Glossary · Term

fixed point

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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

“The collapse to a trivial fixed point — and it's the most important practical lesson in the paper.”
Episode 152 — Training a Model to Mean What It Says, And Why That Isn't the Same as Being Good

Mentioned in 6 episodes

  1. 152
    Training a Model to Mean What It Says, And Why That Isn't the Same as Being Good
  2. 147
    Agents Fail at the Body, Not the Brain: A Self-Rewriting Scaffold That Lifts a 9B Model 44 Points
  3. 088
    Two Levers for Self-Improving AI: When Rewriting Code Isn't Enough
  4. 041
    When the Iteration Teaches the Model to Skip the Iteration
  5. 032
    A Sticky-Note for Every Layer: Letting Transformers Remember What They Were Just Thinking
  6. 015
    The Audit Number Isn't What You Think: Sycophancy and the Case Against Single-Prompt Bias Tests

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