Beyond Fixed Representations: The Vocabulary and Verifier Gaps in Open-Ended AI

Jul 16, 2026

Modern AI systems are assessed on reasoning, coding, theorem proving, tool use, and long-horizon research, yet they face a structural constraint: the representational frame—conceptual vocabulary, admissible search space, and success criteria—is fixed in advance. This work argues that open-ended innovation needs new operations that create, stabilize, and reuse representational primitives, thereby changing the search space itself. It identifies a vocabulary gap and a verifier gap and unifies them as cognitive discrepancy reduction.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages25

Reading Time1 h 3 min

Introduction

Two Types of Intelligent Activity

Limits of Framed Benchmarks

Representational Space Expansion and Progress

Beyond Fixed Representations: The Vocabulary and Verifier Gaps in Open-Ended AI Yuan Cao [realcaoyuan@gmail.com](realcaoyuan@gmail.com) Haiqian Yang [hqyang@mit.edu](hqyang@mit.edu) arXiv :2607 .09560v 1 [ cs .AI] 10 Jul 2026 July 13, 2026 Abstract Modern AI systems are increasingly being evaluated for their ability to reason, code, prove theorems, use tools, and long-horizon research tasks. These are powerful capabilities, but they share a structural limitation: the representational frame within which the model operates, including its conceptual vocabulary, the space of admissible solutions it can search, and the criteria by which success is evaluated, is typically fixed and supplied in advance. This paper argues that building stronger intelligent systems capable of open-ended innovation requires additional classes of operations: the creation, stabilization, and reuse of new representational primitives, which alter the space being searched rather than simply searching within it. We characterize the distance between current AI systems and genuinely open-ended intelligence through two gaps. The first is the vocabulary gap, the difficulty of inventing and stabilizing new representational primitives rather than merely recombining existing ones. The second is the verifier gap, the difficulty of judging the value of a new primitive when its full payoff maybe visible only after future reuse. We interpret both gaps through a unified framework of intelligence as cognitive discrepancy reduction. By viewing intelligent behaviors as a sequence of cognitive transformations, we distinguish intra-space transformations which operate within a fixed representational frame, from generative transformations which may modify the frame itself. On this basis, we propose a ladder of innovation autonomy and outline several directions for advancing open-ended AI, including objectives that reward useful representational change, persistent memory architectures for invented primitives, and adaptive verification mechanisms capable of evolving alongside the representations they evaluate. 1 Introduction There are two types of “intelligent” activities that are often conflated. The first is solving problems within a given frame: given a goal, a trained model with fixed representation space, and a way to check answers, find a good solution. The second requires changing the frame itself, for example creating new concepts, relations, measurements, abstractions, or evaluators that makes a class of problems previously unsolvable under pre-existing frames expressible and solvable. The first activity searches within a space, while the second changes the space being searched itself. Contemporary AI excels at the first type and is still primarily benchmarked on tasks in this category. Reasoning puzzles, competition mathematics, code generation, theorem proving, tool use, and agentic task completion all evaluate performance within problems whose representational frame is largely fixed in advance—a model’s weights are fixed by training data distribution; A benchmark supplies the task, the admissible form of an answer, and the standard of success; A coding environment supplies a programming language and tests; A theorem prover provides a formal language and a checker. An AI-for-science pipeline supplies a topic, a tool stack, a literature corpus, and procedures for validation. Such framed problems are useful for measuring progress, but they also impose an important limitation: our headline metrics are, by construction, weak tests of the second that require stronger capability. They tell us relatively little about whether a system can tackle genuinely open-ended innovation tasks in which the crucial step is not merely finding a solution within a given space, but recognizing that the space itself is inadequate and that a new representational primitive must be introduced. The history of scientific and social progress can be understood, in large part,

FAQs

What structural limitation do current AI systems share during evaluation?

Their representational frame—concept vocabulary, admissible solution space, and evaluation criteria—is typically fixed and provided in advance, so performance largely reflects searching within that frame.

What are the two gaps identified for open-ended intelligence?

The vocabulary gap is the difficulty of inventing and stabilizing new representational primitives, while the verifier gap is the difficulty of judging a primitive’s value when its payoff may appear only after future reuse.

How does the paper distinguish between intra-space and generative transformations?

It views intelligent behavior as cognitive transformations: intra-space transformations operate within a fixed representational frame, whereas generative transformations can modify the frame by creating new primitives or evaluators.

Jul 16, 2026

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