Graph database systems play a vital role in graph structure analysis across a wide range of application domains. Queries with set-level constraints on community structures are increasingly demanded in real-world applications. However, existing graph databases lack native support for both efficient monadic second-order logic (MSOL) query processing and fast community retrieval, hindering their applicability to such analytical tasks. In this paper, we present Monac- Graph, a graph database system that enables practical MSOL queries. MonacGraph features an efficient two-phase execution engine that minimizes redundant first-order clause evaluations. We propose SO-Gremlin, an extension of the Gremlin graph traversal language with intuitive syntax for set quantification. The system adopts LSM-Community as its storage backend, enabling efficient queries over precomputed graph structures. Additionally, MonacGraph provides a user-friendlyWeb interface for composing complex set-level queries and visualizing results in real time. A demonstration video can be found at https://www.youtube.com/watch?v=Eezdq9tzbJE.
Reinforcement learning from verifiable rewards (RLVR) drives chain-of-thought reasoning in large language models, yet its binary outcome reward cannot distinguish among correct trajectories. Existing dense reward alternatives, from surface heuristics to process reward models, either ignore the expert solutions already present in training corpora or require expensive offline annotation. We propose Gradient-Aligned Reward (GAR), which operates in the policy's own gradient space: truncated backpropagation through the output projection layer extracts a compact gradient vector for each rollout, and cosine similarity with an expert-anchor gradient yields a dense, reasoning-aware reward with less than 9% wall-clock overhead. We prove that this cosine admits a multiplicative decomposition into prediction-error and activation-pattern factors, providing a concrete characterization of what the alignment signal measures. On Qwen3-4B and Qwen3-8B, GAR consistently improves over GRPO and other baselines on competition-level math benchmarks and transfers to GPQA Diamond and MMLU-Pro without domain-specific data. Code and data are available at https://github.com/LQgdwind/GAR.
Le-Qi Zheng, Jin-Bo Su, Fang Niu et al.· 2 citations
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