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Entropic Claim Resolution: Uncertainty-Driven Evidence Selection for RAG

🕒 Published (v1): 2026-03-30 13:49 UTC · Source: Arxiv · link

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TL;DR

ECR is an inference-time algorithm that replaces relevance-driven retrieval in RAG with a decision-theoretic objective: sequentially selecting atomic evidence claims that maximize Expected Entropy Reduction (EER) over a set of competing answer hypotheses. Retrieval terminates when Shannon entropy over the hypothesis space falls below a threshold \(\epsilon\) (epistemic sufficiency), or exposes irreconcilable contradiction when evidence is inherently conflicting. The paper is primarily theoretical; empirical benchmarks are not reported in the provided text.

Problem

Standard dense retrieval in RAG selects documents by maximizing \(P(D|Q)\) (semantic similarity), leading to epistemic collapse: redundant evidence that confirms the query surface form rather than discriminating among competing answer hypotheses. Existing iterative/agentic approaches (ReAct, Self-RAG, Tree-of-Thoughts) lack a principled stopping criterion and an explicit objective function for choosing which evidence to fetch next, relying instead on heuristic thresholds or prompt-driven self-reflection.

Method

ECR operates as an inference-time controller after a high-recall candidate claim set \(C = \{c_1, \ldots, c_n\}\) has been generated by upstream retrieval.

  1. Hypothesis initialization: An Answer Hypothesis Space \(A = \{a_1, \ldots, a_k\}\) of mutually exclusive macro-answers is generated via LLM prompting or vector clustering. Prior is set uniform: \(P(a) = 1/|A|\).

  2. EER-based selection: At each iteration \(t\), the next claim is chosen by: $\(c^* = \arg\max_{c \in C_{\text{cand}}} \widehat{\text{EER}}(c) + \lambda \cdot \text{ConflictPotential}(c)\)$ The tractable EER proxy is: $\(\widehat{\text{EER}}(c) = \frac{|p_+(c) - p_-(c)|}{p_+(c) + p_-(c)} \cdot H(A|X_{\text{eval}}) \cdot \text{conf}(c)\)$ where \(p_+(c)\) and \(p_-(c)\) are the posterior mass on hypotheses that do/do not cite \(c\) as support. The \(\lambda \cdot \text{ConflictPotential}(c)\) term biases selection toward claims that complete explicit contradiction pairs.

  3. Bayesian posterior update: After verifying claim \(c^*\) against provenance (Laplace-smoothed support/contradiction edge counts in an EAV SQLite store), hypotheses are updated via localized Bayes' rule.

  4. Stopping rule: Terminate when: $\(H(A|X_{\text{eval}}) \leq \epsilon \;\wedge\; \neg\text{Conflict}(X_{\text{eval}})\)$ If contradictions remain unresolved, ECR halts and exposes the competing hypothesis distribution rather than collapsing it.

ECR is integrated into CSGR++ (Context-Seeded Graph Retrieval plus), activated only on analytical query routes; deterministic SQL/tool routes bypass it.

Key Contributions

  • ECR algorithm: decision-theoretic claim selection maximizing EER rather than semantic relevance, with a computationally linear proxy suitable for inference-time use.
  • Principled stopping criterion: formal epistemic sufficiency condition \(H(A|X_{\text{eval}}) \leq \epsilon \wedge \neg\text{Conflict}\), replacing heuristic halting in prior agentic RAG.
  • Contradiction-aware phase transition: the coherence term \(\lambda > 0\) causes ECR to switch from entropy collapse to ambiguity exposure when evidence is inherently inconsistent; behavior saturates for any \(\lambda > 0\).
  • Termination bound (Theorem 1): ECR terminates in at most \(\min(T, |C_{\text{cand}}|)\) steps; under a minimum per-step entropy decrease \(\delta > 0\), epistemic sufficiency is reached in at most \(\lceil(H_0 - \epsilon)/\delta\rceil\) iterations.
  • Topological provenance verification: Laplace-smoothed empirical truth estimate from graph edge counts, with LLM fallback, decoupling verification from pure parametric model confidence.

Results

No empirical benchmark results (accuracy, F1, latency numbers against baselines) are reported in the provided text. The paper characterizes ECR's properties theoretically and describes system integration into CSGR++. The only quantitative claim is the termination bound from Theorem 1 and qualitative statements about \(\lambda\) sensitivity (Appendix Figure A.1, not included).

Limitations

  • No empirical evaluation against standard RAG benchmarks (e.g., HotpotQA, MuSiQue, ASQA) is presented in the provided text; theoretical properties are demonstrated but not validated experimentally.
  • The EER proxy (Eq. 4) is intentionally exploitative (favoring imbalance over balanced splits) rather than a symmetric approximation of classical information gain; its optimality relative to true EER is uncharacterized.
  • Hypothesis space \(A\) quality depends entirely on LLM generation or clustering quality at initialization; poor hypothesis coverage propagates through all downstream reasoning.
  • ConflictPotential is binary and structural (exact negation detection), missing soft or paraphrased contradictions.
  • ECR is only activated on analytical routes within CSGR++; its behavior on the other five query route types (LOOKUP, SQL, etc.) is undefined.
  • Computational cost of Bayesian posterior updates and EAV provenance lookups at scale is not characterized.

Relevance to Harnesses / Meta-Harnesses

ECR functions as a inference-time meta-controller that wraps an upstream retrieval pipeline and governs which evidence a downstream generator sees — precisely the architecture pattern of a reasoning harness. Its formalization of stopping criteria (\(H \leq \epsilon\)) and evidence selection policy (EER maximization) provides a principled template for harness designers who currently rely on ad-hoc iteration counts or prompt-based self-reflection to terminate agent loops. The integration pattern — ECR sitting between ensemble retrieval and response synthesis, activated conditionally by a query router — exemplifies a modular harness layer that can be swapped into existing RAG pipelines without retraining. For researchers building meta-harnesses over multi-step LLM pipelines, ECR demonstrates how information-theoretic objectives can replace prompt engineering as the control signal governing loop termination and sub-task selection.