💬 NLP

Probing the Knowledge Boundary: An Interactive Agentic Framework for Deep Knowledge Extraction

This paper proposes an interactive agentic framework with adaptive exploration policies and a rigorous processing pipeline to systematically extract and quantify the knowledge boundaries of Large Language Models, revealing distinct knowledge scaling laws, performance trade-offs between specialized and general models, and measurable differences in knowledge profiles driven by training data composition.

Original authors: Yuheng Yang, Siqi Zhu, Tao Feng, Ge Liu, Jiaxuan You

Published 2026-05-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yuheng Yang, Siqi Zhu, Tao Feng, Ge Liu, Jiaxuan You

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine Large Language Models (LLMs) as massive, sealed libraries. We know they contain a lot of books (knowledge), but we don't know exactly how many books are on the shelves, which ones are real, and where the shelves end. Usually, we test these libraries by asking a librarian a few random questions from a pre-written list. But this paper argues that method is flawed: it's like checking a library by peeking through a keyhole. You might miss the vast majority of the collection, and you can't tell if the librarian is making things up or just repeating what they've heard a thousand times.

The authors propose a new way to explore these libraries: The Interactive Agentic Framework. Think of this not as a single librarian, but as a team of explorers sent into the library with a specific mission: to find every single unique fact they can, no matter how obscure.

Here is how their system works, broken down into simple concepts:

1. The Four Exploration Strategies (The Explorers)

The team tried four different ways to ask the model for information to see which method dug the deepest:

The "Just Keep Asking" Approach (Sequential): This is like asking a friend, "Tell me about cats," then "Tell me more," then "Tell me even more." The authors found this hits a wall quickly. The model gets bored or stuck in a loop, repeating the same obvious facts.
The "Self-Correcting" Approach (Reflection): Here, the model is asked to review its own previous answers, find the holes, and fill them. It's like a student checking their homework before handing it in. It helps a bit, but it still struggles to find the deep, hidden facts.
The "Panel of Experts" Approach (Multi-Perspective): The system creates different personas (e.g., a lawyer, an engineer, a historian) and asks them all to talk about the same topic. This brings in different angles, but it can get messy and redundant.
The "Tree Climber" Approach (Recursive Taxonomy): This was the winner. Imagine the library is organized by a giant tree. You start at the trunk (the main topic), then climb a branch (a sub-topic), then a smaller twig (a specific detail), and finally reach the leaves (tiny, specific facts). By forcing the model to break a big topic down into smaller and smaller pieces, it is forced to leave its "comfort zone" and dig up rare, long-tail knowledge that it usually hides.

2. The Quality Control Team (The Knowledge Processor)

Once the explorers bring back a mountain of information, it's a mess. Some facts are duplicates, some are nonsense, and some are just the model saying "This is important" without actually saying what is important. The authors built a three-stage filter to clean this up:

Stage 1: The Fast Scan (Vector Filtering): A computer program quickly scans the list and throws out anything that looks 92% identical to something already found. It's like a bouncer at a club checking IDs to stop obvious duplicates.
Stage 2: The Smart Judge (LLM Adjudication): Sometimes, two facts look different but mean the same thing, or look similar but mean opposite things. A smarter AI (the "Judge") reads these tricky pairs and decides if they are truly unique or just rephrased versions of the same fact.
Stage 3: The Relevance Check (Domain Auditing): The final filter checks: "Is this actually useful knowledge?" It throws out "fluff" (like "Deep learning is cool") and keeps only concrete facts, principles, or step-by-step methods.

3. What They Discovered (The Findings)

The "Size Matters" Law
They tested models of different sizes (small, medium, and huge). They found a clear pattern: Bigger models know more. As the model got larger, it could retrieve significantly more unique facts. However, the biggest model didn't just know more; it knew deeper facts that the smaller models completely missed.

The "Specialist vs. Generalist" Trade-off
They compared a "General" model (good at everything) with a "Specialist" model (trained specifically for coding).

The Specialist: In its own lane (coding), it started off very accurate and confident. But as the team kept asking for more facts, the specialist's performance crashed. It ran out of things to say and started repeating itself or making mistakes.
The Generalist: It started slightly less confident but kept a steady pace. It didn't run out of steam and could keep digging up new facts for much longer.
The Lesson: Specializing a model makes it great at the start, but it narrows its world. If you ask a coding specialist about math, it forgets almost everything it knew.

The "Training Data" Fingerprints
Finally, they looked at models from different companies (Meta, Alibaba, DeepSeek) that were roughly the same size. Even though they were the same size, they had very different "knowledge profiles."

One model was great at engineering and code but weaker on theory.
Another was a theory whiz but less practical.
The Takeaway: It's not just about how big the brain is; it's about what books were fed into it during training. The training data leaves a permanent fingerprint on what the model knows and how well it knows it.

Summary

This paper introduces a new way to "map" the knowledge inside AI. Instead of just asking a few questions, they use a smart, recursive tree-climbing strategy to exhaustively dig for facts, then use a strict three-step filter to ensure only real, unique knowledge is counted. They found that structure beats randomness, bigger models know more, and specializing a model can make it brittle, while the specific data used to train it shapes its entire personality.

Technical Summary: Probing the Knowledge Boundary

Problem Formulation

Large Language Models (LLMs) function as compressed knowledge bases, yet the extent and nature of their internal knowledge remain opaque. Existing evaluation paradigms rely heavily on static benchmarks (e.g., MMLU) and predefined question sets, which suffer from data contamination risks and fail to actively explore the continuous landscape of a model's knowledge coverage. Furthermore, LLMs exhibit a strong inertia to remain within a "comfort zone" of high-probability tokens, often outputting generic or repetitive shallow knowledge when queried directly.

The core challenge is to define and measure the Extractable Knowledge Frontier: the set of unique, valid knowledge atoms retrievable from a black-box LLM under a fixed interactive pipeline. This requires moving beyond simple accuracy metrics to a saturation-based evaluation that distinguishes between latent capacity (what the model knows) and surface realization (what the model is willing to express).

Methodology

The authors propose an Interactive Agentic Framework designed to systematically extract and quantify LLM knowledge. The system operates as a closed-loop pipeline comprising two core modules:

1. Agentic Exploration Policies

To overcome output inertia, the framework employs four adaptive strategies to probe knowledge at different granularities:

Sequential Associative Probing: A baseline where the agent iteratively asks for more points based on flat interaction history.
Self-Reflective Refinement: A critic-actor loop where the model audits its previous outputs to identify missing sub-domains and generates targeted prompts to fill gaps.
Recursive Taxonomy Explorer: A hierarchical search strategy that recursively decomposes a topic domain into a tree of sub-fields. Agents exhaustively mine leaf nodes to force the model beyond dominant concepts into long-tail parametric memory.
Multi-Perspective Parallel Probing: The instantiation of multiple distinct expert personas (e.g., Engineer, Ethicist) to surface nuances a single neutral agent might overlook.

2. Knowledge Processing Pipeline

To ensure the quality of extracted knowledge, a three-stage pipeline filters raw outputs:

Vector-Based Filtering: Uses embedding models to merge pairs with high cosine similarity ( $S > 0.92$ ), removing strict duplicates.
LLM-Based Adjudication: A reasoning-heavy model acts as a judge for ambiguous pairs ( $0.70 < S < 0.92$ ) to resolve semantic overlaps and logical negations.
Domain Relevance Auditing: A final filter validates atoms against Bloom's Taxonomy criteria (Factual, Conceptual, Procedural). It rejects meta-statements, generic assertions, and incomplete fragments, ensuring only valid domain knowledge is retained.

Termination Criteria: Extraction stops when knowledge saturation is detected, defined by a growth rate $<1\%$ , efficiency $<10\%$ , fewer than 3 new atoms, or reaching a maximum of 15 turns.

Key Contributions

Formal Problem Definition: The paper establishes a formal formulation for black-box knowledge boundary probing, shifting from static benchmark testing to dynamic, saturation-based interactive evaluation.
Novel Framework: It introduces a multi-agent framework that adaptively navigates knowledge space, significantly outperforming naive prompting and standard Chain-of-Thought baselines in uncovering deep, long-tail knowledge.
Empirical Characterization: Through four systematic experiments, the authors characterize the knowledge topology of black-box LLMs, revealing scaling laws, trade-offs in specialization, and the impact of training data.

Experimental Results

1. Strategy Efficacy

The Recursive Taxonomy strategy (specifically with a branching factor of 5 and depth of 5) proved to be the Pareto-optimal extraction strategy. It achieved a yield ratio approximately 6.0 times higher than the baseline sequential probing. In contrast, naive sequential and reflection strategies plateaued prematurely, failing to access long-tail parametric memory without explicit structural guidance.

2. Knowledge Scaling Law

A clear positive correlation exists between model size and extractable knowledge. Using the optimal taxonomy strategy, recall increased from 27.3% (8B model) to 36.9% (70B) and 39.0% (405B). However, diminishing returns were observed at larger scales (the gain from 70B to 405B was smaller than from 8B to 70B). Accuracy also improved with size, though the largest model showed a slight regression in precision, suggesting a potential trade-off between volume and accuracy at extreme scales.

3. Specialization and the Pass@1 vs. Pass@k Trade-off

Comparing a general-purpose model (Qwen-2.5-7B) with a domain-specialized RL-tuned model (Coder variant) revealed a critical trade-off:

In-Distribution: The specialized model achieved higher initial accuracy but experienced rapid degradation as the "high-confidence zone" was exhausted. The general model eventually overtook it in accuracy and maintained stable performance.
Out-of-Distribution: The specialized model suffered catastrophic forgetting, with accuracy collapsing significantly compared to the general model.
This confirms that domain-specific fine-tuning narrows the effective knowledge boundary, improving initial precision at the cost of long-term recall and diversity.

4. Training Data Composition

Cross-series analysis of ~7B models from different organizations (Meta, Alibaba, DeepSeek) showed that while recall patterns remained stable (reflecting intrinsic model characteristics), accuracy varied dramatically by domain.

Llama-3.1 excelled in engineering/code-adjacent domains.
Qwen-2.5 dominated theoretical/mathematical domains.
DeepSeek-R1 showed uniformly degraded accuracy, suggesting that reasoning-oriented distillation may compress the knowledge distribution, sacrificing domain-specific expertise.
These results indicate that training data composition fundamentally shapes a model's knowledge profile, governing the quality of extractable knowledge more than architecture alone.

Significance and Claims

The paper claims to provide a robust methodology for auditing model knowledge prior to deployment, addressing the gap between what models can do and what they actually know. By treating the LLM as an environment to be explored rather than a static oracle, the framework offers a way to:

Distinguish between latent knowledge access and hallucination.
Predict failure modes in deployment by understanding knowledge boundaries.
Understand how pretraining choices and fine-tuning strategies shape the topology of machine knowledge.

The authors note that their measurements are operational and pipeline-dependent. While the LLM audit stage showed substantial agreement with human annotators ( $\kappa = 0.79$ ), it does not replace expert verification in high-stakes settings. The work serves as a foundational step toward systematic, saturation-based knowledge evaluation, moving beyond the limitations of current static benchmarks.