Can fixed points replace learned halt tokens in reasoning models?

Adaptive test-time compute needs two things: flexibility (the option to spend variable compute) and adaptivity (a rule for when to stop). Chain-of-thought supplies both, but it pays for them with a special training regime and a learned halt token predicted from hand-crafted traces. FPRM (Fixed-Point Reasoning Model) proposes that a looped transformer already carries an intrinsic stopping signal: keep applying the shared block until the latent state stops moving — until it reaches a fixed point — then halt. The halting decision becomes a property of the computation itself rather than an extra prediction head bolted on top.

This is a sharper version of an observation the vault already holds. Since How do looped language models actually improve reasoning in depth?, the fixed-point structure of looped models is not incidental — it is what FPRM converts into a control mechanism. The payoff is difficulty calibration: FPRM reportedly halts closer to the accuracy-saturation point than Can tiny recursive networks outperform massive language models?'s ACT-style halting, which tends to stop too early (losing accuracy) or too late (wasting compute). It also reframes Can we allocate inference compute based on prompt difficulty? at the architectural rather than orchestration level: depth is allocated per-input by convergence, not by an external budget controller.

The honest caveat: fixed-point halting only works if the loop is built to converge. FPRM's gains lean on pre-norm layers and residual scaling to fix the signal-propagation problem that deferred halting otherwise induces. So "stop when stable" is not free — it presupposes architectural work to make stability a reliable signal rather than premature collapse. The strongest counterargument is that convergence and correctness can diverge: a model can settle confidently on a wrong fixed point, in which case stability becomes a false halt.