reasoning chains

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

The use of Large Language Models (LLMs) for reasoning and planning tasks has drawn increasing attention in Artificial Intelligence research. Despite their remarkable progress, these models still exhibit limitations in multi-step inference scenarios, particularly in mathematical and logical reasoning. We introduce PREGU (Partial Reasoning Guided by Uncertainty). PREGU monitors the entropy of the output distribution during autoregressive generation and halts the process whenever entropy exceeds a defined threshold, signaling uncertainty. From that point, a localized search is performed in the latent space to refine the partial reasoning and select the most coherent answer, using the Soft Reasoning method. Experiments conducted with LLaMA-3-8B, Mistral-7B, and Qwen2-7B across four reasoning benchmarks (GSM8K, GSM-Hard, SVAMP, and StrategyQA) showed performance greater than or similar to Soft Reasoning, indicating that entropy can serve as an effective signal to trigger selective refinement during reasoning.

Prompting language models to provide step-by-step answers (e.g., “Chain-of-Thought”) is the prominent approach for complex reasoning tasks, where more accurate reasoning chains typically improve downstream task performance. Recent literature discusses automatic methods to verify reasoning steps to evaluate and improve their correctness. However, no fine-grained step-level datasets are available to enable thorough evaluation of such verification methods, hindering progress in this direction. We introduce REVEAL: Reasoning Verification Evaluation, a new dataset to benchmark automatic verifiers of complex Chain-of-Thought reasoning in open-domain question answering settings. REVEAL includes comprehensive labels for the relevance, attribution to evidence passages, and logical correctness of each reasoning step in a language model’s answer, across a wide variety of datasets and state-of-the-art language models. Available at reveal-dataset.github.io.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like “Let’s think step by step” or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with hallucinations, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F²-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks¹.

Recent progress in LLMs discussion suggests that multi-agent discussion improves the reasoning abilities of LLMs. In this work, we reevaluate this claim through systematic experiments, where we propose a novel group discussion framework to enrich the set of discussion mechanisms. Interestingly, our results show that a single-agent LLM with strong prompts can achieve almost the same performance as the best existing discussion approach on a wide range of reasoning tasks and backbone LLMs. We observe that the multi-agent discussion performs better than a single agent only when there is no demonstration in the prompt. Further study reveals the common interaction mechanisms of LLMs during the discussion.

In context learning (ICL) underpins recent advances in large language models (LLMs), although its role and performance in causal reasoning remains unclear. Causal reasoning demands multihop composition and strict conjunctive control, and reliance on spurious lexical relations of the input could provide misleading results. We hypothesize that, due to their ability to project the input into a latent space, encoder and encoder decoder architectures are better suited for said multihop conjunctive reasoning versus decoder only models. To do this, we compare fine-tuned versions of all the aforementioned architectures with zero and few shot ICL in both natural language and non natural language scenarios. We find that ICL alone is insufficient for reliable causal reasoning, often overfocusing on irrelevant input features. In particular, decoder only models are noticeably brittle to distributional shifts, while finetuned encoder and encoder decoder models can generalize more robustly across our tests, including the non natural language split. Both architectures are only matched or surpassed by decoder only architectures at large scales. We conclude by noting that for cost effective, short horizon robust causal reasoning, encoder or encoder decoder architectures with targeted finetuning are preferable.

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Existing approaches either require expensive labelled supervision with inconsistent cross-task performance or aggregate scores from multiple sources by simple aggregations, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We formalise this as a coupled scoring problem among disparate, frozen verifiers, interpretable as a coordination game with a unique closed-form equilibrium where agreement signals valid steps while disagreement reveals instability. Towards this end, we propose a training-free domain-agnostic step-wise verification approach we call VERDICT: VERification via Disagreement-Informed Coupled Thresholding. To our knowledge, VERDICT is the first training-free verifier that makes the structure of cross-modal disagreement explicit and actionable. It computes consensus scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, \method consistently improves over the base model by up to +5.95%, and performs competitively with domain-specific critics that demand extensive supervision, demonstrating that cross-modal agreement provides robust verification signals without task-specific adaptation and Training-Free Verification

We introduce Phi-4-reasoning, a 14-billion parameter reasoning model that achieves strong performance on complex reasoning tasks. Trained via supervised fine-tuning of Phi-4 on carefully curated set of “teachable” prompts–selected for the right level of complexity and diversity–and reasoning demonstrations generated using o3-mini, Phi-4-reasoning generates detailed reasoning chains that effectively leverage inference-time compute. We further develop Phi-4-reasoning-plus, a variant enhanced through a short phase of outcome-based reinforcement learning that offers higher performance by generating longer reasoning traces. Across a wide range of reasoning tasks, both models outperform significantly larger open-weight models such as DeepSeek-R1-Distill-Llama-70B model and approach the performance levels of full DeepSeek-R1 model. Our comprehensive evaluations span benchmarks in math and scientific reasoning, coding, algorithmic problem solving, planning, and spatial understanding. Interestingly, we observe a non-trivial transfer of improvements to general-purpose benchmarks as well. In this report, we provide insights into our training data, our training methodologies, and our evaluations. We show that the benefit of careful data curation for supervised fine-tuning (SFT) extends to reasoning language models, and can be further amplified by reinforcement learning (RL). Finally, our evaluation points to opportunities for improving how we assess the performance and robustness of reasoning models.

Large language models (LLMs) have demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time (“few-shot prompting”). Much of this success can be attributed to prompting methods such as “chain-of-thought”, which employ LLMs for both understanding the problem description by decomposing it into steps, as well as solving each step of the problem. While LLMs seem to be adept at this sort of step-by-step decomposition, LLMs often make logical and arithmetic mistakes in the solution part, even when the problem is decomposed correctly. In this paper, we present Program-Aided Language models (PAL): a novel approach that uses the LLM to read natural language problems and generate programs as the intermediate reasoning steps, but offloads the solution step to a runtime such as a Python interpreter. With PAL, decomposing the natural language problem into runnable steps remains the only learning task for the LLM, while solving is delegated to the interpreter. We demonstrate this synergy between a neural LLM and a symbolic interpreter across 13 mathematical, symbolic, and algorithmic reasoning tasks from BIG-Bench Hard and others. In all these natural language reasoning tasks, generating code using an LLM and reasoning using a Python interpreter leads to more accurate results than much larger models. For example, PAL using CODEX achieves state-of-the-art few-shot accuracy on GSM8K, surpassing PaLM-540B which uses chain-of-thought by absolute 15% top-1.

We present SCIENCEWORLD, a benchmark to test agents’ scientific reasoning abilities in a new interactive text environment at the level of a standard elementary school science curriculum. Despite the transformer-based progress seen in question-answering and scientific text processing, we find that current models cannot reason about or explain learned science concepts in novel contexts. For instance, models can easily answer what the conductivity of a known material is but struggle when asked how they would conduct an experiment in a grounded environment to find the conductivity of an unknown material. This begs the question of whether current models are simply retrieving answers by way of seeing a large number of similar examples or if they have learned to reason about concepts in a reusable manner. We hypothesize that agents need to be grounded in interactive environments to achieve such reasoning capabilities. Our experiments provide empirical evidence supporting this hypothesis—showing that a 1.5 million parameter agent trained interactively for 100k steps outperforms a 11 billion parameter model statically trained for scientific question-answering and reasoning from millions of expert demonstrations.12

Augmenting large language models (LLMs) with external tools has emerged as a promising approach to solving complex problems. However, traditional methods, which fine-tune LLMs with tool demonstration data, can be both costly and restricted to a predefined set of tools. Recent in-context learning paradigm alleviates these issues, but the limited context length only allows for a few shots of demonstrations, leading to suboptimal understandings of the tools. Moreover, when there are numerous tools to choose from, in-context learning could completely fail to work. In this paper, we propose an alternative approach, ToolkenGPT, which combines the benefits of both sides. Our approach represents each tool as a token (“toolken”) and learns an embedding for it, enabling tool calls in the same way as generating a regular word token. Once a toolken is triggered, the LLM is prompted to complete arguments for the tool to execute. ToolkenGPT offers the flexibility to plug in an arbitrary number of tools by expanding the set of toolkens on the fly. In addition, it improves tool use by allowing extensive demonstration data for learning the toolken embeddings. In diverse domains, including numerical reasoning, knowledge-based question answering, and embodied plan generation, our approach effectively augments LLMs with tools and substantially outperforms various latest baselines. ToolkenGPT demonstrates the promising ability to use relevant tools from a large tool set in complex scenarios.

Multi-step reasoning ability is fundamental to many natural language tasks, yet it is unclear what constitutes a good reasoning chain and how to evaluate them. Most existing methods focus solely on whether the reasoning chain leads to the correct conclusion, but this answer-oriented view may confound reasoning quality with other spurious shortcuts to predict the answer. To bridge this gap, we evaluate reasoning chains by viewing them as informal proofs that derive the final answer. Specifically, we propose RECEVAL (Reasoning Chain Evaluation), a framework that evaluates reasoning chains via two key properties: (1) correctness, i.e., each step makes a valid inference based on information contained within the step, preceding steps, and input context, and (2) informativeness, i.e., each step provides new information that is helpful towards deriving the generated answer. We evaluate these properties by developing metrics using natural language inference models and V-Information. On multiple datasets, we show that RECEVAL effectively identifies various error types and yields notable improvements compared to prior methods. We analyze the impact of step boundaries, and previous steps on evaluating correctness and demonstrate that our informativeness metric captures the expected flow of information in high-quality reasoning chains. Finally, we show that scoring reasoning chains based on RECEVAL improves downstream task performance.1

With the recent advance in large pre-trained language models, researchers have achieved record performances in NLP tasks that mostly focus on language pattern matching. The community is experiencing the shift of the challenge from how to model language to the imitation of complex reasoning abilities like human beings. In this work, we investigate the application domain of finance that involves real-world, complex numerical reasoning. We propose a new large-scale dataset, CONVFINQA, aiming to study the chain of numerical reasoning in conversational question answering. Our dataset poses great challenge in modeling long-range, complex numerical reasoning paths in real-world conversations. We conduct comprehensive experiments and analyses with both the neural symbolic methods and the prompting-based methods, to provide insights into the reasoning mechanisms of these two divisions. We believe our new dataset should serve as a valuable resource to push forward the exploration of real-world, complex reasoning tasks as the next research focus. Our dataset and code is publicly available¹.

Large language models (LLMs) have demonstrated impressive capabilities across diverse tasks, yet their ability to perform structured symbolic planning remains limited, particularly in domains requiring formal representations like the Planning Domain Definition Language (PDDL). In this paper, we present a novel instruction tuning framework, PDDL-Instruct, designed to enhance LLMs' symbolic planning capabilities through logical chain-of-thought reasoning. Our approach focuses on teaching models to rigorously reason about action applicability, state transitions, and plan validity using explicit logical inference steps. By developing instruction prompts that guide models through the precise logical reasoning required to determine when actions can be applied in a given state, we enable LLMs to self-correct their planning processes through structured reflection. The framework systematically builds verification skills by decomposing the planning process into explicit reasoning chains about precondition satisfaction, effect application, and invariant preservation. Experimental results on multiple planning domains show that our chain-of-thought reasoning based instruction-tuned models are significantly better at planning, achieving planning accuracy of up to 94% on standard benchmarks, representing a 66% absolute improvement over baseline models. This work bridges the gap between the general reasoning capabilities of LLMs and the logical precision required for automated planning, offering a promising direction for developing better AI planning systems.