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arxiv: 2606.23668 · v1 · pith:AMMQWDHQnew · submitted 2026-06-22 · 💻 cs.LG

On the Limits of Prompt-Conditioned Language Models as General-Purpose Learners

David Mguni , Julian Ma , Jun Wang This is my paper

Pith reviewed 2026-06-26 09:11 UTC · model grok-4.3

classification 💻 cs.LG
keywords large language modelspromptingexpressivity floorPAC-Bayes boundscheap-talk gamealignment constraintsgeneralization limitstask inference
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The pith

Prompt-conditioned language models face an expressivity floor from language's limited capacity, making correct behavior unattainable for some task families even with infinite data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models user-LLM interactions as a bilevel cheap-talk game to show how prompts encode and reinterpret tasks under constraints. It decomposes task inference from execution and applies PAC-Bayes bounds to separate removable estimation error from fixed structural limits. This produces an expressivity floor where language channel capacity is exceeded by task complexity, rendering some tasks indistinguishable, plus an objective-misalignment floor from restricted output sets. If these floors hold, prompt-only LLMs cannot serve as universal solvers because certain task families retain positive error no matter the data volume, optimization, or scale. The work indicates that richer interfaces beyond language prompts are needed to supply more task information.

Core claim

Prompt-conditioned LLMs are not universal problem solvers through prompting alone, as there exist task families for which correct behaviour is provably unattainable even in the infinite-data regime. This follows from language acting as a capacity-limited communication channel; when the informational complexity of a task family exceeds the capacity of that channel, distinct tasks become unavoidably indistinguishable to the solver, inducing a strictly positive error floor that cannot be eliminated by additional data, optimisation, or model scaling alone. Alignment constraints add a second irreducible distortion when the user-ideal distribution lies outside the admissible output set.

What carries the argument

The bilevel cheap-talk game that models how latent tasks are encoded into prompts and reinterpreted under alignment constraints, from which PAC-Bayes bounds derive the expressivity floor separating estimation error from structural limitations.

Load-bearing premise

Language functions as a capacity-limited communication channel whose informational capacity can be strictly exceeded by the complexity of certain task families.

What would settle it

A demonstration that error on every task family can be driven to zero by increasing data volume and model size alone would falsify the existence of an expressivity floor.

Figures

Figures reproduced from arXiv: 2606.23668 by David Mguni, Julian Ma, Jun Wang.

Figure 1
Figure 1. Figure 1: Conceptual Diagram informational and objective bottlenecks that arise in prompt-based interaction, without making claims about internal and physical modularity within the model (see [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

Large Language Models (LLMs) are frequently portrayed as general-purpose solvers capable of solving arbitrary tasks. We argue that this view overlooks a fundamental constraint: language is a compressed and capacity-limited interface for conveying task information. Modelling User--System interaction as a bilevel \emph{cheap-talk} game, we analyse how latent tasks are encoded into prompts and reinterpreted under alignment and safety constraints. We introduce a conceptual decomposition separating task inference from execution and derive PAC-Bayes bounds that distinguish finite-sample estimation error from irreducible structural limitations. Our first main result establishes an \emph{expressivity floor}: language acts as a capacity-limited communication channel, and whenever the informational complexity of a task family exceeds the capacity of that channel, distinct tasks become unavoidably indistinguishable to the Solver, inducing a strictly positive error floor that cannot be eliminated by additional data, optimisation, or model scaling alone. We then establish an \emph{objective-misalignment floor}: when alignment constraints restrict the admissible output set, the User-ideal distribution may lie outside the feasible class, inducing an irreducible distortion. Together, these results yield a formal negative conclusion: prompt-conditioned LLMs are not universal problem solvers through prompting alone, as there exist task families for which correct behaviour is provably unattainable even in the infinite-data regime. More broadly, our analysis shows the limits of prompt-based generalisation arise from information-constrained communication and alignment-constrained objectives. This suggests that interfaces beyond natural language, including multimodal observations and, external memory, may reduce the inherent LLM limitations by increasing the task-relevant information available to the System.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper models User-System interactions as a bilevel cheap-talk game under alignment constraints and applies PAC-Bayes analysis to derive two floors: an expressivity floor (when task-family complexity exceeds the fixed capacity of the language channel, tasks become indistinguishable and a positive error floor persists at infinite data) and an objective-misalignment floor (when alignment restricts the output set away from the User-ideal distribution). The central conclusion is that prompt-conditioned LLMs cannot be universal solvers, as certain task families are provably unsolvable through prompting alone.

Significance. If the bounds are valid, the work supplies a formal information-theoretic account of why prompting cannot overcome all generalization limits, distinguishing estimation error from irreducible structural error and motivating non-linguistic interfaces. The use of cheap-talk games and PAC-Bayes tools to obtain explicit negative results on universality is a constructive contribution to the theory of LLM capabilities.

major comments (2)
  1. [bilevel cheap-talk game and expressivity floor derivation] The derivation of the expressivity floor (abstract and the bilevel cheap-talk game section) treats the language channel capacity as strictly finite and independent of prompt length. This modeling choice is load-bearing: if effective capacity can grow without bound via longer or structured prompts, the claimed separation between finite-sample error and an irreducible positive floor does not follow from the stated premises.
  2. [PAC-Bayes bounds] The PAC-Bayes bounds that separate estimation error from structural limitations (the section introducing the bounds) rely on the capacity bound remaining fixed once alignment/safety constraints are imposed. The manuscript should supply the explicit dependence (or independence) of the capacity term on prompt length and show that the floor remains positive when prompt length is allowed to vary.
minor comments (2)
  1. Notation for the task family complexity measure and the channel capacity should be introduced with a single consistent symbol and cross-referenced to the game definition.
  2. The discussion of related work on communication complexity and alignment constraints is brief; adding two or three key citations would clarify the novelty of the bilevel formulation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the modeling assumptions around channel capacity that underpin our negative results. We address each major comment below.

read point-by-point responses

  1. Referee: [bilevel cheap-talk game and expressivity floor derivation] The derivation of the expressivity floor (abstract and the bilevel cheap-talk game section) treats the language channel capacity as strictly finite and independent of prompt length. This modeling choice is load-bearing: if effective capacity can grow without bound via longer or structured prompts, the claimed separation between finite-sample error and an irreducible positive floor does not follow from the stated premises.

    Authors: The manuscript models the language channel capacity as finite for any given prompt to isolate the structural information bottleneck. We agree that the current text does not supply an explicit functional dependence on prompt length. In the revision we will add a paragraph in the bilevel cheap-talk game section stating the capacity term explicitly as a function of prompt length (via the mutual-information bound) and showing that the expressivity floor remains strictly positive for every finite length. revision: yes

  2. Referee: [PAC-Bayes bounds] The PAC-Bayes bounds that separate estimation error from structural limitations (the section introducing the bounds) rely on the capacity bound remaining fixed once alignment/safety constraints are imposed. The manuscript should supply the explicit dependence (or independence) of the capacity term on prompt length and show that the floor remains positive when prompt length is allowed to vary.

    Authors: The PAC-Bayes derivation conditions on a fixed capacity once the language interface and alignment constraints are chosen. We accept that the dependence on prompt length must be stated explicitly. The revised manuscript will include this dependence in the bounds section and verify that the objective-misalignment floor (and the expressivity floor) stay positive for any finite prompt length, while noting that unbounded lengths fall outside the prompt-conditioned setting analyzed in the paper. revision: yes

Circularity Check

0 steps flagged

No circularity; bounds derived from explicit modeling assumptions and PAC-Bayes analysis

full rationale

The paper models User-System interaction as a bilevel cheap-talk game, introduces a decomposition of task inference from execution, and applies PAC-Bayes bounds to separate estimation error from structural limits induced by a capacity-limited language channel. The expressivity floor and objective-misalignment floor are presented as direct consequences of these modeling choices and the assumption that task complexity can exceed channel capacity. No equations reduce to self-definition, no parameters are fitted and relabeled as predictions, and no self-citations or imported uniqueness theorems are invoked as load-bearing steps. The negative result holds conditionally under the stated premises rather than by tautology. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that language is a capacity-limited channel and that task families possess measurable informational complexity that can exceed it; no free parameters or invented entities are stated in the abstract.

axioms (2)
  • domain assumption language acts as a capacity-limited communication channel
    Invoked to establish the expressivity floor when task complexity exceeds channel capacity.
  • domain assumption alignment constraints restrict the admissible output set
    Used to derive the objective-misalignment floor when the user-ideal distribution lies outside the feasible class.

pith-pipeline@v0.9.1-grok · 5819 in / 1383 out tokens · 25058 ms · 2026-06-26T09:11:48.666236+00:00 · methodology

discussion (0)

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Reference graph

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