be designed as carefully as the loop it scores.
03 / language
Anything checkable becomes improvable
Proofs, specs, schemas, plans. The limit is not what can be written down but what can be checked. Finding can stay expensive here while checking stays cheap, and a loop can live on that gap alone. It stalls wherever taste is the only judge.
about / 03
What we are building.
Nonlinearity is an independent research effort on self-influencing systems. We build systems that run the loop end to end — proposing, executing and evaluating their own work — and the infrastructure that makes those loops cheap enough to leave running. Our bet is that the self-influence term is already switching on, unevenly, across everything that can be represented as text.
Generation is not the bottleneck. Evaluation is — and a loop is only worth leaving running where the verdict is both cheap and honest.
Working on the same problem?
We want to hear from people who run a lot of experiments and would rather the loop kept moving overnight.