Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Large Language Models (LLMs), such as OpenAI's o1 and DeepSeek's R1, excel at advanced reasoning tasks like math and coding via Reinforcement Learning with Verifiable Rewards (RLVR), but still struggle with puzzles solvable by humans without domain knowledge. We introduce Enigmata, the first comprehensive suite tailored for improving LLMs with puzzle reasoning skills. It includes 36 tasks across seven categories, each with 1) a generator that produces unlimited examples with controllable difficulty and 2) a rule-based verifier for automatic evaluation. This generator-verifier design supports scalable, multi-task RL training, fine-grained analysis, and seamless RLVR integration. We further propose Enigmata-Eval, a rigorous benchmark, and develop optimized multi-task RLVR strategies. Our trained model, Qwen2.5-32B-Enigmata, consistently surpasses o3-mini-high and o1 on the puzzle reasoning benchmarks like Enigmata-Eval, ARC-AGI (32.8%), and ARC-AGI 2 (0.6%). It also generalizes well to out-of-domain puzzle benchmarks and mathematical reasoning, with little multi-tasking trade-off. When trained on larger models like Seed1.5-Thinking (20B activated parameters and 200B total parameters), puzzle data from Enigmata further boosts SoTA performance on advanced math and STEM reasoning tasks such as AIME (2024-2025), BeyondAIME and GPQA (Diamond), showing nice generalization benefits of Enigmata. This work offers a unified, controllable framework for advancing logical reasoning in LLMs. Resources of this work can be found at https://seed-enigmata.github.io.

KORGym: A Dynamic Game Platform for LLM Reasoning Evaluation

Recent advancements in large language models (LLMs) underscore the need for more comprehensive evaluation methods to accurately assess their reasoning capabilities. Existing benchmarks are often domain-specific and thus cannot fully capture an LLM's general reasoning potential. To address this limitation, we introduce the Knowledge Orthogonal Reasoning Gymnasium (KORGym), a dynamic evaluation platform inspired by KOR-Bench and Gymnasium. KORGym offers over fifty games in either textual or visual formats and supports interactive, multi-turn assessments with reinforcement learning scenarios. Using KORGym, we conduct extensive experiments on 19 LLMs and 8 VLMs, revealing consistent reasoning patterns within model families and demonstrating the superior performance of closed-source models. Further analysis examines the effects of modality, reasoning strategies, reinforcement learning techniques, and response length on model performance. We expect KORGym to become a valuable resource for advancing LLM reasoning research and developing evaluation methodologies suited to complex, interactive environments.

Order Doesn't Matter, But Reasoning Does: Training LLMs with Order-Centric Augmentation

Logical reasoning is essential for large language models (LLMs) to ensure accurate and coherent inference. However, LLMs struggle with reasoning order variations and fail to generalize across logically equivalent transformations. LLMs often rely on fixed sequential patterns rather than true logical understanding. To address this issue, we introduce an order-centric data augmentation framework based on commutativity in logical reasoning. We first randomly shuffle independent premises to introduce condition order augmentation. For reasoning steps, we construct a directed acyclic graph (DAG) to model dependencies between steps, which allows us to identify valid reorderings of steps while preserving logical correctness. By leveraging order-centric augmentations, models can develop a more flexible and generalized reasoning process. Finally, we conduct extensive experiments across multiple logical reasoning benchmarks, demonstrating that our method significantly enhances LLMs' reasoning performance and adaptability to diverse logical structures. We release our codes and augmented data in https://anonymous.4open.science/r/Order-Centric-Data-Augmentation-822C/.

Order Matters: Investigate the Position Bias in Multi-constraint Instruction Following

Real-world instructions with multiple constraints pose a significant challenge to existing large language models (LLMs). An observation is that the LLMs exhibit dramatic performance fluctuation when disturbing the order of the incorporated constraints. Yet, none of the existing works has systematically investigated this position bias problem in the field of multi-constraint instruction following. To bridge this gap, we design a probing task where we quantitatively measure the difficulty distribution of the constraints by a novel Difficulty Distribution Index (CDDI). Through the experimental results, we find that LLMs are more performant when presented with the constraints in a ``hard-to-easy'' order. This preference can be generalized to LLMs with different architecture or different sizes of parameters. Additionally, we conduct an explanation study, providing an intuitive insight into the correlation between the LLM's attention and constraint orders. Our code and dataset are publicly available at https://github.com/meowpass/PBIF.

Application of machine learning algorithm in temperature field reconstruction

This study focuses on the stratification patterns and dynamic evolution of reservoir water temperatures, aiming to estimate and reconstruct the temperature field using limited and noisy local measurement data. Due to complex measurement environments and technical limitations, obtaining complete temperature information for reservoirs is highly challenging. Therefore, accurately reconstructing the temperature field from a small number of local data points has become a critical scientific issue. To address this, the study employs Proper Orthogonal Decomposition (POD) and sparse representation methods to reconstruct the temperature field based on temperature data from a limited number of local measurement points. The results indicate that satisfactory reconstruction can be achieved when the number of POD basis functions is set to 2 and the number of measurement points is 10. Under different water intake depths, the reconstruction errors of both POD and sparse representation methods remain stable at around 0.15, fully validating the effectiveness of these methods in reconstructing the temperature field based on limited local temperature data. Additionally, the study further explores the distribution characteristics of reconstruction errors for POD and sparse representation methods under different water level intervals, analyzing the optimal measurement point layout scheme and potential limitations of the reconstruction methods in this case. This research not only effectively reduces measurement costs and computational resource consumption but also provides a new technical approach for reservoir temperature analysis, holding significant theoretical and practical importance.

Step-by-Step Mastery: Enhancing Soft Constraint Following Ability of Large Language Models

It is crucial for large language models (LLMs) to follow instructions that involve multiple constraints. However, soft constraints are semantically related and difficult to verify through automated methods. These constraints remain a significant challenge for LLMs. To enhance the ability of LLMs to follow soft constraints, we initially design a pipeline to obtain high-quality outputs automatically. Additionally, to fully utilize the acquired data, we introduce a training paradigm based on curriculum learning. We experimentally evaluate the effectiveness of our methods in improving LLMs' soft constraint following ability and analyze the factors driving the improvements. The datasets and code are publicly available at https://github.com/Rainier-rq/FollowSoftConstraints.

QUILL: Quotation Generation Enhancement of Large Language Models

While Large language models (LLMs) have become excellent writing assistants, they still struggle with quotation generation. This is because they either hallucinate when providing factual quotations or fail to provide quotes that exceed human expectations. To bridge the gap, we systematically study how to evaluate and improve LLMs' performance in quotation generation tasks. We first establish a holistic and automatic evaluation system for quotation generation task, which consists of five criteria each with corresponding automatic metric. To improve the LLMs' quotation generation abilities, we construct a bilingual knowledge base that is broad in scope and rich in dimensions, containing up to 32,022 quotes. Moreover, guided by our critiria, we further design a quotation-specific metric to rerank the retrieved quotations from the knowledge base. Extensive experiments show that our metrics strongly correlate with human preferences. Existing LLMs struggle to generate desired quotes, but our quotation knowledge base and reranking metric help narrow this gap. Our dataset and code are publicly available at https://github.com/GraceXiaoo/QUILL.

Think Thrice Before You Act: Progressive Thought Refinement in Large Language Models

Recent advancements in large language models (LLMs) have demonstrated that progressive refinement, rather than providing a single answer, results in more accurate and thoughtful outputs. However, existing methods often rely heavily on supervision signals to evaluate previous responses, making it difficult to assess output quality in more open-ended scenarios effectively. Additionally, these methods are typically designed for specific tasks, which limits their generalization to new domains. To address these limitations, we propose Progressive Thought Refinement (PTR), a framework that enables LLMs to refine their responses progressively. PTR operates in two phases: (1) Thought data construction stage: We propose a weak and strong model collaborative selection strategy to build a high-quality progressive refinement dataset to ensure logical consistency from thought to answers, and the answers are gradually refined in each round. (2) Thought-Mask Fine-Tuning Phase: We design a training structure to mask the "thought" and adjust loss weights to encourage LLMs to refine prior thought, teaching them to implicitly understand "how to improve" rather than "what is correct." Experimental results show that PTR significantly enhances LLM performance across ten diverse tasks (avg. from 49.6% to 53.5%) without task-specific fine-tuning. Notably, in more open-ended tasks, LLMs also demonstrate substantial improvements in the quality of responses beyond mere accuracy, suggesting that PTR truly teaches LLMs to self-improve over time.

Light Up the Shadows: Enhance Long-Tailed Entity Grounding with Concept-Guided Vision-Language Models

Multi-Modal Knowledge Graphs (MMKGs) have proven valuable for various downstream tasks. However, scaling them up is challenging because building large-scale MMKGs often introduces mismatched images (i.e., noise). Most entities in KGs belong to the long tail, meaning there are few images of them available online. This scarcity makes it difficult to determine whether a found image matches the entity. To address this, we draw on the Triangle of Reference Theory and suggest enhancing vision-language models with concept guidance. Specifically, we introduce COG, a two-stage framework with COncept-Guided vision-language models. The framework comprises a Concept Integration module, which effectively identifies image-text pairs of long-tailed entities, and an Evidence Fusion module, which offers explainability and enables human verification. To demonstrate the effectiveness of COG, we create a dataset of 25k image-text pairs of long-tailed entities. Our comprehensive experiments show that COG not only improves the accuracy of recognizing long-tailed image-text pairs compared to baselines but also offers flexibility and explainability.

From Complex to Simple: Enhancing Multi-Constraint Complex Instruction Following Ability of Large Language Models

It is imperative for Large language models (LLMs) to follow instructions with elaborate requirements (i.e. Complex Instructions Following). Yet, it remains under-explored how to enhance the ability of LLMs to follow complex instructions with multiple constraints. To bridge the gap, we initially study what training data is effective in enhancing complex constraints following abilities. We found that training LLMs with instructions containing multiple constraints enhances their understanding of complex instructions, especially those with lower complexity levels. The improvement can even generalize to compositions of out-of-domain constraints. Additionally, we further propose methods addressing how to obtain and utilize the effective training data. Finally, we conduct extensive experiments to prove the effectiveness of our methods in terms of overall performance, training efficiency, and generalization abilities under four settings.