Weakness Localization Is Not Enough: State-Aware Recursive Knowledge Improvement for Large Language Models

Runze Jiang; Yan Wang; Boran Jin; Bingyu Zhu; Longtao Huang

cs.CLOct 27, 2026

Weakness Localization Is Not Enough: State-Aware Recursive Knowledge Improvement for Large Language Models

Authors: Runze Jiang, Yan Wang, Boran Jin, Bingyu Zhu, Longtao Huang

Organizations: Peking University · Alibaba Group · Delft University of Technology

Abstract

Knowledge improvement in large language models is shifting from predefined knowledge incorporation pipelines toward evaluation-guided updating. Existing methods use evaluation to localize model-specific knowledge weaknesses and guide targeted post-training. However, identifying what to improve does not necessarily provide sufficient information for deciding how to improve it. The same localized weakness can be compatible with distinct operational knowledge states: the relevant knowledge may be unavailable, available but difficult to access reliably, or accessible but ineffective for downstream use. We call this ambiguity knowledge-state aliasing. When compatible states favor different interventions, greater diagnostic resolution alone is insufficient for intervention selection. Moreover, model updates can change the underlying knowledge state before the observed weakness disappears, such that an intervention appropriate in one round may no longer address the bottleneck in the next. To address these challenges, we propose Recursive Knowledge Improvement (RKI), which formulates knowledge improvement as a sequential, state-aware intervention process. RKI organizes knowledge into graph-structured units that provide a shared basis for diagnostic evaluation and targeted intervention across rounds. At each round, RKI localizes knowledge weaknesses, estimates the model's operational knowledge state from diagnostic evidence and intervention history, selects a corresponding intervention, and re-evaluates the updated model before determining the next intervention. On HotpotEval and SafeInternalEval, RKI outperforms existing knowledge incorporation methods by 18.41 points on average. Further analyses show that knowledge states provide additional guidance for intervention selection beyond weakness localization and can change across model updates even when the observed weakness persists.

Figures & tables

Figure 1: From weakness localization to state-aware knowledge improvement. RKI estimates operational knowledge states to guide interventions and re-estimates them after each model update.

Figure 2: Overview of RKI. RKI aligns diagnosis and intervention over graph-structured knowledge units and recursively adapts interventions to the model’s evolving operational knowledge state.

Dataset	Domain	Language	Samples		Avg. Tokens		Max. Tokens
Dataset	Domain	Language	Corpus	Test	Corpus	Test	Corpus	Test
HotpotEval	General	English	9,990	1,000	137.5	21.3	1,984	74
SafeInternalEval	Security & Compliance	Chinese	1,000	600	352.4	41.2	701	139

Table 1: Statistics of the datasets used in our experiments. The corpus serves as the knowledge source for graph construction, diagnostic evaluation, and knowledge incorporation, while the test set is used for closed-book evaluation.

Unit Type	Units	Proportion
Relation	14,439	44.45%
Ego	1,340	4.12%
Contrast	1,066	3.28%
Cycle	975	3.00%
Chain	13,494	41.54%
Tree	1,171	3.60%

Table 2: Distribution of graph-structured knowledge units constructed from SafeInternalEval .

Figure 3: Knowledge-state aliasing under the same localized failure signal. Left: recognition outcomes for recall-failure instances. Right: recognition and recall patterns for understanding-, reasoning-, and application-failure units.

Method	HotpotEval	SafeInternalEval	Avg.
GENIE	23.00	9.75	16.38
LongForm	24.40	11.17	17.79
WRAP	22.90	9.75	16.33
Self-QA	26.80	28.00	27.40
EntiGraph	26.50	21.50	24.00
GraphGen	23.70	22.33	23.02

Table 3: Performance of different knowledge incorporation methods. Bold marks the best result.

Method	Average Score
Random Intervention	29.33
Fixed Access	23.17
Fixed Utilization	48.00
Full-Data Training	50.50
Weakness Only	53.75
Frozen State	39.00

Table 4: Ablation study on intervention selection on SafeInternalEval . Bold marks the best result.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Unit	Role
Relation	Represents a direct relational fact between two entities as the basic unit of relational knowledge.
Contrast	Organizes related facts or local structures along a shared comparison dimension.
Ego	Represents the local relational neighborhood centered on a focal entity.
Cycle	Represents a closed relational path formed by multiple entities and their relations.
Chain	Represents a multi-hop relational path connecting a sequence of entities.
Tree	Represents a branching relational structure extending from a shared local context.

Appendix

Table 5: Graph-structured knowledge units in RKI and their functional roles.

Dimension	Aspect	Interpretation
Acquisition	Availability	Whether the relevant knowledge shows evidence of having been incorporated into the model.
Recognition	Accessibility	Whether the model can identify the relevant knowledge when candidate information or relevant cues are provided.
Recall	Accessibility	Whether the model can reliably retrieve the relevant knowledge without explicit candidate cues.
Understanding	Usability	Whether the model can correctly interpret the relations and meaning expressed by the relevant knowledge.
Reasoning	Usability	Whether the model can combine and derive information from the relevant knowledge through reasoning.
Application	Usability	Whether the model can effectively use the relevant knowledge in downstream tasks or problem settings.

Appendix

Table 6: Diagnostic dimensions, operational aspects, and interpretations for knowledge-state estimation.

Figure 8: Local structure of the knowledge graph constructed from the Hotpot corpus. (a) The complete two-hop neighborhood of Star Wars , with 130 entities and 162 edges. Outlined nodes are expanded in (b). (b) The induced subgraph of 15 selected entities and their 25 edges. Colors and markers denote entity types. All edges are undirected.

Parameter	CPT	SFT
Context Length	2,048	2,048
Global Batch Size	16	64
Epochs	1	1
Peak Learning Rate	$5\times 10^{-6}$	$2\times 10^{-5}$
LR Scheduler	Cosine	Linear
Warmup Ratio	0.05	0.03

Appendix

Table 7: Training configurations for CPT and SFT.

Dataset	Corpus	Test
HotpotEval	Bolax is a genus of flowering plants in the Apiaceae, with four or five species, and is endemic to temperate South America. Jovibarba heuffelii, commonly known as Hen-and-chickens, is a plant species native to the Balkans and the Carpathians in Europe. …	Question: Which plant has more species, Bolax or Jovibarba? Answer: Bolax.

Appendix

Table 8: Representative source-corpus and evaluation examples from the public benchmarks.

Benchmark	Dimension	Evaluation Criterion
HotpotEval	final_fact	Whether the final answer states the same fact as the reference answer.
	completeness	Whether the answer covers the required constituents and qualifiers of the reference answer.
SafeInternalEval Understanding	factual_accuracy	Whether every fact stated in the answer is correct; hallucinated facts lose points.
	association_coverage	How many of the required answer points the answer covers. Paraphrase and superordinate summaries count as coverage; a point mentioned with a wrong association does not.
	conclusion_correctness	Whether the core judgment (overall positioning, the difference identified, or the misconception clarified) matches the reference, with the correct characterisation basis.
SafeInternalEval Reasoning and Application	factual_accuracy	Whether every fact stated in the answer is correct; hallucinated facts lose points.

Appendix

Table 9: Judging rubrics across benchmarks. Each dimension is scored from 0 to 10, with scores of at least 6 considered passing. For the internal benchmark, understanding evaluates association coverage, while reasoning and application evaluate reasoning coverage.

Benchmark	Pass Agreement	Cohen’s $\kappa$
HotpotEval	98%	$0.95$
SafeInternalEval	96%	$0.89$

Appendix

Table 10: Agreement between LLM judgments and human annotations on 100 stratified instances per benchmark.

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LLMs are widely used in knowledge-intensive tasks where the same fact may be revised multiple times within context. Unlike prior work focusing on one-shot updates or single conflicts, multi-update scenarios contain multiple historically valid versions that compete at retrieval, yet remain underexplored. This challenge resembles the AB-AC interference paradigm in cognitive psychology: when the same cue A is successively associated with B and C, the old and new associations compete during retrieval, leading to bias. Inspired by this, we introduce a Dynamic Knowledge Instance (DKI) evaluation framework, modeling multi-updates of the same fact as a cue paired with a sequence of updated values, and assess models via endpoint probing of the earliest (initial) and latest (current) states. Across diverse LLMs, we observe that retrieval bias intensifies as updates increase, earliest-state accuracy stays high while latest-state accuracy drops substantially. Diagnostic analyses of attention, hidden-state similarity, and output logits further reveal that these signals become flatter and weakly discriminative on errors, providing little stable basis for identifying the latest update. Finally, cognitively inspired heuristic intervention strategies yield only modest gains and do not eliminate the bias. Our results reveal a persistent challenge in tracking and following knowledge updates in long contexts.

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