LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this question in context of mathematical inequalities -- specifically the prover's ability to recognize that the given problem simplifies by applying a known inequality such as AM/GM. Specifically, we are interested in their ability to do this in a compositional setting where multiple inequalities must be applied as part of a solution. We introduce Ineq-Comp, a benchmark built from elementary inequalities through systematic transformations, including variable duplication, algebraic rewriting, and multi-step composition. Although these problems remain easy for humans, we find that most provers -- including Goedel, STP, and Kimina-7B -- struggle significantly. DeepSeek-Prover-V2-7B shows relative robustness, but still suffers a 20% performance drop (pass@32). Even for DeepSeek-Prover-V2-671B model, the gap between compositional variants and seed problems exists, implying that simply scaling up the model size alone does not fully solve the compositional weakness. Strikingly, performance remains poor for all models even when formal proofs of the constituent parts are provided in context, revealing that the source of weakness is indeed in compositional reasoning. Our results expose a persisting gap between the generalization behavior of current AI provers and human mathematical intuition. All data and evaluation code can be found at https://github.com/haoyuzhao123/LeanIneqComp.

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of candidates, this method incurs prohibitive computational costs, limiting its practicality. In this work, we shift the focus to a more budget-aware paradigm: discriminative verification. We conduct a thorough empirical analysis and demonstrate that while discriminative verifiers may underperform in isolation, combining them with self-consistency in a hybrid approach creates a powerful and efficient test-time scaling mechanism. Notably, under a fixed compute budget, this hybrid approach surpasses state-of-the-art generative verification by a significant margin: achieving up to 15.3\% higher accuracy on AIME2025. Our findings establish that for practical, real-world applications, budget-aware scaling with discriminative verifiers is not only a "free" upgrade over self-consistency, but also a more effective and efficient alternative to costly generative techniques. Code is available at https://github.com/wang-research-lab/verification.

Recently, the development of large language models (LLMs) and reasoning large language models (RLLMs) have gained considerable attention from many researchers. RLLMs enhance the reasoning capabilities of LLMs through Long Chain-of-Thought (Long CoT) processes, significantly improving the performance of LLMs in addressing complex problems. However, there are few works that systematically explore what methods can fully unlock the performance of LLMs and RLLMs within the financial domain. To investigate the impact of various methods on LLMs and RLLMs, we utilize five LLMs and three RLLMs to assess the effects of prompting methods, agentic frameworks, and multilingual alignment methods on financial question-answering tasks. Our research findings indicate: (1) Current prompting methods and agent frameworks enhance the performance of LLMs in financial question answering by simulating Long CoT; (2) RLLMs possess inherent Long CoT capabilities, which limits the effectiveness of conventional methods in further enhancing their performance; (3) Current advanced multilingual alignment methods primarily improve the multilingual performance of LLMs by extending the reasoning length, which yields minimal benefits for RLLMs. Additionally, we discuss strategies for enhancing the performance of LLMs and RLLMs in financial question answering, which may serve as a inspiration for future improvements. We hope that this study can serve as an important reference for LLMs and RLLMs in the field of financial question answering. Recently, large language models (LLMs) have significantly advanced the field of natural language processing (NLP), and more and more researchers utilize LLMs to solve complex tasks in various domains (Zhou et al., 2023; Nie et al., 2024; Qin et al., 2024; Chang et al., 2024; Wang et al., 2025a).

Current Large Language Models (LLMs) are usually post-trained on large-scale carefully curated datasets (data & training scaling) and doing reasoning in test time (inference time scaling). In this work, we present a new scaling paradigm, Input-Time Scaling, to complement previous scaling methods by putting resources on queries (input time). During training and testing, we utilize meta-knowledge from LLMs to refine inputs with different strategies. We also discover a new phenomenon, train-test co-design. It requires us to apply query strategies during training and testing as a whole. Only applying strategies on training or testing would seriously degrade the performance gained. We are also surprised to find that seemingly low data quality datasets can perform better. We can get the best performance even by adding irrelevant information to the queries, with randomly selected 1k examples from a minimally filtered dataset. These findings contradict the widely held inductive bias, "garbage in, garbage out". Curating datasets with seemingly high-quality data can even potentially limit the performance ceiling. In addition, models trained on more data with similar quality (15k VS 1k) perform worse, the intuition of simply scaling the size should also be carefully inspected. The good news is that our findings are compatible with the Less is More phenomenon. 1K examples are enough to invoke high-level reasoning ability. With experiments on Qwen2.5-32B-Instruct, we are able to reach SOTA performance among 32B models on AIME24(76.7%) and AIME25(76.7%) pass@1. We can further achieve AIME24(76.7%) and AIME25(80%) with a majority vote of three models. Starting from DeepSeek-R1-Distill-Qwen-32B, the result would be 90.0% on AIME24 and 80.0% on AIME25. To facilitate reproducibility and further research, we are working on open-source our datasets, data pipelines, evaluation results, and checkpoints.

Reasoning Large Language Models (RLLMs) have demonstrated impressive performance on complex tasks, largely due to the adoption of Long Chain-of-Thought (Long CoT) reasoning. However, they often exhibit overthinking -- performing unnecessary reasoning steps even after arriving at the correct answer. Prior work has largely focused on qualitative analyses of overthinking through sample-based observations of long CoTs. In contrast, we present a quantitative analysis of overthinking from the perspective of self-doubt, characterized by excessive token usage devoted to re-verifying already-correct answer. We find that self-doubt significantly contributes to overthinking. In response, we introduce a simple and effective prompting method to reduce the model's over-reliance on input questions, thereby avoiding self-doubt. Specifically, we first prompt the model to question the validity of the input question, and then respond concisely based on the outcome of that evaluation. Experiments on three mathematical reasoning tasks and four datasets with missing premises demonstrate that our method substantially reduces answer length and yields significant improvements across nearly all datasets upon 4 widely-used RLLMs. Further analysis demonstrates that our method effectively minimizes the number of reasoning steps and reduces self-doubt.

LLM-based multi-agent systems (MAS) extend the capabilities of single LLMs by enabling cooperation among multiple specialized agents. However, most existing MAS frameworks rely on a single LLM to drive all agents, constraining the system's intelligence to the limit of that model. This paper explores the paradigm of heterogeneous LLM-driven MAS (X-MAS), where agents are powered by diverse LLMs, elevating the system's potential to the collective intelligence of diverse LLMs. We introduce X-MAS-Bench, a comprehensive testbed designed to evaluate the performance of various LLMs across different domains and MAS-related functions. As an extensive empirical study, we assess 27 LLMs across 5 domains (encompassing 21 test sets) and 5 functions, conducting over 1.7 million evaluations to identify optimal model selections for each domain-function combination. Building on these findings, we demonstrate that transitioning from homogeneous to heterogeneous LLM-driven MAS can significantly enhance system performance without requiring structural redesign. Specifically, in a chatbot-only MAS scenario, the heterogeneous configuration yields up to 8.4\% performance improvement on the MATH dataset. In a mixed chatbot-reasoner scenario, the heterogeneous MAS could achieve a remarkable 47\% performance boost on the AIME dataset. Our results underscore the transformative potential of heterogeneous LLMs in MAS, highlighting a promising avenue for advancing scalable, collaborative AI systems.

The challenge of slang translation lies in capturing context-dependent semantic extensions, as slang terms often convey meanings beyond their literal interpretation. While slang detection, explanation, and translation have been studied as isolated tasks in the era of large language models (LLMs), their intrinsic interdependence remains underexplored. The main reason is lacking of a benchmark where the two tasks can be a prerequisite for the third one, which can facilitate idiomatic translation. In this paper, we introduce the interpretative slang translation task (named SlangDIT) consisting of three sub-tasks: slang detection, cross-lingual slang explanation, and slang translation within the current context, aiming to generate more accurate translation with the help of slang detection and slang explanation. To this end, we construct a SlangDIT dataset, containing over 25k English-Chinese sentence pairs. Each source sentence mentions at least one slang term and is labeled with corresponding cross-lingual slang explanation. Based on the benchmark, we propose a deep thinking model, named SlangOWL. It firstly identifies whether the sentence contains a slang, and then judges whether the slang is polysemous and analyze its possible meaning. Further, the SlangOWL provides the best explanation of the slang term targeting on the current context. Finally, according to the whole thought, the SlangOWL offers a suitable translation. Our experiments on LLMs (\emph{e.g.}, Qwen2.5 and LLama-3.1), show that our deep thinking approach indeed enhances the performance of LLMs where the proposed SLangOWL significantly surpasses the vanilla models and supervised fine-tuned models without thinking.

The challenge of reducing the size of Large Language Models (LLMs) while maintaining their performance has gained significant attention. However, existing methods, such as model distillation and transfer learning, often fail to achieve high accuracy. To address this limitation, we introduce the Branch-Merge distillation approach, which enhances model compression through two phases: (1) the Branch Phase, where knowledge from a large teacher model is \textit{selectively distilled} into specialized student models via domain-specific supervised fine-tuning (SFT); And (2) the Merge Phase, where these student models are merged to enable cross-domain knowledge transfer and improve generalization. We validate our distillation approach using DeepSeek-R1 as the teacher and DeepSeek-R1-Distill-Qwen-32B as the student. The resulting merged model, TinyR1-32B-Preview, outperforms its counterpart DeepSeek-R1-Distill-Qwen-32B across multiple benchmarks, including Mathematics (+5.5 points), Coding (+4.4 points) and Science (+2.9 points), while achieving near-equal performance to DeepSeek-R1 on AIME 2024. The Branch-Merge distillation approach provides a scalable solution for creating smaller, high-performing LLMs with reduced computational cost and time.

Recent advancements in slow-thinking reasoning models have shown exceptional performance in complex reasoning tasks. However, these models often exhibit overthinking-generating redundant reasoning steps for simple problems, leading to excessive computational resource usage. While current mitigation strategies uniformly reduce reasoning tokens, they risk degrading performance on challenging tasks that require extended reasoning. This paper introduces Difficulty-Adaptive Slow-Thinking (DAST), a novel framework that enables models to autonomously adjust the length of Chain-of-Thought(CoT) based on problem difficulty. We first propose a Token Length Budget (TLB) metric to quantify difficulty, then leveraging length-aware reward shaping and length preference optimization to implement DAST. DAST penalizes overlong responses for simple tasks while incentivizing sufficient reasoning for complex problems. Experiments on diverse datasets and model scales demonstrate that DAST effectively mitigates overthinking (reducing token usage by over 30\% on average) while preserving reasoning accuracy on complex problems.

In the recent development of AI reasoning, large language models (LLMs) are trained to automatically generate chain-of-thought reasoning steps, which have demonstrated compelling performance on math and coding tasks. However, when bias is mixed within the reasoning process to form strong logical arguments, it could cause even more harmful results and further induce hallucinations. In this paper, we have evaluated the 8B and 32B variants of DeepSeek-R1 against their instruction tuned counterparts on the BBQ dataset, and investigated the bias that is elicited out and being amplified through reasoning steps. To the best of our knowledge, this empirical study is the first to assess bias issues in LLM reasoning.