Large language models (LLMs) have achieved impressive human-like performance across various reasoning tasks. However, their mastery of underlying inferential rules still falls short of human capabilities. To investigate this, we propose a logic scaffolding inferential rule generation framework, to construct an inferential rule base, ULogic, comprising both primitive and compositional rules across five domains. Our analysis of GPT-series models over a rule subset reveals significant gaps in LLMs' logic understanding compared to human performance, especially in compositional and structural complex rules with certain bias patterns. We further distill these rules into a smaller-scale inference engine for flexible rule generation and enhancing downstream reasoning. Through a multi-judger evaluation, our inference engine proves effective in generating accurate, complex and abstract conclusions and premises, and improve various commonsense reasoning tasks. Overall, our work sheds light on LLMs' limitations in grasping inferential rule and suggests ways to enhance their logical reasoning abilities~\footnote{Code and data are available at \url{//github.com/SiyuanWangw/ULogic}.}.
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Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful proof paths, faces a discrepancy at the inference stage, as it must sample and try various tactics at each proof state until finding success, unlike its training which does not incorporate learning from failed attempts. Intuitively, a tactic that leads to a failed search path would indicate that similar tactics should receive less attention during the following trials. In this paper, we demonstrate the benefit of training models that additionally learn from failed search paths. Facing the lack of such trial-and-error data in existing open-source theorem-proving datasets, we curate a dataset on intuitionistic propositional logic theorems and formalize it in Lean, such that we can reliably check the correctness of proofs. We compare our model trained on relatively short trial-and-error information (TrialMaster) with models trained only on the correct paths and discover that the former solves more unseen theorems with lower trial searches.
The Path-dependent Neural Jump ODE (PD-NJ-ODE) is a model for online prediction of generic (possibly non-Markovian) stochastic processes with irregular (in time) and potentially incomplete (with respect to coordinates) observations. It is a model for which convergence to the $L^2$-optimal predictor, which is given by the conditional expectation, is established theoretically. Thereby, the training of the model is solely based on a dataset of realizations of the underlying stochastic process, without the need of knowledge of the law of the process. In the case where the underlying process is deterministic, the conditional expectation coincides with the process itself. Therefore, this framework can equivalently be used to learn the dynamics of ODE or PDE systems solely from realizations of the dynamical system with different initial conditions. We showcase the potential of our method by applying it to the chaotic system of a double pendulum. When training the standard PD-NJ-ODE method, we see that the prediction starts to diverge from the true path after about half of the evaluation time. In this work we enhance the model with two novel ideas, which independently of each other improve the performance of our modelling setup. The resulting dynamics match the true dynamics of the chaotic system very closely. The same enhancements can be used to provably enable the PD-NJ-ODE to learn long-term predictions for general stochastic datasets, where the standard model fails. This is verified in several experiments.
Common methods for aligning large language models (LLMs) with desired behaviour heavily rely on human-labelled data. However, as models grow increasingly sophisticated, they will surpass human expertise, and the role of human evaluation will evolve into non-experts overseeing experts. In anticipation of this, we ask: can weaker models assess the correctness of stronger models? We investigate this question in an analogous setting, where stronger models (experts) possess the necessary information to answer questions and weaker models (non-experts) lack this information. The method we evaluate is debate, where two LLM experts each argue for a different answer, and a non-expert selects the answer. We find that debate consistently helps both non-expert models and humans answer questions, achieving 76% and 88% accuracy respectively (naive baselines obtain 48% and 60%). Furthermore, optimising expert debaters for persuasiveness in an unsupervised manner improves non-expert ability to identify the truth in debates. Our results provide encouraging empirical evidence for the viability of aligning models with debate in the absence of ground truth.
Large language models (LLMs) and their fine-tuning techniques have demonstrated superior performance in various language understanding and generation tasks. This paper explores fine-tuning LLMs for stock return forecasting with financial newsflow. In quantitative investing, return forecasting is fundamental for subsequent tasks like stock picking, portfolio optimization, etc. We formulate the model to include text representation and forecasting modules. We propose to compare the encoder-only and decoder-only LLMs, considering they generate text representations in distinct ways. The impact of these different representations on forecasting performance remains an open question. Meanwhile, we compare two simple methods of integrating LLMs' token-level representations into the forecasting module. The experiments on real news and investment universes reveal that: (1) aggregated representations from LLMs' token-level embeddings generally produce return predictions that enhance the performance of long-only and long-short portfolios; (2) in the relatively large investment universe, the decoder LLMs-based prediction model leads to stronger portfolios, whereas in the small universes, there are no consistent winners. Among the three LLMs studied (DeBERTa, Mistral, Llama), Mistral performs more robustly across different universes; (3) return predictions derived from LLMs' text representations are a strong signal for portfolio construction, outperforming conventional sentiment scores.
With the introduction of large language models (LLMs), automatic math reasoning has seen tremendous success. However, current methods primarily focus on providing solutions or using techniques like Chain-of-Thought to enhance problem-solving accuracy. In this paper, we focus on improving the capability of mathematics teaching via a Socratic teaching-based LLM (\texttt{SocraticLLM}), which guides learners toward profound thinking with clarity and self-discovery via conversation. We collect and release a high-quality mathematical teaching dataset, named \texttt{SocraticMATH}, which provides Socratic-style conversations of problems with extra knowledge. Also, we propose a knowledge-enhanced LLM as a strong baseline to generate reliable responses with review, guidance/heuristic, rectification, and summarization. Experimental results show the great advantages of \texttt{SocraticLLM} by comparing it with several strong generative models. The codes and datasets are available on \url{//github.com/ECNU-ICALK/SocraticMath}.
Large language models (LLMs) are known to effectively perform tasks by simply observing few exemplars. However, in low-resource languages, obtaining such hand-picked exemplars can still be challenging, where unsupervised techniques may be necessary. Moreover, competent generative capabilities of LLMs are observed only in high-resource languages, while their performances among under-represented languages fall behind due to pre-training data imbalance. To elicit LLMs' ability onto low-resource languages without any supervised data, we propose to assemble synthetic exemplars from a diverse set of high-resource languages to prompt the LLMs to translate from any language into English. These prompts are then used to create intra-lingual exemplars to perform tasks in the target languages. Our unsupervised prompting method performs on par with supervised few-shot learning in LLMs of different sizes for translations between English and 13 Indic and 21 African low-resource languages. We also show that fine-tuning a 7B model on data generated from our method helps it perform competitively with a 175B model. In non-English translation tasks, our method even outperforms supervised prompting by up to 3 chrF++ in many low-resource languages. When evaluated on zero-shot multilingual summarization, our method surpasses other English-pivoting baselines by up to 4 ROUGE-L and is also favored by GPT-4.
Large language models (LLMs) have demonstrated great success in various fields, benefiting from their huge amount of parameters that store knowledge. However, LLMs still suffer from several key issues, such as hallucination problems, knowledge update issues, and lacking domain-specific expertise. The appearance of retrieval-augmented generation (RAG), which leverages an external knowledge database to augment LLMs, makes up those drawbacks of LLMs. This paper reviews all significant techniques of RAG, especially in the retriever and the retrieval fusions. Besides, tutorial codes are provided for implementing the representative techniques in RAG. This paper further discusses the RAG training, including RAG with/without datastore update. Then, we introduce the application of RAG in representative natural language processing tasks and industrial scenarios. Finally, this paper discusses the future directions and challenges of RAG for promoting its development.
Large language models (LLMs) exhibit superior performance on various natural language tasks, but they are susceptible to issues stemming from outdated data and domain-specific limitations. In order to address these challenges, researchers have pursued two primary strategies, knowledge editing and retrieval augmentation, to enhance LLMs by incorporating external information from different aspects. Nevertheless, there is still a notable absence of a comprehensive survey. In this paper, we propose a review to discuss the trends in integration of knowledge and large language models, including taxonomy of methods, benchmarks, and applications. In addition, we conduct an in-depth analysis of different methods and point out potential research directions in the future. We hope this survey offers the community quick access and a comprehensive overview of this research area, with the intention of inspiring future research endeavors.
Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.
Pre-trained deep neural network language models such as ELMo, GPT, BERT and XLNet have recently achieved state-of-the-art performance on a variety of language understanding tasks. However, their size makes them impractical for a number of scenarios, especially on mobile and edge devices. In particular, the input word embedding matrix accounts for a significant proportion of the model's memory footprint, due to the large input vocabulary and embedding dimensions. Knowledge distillation techniques have had success at compressing large neural network models, but they are ineffective at yielding student models with vocabularies different from the original teacher models. We introduce a novel knowledge distillation technique for training a student model with a significantly smaller vocabulary as well as lower embedding and hidden state dimensions. Specifically, we employ a dual-training mechanism that trains the teacher and student models simultaneously to obtain optimal word embeddings for the student vocabulary. We combine this approach with learning shared projection matrices that transfer layer-wise knowledge from the teacher model to the student model. Our method is able to compress the BERT_BASE model by more than 60x, with only a minor drop in downstream task metrics, resulting in a language model with a footprint of under 7MB. Experimental results also demonstrate higher compression efficiency and accuracy when compared with other state-of-the-art compression techniques.
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