TL;DR
KnowRL addresses reward sparsity in LLM reasoning RL by identifying minimal sufficient knowledge point subsets via Constrained Subset Search. Achieving 70.08 average accuracy across eight benchmarks with only 2.57 KPs per problem, it reduces zero-correct queries from 41.21% to 13.00%.
KnowRL addresses reward sparsity in LLM reasoning RL by identifying minimal sufficient knowledge point subsets via Constrained Subset Search. Achieving 70.08 average accuracy across eight benchmarks with only 2.57 KPs per problem, it reduces zero-correct queries from 41.21% to 13.00%.
39
已证实
3
证据不足
0
无法验证
N/A
可复现性
核心问题
How can minimal, sufficient knowledge guidance be provided to overcome reward sparsity in reinforcement learning for LLM reasoning without introducing hint redundancy?
核心方法
{'approach': 'KnowRL decomposes guidance into atomic knowledge points (KPs) extracted from correct solutions, removes leakage through automated verification, and selects minimal sufficient KP subsets using Constrained Subset Search (CSS) that addresses the pruning interaction paradox where removing single KPs may improve accuracy while removing multiple KPs together can reduce it.', 'key_components': [], 'section_ids': []}
论点验证
已证实 (85%)
we propose Knowledge-Guided Reinforcement Learning (KnowRL), a framework that formulates hint design as a minimal sufficient guidance problem
The KnowRL framework is fully specified in p_10 and detailed throughout Section 3. The paper describes the complete methodology including KP construction pipeline (p_23-p_27), selection strategies (p_27-p_42), and integration with RL training. The fr
The KnowRL framework is fully specified in p_10 and detailed throughout Section 3. The paper describes the complete methodology including KP construction pipeline (p_23-p_27), selection strategies (p_27-p_42), and integration with RL training. The fr
已证实 (85%)
KnowRL decomposes guidance into atomic knowledge points (KPs) and identifies the minimal subset required to unlock reward learning
The decomposition into KPs is described in detail in p_23-p_27, and multiple selection strategies (Max-Score, S-LOO, T-LOO, CSS, CBRS) are presented in p_27-p_42 to identify minimal subsets. Table 1 shows CSS achieves 63.90 accuracy with only 2.57 KP
The decomposition into KPs is described in detail in p_23-p_27, and multiple selection strategies (Max-Score, S-LOO, T-LOO, CSS, CBRS) are presented in p_27-p_42 to identify minimal subsets. Table 1 shows CSS achieves 63.90 accuracy with only 2.57 KP
已证实 (80%)
We introduce a minimal-sufficiency perspective on hint-based RL and empirically demonstrate a non-linear, jump-like performance pattern (critical-segment effect), revealing that effective guidance depends on selective key knowledge rather than cumulative hint length
The critical-segment effect is empirically demonstrated through controlled experiments. Figure 1a is referenced in p_7, and a detailed controlled prefix-ratio study is described in p_57-p_58 with Figure 7 showing the non-linear, jump-like pattern. Th
The critical-segment effect is empirically demonstrated through controlled experiments. Figure 1a is referenced in p_7, and a detailed controlled prefix-ratio study is described in p_57-p_58 with Figure 7 showing the non-linear, jump-like pattern. Th
已证实 (85%)
We design several KP selection pipelines that ensure minimal, non-redundant, and interaction-compatible KP subsets for each problem. We further conduct detailed comparative analyses and finally identify CSS as the optimal selection strategy
Multiple KP selection pipelines are described: Max-Score (p_29), S-LOO and T-LOO (p_32), CSS (p_37-p_38), and CBRS (p_39-p_41). Table 1 provides comparative analysis showing CSS achieves best performance (63.90 accuracy) with fewest KPs (2.57). The c
Multiple KP selection pipelines are described: Max-Score (p_29), S-LOO and T-LOO (p_32), CSS (p_37-p_38), and CBRS (p_39-p_41). Table 1 provides comparative analysis showing CSS achieves best performance (63.90 accuracy) with fewest KPs (2.57). The c
证据不足 (60%)
We integrate minimal KP subsets into RL training via difficulty-aware prompt injection, achieving new state-of-the-art results across benchmarks while significantly reducing hint length and computational overhead
The state-of-the-art results are well-documented (70.08 average accuracy in p_49), and hint length reduction is quantified (from 5.86 to 2.57 KPs per problem in Table 1). However, the claim of 'significantly reducing computational overhead' is not qu
The state-of-the-art results are well-documented (70.08 average accuracy in p_49), and hint length reduction is quantified (from 5.86 to 2.57 KPs per problem in Table 1). However, the claim of 'significantly reducing computational overhead' is not qu
已证实 (80%)
we observe the critical-segment effect: performance does not increase proportionally with hint ratio. Instead, accuracy exhibits a sharp jump once a short key segment appears, followed by diminishing gains
The critical-segment effect is empirically demonstrated through controlled experiments described in p_57-p_58. The study varies prefix ratio from 0 to 90% on 100 randomly sampled instances and observes that 'accuracy does not increase linearly... exh
The critical-segment effect is empirically demonstrated through controlled experiments described in p_57-p_58. The study varies prefix ratio from 0 to 90% on 100 randomly sampled instances and observes that 'accuracy does not increase linearly... exh
已证实 (75%)
we identify cross-hint inconsistency: longer prefixes or abstract templates may introduce branching and conceptual ambiguity, complicating policy updates
Cross-hint inconsistency is identified and quantified. Figure 1b is referenced in p_7, and p_35 provides quantitative evidence: 'cross-hint inconsistency occurs frequently (typically p_m ∈ [40%, 60%]), with substantial performance drops.' The paper d
Cross-hint inconsistency is identified and quantified. Figure 1b is referenced in p_7, and p_35 provides quantitative evidence: 'cross-hint inconsistency occurs frequently (typically p_m ∈ [40%, 60%]), with substantial performance drops.' The paper d
证据不足 (50%)
we observe a trade-off between guidance independence and training efficiency. Abstraction-based hints often rely on teacher-generated guidance, interrupting online RL and increasing computational cost
The trade-off between guidance independence and training efficiency is mentioned in p_7 with reference to Figure 1c, but no quantitative measurements of computational cost or training efficiency are provided. The claim that abstraction-based hints 'i
The trade-off between guidance independence and training efficiency is mentioned in p_7 with reference to Figure 1c, but no quantitative measurements of computational cost or training efficiency are provided. The claim that abstraction-based hints 'i
已证实 (80%)
we model a pruning interaction paradox: removing a single KP may improve accuracy, while removing multiple such "bad" KPs together can reduce accuracy due to inter-KP dependencies
The pruning interaction paradox is formally defined in p_10 and empirically demonstrated in p_33-p_35. The paper quantifies it: 'removing each of m KPs individually improves performance, but removing them jointly degrades performance.' Figure 2a show
The pruning interaction paradox is formally defined in p_10 and empirically demonstrated in p_33-p_35. The paper quantifies it: 'removing each of m KPs individually improves performance, but removing them jointly degrades performance.' Figure 2a show
已证实 (85%)
Our final method adopts Constrained Subset Search (CSS), which prunes first and then performs global search over the remaining candidates, achieving the best performance with the fewest KPs
CSS is fully described in p_37-p_38 with the two-step process: (1) prune non-degrading KPs (set N) first, (2) enumerate subsets within C for global search. Table 1 shows CSS achieves best performance (63.90 accuracy) with fewest KPs (2.57), justifyin
CSS is fully described in p_37-p_38 with the two-step process: (1) prune non-degrading KPs (set N) first, (2) enumerate subsets within C for global search. Table 1 shows CSS achieves best performance (63.90 accuracy) with fewest KPs (2.57), justifyin
证据不足 (55%)
In practice, simple problems receive no hints, while minimal KP subsets are injected only for harder samples during training
The claim is stated in p_11 but the criteria for determining which problems are 'simple' vs 'harder' is not explicitly defined. While the selection strategies (like CSS) may result in some problems receiving no KPs (when optimal configuration is ∅),
The claim is stated in p_11 but the criteria for determining which problems are 'simple' vs 'harder' is not explicitly defined. While the selection strategies (like CSS) may result in some problems receiving no KPs (when optimal configuration is ∅),
已证实 (85%)
KnowRL follows a simple end-to-end workflow: for each training problem, it first constructs candidate knowledge points (KPs), then removes leakage and redundancy to obtain a compact problem-specific subset, and finally uses the curated subset as hint data for RL training only when guidance is needed
The workflow is clearly described in p_21 and detailed throughout Section 3. The three-stage pipeline is specified: (1) construct candidate KPs (p_23-p_27), (2) remove leakage and redundancy via selection strategies (p_27-p_42), (3) use curated subse
The workflow is clearly described in p_21 and detailed throughout Section 3. The three-stage pipeline is specified: (1) construct candidate KPs (p_23-p_27), (2) remove leakage and redundancy via selection strategies (p_27-p_42), (3) use curated subse
已证实 (90%)
We curate and analyze KP annotations over eight mathematical reasoning benchmarks: AIME24, AIME25, BRUMO25, HMMT-Feb-25, AMC23, CMIMC25, MATH-500, and Olympiad-Bench, totaling 1,374 problems
The eight benchmarks and total problem count are explicitly listed in p_22: AIME24, AIME25, BRUMO25, HMMT-Feb-25, AMC23, CMIMC25, MATH-500, and Olympiad-Bench, totaling 1,374 problems. This is a factual statement about the experimental setup.
The eight benchmarks and total problem count are explicitly listed in p_22: AIME24, AIME25, BRUMO25, HMMT-Feb-25, AMC23, CMIMC25, MATH-500, and Olympiad-Bench, totaling 1,374 problems. This is a factual statement about the experimental setup.
已证实 (85%)
All construction and selection procedures are performed via offline evaluation before RL training, ensuring reproducibility and computational efficiency
Stated in p_22: 'All construction and selection procedures are performed via offline evaluation before RL training, ensuring reproducibility and computational efficiency.' This is a factual description of the methodology.
Stated in p_22: 'All construction and selection procedures are performed via offline evaluation before RL training, ensuring reproducibility and computational efficiency.' This is a factual description of the methodology.
已证实 (85%)
For each problem, we sample responses from DeepSeek-R1 until at least one correct solution is obtained
Stated in p_24: 'For each problem, we sample responses from DeepSeek-R1 until at least one correct solution is obtained.' This is a factual description of the methodology.
Stated in p_24: 'For each problem, we sample responses from DeepSeek-R1 until at least one correct solution is obtained.' This is a factual description of the methodology.
已证实 (85%)
Given a problem and a verified correct solution, we prompt DeepSeek-R1 to extract only the indispensable mathematical principles required to solve the problem
Stated in p_25: 'Given a problem and a verified correct solution, we prompt DeepSeek-R1 to extract only the indispensable mathematical principles required to solve the problem.' This is a factual description of the methodology.
Stated in p_25: 'Given a problem and a verified correct solution, we prompt DeepSeek-R1 to extract only the indispensable mathematical principles required to solve the problem.' This is a factual description of the methodology.
已证实 (85%)
To prevent information leakage, we verify each KP using DeepSeek-R1 as an automated reviewer. Failed cases are manually revised to ensure all retained KPs are generalizable and not instance-bound
Stated in p_26: 'To prevent information leakage, we verify each KP using DeepSeek-R1 as an automated reviewer. Failed cases are manually revised to ensure all retained KPs are generalizable and not instance-bound.' This is a factual description of th
Stated in p_26: 'To prevent information leakage, we verify each KP using DeepSeek-R1 as an automated reviewer. Failed cases are manually revised to ensure all retained KPs are generalizable and not instance-bound.' This is a factual description of th
已证实 (85%)
As shown in Table 1, the average performance improves from 60.46 to 61.03, but each problem uses 5.86 KPs on average
Stated in p_27 with specific numbers: 'the average performance improves from 60.46 to 61.03, but each problem uses 5.86 KPs on average.' Table 1 is referenced for these results.
Stated in p_27 with specific numbers: 'the average performance improves from 60.46 to 61.03, but each problem uses 5.86 KPs on average.' Table 1 is referenced for these results.
已证实 (85%)
All accuracy estimates are computed using 8 × 32 samples to reduce variance
Stated in p_28: 'All accuracy estimates are computed using 8 × 32 samples to reduce variance.' This is a factual description of the methodology.
Stated in p_28: 'All accuracy estimates are computed using 8 × 32 samples to reduce variance.' This is a factual description of the methodology.
已证实 (85%)
we introduce a tolerance parameter ε ≥ 0, which controls how strictly we treat borderline cases when selecting the optimal configuration
Described in p_30-p_31: 'we introduce a tolerance parameter ε ≥ 0, which controls how strictly we treat borderline cases when selecting the optimal configuration.' The formalization is provided.
Described in p_30-p_31: 'we introduce a tolerance parameter ε ≥ 0, which controls how strictly we treat borderline cases when selecting the optimal configuration.' The formalization is provided.
... 共 42 个论点
可复现性评估
较低可复现性 (0%)
缺失的复现细节
- 代码不可用 - 未找到任何代码仓库或实现
- 数据不可用 - 训练数据集未公开，无法获取精心策划的训练集
- 知识点(KPs)构建方法缺失 - 论文提到使用预策划的知识点，但未详细说明如何构建、格式和具体内容
- 知识点选择策略(CSS/CBRS)的具体算法实现未详细描述
- 随机种子未指定
- 训练数据的具体来源、规模和划分方式未说明
- 模型初始化细节不够具体 - 虽然提到OpenMath-Nemotron-1.5B作为backbone，但未说明具体初始化方式
- 附录B和C.2中提到的额外细节（如退火对比实验、增强提示示例）不可获取
- CompassVerifier-3B的具体使用细节仅通过引用说明
- 数据预处理步骤未详细描述
局限性（作者自述）
- Training KnowRL-Nemotron-1.5B required approximately 13 days of wall-clock time
本分析由 PDF 阅读助手 自动生成，仅供参考，不构成学术评审意见。验证结论和可复现性评估基于论文文本自动分析，可能存在偏差。原始论文请参阅 arXiv。
分析时间：2026-04-19T13:18:40+00:00 · 数据来源：Paper Collector