Jinhao Liu

Dengyun Peng, Qiguang Chen, Bofei Liu et al.

Ensuring LLM reliability requires not only solving complex problems but also recognizing when a problem is unsolvable. Current models often struggle to distinguish objective unsolvability (inherent contradictions in the problem) from subjective capability limitations (problems beyond the model's competence), which leads to hallucinations and overconfidence. To address this, we propose UnsolvableQA and UnsolvableRL to solve feasible problems, detect inherent contradictions, and prudently refuse tasks beyond capability. Specifically, we construct UnsolvableQA, a dataset of paired solvable and unsolvable instances derived via a dual-track methodology: programmatic generation for logic puzzles and a novel "Reverse Construction" method that injects contradictions into valid reasoning chains for mathematics. Building on this dataset, we introduce UnsolvableRL, a reinforcement learning framework with three reward components jointly accounting for accuracy, unsolvability, and difficulty. Empirical results show that our approach achieves near-perfect unsolvability detection while also improving accuracy on solvable tasks. Crucially, we identify Capability Collapse, demonstrating that explicit exposure to unsolvable data is indispensable for preventing models from becoming systematically overconfident. Our code and data are available at https://github.com/sfasfaffa/unsolvableQA.

Jiannan Guan, Qiguang Chen, Libo Qin et al.

Large Language Models (LLMs) excel in reasoning tasks requiring a single correct answer, but they perform poorly in multi-solution tasks that require generating comprehensive and diverse answers. We attribute this limitation to \textbf{reasoning overconfidence}: a tendency to express undue certainty in an incomplete solution set. To examine the effect, we introduce \textit{MuSoBench}, a benchmark of multi-solution problems. Experiments show that the conventional short chain-of-thought (Short-CoT) prompting paradigm exhibits pronounced overconfidence, whereas the emerging long chain-of-thought (Long-CoT) approach mitigates it through iterative exploration and self-reflection. We further characterise observable behaviours and influential factors. To probe the underlying cause, we propose the \textbf{cognitive-rigidity hypothesis}, which posits that overconfidence arises when the reasoning process prematurely converges on a narrow set of thought paths. An attention-entropy analysis offers preliminary support for this view. These findings provide tools for assessing the completeness of LLM reasoning and highlight the need to move evaluation beyond single-answer accuracy toward comprehensive exploration.

Qiguang Chen, Libo Qin, Jinhao Liu et al.

Chain-of-Thought (CoT) reasoning has proven effective in enhancing large language models (LLMs) on complex tasks, spurring research into its underlying mechanisms. However, two primary challenges remain for real-world applications: (1) the lack of quantitative metrics and actionable guidelines for evaluating and optimizing measurable boundaries of CoT capability, and (2) the absence of methods to assess boundaries of unmeasurable CoT capability, such as multimodal perception. To address these gaps, we introduce the Reasoning Boundary Framework++ (RBF++). To tackle the first challenge, we define the reasoning boundary (RB) as the maximum limit of CoT performance. We also propose a combination law for RBs, enabling quantitative analysis and offering actionable guidance across various CoT tasks. For the second challenge, particularly in multimodal scenarios, we introduce a constant assumption, which replaces unmeasurable RBs with scenario-specific constants. Additionally, we propose the reasoning boundary division mechanism, which divides unmeasurable RBs into two sub-boundaries, facilitating the quantification and optimization of both unmeasurable domain knowledge and multimodal perception capabilities. Extensive experiments involving 38 models across 13 tasks validate the feasibility of our framework in cross-modal settings. Additionally, we evaluate 10 CoT strategies, offer insights into optimization and decay from two complementary perspectives, and expand evaluation benchmarks for measuring RBs in LLM reasoning. We hope this work advances the understanding of RBs and optimization strategies in LLMs. Code and data are available at https://github.com/LightChen233/reasoning-boundary.

Dengyun Peng, Yuhang Zhou, Qiguang Chen et al.

Large Language Models (LLMs) have achieved remarkable success across diverse tasks, largely driven by well-designed prompts. However, crafting and selecting such prompts often requires considerable human effort, significantly limiting its scalability. To mitigate this, recent studies have explored automated prompt optimization as a promising solution. Despite these efforts, existing methods still face critical challenges in robustness, efficiency, and generalization. To systematically address these challenges, we first conduct an empirical analysis to identify the limitations of current reflection-based prompt optimization paradigm. Building on these insights, we propose 7 innovative approaches inspired by traditional deep learning paradigms for prompt optimization (DLPO), seamlessly integrating these concepts into text-based gradient optimization. Through these advancements, we progressively tackle the aforementioned challenges and validate our methods through extensive experimentation. We hope our study not only provides valuable guidance for future research but also offers a comprehensive understanding of the challenges and potential solutions in prompt optimization. Our code is available at https://github.com/sfasfaffa/DLPO.

Qiguang Chen, Libo Qin, Jinhao Liu et al.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "inference-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and inference-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Qiguang Chen, Libo Qin, Jinhao Liu et al.

Large language models (LLMs) such as DeepSeek-R1 have achieved remarkable performance across diverse reasoning tasks. To uncover the principles that govern their behaviour, we introduce the Electronic Circuit Principles (ECP), which maps inference-time learning (ITL) onto a semantic electromotive force and inference-time reasoning (ITR) onto a resistive network governed by Ohm's and Faraday's laws. This circuit-based modelling yields closed-form predictions of task performance and reveals how modular prompt components interact to shape accuracy. We validated ECP on 70,000 samples spanning 350 reasoning tasks and 9 advanced LLMs, observing a about 60% improvement in Pearson correlation relative to the conventional inference-time scaling law. Moreover, ECP explains the efficacy of 15 established prompting strategies and directs the development of new modular interventions that exceed the median score of the top 80% of participants in both the International Olympiad in Informatics and the International Mathematical Olympiad. By grounding LLM reasoning in electronic-circuit principles, ECP provides a rigorous framework for predicting performance and optimising modular components.

Qiguang Chen, Hanjing Li, Libo Qin et al.

Recently, Diffusion Large Language Models (DLLMs) have offered high throughput and effective sequential reasoning, making them a competitive alternative to autoregressive LLMs (ALLMs). However, parallel decoding, which enables simultaneous token updates, conflicts with the causal order often required for rigorous reasoning. We first identify this conflict as the core Parallel-Sequential Contradiction (PSC). Behavioral analyses in both simple and complex reasoning tasks show that DLLMs exhibit genuine parallelism only for directly decidable outputs. As task difficulty increases, they revert to autoregressive-like behavior, a limitation exacerbated by autoregressive prompting, which nearly doubles the number of decoding steps with remasking without improving quality. Moreover, PSC restricts DLLMs' self-reflection, reasoning depth, and exploratory breadth. To further characterize PSC, we introduce three scaling dimensions for DLLMs: parallel, diffusion, and sequential. Empirically, while parallel scaling yields consistent improvements, diffusion and sequential scaling are constrained by PSC. Based on these findings, we propose several practical mitigations, parallel-oriented prompting, diffusion early stopping, and parallel scaling, to reduce PSC-induced ineffectiveness and inefficiencies.