finding

active

finding:pre-bifurcation-all-finite-time-lyapunov-exponents-are-negative-so-no-transient-chaos-occurs

Pre-bifurcation, all finite-time Lyapunov exponents are negative, so no transient chaos occurs

Establishes the baseline (non-chaotic) regime before the bifurcation.

Source paper

extracted_from

Fractal basins trap latent reasoning

(2026) · Jeffrey Lai · Anthony Bao · J. Quinn · William Gilpin

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Papers (1)

paper

Fractal basins trap latent reasoning
mentions

Claims (1)

claim

Fractal basins form because reasoning trajectories become trapped near weakly-unstable saddle points for extended durations
supports
The paper's core mechanistic claim connecting saddle dynamics to basin fractality.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Finite-Time Lyapunov Exponents (FTLE)method0.768
Spectrum quantifying amplification/suppression of perturbations along independent latent directions, used to detect transient chaos onset during training.
Most reasoning models are expected to exhibit some form of doubly transient chaos, because properties like convergence-to-fixed-answers act as a dissipation-like mechanismhypothesis0.754
Forward-looking predictive claim about reasoning models generally, based on the analogy to damped physical systems.
Fractal basins and transient chaos are the generic manner in which computational complexity manifests in analogue systemsclaim0.746
Generalizing interpretation connecting this paper's AI findings to physical analogue computation broadly.
Fast Lyapunov indicator λF strongly correlates with the number of distinct solutions a reasoning trajectory passes through before convergingfinding0.734
Links saddle-crossing intensity to the number of candidate-answer switches during reasoning.
Bayes-optimal perception inherently produces self-organised instability (local Lyapunov exponents fluctuating around zero), so FEP drives the system toward criticality (Friston et al. 2012)finding0.732
Establishes the mechanistic link between lower VFE and critical dynamics, supporting the paper's criticality prediction
Even mathematical catastrophes always begin as features consistent with the symmetries of the earlier state and develop smoothly from within the existing wholeness.claim0.717
Alexander's response to the apparent counter-examples from catastrophe theory: discontinuities are themselves structure-preserving at a deeper level
"Here, we show that reasoning models exhibit transient chaos, a physical consequence of the computational complexity of difficult tasks."quote0.715
Load-bearing abstract sentence stating the paper's central discovery.
Purely local autoregressive systems cannot maintain long-range coherence at finite temperature.claim0.714