Large Language Models (LLMs) have been shown to achieve breakthrough performances on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs for deriving reliable reasoning paths, with systematic evaluations of these capabilities still being limited. In this paper, we aim to conduct a comprehensive evaluation of LLMs across various logical reasoning problems utilizing formal languages. From the perspective of three dimensions, i.e., spectrum of LLMs, taxonomy of tasks, and format of trajectories, our key findings are: 1. \textit{Thinking} models significantly outperform \textit{Instruct} models, especially when formal language is employed; 2. All LLMs exhibit limitations in inductive reasoning capability, irrespective of whether they use a formal language; 3. Data with PoT format achieves the best generalization performance across other languages. Additionally, we also curate the formal-relative training data to further enhance the small language models, and the experimental results indicate that a simple rejected fine-tuning method can better enable LLMs to generalize across formal languages and achieve the best overall performance.

Do Large Language Models excel in Complex Logical Reasoning with Formal Language?

In this paper, we introduce a new \emph{process prejudge} strategy in LLM reasoning to demonstrate that bootstrapping with process prejudge allows the LLM to adaptively anticipate the errors encountered when advancing the subsequent reasoning steps, similar to people sometimes pausing to think about what mistakes may occur and how to avoid them, rather than relying solely on trial and error. Specifically, we define a prejudge node in the rationale, which represents a reasoning step, with at least one step that follows the prejudge node that has no paths toward the correct answer. To synthesize the prejudge reasoning process, we present an automated reasoning framework with a dynamic tree-searching strategy. This framework requires only one LLM to perform answer judging, response critiquing, prejudge generation, and thought completion. Furthermore, we develop a two-phase training mechanism with supervised fine-tuning (SFT) and reinforcement learning (RL) to further enhance the reasoning capabilities of LLMs. Experimental results from competition-level complex reasoning demonstrate that our method can teach the model to prejudge before thinking and significantly enhance the reasoning ability of LLMs~\footnote{Code and data is released at \url{https://github.com/xxx}.}.

Prejudge-Before-Think: Enhancing Large Language Models at Test-Time by Process Prejudge Reasoning

In this paper, we propose a new data synthesis method called \textbf{LogicPro}, which leverages LeetCode-style algorithm \underline{Pro}blems and their corresponding \underline{Pro}gram solutions to synthesize Complex \underline{Logic}al Reasoning data in text format. First, we synthesize complex reasoning problems through source algorithm problems and test cases. Then, standard answers and intermediate variable outputs are obtained for each problem based on standard python solutions and test cases. Finally, with the guidance of code intermediate variables, we synthesize the text reasoning process for each reasoning problems. Through this method, we can synthesize data that is difficult, scalable, effective, and comes with golden standard answers and high-quality reasoning processes. As a result, with our 540K synthesized dataset constructed solely from 2,360 algorithm problems, our approach achieves significant improvements in multiple models for the datasets \textit{BBH^27}, \textit{LogicBench}, \textit{DROP}, \textit{AR-LSAT}, and \textit{GSM8K}, etc. outperforming a wide range of existing reasoning datasets.

LogicPro: Improving Complex Logical Reasoning via Program-Guided Learning

Recent research has increasingly focused on multimodal mathematical reasoning, particularly emphasizing the creation of relevant datasets and benchmarks. Despite this, the role of visual information in reasoning has been underexplored. Our findings show that existing multimodal mathematical models minimally leverage visual information, and model performance remains largely unaffected by changes to or removal of images in the dataset. We attribute this to the dominance of textual information and answer options that inadvertently guide the model to correct answers. To improve evaluation methods, we introduce the HC-M3D dataset, specifically designed to require image reliance for problem-solving and to challenge models with similar, yet distinct, images that change the correct answer. In testing leading models, their failure to detect these subtle visual differences suggests limitations in current visual perception capabilities. Additionally, we observe that the common approach of improving general VQA capabilities by combining various types of image encoders does not contribute to math reasoning performance. This finding also presents a challenge to enhancing visual reliance during math reasoning.

The Role of Visual Modality in Multimodal Mathematical Reasoning: Challenges and Insights

Do current large language models (LLMs) better solve graph reasoning and generation tasks with parameter updates? In this paper, we propose \textbf{InstructGraph}, a framework that empowers LLMs with the abilities of graph reasoning and generation by instruction tuning and preference alignment. Specifically, we first propose a structured format verbalizer to unify all graph data into a universal code-like format, which can simply represent the graph without any external graph-specific encoders. Furthermore, a graph instruction tuning stage is introduced to guide LLMs in solving graph reasoning and generation tasks. Finally, we identify potential hallucination problems in graph tasks and sample negative instances for preference alignment, the target of which is to enhance the output's reliability of the model. Extensive experiments across multiple graph-centric tasks exhibit that InstructGraph can achieve the best performance and outperform GPT-4 and LLaMA2 by more than 13\% and 38\%, respectively.

InstructGraph: Boosting Large Language Models via Graph-centric Instruction Tuning and Preference Alignment

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 an 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 tasks.

Boosting Language Models Reasoning with Chain-of-Knowledge Prompting

Neural sequence labeling (NSL) aims at assigning labels for input language tokens, which covers a broad range of applications, such as named entity recognition (NER) and slot filling, etc. However, the satisfying results achieved by traditional supervised-based approaches heavily depend on the large amounts of human annotation data, which may not be feasible in real-world scenarios due to data privacy and computation efficiency issues. This paper presents SeqUST, a novel uncertain-aware self-training framework for NSL to address the labeled data scarcity issue and to effectively utilize unlabeled data. Specifically, we incorporate Monte Carlo (MC) dropout in Bayesian neural network (BNN) to perform uncertainty estimation at the token level and then select reliable language tokens from unlabeled data based on the model confidence and certainty. A well-designed masked sequence labeling task with a noise-robust loss supports robust training, which aims to suppress the problem of noisy pseudo labels. In addition, we develop a Gaussian-based consistency regularization technique to further improve the model robustness on Gaussian-distributed perturbed representations. This effectively alleviates the over-fitting dilemma originating from pseudo-labeled augmented data. 
Extensive experiments over six benchmarks demonstrate that our SeqUST framework effectively improves the performance of self-training, and consistently outperforms strong baselines by a large margin in low-resource scenarios. 

Uncertainty-aware Self-training for Low-resource Neural Sequence Labeling

Extractive Question Answering (EQA) is one of the most essential tasks in Machine Reading Comprehension (MRC), which can be solved by fine-tuning the span selecting heads of Pre-trained Language Models (PLMs). However, most existing approaches for MRC may perform poorly in the few-shot learning scenario. To solve this issue, we propose a novel framework named Knowledge Enhanced Contrastive Prompt-tuning (KECP). Instead of adding pointer heads to PLMs, we introduce a seminal paradigm for EQA that transforms the task into a non-autoregressive Masked Language Modeling (MLM) generation problem. Simultaneously, rich semantics from the external knowledge base (KB) and the passage context support enhancing the query's representations. In addition, to boost the performance of PLMs, we jointly train the model by the MLM and contrastive learning objectives. Experiments on multiple benchmarks demonstrate that our method consistently outperforms state-of-the-art approaches in few-shot settings by a large margin.

KECP: Knowledge Enhanced Contrastive Prompting for Few-shot Extractive Question Answering

Few-shot Named Entity Recognition (NER) aims to identify named entities with very little annotated data. Previous methods solve this problem based on token-wise classification, which ignores the information of entity boundaries, and inevitably the performance is affected by the massive non-entity tokens. To this end, we propose a seminal span-based prototypical network (SpanProto) that tackles few-shot NER via a two-stage approach, including span extraction and mention classification. 
In the span extraction stage, we transform the sequential tags into a global boundary matrix, enabling the model to focus on the explicit boundary information. For mention classification, we leverage prototypical learning to capture the semantic representations for each labeled span and make the model better adapt to novel-class entities. To further improve the model performance, we split out the false positives generated by the span extractor but not labeled in the current episode set, and then present a margin-based loss to separate them from each prototype region. Experiments over multiple benchmarks demonstrate that our model outperforms strong baselines by a large margin.

SpanProto: A Two-stage Span-based Prototypical Network for Few-shot Named Entity Recognition

Knowledge-enhanced Pre-trained Language Model (PLM) has recently received significant attention, which aims to incorporate factual knowledge into PLMs. However, most existing methods modify the internal structures of fixed types of PLMs by stacking complicated modules, and introduce redundant and irrelevant factual knowledge from knowledge bases (KBs). In this paper, to address these problems, we introduce a seminal knowledge prompting paradigm and further propose a knowledge-prompting-based PLM framework KP-PLM. This framework can be flexibly combined with existing mainstream PLMs. Specifically, we first construct a knowledge sub-graph from KBs for each context. Then we design multiple continuous prompts rules and transform the knowledge sub-graph into natural language prompts. To further leverage the factual knowledge from these prompts, we propose two novel knowledge-aware self-supervised tasks including prompt relevance inspection and masked prompt modeling. Extensive experiments on multiple natural language understanding (NLU) tasks show the superiority of KP-PLM over other state-of-the-art methods in both full-resource and low-resource settings. Our source codes will be released upon the acceptance of the paper.

Jianing Wang

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