Multi-turn instruction following is essential for building intelligent conversational systems that can consistently adhere to instructions across dialogue turns. However, existing approaches to enhancing multi-turn instruction following primarily rely on collecting or generating large-scale multi-turn dialogue datasets to fine-tune large language models (LLMs), which treat each response generation as an isolated task and fail to explicitly incorporate multi-turn instruction following into the optimization objectives. As a result, instruction-tuned LLMs often struggle with complex long-distance constraints. In multi-turn dialogues, relational constraints across turns can be naturally modeled as labeled directed edges, making graph structures particularly suitable for modeling multi-turn instruction following. Despite this potential, leveraging graph structures to enhance the multi-turn instruction following capabilities of LLMs remains unexplored. To bridge this gap, we propose GraphIF, a plug-and-play framework that models multi-turn dialogues as directed relation graphs and leverages graph prompts to enhance the instruction following capabilities of LLMs. GraphIF comprises three key components: (1) an agent-based relation extraction module that captures inter-turn semantic relations via action-triggered mechanisms to construct structured graphs; (2) a relation graph prompt generation module that converts structured graph information into natural language prompts; and (3) a response rewriting module that refines initial LLM outputs using the generated graph prompts. Extensive experiments on two long multi-turn dialogue datasets demonstrate that GraphIF can be seamlessly integrated into instruction-tuned LLMs and leads to significant improvements across all four multi-turn instruction-following evaluation metrics.

Recent advancements in neural theorem proving integrate large language models with tree search algorithms like Monte Carlo Tree Search (MCTS), where the language model suggests tactics and the tree search finds the complete proof path. However, many tactics proposed by the language model converge to semantically or strategically similar, reducing diversity and increasing search costs by expanding redundant proof paths. This issue exacerbates as computation scales and more tactics are explored per state. Furthermore, the trained value function suffers from false negatives, label imbalance, and domain gaps due to biased data construction. To address these challenges, we propose CARTS (diversified tactic CAlibration and bias-Resistant Tree Search), which balances tactic diversity and importance while calibrating model confidence. CARTS also introduce preference modeling and an adjustment term related to the ratio of valid tactics to improve the bias-resistance of the value function. Experimental results demonstrate that CARTS consistently outperforms previous methods achieving a pass@l rate of 49.6\% on the miniF2F-test benchmark. Further analysis confirms that CARTS improves tactic diversity and leads to a more balanced tree search.

Abductive Learning (ABL), a prominent neural-symbolic learning algorithm, integrates perception models with logical reasoning via intermediate symbolic concepts, substantially improving the interpretability and generalization of AI systems. However, a significant challenge in this domain is the issue of reasoning shortcuts, where the system achieve high final prediction accuracy but generate incorrect intermediate concept inferences, severely undermining ABL’s interpretability and generalization capabilities. Current mitigation methods to this problem often neglect potential correlations among training samples, leading to suboptimal performances. This paper innovatively reveals that simple samples can facilitate the learning of intermediate concepts in complex samples, prompting our proposed method Curriculum Abductive Learning (CurABL) technique. This approach employs a curriculum training strategy, integrating a knowledge transfer mechanism from simple to complex samples, effectively addressing the issue of reasoning shortcuts. Comprehensive experimental results demonstrate that the CurABL method substantially improves the ABL framework’s capability to extract intermediate concepts especially in difficult tasks and accelerates the training convergence rate, thus markedly enhancing its robustness against reasoning shortcuts.