Prompt–Model Interaction Reaches the Fixed Points - A deterministic, task-free structural readout—and the factorizations of it that failed

Sep 15, 2026

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Prompts optimized for one language model degrade on another, and prompt formats lack model-independent meaning, causing benchmark rankings to reorder under semantically neutral reformatting. Evidence based on task accuracy cannot determine whether the interaction resides in task-acting machinery or in the conditional distribution itself. The study uses a task-free deterministic short-window argmax fixed-point readout, then tests whether interactions persist across prefixes, model factors, and a proposed mechanistic attention-sink account.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Abstract

1 Introduction

1.1 What is already known

1.2 The open question

1.3 The claim, and the ladder

2 Prefix-side factors fail

3 Model-side factors fail

arXiv : 2608 .2 13 15v 1 [cs .CL] 2 1 Aug 2026 Prompt–Model Interaction Reaches the Fixed Points A deterministic, task-free structural readout—and the factorizations of it that failed Nicolás Vera Zúñiga Independent Researcher, Chile [nicovera@quetru. cl](nicovera@quetru. cl) Abstract That a prompt’s effect on a language model is not a property of the prompt is established: prompts optimised for one model degrade on another, formats have no model-independent valence, and benchmark rankings reorder under semantically neutral reformatting. All of that evidence is about task accuracy, and a task readout cannot say where the interaction lives — in the machinery of performing tasks, or in the conditional distribution itself. We ask on a readout with no task in it: the fixed-point structure of the short-window argmax map xt+1 = arg maxxp (x | xt−1, xt), censused from 96 starts. It is deterministic, so nothing can be helped or hurt; and it exists only at short windows—four of six models lose it entirely by window 16—so everything here is a statement about how a model reads a fragment. Two results. First, the interaction reaches this readout at full magnitude: nine tokens of conditioning move the fixed-point fraction across most of its range, change a four-way structural class, and reorder models, while an instruction-tuning intervention that moves IFEval by 60.5 points moves the class by zero. Second, nothing we proposed carries the effect. Prefix length fails: the effect isnot monotone. Four phenomenological factors — prose-versus-markup, a universal direction, bidirectionality as a model property, instruct-resistance—were each withdrawn within one run of being proposed, dissolved by widening the sample. And the nearest mechanistic account, attention-sink dominance of early tokens, predicts the sign of the shift on 2 of 5 models —chance—with a length-by-content cross showing why: the account holds on real text and failson the uniformly random input our probe feeds it, so we operate outside its regime rather than against it. One fixed nine-token prefix drives four models toward fixed-point fraction 0 and two toward 1; a single beginning-of-sequence token takes one model from 0.21 to 0.91 while collapsing others; the bidirectionality survives in-distribution starts. On this readout the unit of explanation is the prompt–model pair. We close with the discipline that caught our own four factors, whose recurring error has a name: a criterion with a shape applied to a quantity with no room to vary. 1 Introduction 1.1 What is already known Language model evaluations are sensitive to the prompt in ways that are not nuisances. Semantically neutral reformatting reorders leaderboards by up to eight positions[Alzahrani et al. , 2024]; under adversarial prompt selection “any model can be promoted to first place” in a six-model, elevendataset embedding benchmark[Kostiuk and Enevoldsen, 2026]; per-prompt performance rankings agree across models only weakly, at Kendall’s W = 0 .238 [Cao et al. , 2024]; format performance“only weakly correlates between models”[Sclar et al. , 2024] . A prompt optimised for one model is suboptimal on another — named Model Drifting [Wang et al. , 2025a], and anticipated by earlier work establishing that a good prompt “binds to the nature of the LLM in question”[Chen et al. , 2023] . The best prompt templates do not transfer between models, even within a single model family[Voronov et al. , 2024] . Adjacent to the axis we vary, though on a different readout, Mahaut and Franzon [2025] find that prompt type changes the mechanism of repetition itself: repetition induced by in-context learning setups that explicitly require copying “relies on a dedicated network of attention heads that progressively specialize over training, whereas naturally occurring repetition emerges early and lacks a defined circuitry”. That work measures no fixed points. We take all of this as given. This paper does not claim

FAQs

Why can’t task performance benchmarks fully explain prompt–model interaction?

Task readouts conflate where the interaction lives: either in task-execution machinery or in the conditional distribution itself. Semantically neutral reformatting can reorder leaderboards, but that evidence does not isolate the locus.

What is the task-free readout used to study the interaction?

The paper iterates a short-window argmax map deterministically: x_{t+1} = argmax_x p(x | x_{t-1}, x_t). Its fixed-point structure reflects properties of the conditional distribution alone.

What do the experiments conclude about proposed factors and mechanistic accounts?

When the sample is widened, the factorized explanations proposed for prefix-side and model-side effects fail, and the nearest mechanistic account based on attention-sink dominance predicts correct shift signs only on 2 of 5 models.

Sep 15, 2026

Uploaded by Ophelia