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.

Large Language Models (LLMs) have shown promising results across various tasks, yet their reasoning capabilities remain a fundamental challenge. Developing AI systems with strong reasoning capabilities is regarded as a crucial milestone in the pursuit of Artificial General Intelligence (AGI) and has garnered considerable attention from both academia and industry. Various techniques have been explored to enhance the reasoning capabilities of LLMs, with neuro-symbolic approaches being a particularly promising way. This paper comprehensively reviews recent developments in neuro-symbolic approaches for enhancing LLM reasoning. We first present a formalization of reasoning tasks and give a brief introduction to the neuro-symbolic learning paradigm. Then, we discuss neuro-symbolic methods for improving the reasoning capabilities of LLMs from three perspectives: Symbolic->LLM, LLM->Symbolic, and LLM+Symbolic. Finally, we discuss several key challenges and promising future directions. We have also released a GitHub repository including papers and resources related to this survey: https://github.com/LAMDASZ-ML/Awesome-LLM-Reasoning-with-NeSy.

Recent advancements in instruction tuning for large language models (LLMs) suggest that a small, high-quality dataset can significantly equip LLMs with instruction-following capabilities, outperforming large datasets often burdened by quality and redundancy issues. However, the challenge lies in automatically identifying valuable subsets from large datasets to boost both the effectiveness and efficiency of instruction tuning. In this paper, we first establish data selection criteria based on three distinct aspects of data value: diversity, difficulty, and dependability, and then propose the D3 method comprising two key steps of scoring and selection. Specifically, in the scoring step, we define the diversity function to measure sample distinctiveness and introduce the uncertainty-based prediction difficulty to evaluate sample difficulty by mitigating the interference of context-oriented generation diversity. Additionally, we integrate an external LLM for dependability assessment. In the selection step, we formulate the D3 weighted coreset objective, which jointly optimizes three aspects of data value to solve for the most valuable subset. The two steps of D3 can iterate multiple rounds, incorporating feedback to refine the selection focus adaptively. Experiments on both public datasets and the real-world Taobao Live application demonstrate the effectiveness of D3 in endowing LLMs with competitive or even superior instruction-following capabilities using less than 10% of the entire dataset.

Recent learning-to-imitation methods have shown promise in planning by imitating within the observation-action space, yet they remain constrained in open environments, especially for long-horizon tasks. In contrast, while traditional symbolic planning excels in such tasks through logical reasoning over human-defined symbolic spaces, it struggles with high-dimensional visual inputs encountered in real-world scenarios. In this work, we draw inspiration from abductive learning and introduce a novel framework ABductive Imitation Learning (ABIL) that integrates the benefits of data-driven learning and symbolic-based reasoning, enabling long-horizon planning. Specifically, we employ abductive reasoning to understand the demonstrations in symbolic space and design the principles of sequential consistency to resolve the conflicts between perception and reasoning. ABIL generates predicate candidates to facilitate the perception from raw observations to symbolic space without laborious predicate annotations, providing a groundwork for symbolic planning. With the symbolic understanding, we develop a policy ensemble with base policies designed around different logical objectives, managed through symbolic reasoning. Experiments demonstrate that our method successfully comprehends observations with task-relevant symbolics to aid imitation learning. Importantly, ABIL demonstrates improved data efficiency and generalization across various long-horizon tasks, highlighting it as a promising solution for long-horizon planning. Project website: https://www.lamda.nju.edu.cn/shaojj/KDD25_ABIL/.