Reasoning Models

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learning complex reasoning, we propose *Difficulty-Aware Rejection Tuning* (`DART`), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing `DART`, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called `DART-Math`. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, `DART-Math` outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving. Our datasets, models and code are publicly available at https://github.com/hkust-nlp/dart-math.

Studying protein mutations within amino acid sequences holds tremendous significance in life sciences. Protein language models (PLMs) have demonstrated strong capabilities in broad biological applications. However, due to architectural design and lack of supervision, PLMs model mutations implicitly with evolutionary plausibility, which is not satisfactory to serve as explainable and engineerable tools in real-world studies. To address these issues, we present MutaPLM, a unified framework for interpreting and navigating protein mutations with protein language models. MutaPLM introduces a protein *delta* network that captures explicit protein mutation representations within a unified feature space, and a transfer learning pipeline with a chain-of-thought (CoT) strategy to harvest protein mutation knowledge from biomedical texts. We also construct MutaDescribe, the first large-scale protein mutation dataset with rich textual annotations, which provides cross-modal supervision signals. Through comprehensive experiments, we demonstrate that MutaPLM excels at providing human-understandable explanations for mutational effects and prioritizing novel mutations with desirable properties. Our code, model, and data are open-sourced at https://github.com/PharMolix/MutaPLM.

As Large Language Models (LLMs) are integrated into critical real-world applications, their strategic and logical reasoning abilities are increasingly crucial. This paper evaluates LLMs' reasoning abilities in competitive environments through game-theoretic tasks, e.g., board and card games that require pure logic and strategic reasoning to compete with opponents. We first propose GTBench, a language-driven environment composing 10 widely-recognized tasks, across a comprehensive game taxonomy: complete versus incomplete information, dynamic versus static, and probabilistic versus deterministic scenarios. Then, we (1) Characterize the game-theoretic reasoning of LLMs; and (2) Perform LLM-vs.-LLM competitions as reasoning evaluation. We observe that (1) LLMs have distinct behaviors regarding various gaming scenarios; for example, LLMs fail in complete and deterministic games yet they are competitive in probabilistic gaming scenarios; (2) Most open-source LLMs, e.g., CodeLlama-34b-Instruct and Llama-2-70b-chat, are less competitive than commercial LLMs, e.g., GPT-4, in complex games, yet the recently released Llama-3-70b-Instruct makes up for this shortcoming. In addition, code-pretraining greatly benefits strategic reasoning, while advanced reasoning methods such as Chain-of-Thought (CoT) and Tree-of-Thought (ToT) do not always help. We further characterize the game-theoretic properties of LLMs, such as equilibrium and Pareto Efficiency in repeated games. Detailed error profiles are provided for a better understanding of LLMs' behavior. We hope our research provides standardized protocols and serves as a foundation to spur further explorations in the strategic reasoning of LLMs.

Instruction tuning improves the reasoning abilities of large language models (LLMs), with data quality and scalability being the crucial factors. Most instruction tuning data come from human crowd-sourcing or GPT-4 distillation. We propose a paradigm to efficiently harvest 10 million naturally existing instruction data from the pre-training web corpus to enhance LLM reasoning. Our approach involves (1) recalling relevant documents, (2) extracting instruction-response pairs, and (3) refining the extracted pairs using open-source LLMs. Fine-tuning base LLMs on this dataset, we build MAmmoTH2 models, which significantly boost performance on reasoning benchmarks. Notably, MAmmoTH2-7B’s (Mistral) performance increases from 11% to 36.7% on MATH and from 36% to 68.4% on GSM8K without training on any in-domain data. Further training MAmmoTH2 on public instruction tuning datasets yields MAmmoTH2-Plus, achieving state-of-the-art performance on several reasoning and chatbot benchmarks. Our work demonstrates how to harvest large-scale, high-quality instruction data without costly human annotation or GPT-4 distillation, providing a new paradigm for building better instruction tuning data.

Social relation reasoning aims to identify relation categories such as friends, spouses, and colleagues from images. While current methods adopt the paradigm of training a dedicated network end-to-end using labeled image data, they are limited in terms of generalizability and interpretability. To address these issues, we first present a simple yet well-crafted framework named SocialGPT, which combines the perception capability of Vision Foundation Models (VFMs) and the reasoning capability of Large Language Models (LLMs) within a modular framework, providing a strong baseline for social relation recognition. Specifically, we instruct VFMs to translate image content into a textual social story, and then utilize LLMs for text-based reasoning. SocialGPT introduces systematic design principles to adapt VFMs and LLMs separately and bridge their gaps. Without additional model training, it achieves competitive zero-shot results on two databases while offering interpretable answers, as LLMs can generate language-based explanations for the decisions. The manual prompt design process for LLMs at the reasoning phase is tedious and an automated prompt optimization method is desired. As we essentially convert a visual classification task into a generative task of LLMs, automatic prompt optimization encounters a unique long prompt optimization issue. To address this issue, we further propose the Greedy Segment Prompt Optimization (GSPO), which performs a greedy search by utilizing gradient information at the segment level. Experimental results show that GSPO significantly improves performance, and our method also generalizes to different image styles. The code is available at https://github.com/Mengzibin/SocialGPT.

Pretrained language models can encode a large amount of knowledge and utilize it for various reasoning tasks, yet they can still struggle to learn novel factual knowledge effectively from finetuning on limited textual demonstrations. In this work, we show that the reason for this deficiency is that language models are biased to learn word co-occurrence statistics instead of true factual associations. We identify the differences between two forms of knowledge representation in language models: knowledge in the form of co-occurrence statistics is encoded in the middle layers of the transformer model and does not generalize well to reasoning scenarios beyond simple question answering, while true factual associations are encoded in the lower layers and can be freely utilized in various reasoning tasks. Based on these observations, we propose two strategies to improve the learning of factual associations in language models. We show that training on text with implicit rather than explicit factual associations can force the model to learn factual associations instead of co-occurrence statistics, significantly improving the generalization of newly learned knowledge. We also propose a simple training method to actively forget the learned co-occurrence statistics, which unblocks and enhances the learning of factual associations when training on plain narrative text. On both synthetic and real-world corpora, the two proposed strategies improve the generalization of the knowledge learned during finetuning to reasoning scenarios such as indirect and multi-hop question answering.

Trained on vast corpora of human language, language models demonstrate emergent human-like reasoning abilities. Yet they are still far from true intelligence, which opens up intriguing opportunities to explore the parallels of humans and model behaviors. In this work, we study the ability to skip steps in reasoning—a hallmark of human expertise developed through practice. Unlike humans, who may skip steps to enhance efficiency or to reduce cognitive load, models do not inherently possess such motivations to minimize reasoning steps. To address this, we introduce a controlled framework that stimulates step-skipping behavior by iteratively refining models to generate shorter and accurate reasoning paths. Empirical results indicate that models can develop the step skipping ability under our guidance. Moreover, after fine-tuning on expanded datasets that include both complete and skipped reasoning sequences, the models can not only resolve tasks with increased efficiency without sacrificing accuracy, but also exhibit comparable and even enhanced generalization capabilities in out-of-domain scenarios. Our work presents the first exploration into human-like step-skipping ability and provides fresh perspectives on how such cognitive abilities can benefit AI models.

While multi-modal large language models (MLLMs) have shown significant progress across popular visual reasoning benchmarks, whether they possess abstract visual reasoning abilities remains an open question. Similar to the Sudoku puzzles, abstract visual reasoning (AVR) problems require finding high-level patterns (e.g., repetition constraints on numbers) that control the input shapes (e.g., digits) in a specific task configuration (e.g., matrix). However, existing AVR benchmarks only consider a limited set of patterns (addition, conjunction), input shapes (rectangle, square), and task configurations (3 × 3 matrices). And they fail to capture all abstract reasoning patterns in human cognition necessary for addressing real-world tasks, such as geometric properties and object boundary understanding in real-world navigation. To evaluate MLLMs’ AVR abilities systematically, we introduce MARVEL founded on the core knowledge system in human cognition, a multi-dimensional AVR benchmark with 770 puzzles composed of six core knowledge patterns, geometric and abstract shapes, and five different task configurations. To inspect whether the model performance is grounded in perception or reasoning, MARVEL complements the standard AVR question with perception questions in a hierarchical evaluation framework. We conduct comprehensive experiments on MARVEL with ten representative MLLMs in zero-shot and few-shot settings. Our experiments reveal that all MLLMs show near-random performance on MARVEL, with significant performance gaps (40%) compared to humans across all patterns and task configurations. Further analysis of perception questions reveals that MLLMs struggle to comprehend the visual features (near-random performance). Although closed-source MLLMs, such as GPT-4V, show a promising understanding of reasoning patterns (on par with humans) after adding textual descriptions, this advantage is hindered by their weak perception abilities. We release our entire code and dataset at https://github.com/1171-jpg/MARVEL_AVR.

Complex visual reasoning and question answering (VQA) is a challenging task that requires compositional multi-step processing and higher-level reasoning capabilities beyond the immediate recognition and localization of objects and events. Here, we introduce a fully neural Iterative and Parallel Reasoning Mechanism (IPRM) that combines two distinct forms of computation -- iterative and parallel -- to better address complex VQA scenarios. Specifically, IPRM's "iterative" computation facilitates compositional step-by-step reasoning for scenarios wherein individual operations need to be computed, stored, and recalled dynamically (e.g. when computing the query “determine the color of pen to the left of the child in red t-shirt sitting at the white table”). Meanwhile, its "parallel'' computation allows for the simultaneous exploration of different reasoning paths and benefits more robust and efficient execution of operations that are mutually independent (e.g. when counting individual colors for the query: "determine the maximum occurring color amongst all t-shirts'"). We design IPRM as a lightweight and fully-differentiable neural module that can be conveniently applied to both transformer and non-transformer vision-language backbones. It notably outperforms prior task-specific methods and transformer-based attention modules across various image and video VQA benchmarks testing distinct complex reasoning capabilities such as compositional spatiotemporal reasoning (AGQA), situational reasoning (STAR), multi-hop reasoning generalization (CLEVR-Humans) and causal event linking (CLEVRER-Humans). Further, IPRM's internal computations can be visualized across reasoning steps, aiding interpretability and diagnosis of its errors.

Mathematical reasoning is an important capability of large language models~(LLMs) for real-world applications. To enhance this capability, existing work either collects large-scale math-related texts for pre-training, or relies on stronger LLMs (\eg GPT-4) to synthesize massive math problems. Both types of work generally lead to large costs in training or synthesis. To reduce the cost, based on open-source available texts, we propose an efficient way that trains a small LLM for math problem synthesis, to efficiently generate sufficient high-quality pre-training data. To achieve it, we create a dataset using GPT-4 to distill its data synthesis capability into the small LLM. Concretely, we craft a set of prompts based on human education stages to guide GPT-4, to synthesize problems covering diverse math knowledge and difficulty levels. Besides, we adopt the gradient-based influence estimation method to select the most valuable math-related texts. The both are fed into GPT-4 for creating the knowledge distillation dataset to train the small LLM. We leverage it to synthesize 6 million math problems for pre-training our JiuZhang3.0 model. The whole process only needs to invoke GPT-4 API 9.3k times and use 4.6B data for training. Experimental results have shown that JiuZhang3.0 achieves state-of-the-art performance on several mathematical reasoning datasets, under both natural language reasoning and tool manipulation settings. Our code and data will be publicly released in \url{https://github.com/RUCAIBox/JiuZhang3.0}.

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model’s internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model’s confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs.

How did humanity coax mathematics from the aether? We explore the Platonic view that mathematics can be discovered from its axioms---a game of conjecture and proof. We describe an agent that jointly learns to pose challenging problems for itself (conjecturing) and solve them (theorem proving). Given a mathematical domain axiomatized in dependent type theory, we first combine methods for constrained decoding and type-directed synthesis to sample valid conjectures from a language model. Our method guarantees well-formed conjectures by construction, even as we start with a randomly initialized model. We use the same model to represent a policy and value function for guiding proof search. Our agent targets generating hard but provable conjectures --- a moving target, since its own theorem proving ability also improves as it trains. We propose novel methods for hindsight relabeling on proof search trees to significantly improve the agent's sample efficiency in both tasks. Experiments on 3 axiomatic domains (propositional logic, arithmetic and group theory) demonstrate that our agent can bootstrap from only the axioms, self-improving in generating true and challenging conjectures and in finding proofs.

Program synthesis with language models (LMs) has unlocked a large set of reasoning abilities; code-tuned LMs have proven adept at generating programs that solve a wide variety of algorithmic symbolic manipulation tasks (e.g. word concatenation). However, not all reasoning tasks are easily expressible as code, e.g. tasks involving commonsense reasoning, moral decision-making, and sarcasm understanding. Our goal is to extend a LM’s program synthesis skills to such tasks and evaluate the results via pseudo-programs, namely Python programs where some leaf function calls are left undefined. To that end, we propose, Code Generation and Emulated EXecution (COGEX). COGEX works by (1) training LMs to generate pseudo-programs and (2) teaching them to emulate their generated program’s execution, including those leaf functions, allowing the LM’s knowledge to fill in the execution gaps; and (3) using them to search over many programs to find an optimal one. To adapt the COGEX model to a new task, we introduce a method for performing program search to find a single program whose pseudo-execution yields optimal performance when applied to all the instances of a given dataset. We show that our approach yields large improvements compared to standard in-context learning approaches on a battery of tasks, both algorithmic and soft reasoning. This result thus demonstrates that code synthesis can be applied to a much broader class of problems than previously considered.

Large language models (LLMs) have demonstrated remarkable capabilities, but their outputs can sometimes be unreliable or factually incorrect. To address this, we introduce Self Logits Evolution Decoding (SLED), a novel decoding framework that enhances the truthfulness of LLMs without relying on external knowledge bases or requiring further fine-tuning. From an optimization perspective, our SLED framework leverages the latent knowledge embedded within the LLM by contrasting the output logits from the final layer with those from early layers. It then utilizes an approximate gradient approach to enable latent knowledge to guide the self-refinement of outputs, thereby effectively improving factual accuracy. Extensive experiments have been conducted on established benchmarks across a diverse range of model families (LLaMA 2, LLaMA 3, Gemma) and scales (from 2B to 70B), including more advanced architectural configurations such as the mixture of experts (MoE). Our evaluation spans a wide variety of tasks, including multi-choice, open-generation, and adaptations to chain-of-thought reasoning tasks. The results demonstrate that SLED consistently improves factual accuracy by up to 20\% compared to existing decoding methods while maintaining natural language fluency and negligible latency overhead. Furthermore, it can be flexibly combined with other decoding methods to further enhance their performance.

Existing benchmarks for multi-hop question answering (QA) primarily evaluate models based on their ability to reason about entities and the relationships between them. However, there's a lack of insight into how these models perform in terms of both events and entities. In this paper, we introduce a novel semi-automatic question generation strategy by composing event structures from information extraction (IE) datasets and present the first Multi-hop Event-centric Question Answering (MEQA) benchmark. It contains (1) 2,243 challenging questions that require a diverse range of complex reasoning over entity-entity, entity-event, and event-event relations; (2) corresponding multi-step QA-format event reasoning chain (explanation) which leads to the answer for each question. We also introduce two metrics for evaluating explanations: completeness and logical consistency. We conduct comprehensive benchmarking and analysis, which shows that MEQA is challenging for the latest state-of-the-art models encompassing large language models (LLMs); and how they fall short of providing faithful explanations of the event-centric reasoning process.

Large language models (LLMs) have recently demonstrated great success in generating and understanding natural language. While they have also shown potential beyond the domain of natural language, it remains an open question as to what extent and in which way these LLMs can plan. We investigate their planning capabilities by proposing \texttt{GameTraversalBenchmark (GTB)}, a benchmark consisting of diverse 2D grid-based game maps. An LLM succeeds if it can traverse through given objectives, with a minimum number of steps and a minimum number of generation errors. We evaluate a number of LLMs on \texttt{GTB} and found that GPT-4-Turbo achieved the highest score of $44.97\%$ on \texttt{GTB\_Score} (GTBS), a composite score that combines the three above criteria. Furthermore, we preliminarily test large reasoning models, namely o1, which scores $67.84\%$ on GTBS, indicating that the benchmark remains challenging for current models. Code, data, and documentation are available at \url{https://github.com/umair-nasir14/Game-Traversal-Benchmark}.

When making decisions under uncertainty, individuals often deviate from rational behavior, which can be evaluated across three dimensions: risk preference, probability weighting, and loss aversion. Given the widespread use of large language models (LLMs) in supporting decision-making processes, it is crucial to assess whether their behavior aligns with human norms and ethical expectations or exhibits potential biases. Although several empirical studies have investigated the rationality and social behavior performance of LLMs, their internal decision-making tendencies and capabilities remain inadequately understood. This paper proposes a framework, grounded in behavioral economics theories, to evaluate the decision-making behaviors of LLMs. With a multiple-choice-list experiment, we initially estimate the degree of risk preference, probability weighting, and loss aversion in a context-free setting for three commercial LLMs: ChatGPT-4.0-Turbo, Claude-3-Opus, and Gemini-1.0-pro. Our results reveal that LLMs generally exhibit patterns similar to humans, such as risk aversion and loss aversion, with a tendency to overweight small probabilities, but there are significant variations in the degree to which these behaviors are expressed across different LLMs. Further, we explore their behavior when embedded with socio-demographic features of human beings, uncovering significant disparities across various demographic characteristics.

Entity alignment (EA) aims to merge two knowledge graphs (KGs) by identifying equivalent entity pairs. While existing methods heavily rely on human-generated labels, it is prohibitively expensive to incorporate cross-domain experts for annotation in real-world scenarios. The advent of Large Language Models (LLMs) presents new avenues for automating EA with annotations, inspired by their comprehensive capability to process semantic information. However, it is nontrivial to directly apply LLMs for EA since the annotation space in real-world KGs is large. LLMs could also generate noisy labels that may mislead the alignment. To this end, we propose a unified framework, LLM4EA, to effectively leverage LLMs for EA. Specifically, we design a novel active learning policy to significantly reduce the annotation space by prioritizing the most valuable entities based on the entire inter-KG and intra-KG structure. Moreover, we introduce an unsupervised label refiner to continuously enhance label accuracy through in-depth probabilistic reasoning. We iteratively optimize the policy based on the feedback from a base EA model. Extensive experiments demonstrate the advantages of LLM4EA on four benchmark datasets in terms of effectiveness, robustness, and efficiency.

Accurate emotion perception is crucial for various applications, including human-computer interaction, education, and counseling. However, traditional single-modality approaches often fail to capture the complexity of real-world emotional expressions, which are inherently multimodal. Moreover, existing Multimodal Large Language Models (MLLMs) face challenges in integrating audio and recognizing subtle facial micro-expressions. To address this, we introduce the MERR dataset, containing 28,618 coarse-grained and 4,487 fine-grained annotated samples across diverse emotional categories. This dataset enables models to learn from varied scenarios and generalize to real-world applications. Furthermore, we propose Emotion-LLaMA, a model that seamlessly integrates audio, visual, and textual inputs through emotion-specific encoders. By aligning features into a shared space and employing a modified LLaMA model with instruction tuning, Emotion-LLaMA significantly enhances both emotional recognition and reasoning capabilities. Extensive evaluations show Emotion-LLaMA outperforms other MLLMs, achieving top scores in Clue Overlap (7.83) and Label Overlap (6.25) on EMER, an F1 score of 0.9036 on MER2023-SEMI challenge, and the highest UAR (45.59) and WAR (59.37) in zero-shot evaluations on DFEW dataset.

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-boundary.