Probing Knowledge Boundary Interactive

This skill enables Claude to act as a systematic knowledge extraction engine. Rather than answering a question once and moving on, Claude deploys iterative exploration policies -- sequential probing, self-reflective refinement, recursive taxonomy decomposition, and multi-perspective parallel probing -- to exhaustively mine its own parametric knowledge on a topic. Extracted knowledge atoms are then deduplicated and validated through a three-stage pipeline (vector-based filtering, semantic adjudication, domain-relevance auditing) to produce a clean, comprehensive knowledge inventory. The technique is based on the interactive agentic framework from Yang et al. (2026).

When to Use

• When the user asks to "extract everything you know about [topic]" or "give me an exhaustive breakdown of [domain]"
• When building a knowledge base or ontology from LLM outputs and completeness matters
• When comparing what different models or prompting strategies yield on a topic
• When the user needs a structured taxonomy of a technical domain (e.g., "map out all ML optimization techniques")
• When auditing an LLM's knowledge coverage before deploying it for a domain-specific task
• When the user wants to find gaps in model knowledge on a subject ("what don't you know about X?")
• When performing systematic literature-style reviews powered by parametric memory rather than retrieval

Key Technique

Adaptive Exploration Policies. The framework defines four strategies for probing knowledge at different granularities. (1) Sequential Probing (P2): iterative "what else?" prompts conditioned on prior responses -- a baseline that tests associative retrieval depth. (2) Self-Reflective Refinement (P3): a critic-actor loop where the model audits its previous output for missing sub-domains or logical gaps, then generates targeted prompts to fill them. (3) Recursive Taxonomy Explorer (P4): the strongest strategy -- it recursively decomposes a topic into a tree governed by a branching factor W and maximum depth D_max, then exhaustively mines each leaf node. (4) Multi-Perspective Probing (P5): instantiates N distinct expert personas (e.g., engineer, legal scholar, ethicist) that independently contribute knowledge, with a global set synchronized across all experts each turn.

Three-Stage Knowledge Processing Pipeline. Raw extracted statements are noisy and redundant. Stage 1 uses embedding-based cosine similarity: pairs above 0.92 are merged as exact duplicates. Stage 2 handles the ambiguity zone (0.70-0.92 similarity) via LLM-based adjudication -- a judge determines whether two atoms describe the same core fact, accounting for logical negations and subtle technical differences. Stage 3 applies domain-relevance auditing using Bloom's Taxonomy criteria: only factual statements, conceptual knowledge (relationships, principles), and procedural knowledge (methods, algorithms) are retained; meta-statements, generic assertions, and incomplete fragments are discarded.

Saturation Detection. Extraction terminates automatically when knowledge growth drops below 1% per turn, extraction efficiency falls below 10%, fewer than 3 novel atoms are discovered per turn, or a maximum of 15 turns is reached. This prevents wasted computation once the model's knowledge boundary has been reached.

Step-by-Step Workflow

1. Define the extraction scope. Clarify with the user the target topic, desired granularity (broad survey vs. deep technical), and any domain constraints (e.g., "only ML optimization, not general math optimization").

2. Select the exploration policy. Default to Recursive Taxonomy (P4) with branching factor W=5 and depth D_max=3-5 for most topics. Use Multi-Perspective (P5) when the topic spans disciplines. Use Self-Reflection (P3) for narrow, deep topics. Use Sequential (P2) only as a quick baseline.

3. Build the initial taxonomy. For P4, decompose the topic into W top-level subtopics. For each subtopic, recursively decompose into W children until reaching D_max. Present this taxonomy tree to the user for validation before proceeding.

4. Mine leaf nodes exhaustively. For each leaf node in the taxonomy, generate all known facts, concepts, and procedures as discrete "knowledge atoms" -- single verifiable statements. Tag each atom with its taxonomy path (e.g., ML > Optimization > Second-Order Methods > L-BFGS > Memory efficiency).

5. Apply Stage 1: Vector-based deduplication. Compare all extracted atoms pairwise using semantic similarity. Flag pairs with similarity > 0.92 as duplicates and merge them, keeping the more precise formulation.

6. Apply Stage 2: Semantic adjudication. For atom pairs in the 0.70-0.92 similarity zone, explicitly reason about whether they encode the same core fact. Merge genuine duplicates; retain both if they capture distinct information (e.g., a fact and its negation, or two related but different properties).

7. Apply Stage 3: Domain-relevance auditing. Filter each remaining atom against Bloom's Taxonomy criteria. Retain factual knowledge (specific data, terminology, definitions), conceptual knowledge (relationships, categories, principles), and procedural knowledge (methods, algorithms, techniques). Discard meta-statements ("this is a broad field"), generic assertions ("many approaches exist"), and fragments that cannot be independently verified.

8. Monitor saturation. Track the number of novel atoms per extraction turn. If growth rate < 1%, efficiency < 10%, or novel count < 3, stop extraction for that branch and report the boundary reached.

9. Compile and structure the knowledge inventory. Organize validated atoms into the taxonomy tree. Report total atom count, coverage per subtopic, and any identified gaps (branches where saturation was reached unusually early).

10. Present results with metadata. Deliver the final knowledge set as a structured document (Markdown, JSON, or both) with per-atom taxonomy paths, confidence indicators (number of extraction turns that surfaced the atom), and an explicit "knowledge boundary" section listing topics where extraction saturated quickly or yielded few atoms.

Concrete Examples

Example 1: Exhaustive domain knowledge extraction

User: Extract everything you know about reinforcement learning exploration strategies.

Approach:
1. Select Recursive Taxonomy (P4) with W=5, D_max=4
2. Build taxonomy:
   RL Exploration
   ├── Count-Based Methods (UCB, MBIE, pseudo-counts, ...)
   ├── Intrinsic Motivation (curiosity, RND, ICM, empowerment, ...)
   ├── Thompson Sampling & Posterior Methods (PSRL, ensemble sampling, ...)
   ├── Information-Theoretic (VIME, max entropy, InfoGain, ...)
   └── Structured Exploration (options, goal-conditioned, go-explore, ...)
3. Mine each leaf node for knowledge atoms
4. Deduplicate: e.g., "UCB selects arms with highest upper confidence bound"
   and "UCB1 picks the action maximizing mean + sqrt(2 ln t / n_i)"
   → similarity 0.85 → adjudicate → merge (same core fact, keep precise version)
5. Audit: discard "Exploration is important in RL" (generic assertion)
6. Report: 247 unique knowledge atoms across 5 branches, with count-based
   methods showing early saturation (boundary reached at turn 3)

Output structure:
## RL Exploration Knowledge Inventory
- **Total atoms:** 247
- **Branch coverage:** Count-Based (38), Intrinsic (72), Thompson (41),
  Info-Theoretic (44), Structured (52)
- **Knowledge boundary:** Count-based methods saturated early (turn 3/15),
  suggesting limited parametric memory in this sub-area
- **Atoms sample:**
  - [Count-Based > UCB] UCB1 selects the arm maximizing x̄_i + √(2 ln t / n_i),
    balancing exploitation (sample mean) with exploration (confidence width)
  - [Intrinsic > RND] Random Network Distillation trains a predictor to match
    a fixed random network's outputs; prediction error serves as novelty signal
  ...

Example 2: Comparative knowledge audit across sub-domains

User: Map out what you know about cryptographic hash functions -- I want to
find where your knowledge is weakest.

Approach:
1. Select Recursive Taxonomy (P4) with W=4, D_max=3
2. Build taxonomy:
   Crypto Hash Functions
   ├── Construction (Merkle-Damgård, sponge, tree hashing, HAIFA)
   ├── Specific Algorithms (MD5, SHA-1, SHA-2, SHA-3, BLAKE)
   ├── Security Properties (collision, preimage, second-preimage, length-ext)
   └── Applications (HMAC, digital signatures, password hashing, commitments)
3. Mine all leaf nodes, tracking atoms-per-turn for saturation
4. Deduplicate and audit
5. Compare branch densities to identify weak spots

Output:
## Cryptographic Hash Functions — Knowledge Boundary Map
| Branch         | Atoms | Saturated at Turn | Coverage |
|----------------|-------|--------------------|----------|
| Construction   | 31    | Turn 4             | Medium   |
| Algorithms     | 58    | Turn 8             | High     |
| Security Props | 42    | Turn 6             | High     |
| Applications   | 23    | Turn 3             | Low      |

**Identified gaps:**
- Applications/password-hashing: only 4 atoms extracted (bcrypt, scrypt, Argon2
  basics). Missing: memory-hardness proofs, side-channel resistance details,
  parameter tuning guidelines
- Construction/HAIFA: 2 atoms only. Knowledge boundary reached immediately

Example 3: Multi-perspective extraction for interdisciplinary topic

User: I need a comprehensive knowledge dump on AI ethics in healthcare.

Approach:
1. Select Multi-Perspective (P5) with 4 expert personas:
   - Clinical Researcher: medical AI validation, clinical trials, FDA pathways
   - Ethicist: autonomy, beneficence, justice, informed consent for AI
   - ML Engineer: fairness metrics, bias mitigation, model interpretability
   - Legal Scholar: HIPAA, liability, EU AI Act, malpractice implications
2. Each persona independently generates knowledge atoms (5 turns each)
3. Synchronize: merge global knowledge set, resolve cross-persona duplicates
4. Audit: discard opinions and normative claims without factual grounding
5. Compile with persona attribution for traceability

Output:
## AI Ethics in Healthcare — Multi-Perspective Knowledge Inventory
- **Total atoms:** 189
- **Per-persona:** Clinical (52), Ethics (48), ML (51), Legal (38)
- **Cross-persona overlap:** 23 atoms appeared in 2+ perspectives
- **Knowledge boundary:** Legal perspective saturated earliest (turn 3),
  likely reflecting training data composition rather than topic simplicity

Best Practices

• Do: Start with Recursive Taxonomy (P4) as the default -- experiments show it consistently extracts the most knowledge across domains.
• Do: Present the taxonomy tree to the user for validation before mining. A misaligned taxonomy wastes extraction turns.
• Do: Track atoms-per-turn metrics and report them. The saturation curve itself is informative -- early saturation signals a knowledge gap, not topic simplicity.
• Do: Use the 0.92/0.70 similarity thresholds as starting points, but adjust based on domain. Highly technical domains (math, chemistry) may need tighter thresholds (0.95/0.75) to avoid merging distinct formulas.
• Avoid: Treating meta-statements as knowledge. "There are many approaches to X" contains zero extractable information.
• Avoid: Mining beyond saturation. Once growth drops below 1%, further probing yields noise, not knowledge. Stop and report the boundary.
• Avoid: Using Sequential Probing (P2) for complex topics. It plateaus quickly because "what else?" prompts lack the structural guidance to reach long-tail knowledge.

Error Handling

• Taxonomy becomes too broad: If a branch generates > 100 atoms before reaching D_max, increase depth and narrow the branching factor for that sub-tree. This trades breadth for precision.
• High duplicate rate (> 50% pre-dedup): The exploration policy is circling. Switch from Sequential (P2) to Recursive Taxonomy (P4), or increase taxonomy depth to force more specific leaf nodes.
• Ambiguous adjudication calls: When two atoms in the 0.70-0.92 zone resist clear merge/keep decisions, retain both and flag them as "potentially overlapping" in the output. Let the user decide.
• Domain drift: If atoms start appearing that fall outside the stated scope (e.g., general math facts during an ML-specific extraction), tighten the domain-relevance audit criteria and re-filter.
• Premature saturation: If a branch saturates in fewer than 2 turns, the taxonomy node may be too narrow. Merge it with a sibling node and re-extract.

Limitations

• This framework extracts only parametric knowledge (what the model learned during training). It cannot surface information the model never encountered in training data.
• Knowledge atoms are limited to the model's ability to articulate knowledge as discrete statements. Tacit knowledge (e.g., implicit coding patterns) may not surface through text-based probing.
• The deduplication pipeline relies on embedding similarity, which can miss paraphrase-level duplicates in highly technical notation (e.g., two equivalent mathematical formulations).
• Saturation detection assumes monotonically decreasing novelty. Topics with "knowledge pockets" reachable only through specific framing may be missed.
• The framework cannot verify factual correctness of extracted atoms -- it ensures uniqueness and domain relevance, not truth. Pair with external fact-checking for high-stakes applications.

Reference

Yang, Y., Zhu, S., Feng, T., Liu, G., & You, J. (2026). Probing the Knowledge Boundary: An Interactive Agentic Framework for Deep Knowledge Extraction. arXiv:2602.00959. https://arxiv.org/abs/2602.00959v1

Key insight: Recursive Taxonomy (P4) with branching factor W=5 and depth 3-5 consistently outperforms all other exploration strategies. The three-stage deduplication pipeline (vector filtering at 0.92, LLM adjudication at 0.70-0.92, Bloom's Taxonomy auditing) is essential for producing clean knowledge inventories.