SynLogic: Synthesizing Verifiable Reasoning Data at Scale for Learning Logical Reasoning and Beyond
Authors: Junteng Liu
Yuanxiang Fan
Zhuo Jiang
Han Ding
Yongyi Hu
Chi Zhang
Yiqi Shi
Shitong Weng
Aili Chen
Shiqi Chen
Mozhi Zhang
Pengyu Zhao
Junxian He
Venue: NeurIPS 2025 poster ()
Keywords: LLM
reinforcement learning
reasoning
logical reasoning
data synthesis
Primary area: deep_learning
TL;DR: We present SynLogic: a data synthesis framework and logical reasoning dataset encompassing 35 tasks.

Abstract: Recent advances such as OpenAI-o1 and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily focused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RL.
We hypothesize that logical reasoning is critical for developing general reasoning capabilities, as logic forms a fundamental building block of reasoning. In this work, we present SynLogic, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SynLogic approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards.
In our experiments, we validate the effectiveness of RL training on the SynLogic dataset based on 7B and 32B models. SynLogic leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1-Distill-Qwen-32B by 6 points on BBEH. Furthermore, mixing SynLogic data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outperforms DeepSeek-R1-Zero-Qwen-32B across multiple benchmarks.
These findings position SynLogic as a valuable resource for advancing the broader reasoning capabilities of LLMs. We will open-source both the data synthesis pipeline and the SynLogic dataset.

SynLogie: Synthesizing Verifiable Reasoning Data at Scale for Learning Logical Reasoning and Beyond
Junteng Liu Yuanxiang Fan', Zhuo Jiang', Han Ding", Yongyi Hu², Chi Zhang", Yiqi Shi?, Shitong Weng", Aili Chen', Shiqi Chen', Yunan Huang,, Mozhi Zhang", Pengyu Zhao', Junjie Yan?, Junxian He!
The Hong Kong University of Science and Technology MiniMax
'The City University of Hong Kong {jliugi, junxianh)@cse ust.
Abstract
Recent advances such OpenAI-ol and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily fo- cused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RI.. We hypothesize that logical reasoning is critical for developing general reasoning capa- bilities, logic forms fundamental building block of reasoning. In this work, we present SYNLOGIC, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SYNLOGIC approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards. In our experiments, we validate the effectiveness of RL training the SYNLOGIC dataset based on 7B and 32B models. SYNLOGIC leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1 -iai-----tsiii--eeeeee points on BBEH. Furthermore, mixing SYNLOGIC data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outper- forms DeepSeek-RR -----eo--weerteet
by 6
across multiple benchmarks. These findings position SYNLOGIC as a valuable resource for advancing the broader reasoning capabilities of LLMs. We open-source both the data synthesis pipeline and the SYNLOGIC dataset in https: //gi /gggttttt..t... thub. cww/ MaapMMnniMax--ai Sann-AIISyyyLooo
Introduction
The success of Deepseek R1 DeepSeek-AA Al et al. 2025 and OpenAl-ol (Jaech et al. 2024 demon- strates the great potential post-training advancing strong reasoning capabilities. These works reveal that the core methodology behind these advancements is reinforcement learning with verifiable rewards (RLVR), inspiring numerous replication efforts focused on RI. training. However, most of these works have concentrated on the mathematics and coding domains, primarily because it is straightforward to design binary reward rules in these areas [Zeng et al.) 2025b al
Yu et al. [025 Hu
al. 2025 Zhang al.) 2025). To foster more general and comprehensive reasoning abilities, is essential to utilize diverse tasks and examples with verifiable rewards. In this work, we concentrate on logical reasoning as promising domain for this objective, hypothesizing that logical reasoning serves as a fundamental building block for developing general reasoning skills. Although prior work
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Bag of Logical Tasks
Our Working Flow
868
Sudoku
Task Selection
Task Verifier
Parameter Identification
Cipher
Difficulty Control
Grid
Here Sudoku
Arrow Maze
Logic Instance
puzzle, w ere X represents a hidden number that be filled in. Please solve it.
Generation
to
Math Path
Prompt Formalization
Figure 1: The framework of logic data synthesis. The process begins with the selection of suitable tasks and the identification of key parameters that control task difficulty. Next, logic instances are generated with appropriate difficulty control (e.g., setting the grid size of Sudoku to 7). These instances are subsequently formalized into natural language instructions. Each task paired with task-specific verifier to check the correctness of responses. This framework enables the systematic synthesis of high-quality logic data, covering a wide range of difficulty levels and 35 task types.
Tong et al. 2025 Jiang et al. 2025), these efforts have typically focused on a single task, leaving the potential of broader and more diverse synthetic logic datasets largely underexplored.
has explored RL training in the context of logic tasks [ic et al. 2025b Pan et al. 2025
Synthetic logic data presents distinet advantages and challenges. Its synthetic nature allows for unlim- ited data generation with controllable difficulty levels, enabling the creation of increasingly challeng- ing samples. Additionally, the intrinsic properties of some logic tasks like Sudoku often require trial and backtracking in the reasoning process, which closely relates to the "aha moments" [DeepSeek-A] jet al., 2025) in problem-solving. Therefore, the primary advantages of synthetic logic data for RLVR lie in its scalability and inherent characteristics that align well with complex reasoning processes. The main challenge, however, the complexity of generating and designing specific rules for different logic tasks, as tasks like Game of 24 and Sudoku each require distinct verifiers.
Recent works primarily focus on logic evaluation [Suzgun al., 2022 Ma al. 2024 Kazemi et al., 2025], but lack high-quality accessible logical reasoning training data. In this work, to address the gap in comprehensive logic tasks, we present SYNLOGIC: logical reasoning data synthesis framework and a comprehensive synthetic logic dataset containing 35 tasks, including typical logical tasks such as Sudoku, Game of 24, and Cipher. For each task, we develop task- task-specific generation code paired with corresponding rule-based verifier, allowing for fine-graines difficulty control through adjustable generation hyperparameters.
To validate the effectiveness of reinforcement learning on the SYNLOGIC data, we run RL training on it with the GRPO algorithm (Shao al., 2024) and implement binary outcome rewards determined by each task's 's verification rules. By adapting recent GRPO training techniques introduced in DAPO Yuu et al. 2025]. we successfully train Qwen2.5 Base models (Yang et al.) (0224 on the SYNLOGIC data in a zero RL training setting, achieving progressively longer COT responses and observing the emergence of reflection behaviors. Starting from Qwen2.5-7B-Ban and Qwen2.5-32B- Base foundations, our models achieve over 8 absolute percentage points improvement on the logic benchmark
[M et al.) 2024) compared to their instruction models. Notably, our 32B model surpasses DeepScek-RI-DD
BBEH Kazemi et al. 2025 tasks by 5 absolute points, establishing S SYNLOGIC as the state-of-the-s open-source dataset for logical reasoning to date. Additionally, both models demonstrate strong generalization to unseen mathematics domains. Beyond the Qwen family, we also conduct experiments on Deinkein -B--aas [Wang et al. 2025 LLaMA-v3.1-88 A @ Meta 2024 mid-trained model, observing similar success.
Furthermore, we explore mixing SYNLOGIC data with mathematics or coding data for RL training. Surprisingly, conducting the mixed training on Diwen.55-B-Baatt model (Yang et al. 20244) incorporating SYNLOGIC data improves training efficiency for developing mathematical and coding skills. For mathematics, mixed training maintains similar mathematics performance under the same

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Table Comparison of SYNLOGIC with existing synthetic logic datasets. "The number of tasks of KOR-Bo MeR-Benchhae is based on the broader categorization in the paper. "Trainable" indicates whether the dataset provides training data.
Dataset
Tasks
Trainable
Adjustable Difficulty
BBH [Suzgun et al.
2022
23
X
Zebra Logic Lin el al. 2024
X
KOR-Bench Ma el al. 2024
X
K&K Xie el al. 2025a
V
BBEH Kazemi al. 2025
23
X
X
SYNLOGIC
35
V
number of training steps, which consume fewer math training samples. Simultaneously, mixed training achieves much higher performance on logic tasks. A similar trend is observed when mixing SYNLOGIC with coding data, further demonstrating the complementary benefits of logical reasoning training. Finally, we conduct large-scale mixed training on the Owen2.5-32B-Ba.. model to enhance the capability of RL. training. Our mixed training achieves superior performance on multiple benchmarks compared to the DeepSeek-R R -i-Zero-Qwee--ee Qwen-32B model, consistently outperforming or matching it on BBEH (azemi et al.] 2025], COR-Bench [Ma et al. 2024], LiveCodeBench [Jain] al., 2025], and by the inclusion of logical reasoning data.
[Rein et al. 2024], validating the generalization benefits provided
2 SYNLOGIC: Synthesizing Logical Reasoning Data at Scale
2.1 Background
Logical reasoning has long been crucial indicator of model intelligence [ai2] 2019 Suzgun et al. 2022]. valued for both its significance and synthetic accessibility. With the advancement of reasoning capabilities in Large Language Models (LLMs), researchers have developed increasingly challenging benchmarks to evaluate logical reasoning abilities [Kazemi et al.) 2025 Ma et al.) 2024). However, illustrated in Table existing benchmarks either lack training support number of tasks. Synthetic logic data serves as an important source of verifiable data and offers straightforward control over task difficulty, presenting the potential for developing scalable stronger models by training on it. Consequently, comprehensive synthetic logic datasets are essential for developing general strong reasoning models [Seed al. 2025
limited to small
2.2 The Data Synthesis Framework
To synthesize scale,scale, diverse synthetic data, develop comprehensive data synthesis frame- work encompassing 35 tasks. While the benchmarks in Table [ include a wide variety of tasks, a significant challenge faced is that nearly all evaluation benchmarks do not open-source their data generation methods. This hinders us from building training data for these logic tasks directly. Therefore, develop these tasks independently, building the SYNLOGIC framework, illustrated in Figure I The framework consists of the following key components:
1. Task Selection We select a diverse set of logic tasks that require non-trivial reasoning, drawing from two carefully curated categories of data sources: (1) widely recognized puzzle problems from logic communities, such as the game of 24, Sudoku, and cryptarithms. Many of these puzzles have been previously highlighted in works like [Kurtic et al. [2024] et al., 20224 Ma et al. 2024). (2) Logic tasks featured in established evaluation benchmarks, including BBH [Suzgun et al.
2022 and BBEH [Kazmi al. 2025). Detailed descriptions and sources for all tasks can be found in the Appendix[A.]
2. Parameter Identification For each task, we identify key parameters that control difficulty, such as grid size in Sudoku or the missing number ratio Math Path. These parameters form the basis for scalable and adjustable difficulty in data synthesis. For instance, a higher grid size in Sudoku typically represents greater difficulty, while a higher ratio of missing numbers in Math Path increases computational complexity.
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3. Logic Instance Generation We formalize the task-specific rules into code by manually imple- menting rule-based logic generators for each task. These generators are designed to encode the specific constraints and rules of the logic problems, ensuring that the generated instances adhere to the intended task structure (e.g., enforeing the unique digits rule in Sudoku). This nule-based approach allows us to efficiently produce large quantities of data and to cover a broad spectrum of difficulty levels by adjusting the difficulty related parameters. All generated instances undergo automated checks for correctness and solvability.
4. Appropriate Difficulty Control To ensure that the generated data is both challenging and learnable, we carefully adjust difficulty-reltted parameters during data generation. We use strong reasoning models, DeepSeek RI [DeepSeek-Al et al.) 2025 and OpenA--o3-mini to set an upper bound on difficulty: the highest difficulty parameters for which RI or 03-mini can solve samples with a pass @ 10 greater than zero, representing the limit of these models' solvability. This approach prevents the inclusion of instances that are too difficult. Similarly, we use Qwen2.5- 32B- Instructt (Yang al.) 2024] to determine the lower bound of difficulty: the lowest difficulty parameters for which the models achieve pass rate between O and 0.5. This dual-bound approach ensures that the dataset includes balanced range of samples, maintaining an appropriate level of complexity and learnability.
5. Prompt Formalization To facilitate training and evaluation with LLMs, we convert abstract logic instances into natural language prompts using task-specific prompt templates. To ensure robustness, we create an average of over 10 prompts per task, covering both English and Chinese versions. This approach guarantees that each instance is accessible to both humans and language models while maintaining consistency across languages and phrasings.
Verification Suite For every task, we implement a dedicated verifier that automatically checks the correctness of model outputs, supporting both RL training supervision and automatic evaluation. Our verifier validates whether the final answer is correct, rather than evaluating intermediate reasoning steps, consistent with other RLVR approaches. For example, in Sudoku, we identify the difficulty parameter as grid size (set to 7x7). Our generator creates instances with missing numbers marked as X, which are then formatted into natural language prompts. The verifier checks whether the model's completed grid complies with Sudoku rules (such as single value rules) to verify correctness. This verification approach ensures accurate and reliable assessment without apparent failing cases across all tasks in SYNLOGIC.
A key innovation in our approach is the development of customized difficulty control mechanisms for each task type. Unlike existing benchmarks that often provide fxed-difficul evaluation data, our system allows precise calibration of problem complexity through task-specific parameters, such as grid size in Sudoku. This difficulty-uunigg capability enables the creation of different difficulty level data, presenting the potential of progressively challenging training curricula. We overcame significant challenges in implementing these controls, as many evaluation benchmarks do not open-source their data generation methods. At last, most tasks in SYNLOGIC are designed with: (1) a data generation code capable of producing varied instances, (2) a corresponding verification rule for evaluating solution correctness, and (3) configurable difficulty parameters to enable controlled difficulty of generated data. We independently develop and generate data for 33 tasks in our dataset, while only the data of 2 tasks (Zebra Puzzle (Lin et al. 2024 and ARC-AGI [Chollet 2019 directly adopted from existing open source resources.
Risk of Data Contamination Although several tasks overlap between our selected tasks and current benchmarks, such as KOR-Bench and BBEH, the synthetic nature of our data, combined with the large synthesis space, makes the probability of generating data identical benchmark test samples very low we have verified that there are no identical samples between our generated datasets and the benchmark test sets.
2.3 The SYNLOGIC Datasets
We synthesized our dataset with controlled difficulty parameters for each task, carefully balancing challenge and learnability to ensure the success of our subsequent experiments $3 To accommodate different model capacities, we developed two distinct versions of our dataset: SYNLogrc-Hard for Qwen2.5-32B training and SasL for Qwen2.5-7B and OctoThinker-8B [Wang et al. 2025) training, SYNLOGIC-Haid presents more complex challenges with its broader difficulty level

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avg@s
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DeepSeck-R -1--ssk-----sst-l--
u6-
Dwen2.5-328-losttuu DeepSeck-RI RI-Ditill33
Models
Models
(a) 7B models on SYNso
(b) 32B models on SYNLoGIC-Hard
Figure 2: Evaluation of task difficulty across dataset versions. (a) Shows the performance of 7B-scale models on the SYNLOGIC-Easy dataset, while (b) demonstrates the performance of 32B-scale models the more challenging TENLOGIC--Hard dataset. Results are measured using avg@8 (average pass rate with eight attempts) and pass@ (success within eight attempts) metrics, illustrating the appropriate difficulty control for each model scale.
for each tasks with difficulty upper bound described in 2.2 For SYNLOGIC-Easy we systematically lower difficulty parameters across all tasks to create easier versions. Despite these adjustments, eight tasks still remain beyond the learning capacity of the 7B model with zero training accuracy after RL, thus we removed them from this easy version, where the details about the removed tasks provided samples and 16k SYNLOGIC-Eand samples used in subsequent experiments for training, along with 10 validation samples per task,
Appendix [A.2] Finally, we synthesized 33k SYNLOGIC-HEE
separately for the Easy and Hard validation splits.
Difficulty Analysis To assess the difficulty of the synthetic data, we conduct an evaluation on the validation splits, assessing model performance using both avg @8 (average pass rate with eight attempts) and pass@t @8 (success within eight attempts) metrics. The results, illustrated in Figure 2 confirm the appropriate difficulty levels for each model scale, demonstrating that our datasets provide suitable training challenges across different model capacities.
Reinforcement Learning on SYNLOGIC
Reinforcement learning with verifiable rewards (RLVR) has emerged highly effective approach for enhancing reasoning capabilities in large language models [Zeng et al., 2025b et al. 2025 Hu al. 2025 Zhang al. (0255. Building these advances, our experimental framework also focuses on applying reinforcement learning techniques to the SYNLOGIC dataset, leveraging the verifiable nature of logical reasoning tasks. In this section, validate the effectiveness of reinforcement learning training on the SYNLOGIC dataset using Qwen2.5-7B- Basse, Qwen2.5-32B -Base, and Octo'Thinker-88. BB--eerr--BBBe,,, 1.LMA-v3.1-88 1-88 mid-trained model.
3.1 Setup Details
Training Template Following the DAPO training prompt Yu et al. 2025], we modify and design the training prompt template for logic training as shown in Figure
Reward Design Our reward function employs a binary scoring mechanism that evaluates both format adherence and answer correctness. Specifically, we assign reward of only when model- generated response satisfies two criteria: (1) it correctly follows the designated format by including both <think> </think> and <answer> </answer> tags, and (2) the final answer provided is correct. Responses that either deviate from the required format or contain incorrect answers receive reward of O.
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SYNLOGIC Training Prompt Template
Solve the following problem step by step. First, think about the reasoning process in the mind and then provide the answer. The reasoning process is enclosed within <think> </think> and the final answer is enclosed within <answer> </answer> tags, respectively, ie., <think> reasoning process here </think> <answer> answer here</answer>.
Figure 3: The prompt template used for training models on SYNLOGIC data.
Table 2: Evaluation accuracy (%) of 7B, 32B and 8B models across logic benchmarks (SYNLOGIC- Val, ReR-Bench, BBH, BBEH) and mathematical benchmarks (AIME 2024, MATH 500, AMC 2023). For 7B and 8B models, SYNLOGIC- Val refers to SYNLoGIC-Easy, while for 32B models, refers SYNLOGIC-Hare described in $ 2.3 All evaluations were conducted under zero-shot conditions, with SYNLOGIC-Vo. and AIME 2024 reported as avg @ to reduce variance.
Logic Benchmarks
Mathematical Benchmarks
Model
SYNLOGIC-Val
BBH
BBEH
AIME 2024
MATH 500
AMC 2023
Qwen2.5-7B-
2.8
11.6
45.2
0.3
64.6
30.0
Qwen2.5-7B-Instrue
9.0
38.6
62.7
12.4
6.3
76.4
52.5
SYNLOGIC-7B
44.4
48.1
66.5
8.0
10.0
71.8
55.0
Dwen2.5-32B-Bal.
1.6
10.9
58.4
3.3
4.5
68.6
45.0
Dwee2.5-32B-Instmen
12.0
54.7
84.5
17.5
10.0
82.2
57.5
D1-Distill-Qwen-B3
33.0
66.6
88.3
19.2
72.6
94.3
85.0
SYNLOGIC-32B
52.9
62.2
85.8
25.5
19.6
82.0
57.5
OctoThinnerr-88 (Base)
4.2
37.2
43.5
4.1
3.3
38.7
20.3
SYNLOGIC-BB
38.0
44.0
55.2
12.0
14.5
68.4
45.0
11 if format(o;) True correct(o,) True
R(o,) = 0, otherwise
(1)
where format(o;) evaluates whether response includes both the required <think> </think> and <answer> </answer> tags, and correct(o;) determines whether the answer provided correct verified by its task's verification rule.
Training Details For experiments, we synthesized approximately 16k SYNLOGIC-ER and 33k Hyrd instances to train the Qwen2.5-7B- Swwe2.5--B-Basse OctoThinker-8B -B-Bas, and Qwen2.5- 32B-Base models with DAPO, respectively, as described in 22.3 During training, employed prompt batch size 128, generated 16 rollouts per prompt, and set maximum rollout lengths of 16.384 tokens for the 7B model and 28,672 tokens for the 32B model. We configured the clip high parameter thigh at 0.28. Additional training hyperparameters and implementation details are provided in Appendix B.1.2
Evaluation Details Our evaluation strategy encompasses distinct benchmark categories. For assessing logical reasoning capabilities, we employ the validation splits of SYNLOGIC alongside established benchmarks including Knowledge- -otogg--tt Reasoning (KORBBench) [Ma et al., [024). BBH (Suzgun et al., 2022], and the substantially more challenging BBEH [Kazemi et al. 2025 J. To investigate cross-domain generalization effects, we incorporate mathematics evaluations on MATH 500 [Hendrycks et al. 2021), AMC 2023, and AIME 2024. All evaluations are conducted in zero-shot setting, with @ metrics computed for AIME 2024 and SYNLOGIC- Val mitigate variance.

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4000
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(a) Avg Length and Reflection of 7B Training.
(b) Avg Length and Reflection of 32B Training.
Figure 4: Response length and reflection ratio across the 7B and 32B training process on the training dataset. The reflection ratio represents the proportion of generated responses containing at least one reflection phrase (including "recheck", "rethink", "try again". "let's correct it", "re-evaluate", "check again", "think again").
3.2 Results
Substantial Improvements in Logical Reasoning The evaluation results presented in Table 2 demonstrate significant improvements across logical reasoning tasks. Beyond the notable gains on SYNLOGIC's validation split, our models demonstrate enhanced performance across multiple logical benchmarks, leading state-of-the-arr results among open-source datasets. Our 7B model achieves 48.1 % KOR-Bench [Ma et al. 2024]. outperforming
(eeen2.5-7B-Intrreee by nearly
by 32B model exceeds I.-iistill-Qwen333 [DeepSeek] Af al. 2025] by 6 percentage points on the challenging BBEH benchmark (Kazemi et al.) 2025].
10 absolute percentage points. Similarly, our 32B model surpasses Qwen2.5- 1-.55---Bnnnntri percentage points on KOR-Ba Bench.. Notably,
showcasing the effectiveness of the SYNLOGIC dataset in driving tate-of-the-ard logical reasoning performance. Beyond the Qwen family, our substantial improvements on the 8B model also validate the effectiveness of our method LLaMA base models.
Generalization to Mathematical Domains Our experimental results demonstrate significant generalization capabilities to mathematical domains, as shown in Table Despite being primarily trained for logical reasoning. SYNLOGIC models exhibit strong performance across mathematical benchmarks over their base models. SYNLOGIC-TH achieves 10.0% on AIME 2024, nearly 10 absolute point improvement compared to Swven.5-7B-Baat (0.3%), 71.8% MATH 500, 7.2 absolute point gain, and 55.0% on AMC 2023, 25-point increase. More remarkably, SYNLOGIC- 32B achieves 19.6% on AIME 2024, 4.4x improvement over Dwwen..5-32B-Baat (4.5%), while its performance on MATH 500 (82.0%) and AMC 2023 (57.5%) shows substantial gains 13.4 and 12.5 points, respectively. Similarly, SYNLOGIC-BB exhibits strong mathematical capabilities, achieving 14.5% on AIME 2024, with 11. absolute improvement. Without mathematics training data, our models nearly match surpass the instruction models, suggesting that enhancements in logical reasoning capabilities transfer effectively to mathematical problem-solvine This aligns with the observation in Lo (Xie et al. 2025b), highlighting the fundamental connection between logical and mathematical reasoning skills.
Increased Chain-of-Thougee Length As shown in Figure recording the response length and reflection ratio during the training process reveals that training on SYNLOGIC data leads to stable increases in response length for both models. The 7B model reaches an average of approximately 2500 tokens, while the 32B model achieves around 4000 tokens. Additionally, the increasing reflection ratios also indicate the emergence of cognitive behaviors during training [Gandhi et al. 2025). Both the extended response lengths and increased prevalence of reflection tokens suggest that synthetic logic reasoning tasks inherently align with the long-thinking paradigm L.LM.. Detailed training accuracy results are provided in Appendix B.1.3
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Training Stepe
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Cansumed Math Data
(a) Acc on COR-Bench.
(b) Avg Ace on Math.
(c) Avg Math Ace vs. Consumed Math Data
Figure 5: Performance comparison of 7B models trained on mixed data (Logic+Math) versus math- only (Math) data. (a) Accuracy on KOR-Bench. (b) Average accuracy across three mathematics benchmarks (MATH 500, AIME 2024, AMC 2023) as a function of training steps. (c) Average accuracy on mathematics benchmarks function of consumed mathematical data volume.
25
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(a) Acc on KOR-Bench.
(b) Avg Acc on Code.
(c) Avg Code Ace vs. Consumed Coding Data.
Figure 6: Performance comparison of 7B models trained on mixed data (Logic+Coding) versus coding-only (Coding) data. (a) Accuracy on KOR-Bench. (b) Average accuracy across coding benchmarks (validation split of our coding data and LiveCodeBench (Jain et al.) 2025) as a function of training steps. (c) Average accuracy coding benchmarks as function of consumed coding data volume.
4 Scaling RL Training with Diverse Verifiable Reasoning Data
Having verified the success of reinforcement training on SYNLOGIC alone, now leverage verifiable reasoning data from math, coding, and logical reasoning domains, scaling RL. training with diverse verifiable reasoning data. Concretely, data, and perform RL training on the mixed datasets. We will study how combining logical reasoning with code and mathematical data influences training efficiency on 7B models and enhances the Zero-RL capabilities for 32B models.
mix SYNLOGIC with mathematical or/and coding training
4.1 Setup Details
For mathematical training data, we directly utilize the 17k samples provided in DAPO Yuu et al. 2025 For coding data, assembled approximately 9k samples from various online coding platforms such as Codeforces. We adapted a similar prompt template to that used in our SYNLOGIC training; the detailed templates presented in Appendix [.I We maintained the same reward design approach as described in $3.II Specifically, for coding tasks, the reward set as if the output is correctly formatted and all test cases pass; otherwise, the reward is 0.
4.2 Mixing SYNLOGIC with Math or Code Data: A Pilot Ablation Study
Mixed Training with Math We sample approximately 17k samples from SYNLOGIC-Fasy and combine them with 17k math data for training on the Qwen2.5-7B-Be model. For controlled comparison, also conduct reinforcement learning using exclusively math data. Both experimental

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Table 3: Performance comparison across multiple benchmarks. The evaluation metrics vary by dataset: BBEH Kazemi et al., 2025) uses pass@1 I, while KOR- Bench [Ma et al., 2024], LiveCodeBench (LCB) al. 2025 and GPOA-Diamond
al. 2024 avg @ 4. AIME 2024 is evaluated
using @v All training configurations (Zero-Mix-2 and Zero-Mix-3) are run for the same number of training steps ensure fair comparison of results.
Model
BBEH KOR-Bench I.B
AIME 2024
GPQA Diamond
DeepSeek RI RI-Distill- Dww.iillllwwnn-33-1 Qwen-32B
19.2
66.6
57.2
72.6
63.1
DeepSeck-Re RI -e-eer--oww--33
40.2
47.0
55.0
Zero-Mix-2 (Math+Coding)
18.5
58.6
39.5
34.5
55.2
Zero-Mix-3 (SYNLoCCCttCWtthCooonnn
28.6
65.0
40.7
35.8
57.5
configurations maintain identical hyperparameters, optimization settings, and computational resources to ensure fair evaluation. Figure presents comparison of training dynamics. Running for the same number of training steps, mixed training (Logic+.Math) achieves comparable performance to math-only training average across three mathematical benchmarks (Figure 5b), while consuming fewer math samples. Under the same volume of processed math data, mixed training achieves higher accuracy (Figure 5c). Moreover, mixed training steadily improves logical reasoning, reflected in rising KOR-Bench scores (Figure 5a), which are nearly 10 absolute percentage points higher than those achieved with math-only training. These results suggest that mixed training facilitates more efficient optimization, potentially due to shared abstract reasoning mechanisms across domains.
Mixed Training with Code Following similar methodology. sample approximately 9k samples from SYNLOGIC-Easy and combine them with 9K code samples to train the Qwen2.5-7B- Base model. As control, conduct parallel training using exclusively coding data. Both training configurations maintain identical parameters to ensure a fair comparison. To measure the coding ability, we include the validation split of our coding data and the LiveCodeBench (Jain et al.) 2025 (the same version as used in DeepSeek's 's report [DeepSeek-Al et al. (0255) for evaluation. As shown in Figure 6. we observe similar phenomenon of more efficient training dynamics when mixing code with SYNLOGIC-Eass on coding benchmarks than code-only training when consuming the same volume of coding data, Simultaneously, mixed training improves logical reasoning, as evidenced by 10 absolute points better KOR-Bench scores (Figure 6a). These findings reinforce the complementary nature of logical reasoning in enhancing domain domain-specific capabilities.
Models trained on Logic+Coding data achieve higher performance
4.3
32B Rero-RI. Training with Diverse Reasoning Data
Building on the previous observation, here we scale up the diverse, verifiable training data by mixing math, coding, and SYNLOGIC datasets, and perform RI. training on the Qwen2.5-32BB- BBase model. Specifically,
a mix of 35k mathematical samples, 9k coding samples, and 1 17k SYNLOGIC samples for training. We term this training configuration as Zero-Mix-3. We additionally conduct Zero-Mix-2 setting that only mixes coding and mathematical data, serving as an ablation baseline to study the effect of SYNLOGIC in such scalable setting. Related to our Zero-Mix-2 setup, Zhang al. 2025 recently demonstrated that combining mathematical data with coding data able to facilitate coding learning. Here we further scale up this trend by including our proposed SYN SYNLOGIC dataset. To evaluate generalization, we include an ofo-oin benchmark, GPQA Diamond [Rein et al. 2024.. to study how the addition of SYNLOGIC impacts broader reasoning capabilities. Both Zero-Min Mix-- and Zero-Mix-2 configurations are run for the same number of training steps to ensure a fair and controlled comparison.
Results As shown in Table g the Zero-RL training in Zero-Mix-3 (SYNLoocc++Math-CCodnng
achieves superior performance across multiple evaluations. On logic benchmarks, Zero-Mix-3 nearly matches the performance of DeepSeek- -eegseee-----istillll RI--Ditill--ween- points on BBEH. Notably, Zero-Mix-3 also matches DeepSeek-R/ 1----o------ Qwen-32B on the coding benchmark LiveCodeBench [Jain et al., 2025) and outperforms on GPQA-Diamond. Compared to the Zero-Mix-2 (Math+Coding) experiment, Zero-Mix-3 consistently delivers higher performance
on
and surpasses it by

---

across all benchmarks. Specifically, Zero-Mix- shows significant improvement of over 10 points on BBEH, 6 points on KOR-Bench, and over points on the out-of-domain benchmark GPQA Diamond. These results strongly validate the significant generalization benefits provided by the inclusion of SYNLOGIC.
Conclusion
We present SYNLOGIC: a data synthesis framework and a comprehensive synthetic logic dataset with 35 diverse tasks, addressing the lack of high-quality logic training data. Using SYNLOGIC, we trained Qwen2.5 models with the GRPO algorithm, achieving significant gains on logic benchmarks like TOR-Bench and strong generalization to unseen mathematical tasks. Notably, our 32B model outperformed DeepSeek-R I-Distii 1--iisill--Qee-3225 on BBEH. Mixed training with SYNLOGIC further improved training efficiency and performance, showcasing the complementary benefits of logical reasoning across domains. We hope SYNLOGIC inspires broader exploration of synthetic datasets and logical reasoning to develop stronger reasoning capability models.
Limitations First, due to limited computational resources, we do not conduct precise difficulty tuning for every task, meaning the curated data may not be fully optimized for training 7B and 32B models. Second, we do not implement training with dynamically adjustable difficulty, where sample complexity progressively increases during training. We hypothesize that such an approach could further enhance the logical reasoning capabilities of LLMss. Both of these directions are left as opportunities for future exploration.
Acknowledgements
This project is partially supported by Hong Kong RGC ECS grant no. 26218125 and NSFC grant no. 62306177.
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A Comprehensive Overview of SYNLOGIC
A.1 Task Composition and Sources
Table 4 presents the diverse collection of tasks incorporated in SYNLOGIC. We have carefully selected
these tasks from established benchmarks including KOR-Bench [Ma al., 2024]. BBH (Suzgun et al."
2022 and BBEH [Kazemi et al. 2025 Additionally, integrated some logical reasoning tasks not
previously featured in these benchmarks, such as Mathador [Krrtc et al. 2024 and Minesweeper [Li
al. 2024].
Our collection comprises 35 distinct tasks, with only two (Zebra Puzzle [Lin et al. 2024 and ARC- AGI [Chollet 2019)) ) using existing data sources. For all remaining tasks, we generated custom datasets. Importantly, we developed and implemented verifiers for all tasks in the collection, ensuring consistent evaluation across the benchmark.
Table 4: Tasks in the Dataset Collection with Descriptions
No. Task Name
Description
ARC-AGI
A collection of general intelligence tasks requiring abstract reasoning and pattern recognition.
2
Arrow Maze
A mare sulving task where arows dictate movement, requiring pathfinding logic. Evaluating logical expressions AND, OR, NOT operators.
Boolean Expressions
4
Buggy Tables
Correcting flawed data tables based on logical constraints. A math-based Sudoku variant with arithmetti constraints.
5
Calcudoko
Campsile
Placing lents grid while satisfying adjacency rules.
7
Cipher
Decoding enerypted messages hased on given rules.
Cryptarithm
Solving arithmetic puzzles where letters represent digits. Validating hracket sequences for correct nesting.
Dyek I Language
Dyek Language Erross
Identifying and correcting errors bracket sequences. Advanced reasoning for errees bracket nesting logic.
11
Dyck Language Reasoning Errors
12
Futoshaki
A grid bused logic puzzle with insquality constraints.
13
Goods Exchange
Trac Tracking item exchanges amony multiple participants. A grid-hased puzzile involving row/column weight sums. math strategy game involving arithmetic operations. Finding correct numbers to satisfy equations in a grid.
14
Kukurasa
Mathador
16
Math Path
17
Minesweeper
Logical deduction to uncover mines on a grid.
18
Notinoei
Placing domino tiles grid with adjacency rules.
19
Number Wall
Constructing walls to separate grid regions bused on rules.
20
Numbrix
Filling prid with consecutive numbers in order.
21
Object Counting
Counting specific objects under given constraints.
Object Properties
Inferring reasoning about object attributes.
23
Operation
Solving puzzles with custom-dee custom-defined mathematical operations.
24
Skyscraper Puzzle
Determining building beights based on visibility clues.
25
Space Reasoning
Reasoning about spatial relationships Advanced spatial reasoming tasks with hierarchical relationships.
grid.
26
Space Reasoning Tree
27
Star Placement Puzzle
Placing stars grid while avoiding adjacency conflicts. Solving the classic number-placement puzzle. Filling grids to satisfy Scheduling tasks or events with overlapping constraints.
28 Sudoku
29
column sum constraints.
30
Time Sequence
31
Web Lies
Deternining truth-tellers and liars through logical statements. Sorting words based Identifying mistakes in word sorting logic or reasoning.
32
Word Sorting
rules construints.
33
Word Sorting Mistake
34
Wordscapes
crossword puzzle where players fill words from lists while matching intersee-
tions.
Solving complex logic puzzles with multiple constraints.
A.2 SYNLoorC--Hrrd and SYNLoGIC-Fasy
The SYNLoGIC-Hard dataset encompasses all 35 tasks, representing a challenging upper bound calibrated to the solvability thresholds of DeepSeek RI and OpenAl-o3-mmni. During our experiments with Qwen2.5-32B- Base we observed consistent training accuracy gains across this comprehensive task set. However, this difficulty level proved excessive for smaller-scale models like Qwen2.5-7B. Base. Despite reducing the difficulty parameters across tasks, eight specific tasks (Arrow Maze, Goods Exchange, Kukurasu, Minesweeper, Norinori, Object Counting, Space Reasoning Tree, and Wordscapes) persistently yielded zero accuracy when training the 7B models. Consequently, we developed SYNLOGIC-Fasy, modified variant that excludes these particularly challenging tasks, to provide more appropriate training dataset for the Dwen2.5-7B-Baat model.
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B Training and Evaluation Details
B.1
Training
B.1.1 Training Template
We provide the training template for math and coding here Figure 7 and Figure
Math Training Prompt Template
You are a helpful assistant. You always first think about the reasoning process in the mind and then provides the user with the answer reasoning process and answer are enclosed within '<think>> "</think>' and '<answer>' "</answer>" tags, respectively, e.g., .g.hinchhnn>>AA detailed reasoning process here, with possible reflections including but limited to reviewing previous steps for errors, exploring alternative approaches, and considering possible refinements, \n</think>> haaninn/innnnsssrnnnneppll to user here..ncc/answe>>. Please reason step by step, and put your final answer within \boxed(). )
Figure 7: The prompt template used for training models on math data.
Coding Training Prompt Template
You are a helpful assistant. You always first think about the reasoning process in the mind and then provides the user with the answer/unTh reasoning process and answer enclosed within '<think>' "</think>' and '<answer>' '</answer>' tags, respectively, .ng.iincthnn detailed reasoning process here, with possihle reflections including but not limited to reviewing previous steps for errors, exploring alternative approaches, and considering possible refinements. refnements.nc//hinklnneee www.:///hiinbbnnnnswweeettteeee here. beceanwr///s Please put your final code following this format:An" "ommattu"[aanguage JJanguageJuffyourr code here ln
to user
Figure 8: The prompt template used for training models on coding data.
B.1.2 Training peper-parameters
For 7B model training, we adopted the following hyper-parameters: with learning rate 1e-6, GRPO group size 16, max prompt length 2048, max response length 16384, prompt batch size 128, mini batch size 64, with clip high 0.28, clip low 0.2.
For 32B model training in 3 we adopted the following syper-parameters: with learning rate 2e-6, GRPO group size 16, max prompt length 2048, max response length 28672, prompt batch size 128, mini batch size 16, with clip high 0.28, clip low 0.2.
For 32B model training in $ we adopted the following hyper- hyper-parameters: with learning rate 2e-6, GRPO group size 16, max prompt length 2048, max response length 12288, prompt batch size 512, mini batch size 16, with clip high 0.28, clip low 0.2.
B.1.3 Training Dynamics Analysis
We present the training accuracy progression of our 7B and 32B models on the SYNLOGIC dataset in Figure 9 The results demonstrate a consistent improvement in accuracy throughout the training process for both model sizes.
B.2
Evaluation
B.2.1
Performance Analysis of Mixed Training with Math
We analyze the training dynamics when combining our logical reasoning dataset with mathematical content. Figure 10 presents performance results across three mathematical benchmarks: MATH 500, AIME 2024, and AMC 2023. These results demonstrate that mixed training can achieve similar performance with the same number of training steps while using less mathematical data. This suggests that mixed training creates more efficient training dynamics.
14

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53
WW
23
Training
(a) Training accuracy of model
(b) Training accuracy of 32B model
Figure 9: Training accuracy progression for both model sizes the SYNLOGGIC dataset. Both models exhibit steady improvement in performance as training progresses.
$3.5
18
65-
78.5-
Accinv (%6)
Accanac (t6)
50-
Legie-Math
Logie+Mark
Legle-Math
Math data
Math data
Math data
63.5
64
256
520
124
256
520
128
256
320
Stepo
(a) Performance on MATH 500.
(b) Performance on AIME 2024.
(c) Performance on AMC 2023.
Figure 10: Comparative accuracy (%) of models trained with mixed data and math-only data across three mathematical benchmarks: MATH 500, AIME 2024, and AMC 2023. All evaluations of figure use avg @8 scoring.
B.3 Performance Analysis of Mixed Training with Coding
We also provide the training dynamics when mixed training with coding data in Figure [1 The observation is similar to mixed training with math, suggesting that mixed training leads to more efficient training dynamics.
Acuracy (N)
Accuraey (%)
Logle-Coding
Lodin Coding data
Coding data
10
Training Steps
Training Steps
(a) Performance on our coding data validation split.
(b) Performance on LiveCodeBench.
Figure 11: Comparative accuracy (%) of models trained with mixed data and coding-only data across two coding benchmarks: our coding data validation split and LiveCodeBench. All evaluations of the figure use avg @8 @v scoring.
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Reviews:
[{"review_id": "AVSDJ013mb", "reviewer": "Reviewer_7q1L", "summary": "The paper introduces SYNLOGIC, a comprehensive data synthesis framework and dataset designed to generate diverse logical reasoning tasks at scale. SYNLOGIC addresses the gap in high-quality logical reasoning training data, which is essential for developing general reasoning capabilities in large language models (LLMs). The dataset includes 35 diverse tasks, each with task-specific generation code, a verification rule, and configurable difficulty parameters. This allows for the creation of data with controlled difficulty levels, making it suitable for reinforcement learning (RL) with verifiable rewards.", "questions": "- Consider implementing a dynamic difficulty adjustment mechanism where the difficulty of the tasks is gradually increased during training. This could involve starting with simpler tasks and gradually introducing more complex ones as the model's performance improves.\n- Conduct additional experiments to compare the generalization performance of the 7B and 32B models when trained with mixed SYNLOGIC, mathematical, and coding data. This could include a more granular analysis of performance on specific benchmarks and tasks.\n- Perform ablation studies to investigate the impact of dataset size on training efficiency and performance. This could involve training models with different sizes of SYNLOGIC data (e.g., 10k, 20k, 30k, 33k samples) and comparing the results.\n- Conduct experiments to investigate the integration of SYNLOGIC with other training techniques. This could include few-shot learning, fine-tuning on specific tasks, or hybrid approaches that combine multiple techniques.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\nThe paper introduces SYNLOGIC, a comprehensive dataset containing 35 diverse logical reasoning tasks. This is a significant contribution to the field, as it addresses the lack of high-quality logical reasoning training data.\nThe framework allows for controlled synthesis of data with adjustable difficulty and quantity, which is crucial for training models effectively.\nAll examples in the dataset can be verified by simple rules, making them ideally suited for reinforcement learning (RL) with verifiable rewards.\nThe authors validate the effectiveness of RL training on the SYNLOGIC dataset using 7B and 32B models, demonstrating state-of-the-art performance on logical reasoning benchmarks.\nhe mixed training approach, combining SYNLOGIC data with mathematical and coding tasks, improves training efficiency and significantly enhances reasoning generalization across multiple domains.\nThe authors provide a detailed description of the SYNLOGIC framework, including task selection, parameter identification, logic instance generation, and verification suite. This makes the work reproducible and transparent.\n\nWeaknesses:\nDue to limited computational resources, the authors do not perform precise difficulty tuning for every task. This could mean that the data is not fully optimized for training 7B and 32B models.\nThe paper does not implement training with dynamically adjustable difficulty, where sample complexity progressively increases during training. This could limit the potential for further enhancing logical reasoning capabilities.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate your thoughtful comments and recognition of the strengths of our work. Below, we address each of your concerns and questions in detail:\n\n\n\n>Q1: Conduct additional experiments to compare the generalization performance of the 7B and 32B models when trained with mixed SYNLOGIC, mathematical, and coding data. This could include a more granular analysis of performance on specific benchmarks and tasks.\n\nA1:  To provide more granular analysis, here we analyze the effect of mixed training on response length and training efficiency beyond accuracy on AIME 2024.  Specifically, based on the 7B model trained on mixed synlogic, math, and code data, we compare its performance to training on math-only data. Results on AIME 2024 are shown below. We find that mixed training leads to higher performance under the same training steps (while consuming less math data).  Also, mixed training leads to longer responses. \n\n| Training Steps | 48 | 96 | 144 | 192 | 240 | 304 |\n|----------------|----|----|----|----|----|----|\n| Response Length (mix-logic vs. math-only) | **1122**/1160 | **1366**/1312 | **1640**/1554 | **2716**/1915 | **3926**/3813 | **8621**/7260 |\n| Performance (mix-logic vs. math-only) | **11.6**/11.6 | **12.5**/12.9 | **15.8**/14.6 | **16.7**/15.4 | **17.1**/16.7 | **18.3**/17.1 |\n\n\n\n>Q2: Perform ablation studies to investigate the impact of dataset size on training efficiency and performance.\n\n\nA2: Thank you for the suggestion.  Here, we conduct ablation studies on different data sizes by controlling the selected task numbers. Using the Qwen2.5-7B-Base model, we conduct RL training varying the logical reasoning tasks: 10 tasks (5K samples), 20 tasks (10K samples), and all 27 tasks (16K samples) under the same training steps. The results are shown below:\n\n| Tasks | SynLogic-val | KOR-Bench | BBH | BBEH | AIME 2024 | MATH 500 | AMC 2023 |\n|-------|-------------|-----------|-----|------|-----------|----------|----------|\n| 10 tasks (5K) | 32.6 | 44.2 | 66.0 | 5.6 | 10.0 | 72.1 | 52.5 |\n| 20 tasks (10K) | 33.4 | 47.7 | 66.0 | 7.3 | 11.25 | 70.1 | 47.1 |\n| All tasks (16K) | **44.4** | **48.1** | **66.5** | **8.0** | 10.0 | 71.8 | **55.0** |\n\nThe results show that increasing the number of tasks generally improves performance across most benchmarks, demonstrating the effectiveness of our diverse task collection.\n\n\n>Q3: Conduct experiments to investigate the integration of SYNLOGIC with other training techniques.\n\nA3: Thanks for your suggestion.  Our paper primarily focuses on the RLVR setting, which we believe is sufficiently substantive to stand on its own. We look forward to investigating the impact of SYNLOGIC in other training paradigms like SFT in future work.\n\n\n>Q4: Consider implementing a dynamic difficulty adjustment mechanism where the difficulty of the tasks is gradually increased during training. \n\nA4: Thank you for your suggestions. Curriculum learning as advised here may indeed help learn logical reasoning greatly. Due to time and resource limitations we were unable to conduct this experiment during rebuttal, but we will consider exploring it in future work."}, {"review_id": "7AWXYfW5hx", "reviewer": "Reviewer_wT7y", "summary": "This paper studies the problems of reinforcement learning from verifiable feedback. The paper introduces a collection of synthetic logical reasoning tasks, called SynLogic, for training LLMs. SynLogic 35 36 logical reasoning tasks, where each of the tasks supports two difficulty levels and rule-based evaluators for reliable evaluation.\n\nUsing SynLogic, the paper trains Qwen-7B and 32B with reinforcement learning, which achieves strong performance on logical reasoning tasks in Big-bench-extra-hard, and also sees a bit of generalization to GPQA.", "questions": "See weakness for concerns.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strength\n\nThe collected data suite, SynthLogic, contains over 30 logical reasoning tasks of multiple types. The tasks have some nice properties of having two difficulty levels and reliable rule-based evaluation.  This collection of data suites can be useful for the research community in the field of RLVR for reasoning.\n\nThe authors also conduct experiments of running RL over the logical reasoning problems, which shows good in-domain results and performance improvements on similar logical reasoning benchmarks (KOR and BBEH also have problems like logical, puzzle, cipher, which, in my opinion, are similar with the proposed data suite). The more interesting findings are including SynthLogic generalizes a bit to GPQA and LiveCodeBench.\n\nThe paper is mostly well-written and easy to follow.\n\n## Weakness\n\nThe generalization to more realistic benchmarks (LiveCode and GPQA) shows observable but modest improvements considering the additional amount of training data.\n\nWhile the paper compiles a set of tasks, most of them can be found in existing resources. The paper does not add new things for testing LLMs.\n\nThe paper presents a collection of logical reasoning models and empirical study on using them for training models. I feel the paper could benefit from a bit more analysis, such as impact of additional training data size, generalization across tasks within SynLogic.\n\nThe experiment only contains one model family (Qwen). It is unsure how the results could generalize across different model families like Llama.", "was_revised": true, "final_justification": "I thank authors for the detailed response. I'd like to retain my score, slightly leaning the positive side. As in my response, I do appreciate the work for collecting this number of tasks and run experiments to study the benefits on RL on these tasks. At the same time, I feel 1) the main improvements on logical reasoning is somewhat in-domain (KOR bench, BBH, BBEH are mostly about games/logical puzzles) which is in some sense. similar to such collection of data. 2) on more OOD tasks like MATH, as in answers to Q3, the improvements are not consistent, 20 tasks < 10 tasks on MATH 500 and AMC 2023, 5 tasks work best on MATH 500.", "rebuttal": "Thanks for your helpful comments; we are glad that you acknowledged our work's strengths! Below we address your concerns:\n\n>Q1: The generalization to more realistic benchmarks (LiveCode and GPQA) shows observable but modest improvements considering the additional amount of training data.\n\nA1: Thank you for the comment. We first note that, in all table comparisons, different RL training runs are always benchmarked using the same number of training steps. Therefore, our model does not consume more training tokens than the baselines, even when additional datasets are incorporated. More importantly, we emphasize that the contribution of SynLogic, as shown in the tables, is that it **greatly improves logical reasoning performance without negatively impacting other domains, all within the same training compute budget**. This means that including our dataset in the training pipeline acts as a free addition—providing significant benefits on logical reasoning without causing negative transfer or requiring extra computation. Consequently, the modest improvements observed on LiveCode and GPQA do not undermine our main contribution or the claims as improving them is not the main goal. \n\n>Q2: While the paper compiles a set of tasks, most of them can be found in existing resources. The paper does not add new things for testing LLMs.\n\nA2: As discussed in Section 2.2 (The Data Synthesis Framework), although most tasks can be found in existing resources, they do not open-source their synthesis code and do not conduct careful difficulty control. We have overcome this challenge through the time-consuming development of these tasks’ generation framework. Furthermore, our work focuses on conducting RLVR on diverse and scalable logical tasks rather than introducing new testing paradigms for LLMs.\n\n>Q3:  I feel the paper could benefit from a bit more analysis, such as impact of additional training data size, generalization across tasks within SynLogic.\n\nA3: Thanks for your suggestions! Here, we conduct ablation studies on different data sizes by controlling the selected task numbers. Using the Qwen2.5-7B-Base model, we conduct RL training varying the logical reasoning tasks: 10 tasks (5K samples), 20 tasks (10K samples), and all 27 tasks (16K samples) under the same training steps. The results are shown below:\n\n| Tasks | SynLogic-val | KOR-Bench | BBH | BBEH | AIME 2024 | MATH 500 | AMC 2023 |\n|-------|-------------|-----------|-----|------|-----------|----------|----------|\n| 10 tasks (5K) | 32.6 | 44.2 | 66.0 | 5.6 | 10.0 | 72.1 | 52.5 |\n| 20 tasks (10K) | 33.4 | 47.7 | 66.0 | 7.3 | 11.25 | 70.1 | 47.1 |\n| All tasks (16K) | **44.4** | **48.1** | **66.5** | **8.0** | 10.0 | 71.8 | **55.0** |\n\nThe results show that increasing the number of tasks generally improves performance across most benchmarks, demonstrating the effectiveness of our diverse task collection.\n\n\n\n\n>Q4: The experiment only contains one model family (Qwen). It is unsure how the results could generalize across different model families like Llama.\n\n\nA4: Thank you for the suggestion! We conduct RL experiments on the mid-trained LLaMA-3.1-8B model [1] and observe significant improvements in both logical reasoning and math generalization performance. The results demonstrate that our SynLogic framework is effective across different model architectures, not limited to Qwen-specific training dynamics.\n\n| Model | SynLogic-val | KOR-Bench | BBH | BBEH | AIME 2024 | MATH 500 | AMC 2023 |\n|-------|-------------|-----------|-----|------|-----------|----------|----------|\n| LLaMA-3.1-8B (Base) | 4.2 | 37.2 | 43.45 | 4.1 | 3.3 | 38.7 | 20.3 |\n| LLaMA-3.1-8B (Trained on SynLogic) | 38.0 | 44.0 | 55.2 | 12.0 | 14.5 | 68.4 | 45.0 |\n| Improvement | +33.8 | +6.8 | +11.75 | +7.9 | +11.2 | +29.7 | +24.7 |\n\n[1] Wang et al. OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling. arXiv preprint. arXiv:2506.20512 2025"}, {"review_id": "KhKlRcwIiq", "reviewer": "Reviewer_GS5X", "summary": "This paper introduces SYNLOGIC, a novel framework and dataset designed to address the scarcity of diverse, high-quality, and verifiable logical reasoning data for training Large Language Models (LLMs). Specifically, the contributions are:\n1. A Data Synthesis Framework: A systematic pipeline for generating logical reasoning problems across 35 diverse tasks (e.g., Sudoku, Cryptarithms, Arrow Maze). This framework allows for controlled synthesis with adjustable difficulty and includes a dedicated verifier for each task, making it ideal for RL with verifiable rewards (RLVR).\n2. The SYNLOGIC Dataset: A large-scale dataset generated by the framework, with two versions tailored for different model sizes (\"Easy\" for 7B models and \"Hard\" for 32B models).\n3. Empirical Validation and State-of-the-Art Results: The authors train Qwen2.5 models (7B and 32B) on SYNLOGIC using the GRPO reinforcement learning algorithm. Their models achieve state-of-the-art performance on logical reasoning benchmarks among open-source models, notably surpassing the strong DeepSeek-R1-Distill-Qwen-32B model by 6 points on BBEH.\n4. Demonstration of Generalization and Efficiency: The paper shows that training on SYNLOGIC not only improves logical reasoning but also generalizes to mathematical tasks. Furthermore, experiments reveal that mixing SYNLOGIC data with math or code data significantly improves the training efficiency and final performance in those domains, highlighting the complementary nature of logical reasoning.\n\nThe authors commit to open-sourcing both the dataset and the synthesis pipeline to foster further research in general reasoning for LLMs.", "questions": "1. Is SYNLOGIC trained from qwen -base model or -instruct model in Table 2?\n2. You may need to cite another paper [FineReason](https://arxiv.org/abs/2502.20238), which also releases the generation pipeline and data for logic data, and possibly compare the effectiveness of your data and this data.\n3. Other questions in Weakness 1 and the difference between consumed math data and training steps mentioned in weakness 3.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n1. Addresses a Clear and Important Problem: The paper correctly identifies a significant bottleneck in advancing general reasoning capabilities in LLMs—the lack of diverse, verifiable training data outside of math and code. Its focus on logical reasoning as a fundamental building block is a well-founded and timely hypothesis.\n2. The authors commit to open-sourcing both the dataset and the synthesis pipeline.\n\nWeakness:\n1. The generation pipeline is too abstract and hard to understand. For example, in Line 102, it is difficult to understand how parameters for each task are used to control the synthesis process. In line 105, what is the output of your generator? Line 111, how do you perform automatic checks? Line 117, what are the chat models? Line 121, what is the conversion prompt? Line 124, Is the verification the same as that in in line 111?\n2. The performance in Table 2 shows that Synlogic still lags behind R1-disill-qwen in 32B, limiting the effectiveness of Synlogic data.\n3. For the experiments in Figure 5 and Figure 6, it seems the constructed logic data only do well on KOR-Bench, which can be the indomain nature of puzzle-related problems in KOR-bench. However, there is no significant effectiveness on math and code tasks.  Particularly, in Table 6-(b), using only code data has a higher effectiveness and greater training efficiency. Meanwhile, I also found it hard to understand the difference between consumed math data and training steps since the range of these two are the same in the figure.", "was_revised": true, "final_justification": "The work is conducted on a large model size and improves the logic reasoning without hurting other capability. The authors say \" The purpose of creating SynLogic is to provide researchers and practitioners with an RL logical reasoning dataset that can be used to enhance models’ logical reasoning performance through RL.\" Therefore, a good data source will be released, which is a good contribution.", "rebuttal": "Thank you for the comments and we address them below.\n\n>Q1:  in Line 102, it is difficult to understand how parameters for each task are used to control the synthesis process.\n\nA1: Each logical reasoning task has specific parameters that control its difficulty level. For Sudoku, the key parameter is grid size (e.g., 5x5, 7x7, 9x9) - larger grids create more complex puzzles. For Cryptarithms, consider this example: SEND + MORE = MONEY, where each letter represents a unique digit, and this task is to find the numerical equation making the equation true. The difficulty parameters include the number of letters used and the length of arithmetic expressions. These parameters are systematically varied during synthesis to create problems of different difficulty levels. We apologize for incomplete details of this process in the submission and we will provide detailed parameter descriptions for all 35 tasks in the appendix in the next revision.\n\n>Q2: In line 105, what is the output of your generator? Line 111, how do you perform automatic checks? \n\nA2: The task generator outputs structured problem instances with specific formats. For Sudoku, it generates a grid with some numbers filled and others marked as \"X\" for missing values. For Cryptarithms, it outputs equations like \"SEND + MORE = MONEY\" where each letter represents a unique digit. The automatic solvability checks use algorithmic verification: Sudoku uses backtracking algorithms to verify solutions exist, while Cryptarithms uses constraint satisfaction to check for valid digit assignments. We will provide detailed output formats for all tasks in the appendix of the next version.\n\n>Q3:   Line 117, what are the chat models?\n\nA3: We use the Qwen-2.5-32B-Instruct model for this step. \n\n>Q4: Line 121, what is the conversion prompt? \n\nA4: The conversion prompt transforms structured problem instances into natural language instructions. For example, in Sudoku: \"Here is a 7x7 Sudoku puzzle, where X represents a hidden number that needs to be filled in. Please solve it step by step.\" as demonstrated in Figure 1. For Cryptarithms, we use \"Solve this cryptarithm: {equation}, where each letter represents a unique digit. Find the digit substitution that makes the equation true.\" We use multiple prompt templates for each task to ensure robust instruction following. We did not include all prompt templates in the submission because there are many of them, and we instead only included certain examples in Figure 1. \n\n>Q5: Line 124, Is the verification the same as that in line 111?\n\nA5: No, they are different steps in our pipeline. The automatic solvability checks (line 111) aim to filter out unsolvable problems before they enter the training dataset. In contrast, verification (line 124) happens during RL training to evaluate model responses and provide rewards. For example, the automatic solvability checks in Sudoku filter out created puzzles with no valid solutions using backtracking algorithms. The verification checks whether the model's final answer is correct (e.g., whether the filled Sudoku grid satisfies all rules).\n\n>Q6: The performance in Table 2 shows that Synlogic still lags behind R1-disill-qwen in 32B, limiting the effectiveness of Synlogic data.\n\nA6: We emphasize that Table 2 includes R1-disill-qwen for reference point only, and it is not fair to compare our RL models to R1-Distill-Qwen-32B due to fundamental differences in training approaches and resources. R1-Distill-Qwen-32B is trained on large-scale trajectory data from R1 models, which includes extensive supervised fine-tuning processes. In contrast, our SynLogic models are trained using only 33K synthetic logical reasoning instances through pure RL training without any additional supervised data.  The purpose of creating SynLogic is to provide researchers and practitioners with an RL logical reasoning dataset that can be used to enhance models’ logical reasoning performance through RL.\n\n\n>Q7: For the experiments in Figure 5 and Figure 6, it seems the constructed logic data only do well on KOR-Bench, which can be the indomain nature of puzzle-related problems in KOR-bench. However, there is no significant effectiveness on math and code tasks. \n\nA7: The key message from Figure 5 and Figure 6 is that our approach significantly enhances logical reasoning without hurting performance on other domains  under the same training compute -- that means including our dataset in the training recipe is like a free gift without negative transfer to other domains or consuming additional compute, as described in line 244-246. The effectiveness is particularly evident when comparing performance under equivalent math/code data consumption (Figures 5-c and 6-c), where mixed training shows clear advantages over training with math or code data alone.\n\n\n>Q8: Meanwhile, I also found it hard to understand the difference between consumed math data and training steps since the range of these two are the same in the figure.\n\nA8: We apologize for the confusion in Figure 5-c and Figure 6-c. The x-axis represents the number of consumed math/code data samples (step×batch_size), not training steps. We will update the axis labels in the next version. To clarify, when we mix logic data with math/code data, the total training steps remain the same, but we consume proportionally less math/code data since logic data occupies some of the training budget. For example, if we train for 1000 steps with pure math data, we consume 1000×batch_size math samples. But with mixed training (50% logic, 50% math), we still train for 1000 steps but only consume 500×batch_size math samples. Therefore, we plot Figures 5-c and 6-c to show performance under equivalent consumed math/code data. The key insight is that mixed training achieves better performance while using less domain-specific data, demonstrating the efficiency of our approach.\n\n\n>Q9: Is SYNLOGIC trained from qwen -base model or -instruct model in Table 2?\n\nA9: As described in line 167, we conduct RL training starting from Qwen-Base models.\n\n>Q10: You may need to cite another paper FineReason, which also releases the generation pipeline and data for logic data, and possibly compare the effectiveness of your data and this data.\n\nA10: Thank you for the suggestion, and we will surely cite it in the next revision. We also tried comparing it empirically during rebuttal. However, FineReason did not release their training data or the source code for their data generation pipeline. Below we describe the relation and distinction between SynLogic and FineReason.\n\nBoth SynLogic and FineReason investigate logical reasoning tasks and conduct RL training experiments. However, there are significant differences between FineReason and SynLogic in both scope and methodology.\n1. **Scale & Diversity**: SynLogic covers 35 distinct logical reasoning tasks (vs. FineReason's 4 puzzle tasks), providing much broader coverage of reasoning patterns and cognitive skills. \n2. **Scalable Synthesis**: SynLogic features adjustable difficulty parameters and automated generation of unlimited training data with verifiable rewards, enabling efficient RL training. FineReason did not open-source their data generation code. \n3. **Strong RL Scaling**: SynLogic conducts large and comprehensive RL experiments on these 35 logical reasoning tasks and math and coding domains over 7B and 32B models, while FineReason only conducts experiments on 4 logical tasks and math domain over smaller 1.5B and 7B models."}, {"review_id": "gYJXpA4Ya5", "reviewer": "Reviewer_cYNo", "summary": "This paper introduces SynLogic, a framework for synthesizing large-scale, verifiable logical reasoning data across 35 diverse task types with controllable difficulty, enabling RLVR. The authors train Qwen2.5-7B and 32B models using this data, demonstrating substantial improvements on logic benchmarks like KOR-Bench and BBEH, surpassing previous SOTA open-source models. They further show that mixing SynLogic data with math and coding tasks enhances training efficiency and generalization across domains, including mathematics and programming.", "questions": "1. In my view, the value of high-quality synthetic data should ideally be demonstrated in the regime where strong models are already saturated with existing training data, and the synthetic data enables further gains. While Section 4.3 partially addresses this through a Zero-RL setup on Qwen2.5-32B, I would encourage the authors to include or discuss results where SynLogic data is used to fine-tune even stronger models, to evaluate whether synthetic logic tasks provide meaningful additional signal beyond what distilled data already offers.\n2. While the authors demonstrate meaningful generalization improvements over base models in math and coding tasks, it would be more informative to compare against the instruct-tuned versions (e.g., Qwen2.5-Instruct), especially given the strong performance those models already exhibit in these domains. This would clarify whether SynLogic training offers significant cross-domain benefits beyond what instruction tuning alone achieves.", "limitations": "The authors rightly acknowledge in the Limitations section that they do not implement training with dynamically adjustable difficulty. Given that SynLogic includes fine-grained difficulty control for each task, this opens up a promising direction for curriculum learning, where samples of increasing complexity could be introduced progressively. Incorporating such a strategy may further improve model performance on harder reasoning tasks, akin to how humans build up reasoning skills through gradual exposure. I encourage the authors to explore this in future work, as it aligns naturally with the design of their dataset and could enhance the effectiveness of RL training.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The SynLogic dataset is designed with adjustable difficulty parameters.\n2. The authors demonstrate that mixing SynLogic data with mathematical and coding datasets improves training efficiency and performance across all domains.\n3. Reinforcement learning on SynLogic significantly boosts the performance of the Qwen2.5-32B model, bringing it close to the level of the state-of-the-art R1-Distill-Qwen-32B on challenging logic benchmarks such as BBEH.\n\n\nWeaknesses\n1. While the SynLogic dataset provides verifiable and diverse task types, the solution traces appear to be rule-based and may lack the richness and diversity of human-like reasoning strategies. Prior work [1] has shown that such diversity in solution paths plays a crucial role in improving LLM reasoning abilities. I would encourage the authors to explore or discuss approaches for enhancing the diversity of reasoning trajectories, which may further boost generalization beyond structured synthetic tasks.\n2. Another concern is that the training contains only fixed-format prompts with strict reward constraints tied to specific tags. This design may inadvertently increase prompt sensitivity, a known weakness of LLMs, where slight variations in prompt phrasing can lead to large performance drops. The paper would benefit from an empirical analysis of prompt robustness or a discussion on potential mitigation strategies (e.g., training with paraphrased prompt templates or evaluating on alternate phrasing).\n3. The paper highlights difficulty control as a key advantage of the SynLogic dataset, but it lacks concrete examples or definitions for how difficulty is parameterized and adjusted across all tasks. Could the authors provide detailed descriptions (possibly in Appendix) of how difficulty is defined and controlled for each task? For instance, what are the concrete parameters, value ranges, and examples across difficulty levels?\n4. The verifier design is central to the reliability of RLVR. However, the paper does not elaborate on how the verifiers ensure all generated questions are solvable and whether the verifiers cover edge cases or complex failure modes. It is also unclear whether the verifiers only check for final answer correctness, or if they also assess the logical validity of intermediate reasoning steps (especially relevant under the chain-of-thought paradigm). Clarification and evidence of thorough verifier validation would significantly strengthen the work.\n5. The proposed SynLogic framework demonstrates strong improvements in logical reasoning tasks when applied to Qwen2.5 models. However, all experiments are limited to the Qwen model family. Including additional results on a distinct open-source model, such as LLaMA or Mistral, would strengthen the paper’s claim beyond Qwen-specific training dynamics.\n\n[1] Peng, Xiangyu, et al. \"ReGenesis: LLMs can Grow into Reasoning Generalists via Self-Improvement.\" In ICLR 2025.", "was_revised": true, "final_justification": "The responses have addressed my concerns.", "rebuttal": "Thank you for the comments and we address them below.\n\n\n>Q1: While the SynLogic dataset provides verifiable and diverse task types, the solution traces appear to be rule-based and may lack the richness and diversity of human-like reasoning strategies.\n\nA1: We agree that logical tasks are more rule-complete, but this is determined by these tasks' inherent properties. However, this does not mean these tasks don’t trigger diverse, human-like reasoning strategies to solve. As demonstrated in Figure 4, during RL training, the ratio of reflection tokens within CoT increases, which is closely related to human-like reasoning processes involving trial and backtracking. We will provide example rollouts in the appendix in the next version to further illustrate this point.\n\n\n>Q2: Another concern is that the training contains only fixed-format prompts with strict reward constraints tied to specific tags.\n\nA2: First, we do not use a single fixed prompt for each task. Instead, we implement over 10 bilingual (English and Chinese) prompts for each task separately to achieve robust prompt-following performance.  We will provide more details about the prompt examples and prompt numbers in the next version. Every generated instance is randomly selected from prompt templates to achieve diverse prompt formats and robust instruction following. Additionally, given that our approach significantly improves performance on diverse benchmarks like BBEH and KOR-Bench, it demonstrates the effectiveness of our training dataset.\n\n\n>Q3: The paper highlights difficulty control as a key advantage of the SynLogic dataset, but it lacks concrete examples or definitions for how difficulty is parameterized and adjusted across all tasks. \n\nA3: Typically, logical tasks contain key parameters that relate to difficulty or complexity. For example, the grid size of Sudoku problems directly correlates with complexity - higher grid sizes correspond to higher difficulty levels. Due to space limitations, we only showed this in Figure 1 and briefly discussed it in lines 102-104. We will definitely include more detailed descriptions of difficulty parameters and value ranges for every task in the appendix of the next version. Figure 1 provides a concrete difficulty example using Sudoku grid size.\n\n\n\n>Q4: Clarification and evidence of thorough verifier validation would significantly strengthen the work.\n\nA4: Thank you for the suggestion! Our verifier validates whether the final answer is correct. Here are two detailed examples of our data construction and verification process:\n\nFor Sudoku, a typical board game, we identify the difficulty parameter as grid size and set it to 7 as example. Our generator creates a 7x7 grid instance with some missing numbers marked as X. We then format the instance with a prompt describing the Sudoku task to create the final question. Given the question, the LLM attempts to reason and solve the task, providing the final grid with filled values. Our verifier then checks whether the response's grid complies with Sudoku rules (such as single value rules) to verify correctness.\n\nFor math path problems, an example instance is: $5-{?}-0 \\times 9+{?} \\times 5-3 \\times ({?} \\bmod {?}) \\times 1-1 = 4$, where each ? represents a number to be solved. The identified difficulty parameter is the missing number ratio in the equation. The verifier validates whether the LLM's solution makes the equation work correctly.\n\nTherefore, our verifier checks answers’ correctness as in other RLVR works (rather than reasoning steps) and the verification is very accurate without apparent failing cases.\n\n\n>Q5: Including additional results on a distinct open-source model, such as LLaMA or Mistral, would strengthen the paper’s claim beyond Qwen-specific training dynamics.\n\nA5: Thank you for the suggestion! We conduct RL experiments on the mid-trained LLaMA-3.1-8B model [1] and observe significant improvements in both logical reasoning and math generalization performance. The results demonstrate that our SynLogic framework is effective across different model architectures, not limited to Qwen-specific training dynamics.\n\n| Model | SynLogic-val | KOR-Bench | BBH | BBEH | AIME 2024 | MATH 500 | AMC 2023 |\n|-------|-------------|-----------|-----|------|-----------|----------|----------|\n| LLaMA-3.1-8B (Base) | 4.2 | 37.2 | 43.5 | 4.1 | 3.3 | 38.7 | 20.3 |\n| LLaMA-3.1-8B (Trained on SynLogic) | 38.0 | 44.0 | 55.2 | 12.0 | 14.5 | 68.4 | 45.0 |\n| Improvement | +33.8 | +6.8 | +11.7 | +7.9 | +11.2 | +29.7 | +24.7 |\n\n\n\n\n>Q6: While the authors demonstrate meaningful generalization improvements over base models in math and coding tasks, it would be more informative to compare against the instruct-tuned versions (e.g., Qwen2.5-Instruct)\n\n>Q7: I would encourage the authors to include or discuss results where SynLogic data is used to fine-tune even stronger models\n\nA6 & A7: As suggested by the reviewer, we conduct RL training based on Qwen2.5-32B-Instruct, which is an instruct-tuned version and stronger than all the base models in our submission version. Results are shown below. Similarly, we observe consistent \nimprovements on logical and math tasks, even though we only trained for 50 steps with 128 batch size due to time constraints.\n\n| Model | SynLogic-val | KOR-Bench | BBH | BBEH | AIME 2024 | MATH 500 | AMC 2023 |\n|-------|-------------|-----------|-----|------|-----------|----------|----------|\n| Qwen2.5-32B-Instruct| 12.0 | 54.7 | 84.5 | 17.5 | 10.0 | 82.2 | 57.5 |\n| Qwen2.5-32B-Instruct (Trained on SynLogic) | 31.7 | 58.1 | 85.7 | 20.3 | 16.25 | 81.8 | 63.4 |\n| Improvement | +19.7 | +3.4 | +1.2 | +2.8 | +6.25 | -0.4 | +5.9 |\n\nThe improvements on logical benchmarks like KOR-Bench (+3.4) and math benchmarks like AIME 2024 (+6.25) validate the effectiveness of SynLogic on stronger, instruction version models.\n\n\n\n[1] Wang et al. OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling.  arXiv preprint. arXiv:2506.20512 2025"}]

Author rebuttal:

Meta-review: The paper introduces a synthetic benchmark combining many logic problems, finetunes LMs with RL on it, and show some cross-domain generalization to benchmarks such as LiveCodeBench. 

All reviewers agreed that the combination of the benchmark and RL training experiments make it a worthy contribution. A weakness is that cross-domain generalization is not strong and consistent across benchmarks, but paper contains an interesting idea that can be explored further. I recommend the authors to include the rebuttal extensions in the updated paper.
Decision: Accept (poster)