Definition
Plain language
A value a process gets pulled toward — feed it in, get it back out.
As stated in the literature
A value x where f(x) = x; in iterative inference, the destination toward which a contractive map converges, allowing implicit solvers to skip explicit unrolling.
Also called: fixed-point, fixed-point iteration
Why it matters: Iterative procedures in neural networks often converge to fixed points, and finding them directly can replace expensive repeated forward passes.
For example, repeatedly hitting the square-root key on a calculator after entering any positive number converges to 1, which is the fixed point of the square-root function.
Heard on the show
“"Political bias in LLMs is therefore not a fixed point on an ideological scale but a response profile that must be mapped across realistic interlocutors.”Episode 015 — The Audit Number Isn't What You Think: Sycophancy and the Case Against Single-Prompt Bias Tests