We introduce a dataset of concept learning tasks that helps uncover implicit biases in large language models. Using in-context concept learning experiments, we found that language models may have a bias toward upward monotonicity in quantifiers; such bias is less apparent when the model is tested by direct prompting without concept learning components. This demonstrates that in-context concept learning can be an effective way to discover hidden biases in language models.

Interactive theorem provers (ITPs) require manual formalization, which is labor-intensive and demands expert knowledge. While automated formalization offers a potential solution, it faces two major challenges: model hallucination (e.g., undefined predicates, symbol misuse, and version incompatibility) and the semantic gap caused by ambiguous or missing premises in natural language descriptions. To address these issues, we propose CRAMF, a Concept-driven Retrieval-Augmented Mathematical Formalization framework. CRAMF enhances LLM-based autoformalization by retrieving formal definitions of core mathematical concepts, providing contextual grounding during code generation. However, applying retrieval-augmented generation (RAG) in this setting is non-trivial due to the lack of structured knowledge bases, the polymorphic nature of mathematical concepts, and the high precision required in formal retrieval. We introduce a framework for automatically constructing a concept-definition knowledge base from Mathlib4, the standard mathematical library for the Lean 4 theorem prover, indexing over 26,000 formal definitions and 1,000+ core mathematical concepts. To address conceptual polymorphism, we propose contextual query augmentation with domain- and application-level signals. In addition, we design a dual-channel hybrid retrieval strategy with reranking to ensure accurate and relevant definition retrieval. Experiments on miniF2F, ProofNet, and our newly proposed AdvancedMath benchmark show that CRAMF can be seamlessly integrated into LLM-based autoformalizers, yielding consistent improvements in translation accuracy, achieving up to 62.1% and an average of 29.9% relative improvement.

The study aims to enhance mathematics education accessibility for hard-of-hearing students by developing an accurate Palestinian sign language PSL recognition system using advanced artificial intelligence techniques. Due to the scarcity of digital resources for PSL, a custom dataset comprising 41 mathematical gesture classes was created, and recorded by PSL experts to ensure linguistic accuracy and domain specificity. To leverage state-of-the-art-computer vision techniques, a Vision Transformer ViTModel was fine-tuned for gesture classification. The model achieved an accuracy of 97.59%, demonstrating its effectiveness in recognizing mathematical signs with high precision and reliability. This study highlights the role of deep learning in developing intelligent educational tools that bridge the learning gap for hard-of-hearing students by providing AI-driven interactive solutions to enhance mathematical comprehension. This work represents a significant step toward innovative and inclusive frosting digital integration in specialized learning environments. The dataset is hosted on Hugging Face at https://huggingface.co/datasets/fidaakh/STEM_data.

Large Language Models have demonstrated remarkable capabilities in natural language processing tasks, including mathematical problem-solving that requires multi-step logical reasoning. However, challenges persist in automating the identification of key mathematical concepts, understanding their interrelations, and formalizing proofs within a rigorous framework. We present a novel framework that leverages knowledge graphs to augment LLMs to construct and formalize mathematical proofs. Our results demonstrate significant performance improvements across multiple datasets, with using knowledge graphs, achieving up to a 34% success rate on the MUSTARDSAUCE dataset on o1-mini and consistently outperforming baseline approaches by 2-11% across different models. We show how this approach bridges the gap between natural language understanding and formal logic proof systems and achieve elevated results for foundation models over baseline.

Mathematics is a highly specialized domain with its own unique set of challenges. Despite this, there has been relatively little research on natural language processing for mathematical texts, and there are few mathematical language resources aimed at NLP. In this paper, we aim to provide annotated corpora that can be used to study the language of mathematics in different contexts, ranging from fundamental concepts found in textbooks to advanced research mathematics. We preprocess the corpora with a neural parsing model and some manual intervention to provide part-of-speech tags, lemmas, and dependency trees. In total, we provide 182397 sentences across three corpora. We then aim to test and evaluate several noteworthy natural language processing models using these corpora, to show how well they can adapt to the domain of mathematics and provide useful tools for exploring mathematical language. We evaluate several neural and symbolic models against benchmarks that we extract from the corpus metadata to show that terminology extraction and definition extraction do not easily generalize to mathematics, and that additional work is needed to achieve good performance on these metrics. Finally, we provide a learning assistant that grants access to the content of these corpora in a context-sensitive manner, utilizing text search and entity linking. Though our corpora and benchmarks provide useful metrics for evaluating mathematical language processing, further work is necessary to adapt models to mathematics in order to provide more effective learning assistants and apply NLP methods to different mathematical domains.

Self-correction is emerging as a promising approach to mitigate the issue of hallucination in Large Language Models (LLMs). To facilitate effective self-correction, recent research has proposed mistake detection as its initial step. However, current literature suggests that LLMs often struggle with reliably identifying reasoning mistakes when using simplistic prompting strategies. To address this challenge, we introduce a unique prompting strategy, termed the Pedagogical Chain-of-Thought (PedCoT), which is specifically designed to guide the identification of reasoning mistakes, particularly mathematical reasoning mistakes. PedCoT consists of pedagogical principles for prompts (PPP) design, two-stage interaction process (TIP) and grounded PedCoT prompts, all inspired by the educational theory of the Bloom Cognitive Model (BCM). We evaluate our approach on two public datasets featuring math problems of varying difficulty levels. The experiments demonstrate that our zero-shot prompting strategy significantly outperforms strong baselines. The proposed method can achieve the goal of reliable mathematical mistake identification and provide a foundation for automatic math answer grading. The results underscore the significance of educational theory, serving as domain knowledge, in guiding prompting strategy design for addressing challenging tasks with LLMs effectively.

MathGloss is a project to create a knowledge graph (KG) for undergraduate mathematics from text, automatically, using modern natural language processing (NLP) tools and resources already available on the web. MathGloss is a linked database of undergraduate concepts in mathematics. So far, it combines five resources: (i) Wikidata, a collaboratively edited, multilingual knowledge graph hosted by the Wikimedia Foundation, (ii) terms covered in mathematics courses at the University of Chicago, (iii) the syllabus of the French undergraduate mathematics curriculum which includes hyperlinks to the automated theorem prover Lean 4, (iv) MuLiMa, a multilingual dictionary of mathematics curated by mathematicians, and (v) the nLab, a wiki for category theory also curated by mathematicians. MathGloss's goal is to bring together resources for learning mathematics and to allow every mathematician to tailor their learning to their own preferences. Moreover, by organizing different resources for learning undergraduate mathematics alongside those for learning formal mathematics, we hope to make it easier for mathematicians and formal tools (theorem provers, computer algebra systems, etc) experts to "understand" each other and break down some of the barriers to formal math.

Machine learning (ML) is everywhere these days. It helps us better detect malware and insider threats by continuously analyzing data to find patterns. It increases our productivity, improves service quality, and can even entertain us by recommending the movies we are likely to enjoy. ML capabilities have pushed a lot of people to start exploring machine learning, but writing algorithms and programs for ML isn't easy and requires significant mathematical knowledge. This track will build the basic foundation required for ML model development. It breaks down complicated mathematical concepts into easy-to-read theory followed by practical tasks.

A collection of resources to learn mathematics for machine learning. This is probably the place you want to start. Pay close attention to the notation and get comfortable with it. Machine learning deals with data and in turn uncertainty which is what statistics aims to teach. Get comfortable with topics like estimators, statistical significance, etc.

Most traders or investors in the financial market dream of having a system that automatically trades for them without the need for them to do anything else trading related. While no such system truly exists, algorithmic trading comes very close. Based on a recent market report, the global algorithmic market valued at $10.3 thousand in 2018 is anticipated to witness a CAGR of 10% over a forecast period (2022-2027). The demand for a fast, reliable, and profitable system is spearheading the growth of algorithmic trading. However, despite the availability of various materials, a beginner with a non-technical background might find it very difficult to follow a systematic approach to learning algorithmic trading.