BELIEFRAG: Making Adaptive RAG State-Aware under Evolving Evidence

Hongji Pu

cs.AISep 30, 2026

BELIEFRAG: Making Adaptive RAG State-Aware under Evolving Evidence

Authors: Hongji Pu

Organizations: University of Illinois Urbana-Champaign

Abstract

Adaptive RAG uses signals such as confidence, relevance, support, and retrieval quality to decide when to search or correct evidence. In multi-step retrieval, however, these local signals must be combined into a persistent view of what the current evidence supports, what remains missing, and which action should follow. Existing methods often use such signals as separate triggers, making it difficult to preserve a coherent evidence state across a trajectory; we call this problem evidence-state fragmentation. We introduce BELIEFRAG, a closed-loop controller that updates an explicit state over sufficiency, reliability, conflict, uncertainty, evidence gaps, and acquisition cost, then chooses among retrieval, query rewriting, verification, answering, stopping, and abstention. Across six QA benchmarks with gpt-oss-120b, BELIEFRAG reaches mean token F1 0.572 with 3.89k tokens per question, outperforming fixed iterative retrieval (0.555 F1) while using 39% fewer tokens. The same quality-cost pattern transfers to Qwen3-32B, where BELIEFRAG reaches 0.552 F1 versus 0.523 for iterative retrieval while using 35% fewer tokens. Analysis shows that the main gains come from corrective re-retrieval rather than pruning alone, while several belief dimensions are redundant and calibrated answerability plays the strongest operational role. Calibration improves threshold stability across related evidence sources, although source shift can still invalidate the same decision signal.

Figures & tables

Figure 1: BeliefRAG as a closed-loop evidence controller. The system converts the current evidence into diagnostic signals and a compact belief state, then applies fixed branch rules to choose among retrieval, rewriting, verification, answering, stopping, and abstention. Retrieval value and verifier feedback determine whether more evidence is worth acquiring and update the next iteration. The controller is non-RL; only the sufficiency and retrieval-value estimates are fitted from data.

	Meaning	Computation
$R_{t}$	Relevance	Softmax-weighted mean of calibrated top- $k$ retrieval scores.
$S_{t}$	Support	Verifier score for how strongly $E_{t}$ supports a complete answer.
$C_{t}$	Conflict	Largest material contradiction within $E_{t}$ or between evidence and the current draft.
$U_{t}$	Uncertainty	Verifier estimate of how uncertain the answer remains given only $E_{t}$ .
$G_{t}$	Gap	Estimated fraction of information required by the question that is still unsupported.
$N_{t}$	Novelty	$1-\mathrm{sim}(\Delta E_{t},E_{t-1})$ ; high when the newest retrieval adds information not already retained.

Table 1: Evidence diagnostics used at each decision step.

Decision	Condition	Default
Correct	Evidence is materially conflicting or clearly unreliable	$b_{t}^{\rm conf}\geq 0.50$ or $b_{t}^{\rm rel}<0.30$
Answer	Current state is operationally answerable and conflict is acceptable	$p_{t}^{\rm ans}\geq 0.50$
Retrieve	Evidence is insufficient, budget remains, and another retrieval has enough chance to make it answerable	$p_{t}^{\rm flip}\geq 0.10$
Rewrite	Another retrieval is useful, but the previous retrieval added little new information	$N_{t}<0.20$
Stop / Abstain	Evidence is still insufficient and further acquisition has low expected value	no useful acquisition

Table 2: Main decision rules. Values are the default operating thresholds; experiment-specific selected values are reported in the Appendix.

Method	Multi-hop QA			Open-domain QA			Mean	Tokens
Method	HotpotQA	2Wiki	MuSiQue	NQ	TriviaQA	PopQA	Mean	Tokens
No-RAG ( Brown et al., 2020 )	.378	.411	.167	.341	.766	.381	.407	0.10k
Static RAG ( Lewis et al., 2020 )	.559	.681	.423	.413	.681	.324	.514	2.82k
Adaptive- $k$ ( Taguchi et al., 2025 )	.535	.558	.360	.347	.715	.348	.477	3.04k
Adaptive-RAG ( Jeong et al., 2024 )	.575	.711	.445	.425	.751	.324	.538	3.59k
Iterative RAG ( Jiang et al., 2023 )	.588	.710	.420	.420	.750	.440	.555	6.35k

Table 3: Main comparison on six QA benchmarks with gpt-oss-120b ( OpenAI, 2025 ) as the language backbone. The primary metric is normalized token-level answer F1; all cells use

n=100

questions. Mean is the simple average across the six datasets and Tokens is mean total token cost per question. Cell color shows the F1 change from Static RAG on the same dataset. Bold marks the best F1 in each column.

Figure 2: F1–cost trade-off. Each point is a method average over the six QA datasets in Table 3 .

Figure 3: Mechanism ablations. (a) Retrieval-control ablations. (b–c) Interventions on

p_{t}^{\mathrm{ans}}

; “sufficiency” is the legacy run label.

Figure 4: Threshold transfer and reachability. (a) Answerability scale. (b) Operating points. (c) Gate reachability. “Sufficiency” is the legacy label for this score.

Figure 5: Belief-state diagnostics. (a) Signal usefulness. (b) Signal dependence. (c) Signal calibration. (d) Actions by belief level.

Figure 6: Robustness to imperfect evidence. (a) Irrelevant noise. (b) Misleading evidence. (c) Evidence-source transfer.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Dimension	$b_{0}$	$\alpha$	$\lambda$	Non-zero weights in $w_{d}^{\top}x_{t}$
Sufficiency	0.35	$-1.6$	0.6	$+2.6S_{t},+1.2R_{t},-2.2G_{t},-1.0U_{t},-0.6C_{t}$
Reliability	0.50	$-1.4$	0.5	$+2.8R_{t},+0.9S_{t},-2.4C_{t}$
Conflict	0.05	$-2.2$	0.6	$+4.4C_{t},-0.5S_{t}$
Uncertainty	0.70	$-1.2$	0.6	$+2.6U_{t},+1.3G_{t},-1.6S_{t},+0.7C_{t}$
Gap	0.90	$-1.0$	0.7	$+3.0G_{t},-1.4S_{t},+0.4N_{t}$
Cost	0.00	—	1.0	observed directly: $b_{t}^{\mathrm{cost}}=K_{t}$

Appendix

Table 4: Default belief-state parameters. Only non-zero coefficients are shown.

Step	Action	Decision and query/evidence change	$\|E_{t}\|$
0	Retrieve	Initial belief is $(0.35,0.50,0.05,0.70,0.90,0.00)$ . With no evidence, the structural diagnostics set uncertainty and gap to $1$ . The fallback $p^{\mathrm{flip}}=0.59$ exceeds the $0.10$ retrieval threshold. Under first_query_is_question , the original question is issued directly as the first query. Five passages are returned; only Private_Music is useful.	5
1	Verify	The verifier reports approximately $R_{t}=0.27$ , $S_{t}=0.30$ , $G_{t}=0.70$ , and $K_{t}=0.21$ , with $P(\mathrm{answerable})=0.49$ . Four passages are flagged unhelpful: Myron__duo_ , Zak_Starkey , Weathermaker_Music , and Oasis_discography . Verification prunes them, leaving only Private_Music .	1
2	Rewrite	The query is reformulated as Private Music signed drummer formerly a member of an English band . Rewriting changes the query but performs no retrieval.	1
3	Retrieve	The evidence-aware query writer reads the retained Private_Music passage, which names Ringo Starr , and makes that bridge entity explicit: Ringo Starr drummer member of which English group?> . Three additional passages are returned, but all are distractors and none mentions Ringo Starr or the Beatles.	4
4	Answer	With approximately $R_{t}=0.34$ , $S_{t}=0.30$ , $G_{t}=0.60$ , $K_{t}=0.45$ , conflict $0.09$ , and $P(\mathrm{answerable})=0.53$ , the answer threshold $0.50$ is crossed. The final answer is The Beatles .	4

Appendix

Table 5: Representative HotpotQA trace.

|E_{t}|

is the number of retained passages after the action.

Budget	Value
Maximum retrieval rounds	3
Passages per retrieval (top- $k$ )	5
Maximum controller actions	6
Token budget	12,000
Answer evidence window	10 passages

Appendix

Table 6: Default budgets used by the controlled harness.

Method	HotpotQA	2Wiki	MuSiQue	NQ	TriviaQA	PopQA	Mean F1
No-RAG	.265/.180/.320	.382/.310/.420	.154/.080/.200	.210/.120/.280	.512/.420/.550	.185/.130/.220	.285
Static	.497/.380/.560	.643/.570/.630	.309/.170/.360	.365/.230/.420	.642/.560/.680	.284/.240/.350	.457
Iterative	.559/.460/.610	.659/.570/.630	.361/.240/.410	.412/.310/.470	.695 /.600/.720	.452/.370/.510	.523
Self-RAG*	.367/.300/.400	.625/.517/.552	.285/.210/.320	.215/.110/.260	.088/.080/.120	.245/.210/.300	.304
CRAG	.512/.410/.570	.680/.590/.660	.352/.230/.400	.388/.250/.440	.665/.580/.700	.410/.340/.460	.501
RL-Search	.278/.180/.310	.285/.100/.310	.198/.100/.230	.092/.010/.120	.248/.180/.290	.210/.110/.250	.219

Appendix

Table 7: Qwen3-32B answer quality. Each dataset cell is F1 / EM / Judge , where Judge is the supplementary LLM-judged semantic accuracy. Mean is mean F1 over six datasets. All dataset cells use

n=100

Method	HotpotQA	2Wiki	MuSiQue	NQ	TriviaQA	PopQA	Mean EM/Judge
Static	.450/.640	.600/.720	.290/.440	.280/.510	.600/.810	.280/.330	.417/.575
Iterative	.452/.660	.670/.750	.355/.520	.350/.620	.625/.860	.410/.530	.477/.657
CRAG	.460/.650	.630/.770	.310/.460	.280/.570	.630/.830	.380/.470	.448/.625
Self-RAG*	.380/.540	.600/.680	.270/.400	.130/.310	.100/.120	.250/.290	.288/.390
RL-Search	.200/.620	.110/.750	.120/.440	.010/.440	.200/.530	.130/.420	.128/.533
BeliefRAG	.480/.630	.660/.810	.370/.520	.290/.580	.650/.850	.340/.430	.465/.637

Appendix

Table 9: gpt-oss-120b secondary answer metrics. Each cell is EM / Judge ; F1 is reported in the main table. Mean gives the simple six-dataset average for each metric.

Figure 7: HoloBench aggregation retrieval. Row recall is the fraction of gold rows recovered in the evidence shown to the model; recall per row read divides that recall by the mean number of rows inspected (scaled by

10^{3}

for display). (a) BeliefRAG reaches row recall

0.145

after reading

9.73

rows on average, versus

0.152

after

22.98

rows for fixed Iterative retrieval. (b) BeliefRAG therefore obtains higher recall per row read. The structural ceiling at 50 rows is

0.985

; absolute recall remains far below it, so this diagnostic supports a selection-efficiency claim rather than a claim that aggregation retrieval is solved. These common-harness HoloBench numbers are not directly comparable with the QA F1 scores in Table 3 .

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May 4, 2026, cs.CLJ/K move · Enter open · S save

AdaGATE: Adaptive Gap-Aware Token-Efficient Evidence Assembly for Multi-Hop Retrieval-Augmented Generation

Yilin Guo, Yinshan Wang, Yixuan Wang

Center for Data Science New York University · Tandon School of Engineering New York University

Agentic Retrieval-Augmented Generation Systems Multi-Hop Reasoning

Open paper AskPDF arXiv

Retrieval-augmented generation (RAG) remains brittle on multi-hop questions in realistic deployment settings, where retrieved evidence may be noisy or redundant and only limited context can be passed to the generator. Existing controllers address parts of this problem, but typically either expand context additively, select from a fixed top-k set, or optimize relevance without explicitly repairing missing bridge facts. We propose AdaGATE, a training-free evidence controller for multi-hop RAG that frames evidence selection as a token-constrained repair problem. AdaGATE combines entity centric gap tracking, targeted micro-query generation, and a utility based selection mechanism that balances gap coverage, corroboration, novelty, redundancy, and direct question relevance. We evaluate AdaGATE on HotpotQA under clean, redundancy, and noise injected retrieval conditions. Across all three settings, AdaGATE achieves the best evidence F1 among the compared controllers, reaching 62.3% on clean data and 71.2% under redundancy injection, while using 2.6x fewer input tokens than Adaptive-k. These results suggest that explicit gap-aware repair, combined with token-efficient evidence selection, improves robustness in multi-hop RAG under imperfect retrieval. Our code and evaluation pipeline are available at https://github.com/eliguo/AdaGATE.

Abstract

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