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Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (\eg, LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose \emph{MetaMath}, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called {MetaMathQA}. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (\ie, GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves $66.4\%$ on GSM8K and $19.4\%$ on MATH, exceeding the state-of-the-art models of the same size by $11.5\%$ and $8.7\%$. Particularly, {MetaMath-70B} achieves an accuracy of $82.3\%$ on {GSM8K}, slightly better than {GPT-3.5-Turbo}. We release the {MetaMathQA} dataset, the {MetaMath} models with different model sizes and the training code for public use.

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Lemmatization holds significance in both natural language processing (NLP) and linguistics, as it effectively decreases data density and aids in comprehending contextual meaning. However, due to the highly inflected nature and morphological richness, lemmatization in Bangla text poses a complex challenge. In this study, we propose linguistic rules for lemmatization and utilize a dictionary along with the rules to design a lemmatizer specifically for Bangla. Our system aims to lemmatize words based on their parts of speech class within a given sentence. Unlike previous rule-based approaches, we analyzed the suffix marker occurrence according to the morpho-syntactic values and then utilized sequences of suffix markers instead of entire suffixes. To develop our rules, we analyze a large corpus of Bangla text from various domains, sources, and time periods to observe the word formation of inflected words. The lemmatizer achieves an accuracy of 96.36% when tested against a manually annotated test dataset by trained linguists and demonstrates competitive performance on three previously published Bangla lemmatization datasets. We are making the code and datasets publicly available at //github.com/eblict-gigatech/BanLemma in order to contribute to the further advancement of Bangla NLP.

Large language models (LLMs) are powerful AI tools that can generate and comprehend natural language text and other complex information. However, the field lacks a mathematical framework to systematically describe, compare and improve LLMs. We propose Hex a framework that clarifies key terms and concepts in LLM research, such as hallucinations, alignment, self-verification and chain-of-thought reasoning. The Hex framework offers a precise and consistent way to characterize LLMs, identify their strengths and weaknesses, and integrate new findings. Using Hex, we differentiate chain-of-thought reasoning from chain-of-thought prompting and establish the conditions under which they are equivalent. This distinction clarifies the basic assumptions behind chain-of-thought prompting and its implications for methods that use it, such as self-verification and prompt programming. Our goal is to provide a formal framework for LLMs that can help both researchers and practitioners explore new possibilities for generative AI. We do not claim to have a definitive solution, but rather a tool for opening up new research avenues. We argue that our formal definitions and results are crucial for advancing the discussion on how to build generative AI systems that are safe, reliable, fair and robust, especially in domains like healthcare and software engineering.

Recently, pre-trained large language models (LLMs) have shown impressive abilities in generating codes from natural language descriptions, repairing buggy codes, translating codes between languages, and retrieving relevant code segments. However, the evaluation of these models has often been performed in a scattered way on only one or two specific tasks, in a few languages, at a partial granularity (e.g., function) level, and in many cases without proper training data. Even more concerning is that in most cases the evaluation of generated codes has been done in terms of mere lexical overlap with a reference code rather than actual execution. We introduce xCodeEval, the largest executable multilingual multitask benchmark to date consisting of $25$M document-level coding examples ($16.5$B tokens) from about $7.5$K unique problems covering up to $11$ programming languages with execution-level parallelism. It features a total of $7$ tasks involving code understanding, generation, translation and retrieval. xCodeEval adopts an execution-based evaluation and offers a multilingual code execution engine, ExecEval that supports unit test based execution in all the $11$ languages. To address the challenge of balancing the distributions of text-code samples over multiple attributes in validation/test sets, we propose a novel data splitting and a data selection schema based on the geometric mean and graph-theoretic principle. Our experiments with OpenAI's LLMs (zero-shot) and open-LLMs (zero-shot and fine-tuned) on the tasks and languages demonstrate **xCodeEval** to be quite challenging as per the current advancements in language models.

Large language models (LLMs) can learn to perform a wide range of natural language tasks from just a handful of in-context examples. However, for generating strings from highly structured languages (e.g., semantic parsing to complex domain-specific languages), it is challenging for the LLM to generalize from just a few exemplars. We propose \emph{grammar prompting}, a simple approach to enable LLMs to use external knowledge and domain-specific constraints, expressed through a grammar in Backus--Naur Form (BNF), during in-context learning. Grammar prompting augments each demonstration example with a specialized grammar that is minimally sufficient for generating the particular output example, where the specialized grammar is a subset of the full DSL grammar. For inference, the LLM first predicts a BNF grammar given a test input, and then generates the output according to the rules of the grammar. Experiments demonstrate that grammar prompting can enable LLMs to perform competitively on a diverse set of DSL generation tasks, including semantic parsing (SMCalFlow, Overnight, GeoQuery), PDDL planning, and SMILES-based molecule generation.

Large language models (LLMs) have achieved remarkable breakthroughs in new dialogue capabilities, refreshing human's impressions on dialogue systems. The long-standing goal of dialogue systems is to be human-like enough to establish long-term connections with users by satisfying the need for communication, affection and social belonging. Therefore, there has been an urgent need to evaluate LLMs as human-like dialogue systems. In this paper, we propose DialogBench, a dialogue evaluation benchmark that currently contains $12$ dialogue tasks to assess the capabilities of LLMs as human-like dialogue systems should have. Specifically, we prompt GPT-4 to generate evaluation instances for each task. We first design the basic prompt based on widely-used design principles and further mitigate the existing biases to generate higher-quality evaluation instances. Our extensive test over $28$ LLMs (including pre-trained and supervised instruction-tuning) shows that instruction fine-tuning benefits improve the human likeness of LLMs to a certain extent, but there is still much room to improve those capabilities for most LLMs as human-like dialogue systems. In addition, experimental results also indicate that LLMs perform differently in various abilities that human-like dialogue systems should have. We will publicly release DialogBench, along with the associated evaluation code for the broader research community.

Large language models (LLMs) have demonstrated impressive language understanding and generation capabilities, enabling them to answer a wide range of questions across various domains. However, these models are not flawless and often produce responses that contain errors or misinformation. These inaccuracies, commonly referred to as hallucinations, render LLMs unreliable and even unusable in many scenarios. In this paper, our focus is on mitigating the issue of hallucination in LLMs, particularly in the context of question-answering. Instead of attempting to answer all questions, we explore a refusal mechanism that instructs LLMs to refuse to answer challenging questions in order to avoid errors. We then propose a simple yet effective solution called Learn to Refuse (L2R), which incorporates the refusal mechanism to enable LLMs to recognize and refuse to answer questions that they find difficult to address. To achieve this, we utilize a structured knowledge base to represent all the LLM's understanding of the world, enabling it to provide traceable gold knowledge. This knowledge base is separate from the LLM and initially empty, and it is progressively expanded with validated knowledge. When an LLM encounters questions outside its domain, the system recognizes its knowledge scope and determines whether it can answer the question independently. Additionally, we introduce a method for automatically and efficiently expanding the knowledge base of LLMs. Through qualitative and quantitative analysis, we demonstrate that our approach enhances the controllability and reliability of LLMs.

Neural language models are probabilistic models of human text. They are predominantly trained using maximum likelihood estimation (MLE), which is equivalent to minimizing the forward cross-entropy between the empirical data distribution and the model distribution. However, various degeneration phenomena are still widely observed when decoding from the distributions learned by such models. We establish that the forward cross-entropy is suboptimal as a distance metric for aligning human and model distribution due to its (1) recall-prioritization (2) negative diversity ignorance and (3) train-test mismatch. In this paper, we propose Earth Mover Distance Optimization (EMO) for auto-regressive language modeling. EMO capitalizes on the inherent properties of earth mover distance to address the aforementioned challenges. Due to the high complexity of direct computation, we further introduce a feasible upper bound for EMO to ease end-to-end training. Upon extensive evaluation of language models trained using EMO and MLE. We find that EMO demonstrates a consistently better language modeling performance than MLE across domains. Moreover, EMO demonstrates noteworthy enhancements in downstream performance with minimal fine-tuning on merely 25,000 sentences. This highlights the tremendous potential of EMO as a lightweight calibration method for enhancing large-scale pre-trained language models.

Large language models (LLMs) have demonstrated impressive capabilities in natural language processing. However, their internal mechanisms are still unclear and this lack of transparency poses unwanted risks for downstream applications. Therefore, understanding and explaining these models is crucial for elucidating their behaviors, limitations, and social impacts. In this paper, we introduce a taxonomy of explainability techniques and provide a structured overview of methods for explaining Transformer-based language models. We categorize techniques based on the training paradigms of LLMs: traditional fine-tuning-based paradigm and prompting-based paradigm. For each paradigm, we summarize the goals and dominant approaches for generating local explanations of individual predictions and global explanations of overall model knowledge. We also discuss metrics for evaluating generated explanations, and discuss how explanations can be leveraged to debug models and improve performance. Lastly, we examine key challenges and emerging opportunities for explanation techniques in the era of LLMs in comparison to conventional machine learning models.

The emergence of large language models (LLMs) has substantially influenced natural language processing, demonstrating exceptional results across various tasks. In this study, we employ ``Introspective Tips" to facilitate LLMs in self-optimizing their decision-making. By introspectively examining trajectories, LLM refines its policy by generating succinct and valuable tips. Our method enhances the agent's performance in both few-shot and zero-shot learning situations by considering three essential scenarios: learning from the agent's past experiences, integrating expert demonstrations, and generalizing across diverse games. Importantly, we accomplish these improvements without fine-tuning the LLM parameters; rather, we adjust the prompt to generalize insights from the three aforementioned situations. Our framework not only supports but also emphasizes the advantage of employing LLM in in-contxt decision-making. Experiments involving over 100 games in TextWorld illustrate the superior performance of our approach.

Pre-trained language representation models, such as BERT, capture a general language representation from large-scale corpora, but lack domain-specific knowledge. When reading a domain text, experts make inferences with relevant knowledge. For machines to achieve this capability, we propose a knowledge-enabled language representation model (K-BERT) with knowledge graphs (KGs), in which triples are injected into the sentences as domain knowledge. However, too much knowledge incorporation may divert the sentence from its correct meaning, which is called knowledge noise (KN) issue. To overcome KN, K-BERT introduces soft-position and visible matrix to limit the impact of knowledge. K-BERT can easily inject domain knowledge into the models by equipped with a KG without pre-training by-self because it is capable of loading model parameters from the pre-trained BERT. Our investigation reveals promising results in twelve NLP tasks. Especially in domain-specific tasks (including finance, law, and medicine), K-BERT significantly outperforms BERT, which demonstrates that K-BERT is an excellent choice for solving the knowledge-driven problems that require experts.

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