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

• URL: http://arxiv.org/abs/2606.23668v1
• Date: Mon, 22 Jun 2026 17:52:59 GMT
• Title: On the Limits of Prompt-Conditioned Language Models as General-Purpose Learners
• Abstract summary: Large Language Models (LLMs) are frequently portrayed as general-purpose solvers capable of solving arbitrary tasks.<n>We argue that this view overlooks a fundamental constraint: language is a compressed and capacity-limited interface for conveying task information.<n>We analyse how latent tasks are encoded into prompts and reinterpreted under alignment and safety constraints.
• Score: 4.675635684281315
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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