Title: SynLogic: Synthesizing Verifiable Reasoning Data at Scale for Learning Logical Reasoning and Beyond
Venue: NeurIPS 2025
Accepted: yes
Keywords: LLM

reinforcement learning

reasoning

logical reasoning

data synthesis
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.

SynLogic: Synthesizing Verifiable Reasoning Data at Scale for Learning Logical Reasoning and Beyond

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 open-source both the data synthesis pipeline and the SYNLOGIC dataset in https://github.com/MiniMax-AI/SynLogic .

1 Introduction

The success of Deepseek R1 [DeepSeek-AI et al., 2025] and OpenAI-o1 [Jaech et al., 2024] demonstrates the great potential of post-training in 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 RL 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,a, Yu et al., 2025, Hu et al., 2025, Zhang et al., 2025]. To foster more general and comprehensive reasoning abilities, it is essential to utilize diverse tasks and examples with verifiable rewards. In this work, we concentrate on logical reasoning as a promising domain for this objective, hypothesizing that logical reasoning serves as a fundamental building block for developing general reasoning skills. Although prior work

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has explored RL training in the context of logic tasks [Xie et al., 2025b, Pan et al., 2025, 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.

Synthetic logic data presents distinct advantages and challenges. Its synthetic nature allows for unlimited data generation with controllable difficulty levels, enabling the creation of increasingly challenging 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-AI et 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, is 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 et al., 2022, Ma et 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: a 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-specific generation code paired with a corresponding rule-based verifier, allowing for fine-grained 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 et al., 2024] and implement binary outcome rewards determined by each task's verification rules. By adapting recent GRPO training techniques introduced in DAPO [Yu et al., 2025], we successfully train Qwen2.5 Base models [Yang et al., 2024] 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-Base and Qwen2.5-32BBase foundations, our models achieve over 8 absolute percentage points improvement on the logic benchmark KOR-Bench [Ma et al., 2024] compared to their instruction models. Notably, our 32B model surpasses DeepSeek-R1-Distill-Qwen-32B on BBEH [Kazemi et al., 2025] tasks by 5 absolute points, establishing SYNLOGIC as the state-of-the-art 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 OctoThinker-8B-Base [Wang et al., 2025], a LLaMA-v3.1-8B [AI@Meta, 2024] mid-trained model, observing similar success.

Furthermore, we explore mixing the SYNLOGIC data with mathematics or coding data for RL training. Surprisingly, conducting the mixed training on Qwen2.5-7B-Base model [Yang et al., 2024], incorporating SYNLOGIC data improves training efficiency for developing mathematical and coding skills. For mathematics, mixed training maintains similar mathematics performance under the same

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 Qwen2.5-32B-Base model to enhance the capability of Zero-RL training. Our mixed training achieves superior performance on multiple benchmarks compared to the DeepSeek-R1-Zero-Qwen-32B model, consistently outperforming or matching it on BBEH [Kazemi et al., 2025], KOR-Bench [Ma et al., 2024], LiveCodeBench [Jain et al., 2025], and GPQA-Diamond [Rein et al., 2024], validating the generalization benefits provided by the inclusion of logical reasoning data.

2 SYNLOGIC: Synthesizing Logical Reasoning Data at Scale

2.1 Background

Logical reasoning has long been a 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, as illustrated in Table 1, existing benchmarks either lack training support or are limited to a small 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 et al., 2025].

2.2 The Data Synthesis Framework

To synthesize large-scale, diverse synthetic data, we develop a comprehensive data synthesis framework encompassing 35 tasks. While the benchmarks in Table 1 include a wide variety of tasks, a significant challenge we 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, we develop these tasks independently, building the SYNLOGIC framework, illustrated in Figure 1. The framework consists of the following key components:

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, Li et al., 2024, Ma et al., 2024]. (2) Logic tasks featured in established evaluation benchmarks, including BBH [Suzgun et al., 2022] and BBEH [Kazemi et al., 2025]. Detailed descriptions and sources for all 35 tasks can be found in the Appendix A.1.

Parameter Identification For each task, we identify key parameters that control difficulty, such as grid size in Sudoku or the missing number ratio in 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.

Logic Instance Generation We formalize the task-specific rules into code by manually implementing 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., enforcing the unique digits rule in Sudoku). This rule-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.

Appropriate Difficulty Control To ensure that the generated data is both challenging and learnable, we carefully adjust difficulty-related parameters during data generation. We use strong reasoning models, DeepSeek R1 [DeepSeek-AI et al., 2025] and OpenAI-o3-mini to set an upper bound on difficulty: the highest difficulty parameters for which R1 or o3-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 Qwen2.532B-Instruct [Yang et al., 2024] to determine the lower bound of difficulty: the lowest difficulty parameters for which the models achieve a pass rate between 0 and 0.5. This dual-bound approach ensures that the dataset includes a balanced range of samples, maintaining an appropriate level of complexity and learnability.

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 7×7). 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 fixed-difficulty evaluation data, our system allows precise calibration of problem complexity through task-specific parameters, such as grid size in Sudoku. This difficulty-tuning 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]) are 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 to 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: SYNLOGIC-Hard for Qwen2.5-32B training and SYNLOGIC-Easy for Qwen2.5-7B and OctoThinker-8B [Wang et al., 2025] training. SYNLOGIC-Hard presents more complex challenges with its broader difficulty level

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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 are provided in Appendix A.2. Finally, we synthesized 33k SYNLOGIC-Hard samples and 16k SYNLOGIC-Easy samples used in subsequent experiments for training, along with 10 validation samples per task, 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@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.

3 Reinforcement Learning on SYNLOGIC

Reinforcement learning with verifiable rewards (RLVR) has emerged as a highly effective approach for enhancing reasoning capabilities in large language models [Zeng et al., 2025b, Yu et al., 2025, Hu et al., 2025, Zhang et al., 2025]. Building on 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, we validate the effectiveness of reinforcement learning training on the SYNLOGIC dataset using Qwen2.5-7B-Base, Qwen2.5-32B-Base, and OctoThinker-8B-Base, a LLaMA-v3.1-8B 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 3:

Reward Design Our reward function employs a binary scoring mechanism that evaluates both format adherence and answer correctness. Specifically, we assign a reward of 1 only when a modelgenerated 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 a reward of 0.

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, i.e., <think> reasoning process here </think> <answer> answer here</answer>.

Table 2: Evaluation accuracy (%) of 7B, 32B and 8B models across logic benchmarks (SYNLOGICVal, KOR-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, it refers to SYNLOGIC-Hard as described in § 2.3. All evaluations were conducted under zero-shot conditions, with SYNLOGIC-Val and AIME 2024 reported as avg@8 to reduce variance.

where format ( o i ) evaluates whether response o i includes both the required <think> </think> and <answer> </answer> tags, and correct ( o i ) determines whether the answer provided is correct verified by its task's verification rule.

Training Details For our experiments, we synthesized approximately 16k SYNLOGIC-Easy and 33k SYNLOGIC-Hard instances to train the Qwen2.5-7B-Base, OctoThinker-8B-Base, and Qwen2.532B-Base models with DAPO, respectively, as described in §2.3. During training, we employed a prompt batch size of 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 ϵ high at 0.28. Additional training hyperparameters and implementation details are provided in Appendix B.1.2.

Evaluation Details Our evaluation strategy encompasses two distinct benchmark categories. For assessing logical reasoning capabilities, we employ the validation splits of SYNLOGIC alongside established benchmarks including Knowledge-Orthogonal Reasoning (KOR-Bench) [Ma et al., 2024], BBH [Suzgun et al., 2022], and the substantially more challenging BBEH [Kazemi et al., 2025]. 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 a zero-shot setting, with avg@8 metrics computed for AIME 2024 and SYNLOGIC-Val to mitigate variance.

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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-art results among open-source datasets. Our 7B model achieves 48.1% on KOR-Bench [Ma et al., 2024], outperforming Qwen2.5-7B-Instruct by nearly 10 absolute percentage points. Similarly, our 32B model surpasses Qwen2.5-32B-Instruct by 7 percentage points on KOR-Bench. Notably, our 32B model exceeds R1-Distill-Qwen32B [DeepSeekAI et al., 2025] by 6 percentage points on the challenging BBEH benchmark [Kazemi et al., 2025], showcasing the effectiveness of the SYNLOGIC dataset in driving state-of-the-art logical reasoning performance. Beyond the Qwen family, our substantial improvements on the 8B model also validate the effectiveness of our method on LLaMA base models.

Generalization to Mathematical Domains Our experimental results demonstrate significant generalization capabilities to mathematical domains, as shown in Table 2. Despite being primarily trained for logical reasoning, SYNLOGIC models exhibit strong performance across mathematical benchmarks over their base models. SYNLOGIC-7B achieves 10.0% on AIME 2024, a nearly 10 absolute point improvement compared to Qwen2.5-7B-Base (0.3%), 71.8% on MATH 500, a 7.2 absolute point gain, and 55.0% on AMC 2023, a 25-point increase. More remarkably, SYNLOGIC32B achieves 19.6% on AIME 2024, a 4.4x improvement over Qwen2.5-32B-Base (4.5%), while its performance on MATH 500 (82.0%) and AMC 2023 (57.5%) shows substantial gains of 13.4 and 12.5 points, respectively. Similarly, SYNLOGIC-8B exhibits strong mathematical capabilities, achieving 14.5% on AIME 2024, with 11.2 absolute improvement. Without mathematics training data, our models nearly match or surpass the instruction models, suggesting that enhancements in logical reasoning capabilities transfer effectively to mathematical problem-solving. This aligns with the observation in Logic-RL [Xie et al., 2025b], highlighting the fundamental connection between logical and mathematical reasoning skills.

Increased Chain-of-Thought Length As shown in Figure 4, 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 of LLM. Detailed training accuracy results are provided in Appendix B.1.3.

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4 Scaling RL Training with Diverse Verifiable Reasoning Data

Having verified the success of reinforcement training on SYNLOGIC alone, we now leverage verifiable reasoning data from math, coding, and logical reasoning domains, scaling RL training with diverse verifiable reasoning data. Concretely, we mix SYNLOGIC with mathematical or/and coding training 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.

4.1 Setup Details

For mathematical training data, we directly utilize the 17k samples provided in DAPO [Yu et al., 2025]. For coding data, we 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 are presented in Appendix B.1. We maintained the same reward design approach as described in §3.1. Specifically, for coding tasks, the reward is set as 1 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-Easy and combine them with 17k math data for training on the Qwen2.5-7B-Base model. For controlled comparison, we also conduct reinforcement learning using exclusively math data. Both experimental

configurations maintain identical hyperparameters, optimization settings, and computational resources to ensure fair evaluation. Figure 5 presents a comparison of training dynamics. Running for the same number of training steps, mixed training (Logic+Math) achieves comparable performance to math-only training on 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, as 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 a similar methodology, we sample approximately 9k samples from SYNLOGIC-Easy and combine them with 9K code samples to train the Qwen2.5-7BBase model. As a control, we 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 report [DeepSeek-AI et al., 2025]) for evaluation. As shown in Figure 6, we observe a similar phenomenon of more efficient training dynamics when mixing code with SYNLOGIC-Easy. Models trained on Logic+Coding data achieve higher performance 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-specific capabilities.

4.3 32B Zero-RL 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 RL training on the Qwen2.5-32B-Base model. Specifically, we use a mix of 35k mathematical samples, 9k coding samples, and 17k SYNLOGIC samples for training. We term this training configuration as Zero-Mix-3 . We additionally conduct a Zero-Mix-2 setting that only mixes coding and mathematical data, serving as an ablation baseline to study the effect of SYNLOGIC in such a scalable setting. Related to our Zero-Mix-2 setup, Zhang et al. [2025] recently demonstrated that combining mathematical data with coding data is able to facilitate coding learning. Here we further scale up this trend by including our proposed SYNLOGIC dataset. To evaluate generalization, we include an out-of-domain benchmark, GPQA Diamond [Rein et al., 2024], to study how the addition of SYNLOGIC impacts broader reasoning capabilities. Both Zero-Mix-3 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 3, the Zero-RL training in Zero-Mix-3 (SYNLOGIC+Math+Coding) achieves superior performance across multiple evaluations. On logic benchmarks, Zero-Mix-3 nearly matches the performance of DeepSeek-R1-Distill-Qwen-32B on KOR-Bench and surpasses it by 8 points on BBEH. Notably, Zero-Mix-3 also matches DeepSeek-R1-Zero-Qwen-32B on the coding benchmark LiveCodeBench [Jain et al., 2025] and outperforms it on GPQA-Diamond. Compared to the Zero-Mix-2 (Math+Coding) experiment, Zero-Mix-3 consistently delivers higher performance

across all benchmarks. Specifically, Zero-Mix-3 shows a significant improvement of over 10 points on BBEH, 6 points on KOR-Bench, and over 2 points on the out-of-domain benchmark GPQA Diamond. These results strongly validate the significant generalization benefits provided by the inclusion of SYNLOGIC.

5 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 KOR-Bench and strong generalization to unseen mathematical tasks. Notably, our 32B model outperformed DeepSeek-R1-Distill-Qwen-32B 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 LLMs. Both of these directions are left as opportunities for future exploration.

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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 et al., 2024], BBH [Suzgun et al., 2022], and BBEH [Kazemi et al., 2025]. Additionally, we integrated some logical reasoning tasks not previously featured in these benchmarks, such as Mathador [Kurtic et al., 2024] and Minesweeper [Li et al., 2024].

Our collection comprises 35 distinct tasks, with only two (Zebra Puzzle [Lin et al., 2024] and ARCAGI [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.

A.2 SYNLOGIC-Hard and SYNLOGIC-Easy

The SYNLOGIC-Hard dataset encompasses all 35 tasks, representing a challenging upper bound calibrated to the solvability thresholds of DeepSeek R1 and OpenAI-o3-mini. 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 Qwen2.5-7BBase. 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-Easy, a modified variant that excludes these particularly challenging tasks, to provide a more appropriate training dataset for the Qwen2.5-7B-Base model.

B Training and Evaluation Details

B.1 Training

B.1.1 Training Template

We provide the training template for math and coding here in Figure 7 and Figure 8.

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.\nThe reasoning process and answer are enclosed within '<think>' '</think>' and '<answer>' '</answer>' tags, respectively, e.g.,\n<think>\nA detailed reasoning process here, with possible reflections including but not limited to reviewing previous steps for errors, exploring alternative approaches, and considering possible refinements.\n</think>\n<answer>\nReply to user here.\n</answer>. Please reason step by step, and put your final answer within \boxed{}.

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.\nThe reasoning process and answer are enclosed within '<think>' '</think>' and '<answer>' '</answer>' tags, respectively, e.g.,\n<think>\nA detailed reasoning process here, with possible reflections including but not limited to reviewing previous steps for errors, exploring alternative approaches, and considering possible refinements.\n</think>\n<answer>\nReply to user here.\n</answer>. Please put your final code following this format:\n''[language]\n#your code here \n''.

B.1.2 Training hyper-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 hyper-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 §4, we adopted the following 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.

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B.3 Performance Analysis of Mixed Training with Coding

We also provide the training dynamics when mixed training with coding data in Figure 11. The observation is similar to mixed training with math, suggesting that mixed training leads to more efficient training dynamics.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\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.\n\nQUESTIONS:\n1. 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.\n\nLIMITATIONS:\nThe 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.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-20"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\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.\n\nQUESTIONS:\n1. 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.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\n## 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.\n\nQUESTIONS:\nSee weakness for concerns.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\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.\n\nQUESTIONS:\n- 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.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-05"}