Andrii Bidochko

• Updated: July 22, 2026
• 7 min read

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

Direct Answer

The paper Beyond Fixed Representations: The Vocabulary and Verifier Gaps in Open-Ended AI introduces a two‑pronged framework that lets AI systems create, stabilize, and reuse new representational primitives—effectively expanding the language and evaluation criteria they operate with. This matters because it moves AI from merely searching within a static problem space to reshaping that space, a prerequisite for genuine open‑ended innovation.

Background: Why This Problem Is Hard

Modern AI agents excel at tasks that can be expressed in a pre‑defined vocabulary: solving math equations, writing code, or navigating a known toolset. Yet, when the problem itself demands new concepts—new data structures, novel proof techniques, or emergent business models—the agent stalls. The bottleneck is twofold:

• Vocabulary Gap: The model’s internal lexicon lacks the symbols needed to describe a fresh idea.
• Verifier Gap: Even if a novel symbol is coined, the system has no reliable way to judge whether the new construct is valid or useful.

Existing pipelines address these gaps indirectly. Prompt‑engineering tricks, retrieval‑augmented generation, or tool‑use APIs can inject external knowledge, but they keep the core representational frame fixed. As a result, agents can only remix existing pieces rather than invent new ones. This limitation becomes stark in long‑horizon research, autonomous product design, or self‑improving codebases where the solution space continuously evolves.

What the Researchers Propose

Cao and Yang propose a unified “Cognitive Discrepancy Reduction” (CDR) framework that explicitly targets the vocabulary and verifier gaps. The framework consists of three interacting modules:

1. Primitive Generator (PG): A meta‑learner that synthesizes new representational primitives—new symbols, data types, or abstraction layers—based on observed gaps in the task.
2. Stabilizer (ST): A consensus‑building component that iteratively refines the freshly minted primitives, ensuring they are internally consistent and compatible with existing knowledge.
3. Verifier (VF): An evaluation engine that constructs task‑specific criteria (e.g., logical soundness, empirical performance) to test the utility of the new primitives.

The three modules form a feedback loop: when the PG detects a missing concept, the ST polishes it, and the VF either accepts it or pushes it back for revision. Over time, the system expands its own representational universe, enabling truly open‑ended problem solving.

How It Works in Practice

At a high level, the CDR workflow proceeds through four stages:

1. Gap Detection

The base model attempts the target task. Failure signals—high loss, incoherent reasoning traces, or tool‑call errors—are logged as “cognitive discrepancies.” These discrepancies are classified as either vocabulary‑related (missing symbols) or verifier‑related (missing evaluation criteria).

2. Primitive Generation

The PG receives the discrepancy description and produces candidate primitives. For a coding task, this could be a new API wrapper; for a theorem‑proving task, a novel lemma; for a business‑strategy task, a fresh market segment definition.

3. Stabilization Loop

The ST runs a multi‑agent consensus protocol. It samples variations of the candidate, checks for contradictions with the existing knowledge graph, and aligns the new primitive with the model’s embedding space. The result is a “stabilized primitive” that can be safely injected back into the model’s reasoning pipeline.

4. Verification & Integration

The VF constructs a task‑specific test suite. In a coding scenario, it compiles and runs unit tests; in a reasoning scenario, it checks logical entailment; in a strategic scenario, it runs a simulation against market data. Successful primitives are cached for future reuse, while failures trigger a new iteration of generation.

What distinguishes this approach from prior tool‑use or retrieval methods is that the system does not merely call external resources—it actively reshapes its own conceptual space. The primitives become first‑class citizens that other downstream agents can invoke without additional prompting.

Evaluation & Results

The authors benchmarked CDR across three domains that epitomize open‑ended challenges:

• Algorithmic Synthesis: Generating novel sorting algorithms for custom data layouts.
• Theorem Proving: Extending a proof assistant to discover and apply new lemmas in number theory.
• Strategic Planning: Designing go‑to‑market strategies for hypothetical products in a simulated economy.

Key findings include:

1. Vocabulary Expansion: In the algorithmic task, the system introduced 12 previously unseen data‑structure primitives, reducing average solution time by 38%.
2. Verifier Effectiveness: For theorem proving, the VF’s automated lemma‑checking raised proof success rates from 62% (baseline) to 87%.
3. Cross‑Domain Reuse: Primitives generated in the strategic planning domain were later reused in a separate business‑simulation benchmark, cutting model fine‑tuning cycles by half.

Beyond raw numbers, the experiments demonstrate that CDR can autonomously grow its own toolbox, a capability that static‑prompt pipelines lack. The results also suggest a positive feedback effect: as the primitive library grows, the model’s ability to detect and fill new gaps improves, hinting at a virtuous cycle of self‑enhancement.

Why This Matters for AI Systems and Agents

For practitioners building autonomous agents, the CDR framework offers a concrete pathway to break out of the “fixed‑frame” trap. Here are three practical takeaways:

• Dynamic Skill Acquisition: Agents can generate and validate new tool interfaces on the fly, reducing the need for exhaustive pre‑programmed SDKs.
• Robust Evaluation Pipelines: The verifier component provides a systematic way to embed domain‑specific success criteria, making agent behavior auditable and safer.
• Reusable Knowledge Assets: Stabilized primitives become shareable modules, enabling a marketplace of AI‑generated building blocks.

Enterprises looking to embed AI into complex workflows can leverage these capabilities to accelerate innovation cycles. For example, a marketing automation platform could let an AI agent invent a new audience segmentation schema, verify its lift through A/B testing, and then expose the schema to human marketers via a UI. This aligns directly with the AI marketing agents offering on the UBOS platform.

Similarly, the Workflow automation studio can integrate a CDR‑style primitive generator to let non‑technical users define custom data transformations that the system then validates and deploys automatically.

What Comes Next

While the CDR framework marks a significant step forward, several open challenges remain:

1. Scalability of Verification: As the primitive library expands, the verifier must handle combinatorial explosion in test generation. Future work could explore hierarchical verification or meta‑learning of test suites.
2. Cross‑Modal Primitive Transfer: Current experiments stay within a single modality (code, logic, or strategy). Enabling primitives that bridge modalities—e.g., a visual pattern translated into a symbolic rule—would unlock richer creativity.
3. Human‑in‑the‑Loop Governance: For high‑stakes domains (finance, healthcare), a transparent audit trail and optional human approval step are essential. Integrating CDR with existing governance frameworks is an active research direction.

Potential applications span from autonomous research assistants that draft and prove new scientific hypotheses to self‑optimizing enterprise AI platforms that continuously evolve their own APIs. Companies interested in experimenting with open‑ended AI can start by exploring the UBOS platform overview, which already supports plug‑in architectures suitable for CDR‑style extensions.

Developers seeking a quick sandbox can try the Ollama integration, which offers a lightweight environment for testing primitive generation and verification loops before scaling to production.

Conclusion

The vocabulary and verifier gaps identified by Cao and Yang expose a fundamental blind spot in today’s AI agents: the inability to reshape the very language and evaluation metrics they rely on. Their Cognitive Discrepancy Reduction framework demonstrates that, by closing these gaps, an AI system can become a true innovator—creating, stabilizing, and reusing new representational primitives. The empirical results across algorithmic, logical, and strategic domains validate the approach and hint at a future where AI agents continuously expand their own problem‑solving horizons.

As the field moves toward open‑ended intelligence, embracing mechanisms for self‑generated representations will be as critical as advances in model scaling. Organizations that embed such capabilities early will gain a decisive edge in rapid prototyping, autonomous research, and adaptive product development.

Call to Action

Ready to experiment with self‑evolving AI primitives? Explore the UBOS homepage for a suite of tools that support dynamic workflow creation, or dive straight into the UBOS templates for quick start. For a hands‑on demo of AI‑driven communication, check out the ChatGPT and Telegram integration. Stay ahead of the innovation curve—let your agents learn to rewrite their own rules.

Andrii Bidochko

CTO UBOS

Andrii Bidochko is an AI entrepreneur and researcher focused on AI agents, reinforcement learning, and autonomous systems. He writes about the technologies shaping the future of machine intelligence, from frontier models and agent architectures to real-world AI applications.