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Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LMMs to change how mathematicians work.

相關內容

大語言模型是基于海量文本數據訓練的深度學習模型。它不僅能夠生成自然語言文本,還能夠深入理解文本含義,處理各種自然語言任務,如文本摘要、問答、翻譯等。2023年,大語言模型及其在人工智能領域的應用已成為全球科技研究的熱點,其在規模上的增長尤為引人注目,參數量已從最初的十幾億躍升到如今的一萬億。參數量的提升使得模型能夠更加精細地捕捉人類語言微妙之處,更加深入地理解人類語言的復雜性。在過去的一年里,大語言模型在吸納新知識、分解復雜任務以及圖文對齊等多方面都有顯著提升。隨著技術的不斷成熟,它將不斷拓展其應用范圍,為人類提供更加智能化和個性化的服務,進一步改善人們的生活和生產方式。

Large language models (LLMs) inevitably exhibit hallucinations since the accuracy of generated texts cannot be secured solely by the parametric knowledge they encapsulate. Although retrieval-augmented generation (RAG) is a practicable complement to LLMs, it relies heavily on the relevance of retrieved documents, raising concerns about how the model behaves if retrieval goes wrong. To this end, we propose the Corrective Retrieval Augmented Generation (CRAG) to improve the robustness of generation. Specifically, a lightweight retrieval evaluator is designed to assess the overall quality of retrieved documents for a query, returning a confidence degree based on which different knowledge retrieval actions can be triggered. Since retrieval from static and limited corpora can only return sub-optimal documents, large-scale web searches are utilized as an extension for augmenting the retrieval results. Besides, a decompose-then-recompose algorithm is designed for retrieved documents to selectively focus on key information and filter out irrelevant information in them. CRAG is plug-and-play and can be seamlessly coupled with various RAG-based approaches. Experiments on four datasets covering short- and long-form generation tasks show that CRAG can significantly improve the performance of RAG-based approaches.

While pretrained language models (PLMs) have been shown to possess a plethora of linguistic knowledge, the existing body of research has largely neglected extralinguistic knowledge, which is generally difficult to obtain by pretraining on text alone. Here, we contribute to closing this gap by examining geolinguistic knowledge, i.e., knowledge about geographic variation in language. We introduce geoadaptation, an intermediate training step that couples language modeling with geolocation prediction in a multi-task learning setup. We geoadapt four PLMs, covering language groups from three geographic areas, and evaluate them on five different tasks: fine-tuned (i.e., supervised) geolocation prediction, zero-shot (i.e., unsupervised) geolocation prediction, fine-tuned language identification, zero-shot language identification, and zero-shot prediction of dialect features. Geoadaptation is very successful at injecting geolinguistic knowledge into the PLMs: the geoadapted PLMs consistently outperform PLMs adapted using only language modeling (by especially wide margins on zero-shot prediction tasks), and we obtain new state-of-the-art results on two benchmarks for geolocation prediction and language identification. Furthermore, we show that the effectiveness of geoadaptation stems from its ability to geographically retrofit the representation space of the PLMs.

Large language models (LLMs), exemplified by ChatGPT, have gained considerable attention for their excellent natural language processing capabilities. Nonetheless, these LLMs present many challenges, particularly in the realm of trustworthiness. Therefore, ensuring the trustworthiness of LLMs emerges as an important topic. This paper introduces TrustLLM, a comprehensive study of trustworthiness in LLMs, including principles for different dimensions of trustworthiness, established benchmark, evaluation, and analysis of trustworthiness for mainstream LLMs, and discussion of open challenges and future directions. Specifically, we first propose a set of principles for trustworthy LLMs that span eight different dimensions. Based on these principles, we further establish a benchmark across six dimensions including truthfulness, safety, fairness, robustness, privacy, and machine ethics. We then present a study evaluating 16 mainstream LLMs in TrustLLM, consisting of over 30 datasets. Our findings firstly show that in general trustworthiness and utility (i.e., functional effectiveness) are positively related. Secondly, our observations reveal that proprietary LLMs generally outperform most open-source counterparts in terms of trustworthiness, raising concerns about the potential risks of widely accessible open-source LLMs. However, a few open-source LLMs come very close to proprietary ones. Thirdly, it is important to note that some LLMs may be overly calibrated towards exhibiting trustworthiness, to the extent that they compromise their utility by mistakenly treating benign prompts as harmful and consequently not responding. Finally, we emphasize the importance of ensuring transparency not only in the models themselves but also in the technologies that underpin trustworthiness. Knowing the specific trustworthy technologies that have been employed is crucial for analyzing their effectiveness.

Multi-modal large language models (MLLMs) have been shown to efficiently integrate natural language with visual information to handle multi-modal tasks. However, MLLMs still face a fundamental limitation of hallucinations, where they tend to generate erroneous or fabricated information. In this paper, we address hallucinations in MLLMs from a novel perspective of representation learning. We first analyzed the representation distribution of textual and visual tokens in MLLM, revealing two important findings: 1) there is a significant gap between textual and visual representations, indicating unsatisfactory cross-modal representation alignment; 2) representations of texts that contain and do not contain hallucinations are entangled, making it challenging to distinguish them. These two observations inspire us with a simple yet effective method to mitigate hallucinations. Specifically, we introduce contrastive learning into MLLMs and use text with hallucination as hard negative examples, naturally bringing representations of non-hallucinative text and visual samples closer while pushing way representations of non-hallucinating and hallucinative text. We evaluate our method quantitatively and qualitatively, showing its effectiveness in reducing hallucination occurrences and improving performance across multiple benchmarks. On the MMhal-Bench benchmark, our method obtains a 34.66% /29.5% improvement over the baseline MiniGPT-4/LLaVA. Our code is available on //github.com/X-PLUG/mPLUG-HalOwl/tree/main/hacl.

Retrieval-augmented language models (RaLM) have demonstrated the potential to solve knowledge-intensive natural language processing (NLP) tasks by combining a non-parametric knowledge base with a parametric language model. Instead of fine-tuning a fully parametric model, RaLM excels at its low-cost adaptation to the latest data and better source attribution mechanisms. Among various RaLM approaches, iterative RaLM delivers a better generation quality due to a more frequent interaction between the retriever and the language model. Despite the benefits, iterative RaLM usually encounters high overheads due to the frequent retrieval step. To this end, we propose RaLMSpec, a speculation-inspired framework that provides generic speed-up over iterative RaLM while preserving the same model outputs through speculative retrieval and batched verification. By further incorporating prefetching, optimal speculation stride scheduler, and asynchronous verification, RaLMSpec can automatically exploit the acceleration potential to the fullest. For naive iterative RaLM serving, extensive evaluations over three language models on four downstream QA datasets demonstrate that RaLMSpec can achieve a speed-up ratio of 1.75-2.39x, 1.04-1.39x, and 1.31-1.77x when the retriever is an exact dense retriever, approximate dense retriever, and sparse retriever respectively compared with the baseline. For KNN-LM serving, RaLMSpec can achieve a speed-up ratio up to 7.59x and 2.45x when the retriever is an exact dense retriever and approximate dense retriever, respectively, compared with the baseline.

While large language models (LLMs) have enabled learning knowledge from the pre-training corpora, the acquired knowledge may be fundamentally incorrect or outdated over time, which necessitates rectifying the knowledge of the language model (LM) after the training. A promising approach involves employing a hyper-network to generate parameter shift, whereas existing hyper-networks suffer from inferior scalability in synchronous editing operation amount. To mitigate the problem, we propose the MAssive Language Model Editing Network (MALMEN), which formulates the parameter shift aggregation as the least square problem, subsequently updating the LM parameters using the normal equation. To accommodate editing multiple facts simultaneously with limited memory budgets, we separate the computation on the hyper-network and LM, enabling arbitrary batch size on both neural networks. Our method is evaluated by editing up to thousands of facts on LMs with different architectures, i.e., BERT-base, GPT-2, T5-XL (2.8B), and GPT-J (6B), across various knowledge-intensive NLP tasks, i.e., closed book fact-checking and question answering. Remarkably, MALMEN is capable of editing hundreds of times more facts than strong baselines with the identical hyper-network architecture and outperforms editor specifically designed for GPT. Our code is available at //github.com/ChenmienTan/malmen.

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.

External knowledge is often useful for natural language understanding tasks. We introduce a contextual text representation model called Conceptual-Contextual (CC) embeddings, which incorporates structured knowledge into text representations. Unlike entity embedding methods, our approach encodes a knowledge graph into a context model. CC embeddings can be easily reused for a wide range of tasks just like pre-trained language models. Our model effectively encodes the huge UMLS database by leveraging semantic generalizability. Experiments on electronic health records (EHRs) and medical text processing benchmarks showed our model gives a major boost to the performance of supervised medical NLP tasks.

External knowledge is often useful for natural language understanding tasks. We introduce a contextual text representation model called Conceptual-Contextual (CC) embeddings, which incorporates structured knowledge into text representations. Unlike entity embedding methods, our approach encodes a knowledge graph into a context model. CC embeddings can be easily reused for a wide range of tasks just like pre-trained language models. Our model effectively encodes the huge UMLS database by leveraging semantic generalizability. Experiments on electronic health records (EHRs) and medical text processing benchmarks showed our model gives a major boost to the performance of supervised medical NLP tasks.

Deep learning has yielded state-of-the-art performance on many natural language processing tasks including named entity recognition (NER). However, this typically requires large amounts of labeled data. In this work, we demonstrate that the amount of labeled training data can be drastically reduced when deep learning is combined with active learning. While active learning is sample-efficient, it can be computationally expensive since it requires iterative retraining. To speed this up, we introduce a lightweight architecture for NER, viz., the CNN-CNN-LSTM model consisting of convolutional character and word encoders and a long short term memory (LSTM) tag decoder. The model achieves nearly state-of-the-art performance on standard datasets for the task while being computationally much more efficient than best performing models. We carry out incremental active learning, during the training process, and are able to nearly match state-of-the-art performance with just 25\% of the original training data.

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