Mathematical error detection in educational settings presents a significant challenge for Multimodal Large Language Models (MLLMs), requiring a sophisticated understanding of both visual and textual mathematical content along with complex reasoning capabilities. Though effective in mathematical problem-solving, MLLMs often struggle with the nuanced task of **identifying and categorizing student errors in multimodal mathematical contexts**. Therefore, we introduce **MathAgent, a novel Mixture-of-Math-Agent framework** specifically designed to address these challenges. Our approach decomposes error detection into three phases with specialized agents: an image-text consistency validator, a visual semantic interpreter, and an integrative error analyzer. This architecture enables more accurate processing of multimodal mathematical content by explicitly modeling the relationships between multimodal problems and student solution steps. We evaluate MathAgent on real-world educational data, demonstrating approximately 5% higher accuracy in error step identification and 3% improvement in error categorization compared to baseline models. Furthermore, MathAgent has been successfully deployed in an educational platform serving over one million K-12 students, achieving nearly 90% student satisfaction while generating significant cost savings by reducing manual error detection.

Mathematical reasoning, a core aspect of human cognition, is vital across many domains, from educational problem-solving to scientific advancements. As artificial general intelligence (AGI) progresses, integrating large language models (LLMs) with mathematical reasoning tasks is becoming increasingly significant. This survey provides **the first comprehensive analysis of mathematical reasoning in the era of multimodal large language models (MLLMs)**. We review over 200 studies published since 2021, and examine the state-of-the-art developments in Math-LLMs, with a focus on multimodal settings. We categorize the field into three dimensions: benchmarks, methodologies, and challenges. In particular, we explore multimodal mathematical reasoning pipeline, as well as the role of (M)LLMs and the associated methodologies. Finally, we identify five major challenges hindering the realization of AGI in this domain, offering insights into the future direction for enhancing multimodal reasoning capabilities. This survey serves as a critical resource for the research community in advancing the capabilities of LLMs to tackle complex multimodal reasoning tasks.

Recent advances in large language models have revolutionized many sectors, including the database industry. One common challenge when dealing with large volumes of tabular data is the pervasive use of abbreviated column names, which can negatively impact performance on various data search, access, and understanding tasks. To address this issue, we introduce a new task, called NameGuess, to expand column names (used in database schema) as a natural language generation problem. We create a training dataset of 384K abbreviated-expanded column pairs using a new data fabrication method and a human-annotated evaluation benchmark that includes 9.2K examples from real-world tables. To tackle the complexities associated with polysemy and ambiguity in NameGuess, we enhance auto-regressive language models by conditioning on table content and column header names – yielding a fine-tuned model (with 2.7B parameters) that matches human performance. Furthermore, we conduct a comprehensive analysis (on multiple LLMs) to validate the effectiveness of table content in NameGuess and identify promising future opportunities. Code has been made available at https://github.com/amazon-science/nameguess.

Given a data lake of tabular data as well as a query table, how can we retrieve all the tables in the data lake that can be unioned with the query table? Table union search constitutes an essential task in data discovery and preparation as it enables data scientists to navigate massive open data repositories. Existing methods identify uniability based on column representations (word surface forms or token embeddings) and column relation represented by column representation similarity. However, the semantic similarity obtained between column representations is often insufficient to reveal latent relational features to describe the column relation between pair of columns and not robust to the table noise. To address these issues, in this paper, we propose a multi-stage self-supervised table union search framework called AutoTUS, which represents column relation as a vector– column relational representation and learn column relational representation in a multi-stage manner that can better describe column relation for unionability prediction. In particular, the large language model powered contextualized column relation encoder is updated by adaptive clustering and pseudo label classification iteratively so that the better column relational representation can be learned. Moreover, to improve the robustness of the model against table noises, we propose table noise generator to add table noise to the training table data. Experiments on real-world datasets as well as synthetic test set augmented with table noise show that AutoTUS achieves 5.2% performance gain over the SOTA baseline.

Large language models have achieved high performance on various question answering (QA) benchmarks, but the explainability of their output remains elusive. Structured explanations, called entailment trees, were recently suggested as a way to explain the reasoning behind a QA system’s answer. In order to better generate such entailment trees, we propose an architecture called Iterative Retrieval-Generation Reasoner (IRGR). Our model is able to explain a given hypothesis by systematically generating a step-by-step explanation from textual premises. The IRGR model iteratively searches for suitable premises, constructing a single entailment step at a time. Contrary to previous approaches, our method combines generation steps and retrieval of premises, allowing the model to leverage intermediate conclusions, and mitigating the input size limit of baseline encoder-decoder models. We conduct experiments using the EntailmentBank dataset, where we outperform existing benchmarks on premise retrieval and entailment tree generation, with around 300% gain in overall correctness.

People frequently interact with information retrieval (IR) systems, however, IR models exhibit biases and discrimination towards various demographics. The in-processing fair ranking methods provides a trade-offs between accuracy and fairness through adding a fairness-related regularization term in the loss function. However, there haven’t been intuitive objective functions that depend on the click probability and user engagement to directly optimize towards this. In this work, we propose the In-Batch Balancing Regularization (IBBR) to mitigate the ranking disparity among subgroups. In particular, we develop a differentiable normed Pairwise Ranking Fairness (nPRF) and leverage the T-statistics on top of nPRF over subgroups as a regularization to improve fairness. Empirical results with the BERT-based neural rankers on the MS MARCO Passage Retrieval dataset with the human-annotated non-gendered queries benchmark (CITATION) show that our IBBR method with nPRF achieves significantly less bias with minimal degradation in ranking performance compared with the baseline.