🤖 AI Summary
This study addresses the confounding influence of probe construction artifacts on self-feedback analyses in language models by proposing a dual-ring co-stochastic evolution framework grounded in cyclic token-cell architectures and Glauber dynamics. Integrating maximal coupling, damage propagation analysis, Lyapunov exponent estimation, and controlled experiments, the approach effectively disentangles spurious signals arising from probe design from genuine model capabilities. The findings reveal that certain phenomena previously attributed to models are in fact artifacts of the probing methodology, identify a model-agnostic damage light cone, and uncover a model-dependent zero-crossing phase transition in Lyapunov exponents. Experimental validation across 19 models and two scale series demonstrates the model-invariance of token-space Lyapunov exponents, accurately reproduces Domany–Kinzel damage fields with high fidelity, and corrects four prior misinterpretations in the literature.
📝 Abstract
A growing class of methods probes a language model by feeding it its own output: self-consistency, iterated refinement, agentic loops. We ask what such a probe measures, in a construction chosen to make the question sharp: a ring of token cells resampled in place by the model's own windowed conditional p_r(x_i | x_{i+-r}). The substrate is Glauber dynamics on token sequences and is not new; what we change is the coupling. Advancing two rings that differ in one token under common random numbers makes undamaged copies diverge by exactly zero, so damage spreading becomes measurable where a maximal coupling gives mixing times instead. The answer is that it measures two different things at once, in readings that look alike. Some quantities are fixed by the construction: the damage light cone is kinematic, and the radius scaling of the token-space Lyapunov exponent lambda_ca(r) is model-invariant across 19 models and two scale ladders spanning 70x. Others genuinely track the model: lambda_ca crosses zero at a reproducible point in training, and the attractor share ranks models consistently however the lattice is built. Left undistinguished, the first kind is readily mistaken for the second -- we did so ourselves for four months, and report a phase transition we measured to three decimal places that belongs to the probe rather than to any language model. We give the test that separates them: hold the construction fixed and vary the model, or hold the model fixed and vary the construction, and see which readings move. We validate the instrument by reproduction first, recovering a Domany-Kinzel damage field bit-exactly against an independent prediction, and we report the estimator failures that this discipline caught -- four retracted verdicts, each on a quantity that looked like a measurement. The methodology ships as a package.