Daily Papers

There is growing evidence that pretraining on high quality, carefully thought-out tokens such as code or mathematics plays an important role in improving the reasoning abilities of large language models. For example, Minerva, a PaLM model finetuned on billions of tokens of mathematical documents from arXiv and the web, reported dramatically improved performance on problems that require quantitative reasoning. However, because all known open source web datasets employ preprocessing that does not faithfully preserve mathematical notation, the benefits of large scale training on quantitive web documents are unavailable to the research community. We introduce OpenWebMath, an open dataset inspired by these works containing 14.7B tokens of mathematical webpages from Common Crawl. We describe in detail our method for extracting text and LaTeX content and removing boilerplate from HTML documents, as well as our methods for quality filtering and deduplication. Additionally, we run small-scale experiments by training 1.4B parameter language models on OpenWebMath, showing that models trained on 14.7B tokens of our dataset surpass the performance of models trained on over 20x the amount of general language data. We hope that our dataset, openly released on the Hugging Face Hub, will help spur advances in the reasoning abilities of large language models.

Mathematical formulas are a fundamental and widely used component in various scientific fields, serving as a universal language for expressing complex concepts and relationships. While state-of-the-art transformer models excel in processing and understanding natural language, they encounter challenges with mathematical notation, which involves a complex structure and diverse representations. This study focuses on the development of specialized training datasets to enhance the encoding of mathematical content. We introduce Math Mutator (MAMUT), a framework capable of generating equivalent and falsified versions of a given mathematical formula in LaTeX notation, effectively capturing the mathematical variety in notation of the same concept. Based on MAMUT, we have generated four large mathematical datasets containing diverse notation, which can be used to train language models with enhanced mathematical embeddings.

This paper surveys and organizes research works in a new paradigm in natural language processing, which we dub "prompt-based learning". Unlike traditional supervised learning, which trains a model to take in an input x and predict an output y as P(y|x), prompt-based learning is based on language models that model the probability of text directly. To use these models to perform prediction tasks, the original input x is modified using a template into a textual string prompt x' that has some unfilled slots, and then the language model is used to probabilistically fill the unfilled information to obtain a final string x, from which the final output y can be derived. This framework is powerful and attractive for a number of reasons: it allows the language model to be pre-trained on massive amounts of raw text, and by defining a new prompting function the model is able to perform few-shot or even zero-shot learning, adapting to new scenarios with few or no labeled data. In this paper we introduce the basics of this promising paradigm, describe a unified set of mathematical notations that can cover a wide variety of existing work, and organize existing work along several dimensions, e.g.the choice of pre-trained models, prompts, and tuning strategies. To make the field more accessible to interested beginners, we not only make a systematic review of existing works and a highly structured typology of prompt-based concepts, but also release other resources, e.g., a website http://pretrain.nlpedia.ai/ including constantly-updated survey, and paperlist.

Recognizing handwritten mathematical expressions (HMER) is a challenging task due to the inherent two-dimensional structure, varying symbol scales, and complex spatial relationships among symbols. In this paper, we present a self-supervised learning (SSL) framework for HMER that eliminates the need for expensive labeled data. Our approach begins by pretraining an image encoder using a combination of global and local contrastive loss, enabling the model to learn both holistic and fine-grained representations. A key contribution of this work is a novel self-supervised attention network, which is trained using a progressive spatial masking strategy. This attention mechanism is designed to learn semantically meaningful focus regions, such as operators, exponents, and nested mathematical notation, without requiring any supervision. The progressive masking curriculum encourages the network to become increasingly robust to missing or occluded visual information, ultimately improving structural understanding. Our complete pipeline consists of (1) self-supervised pretraining of the encoder, (2) self-supervised attention learning, and (3) supervised fine-tuning with a transformer decoder to generate LATEX sequences. Extensive experiments on CROHME benchmarks demonstrate that our method outperforms existing SSL and fully supervised baselines, validating the effectiveness of our progressive attention mechanism in enhancing HMER performance. Our codebase can be found here.

Large-scale data sets on scholarly publications are the basis for a variety of bibliometric analyses and natural language processing (NLP) applications. Especially data sets derived from publication's full-text have recently gained attention. While several such data sets already exist, we see key shortcomings in terms of their domain and time coverage, citation network completeness, and representation of full-text content. To address these points, we propose a new version of the data set unarXive. We base our data processing pipeline and output format on two existing data sets, and improve on each of them. Our resulting data set comprises 1.9 M publications spanning multiple disciplines and 32 years. It furthermore has a more complete citation network than its predecessors and retains a richer representation of document structure as well as non-textual publication content such as mathematical notation. In addition to the data set, we provide ready-to-use training/test data for citation recommendation and IMRaD classification. All data and source code is publicly available at https://github.com/IllDepence/unarXive.

Formula recognition presents significant challenges due to the complicated structure and varied notation of mathematical expressions. Despite continuous advancements in formula recognition models, the evaluation metrics employed by these models, such as BLEU and Edit Distance, still exhibit notable limitations. They overlook the fact that the same formula has diverse representations and is highly sensitive to the distribution of training data, thereby causing the unfairness in formula recognition evaluation. To this end, we propose a Character Detection Matching (CDM) metric, ensuring the evaluation objectivity by designing a image-level rather than LaTex-level metric score. Specifically, CDM renders both the model-predicted LaTeX and the ground-truth LaTeX formulas into image-formatted formulas, then employs visual feature extraction and localization techniques for precise character-level matching, incorporating spatial position information. Such a spatially-aware and character-matching method offers a more accurate and equitable evaluation compared with previous BLEU and Edit Distance metrics that rely solely on text-based character matching. Experimentally, we evaluated various formula recognition models using CDM, BLEU, and ExpRate metrics. Their results demonstrate that the CDM aligns more closely with human evaluation standards and provides a fairer comparison across different models by eliminating discrepancies caused by diverse formula representations.

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature has also led to a lack of unification in notation and language across Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL, and compare the recently published TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.