Large Language Models (LLMs) have achieved human-level proficiency across diverse tasks, but their ability to perform rigorous mathematical problem solving remains an open challenge. In this work, we investigate a fundamental yet computationally intractable problem: determining whether a given multivariate polynomial is nonnegative. This problem, closely related to Hilbert's Seventeenth Problem, plays a crucial role in global polynomial optimization and has applications in various fields. First, we introduce SoS-1K, a meticulously curated dataset of approximately 1,000 polynomials, along with expert-designed reasoning instructions based on five progressively challenging criteria. Evaluating multiple state-of-the-art LLMs, we find that without structured guidance, all models perform only slightly above the random guess baseline 50%. However, high-quality reasoning instructions significantly improve accuracy, boosting performance up to 81%. Furthermore, our 7B model, SoS-7B, fine-tuned on SoS-1K for just 4 hours, outperforms the 671B DeepSeek-V3 and GPT-4o-mini in accuracy while only requiring 1.8% and 5% of the computation time needed for letters, respectively. Our findings highlight the potential of LLMs to push the boundaries of mathematical reasoning and tackle NP-hard problems.

The capabilities of Large Language Models (LLMs) have significantly evolved, extending from natural language processing to complex tasks like code understanding and generation. We expand the scope of LLMs' capabilities to a broader context, using LLMs to execute code snippets to obtain the output. This paper pioneers the exploration of LLMs as code executors, where code snippets are directly fed to the models for execution, and outputs are returned. We are the first to comprehensively examine this feasibility across various LLMs, including OpenAI's o1, GPT-4o, GPT-3.5, DeepSeek, and Qwen-Coder. Notably, the o1 model achieved over 90% accuracy in code execution, while others demonstrated lower accuracy levels. Furthermore, we introduce an Iterative Instruction Prompting (IIP) technique that processes code snippets line by line, enhancing the accuracy of weaker models by an average of 7.22% (with the highest improvement of 18.96%) and an absolute average improvement of 3.86% against CoT prompting (with the highest improvement of 19.46%). Our study not only highlights the transformative potential of LLMs in coding but also lays the groundwork for future advancements in automated programming and the completion of complex tasks.

Large language models (LLMs) such as ChatGPT can produce coherent, cohesive, relevant, and fluent answers for various natural language processing (NLP) tasks. Taking document-level machine translation (MT) as a testbed, this paper provides an in-depth evaluation of LLMs' ability on discourse modeling. The study focuses on three aspects: 1) Effects of Context-Aware Prompts, where we investigate the impact of different prompts on document-level translation quality and discourse phenomena; 2) Comparison of Translation Models, where we compare the translation performance of ChatGPT with commercial MT systems and advanced document-level MT methods; 3) Analysis of Discourse Modelling Abilities, where we further probe discourse knowledge encoded in LLMs and shed light on impacts of training techniques on discourse modeling. By evaluating on a number of benchmarks, we surprisingly find that LLMs have demonstrated superior performance and show potential to become a new paradigm for document-level translation: 1) leveraging their powerful long-text modeling capabilities, GPT-3.5 and GPT-4 outperform commercial MT systems in terms of human evaluation; 2) GPT-4 demonstrates a stronger ability for probing linguistic knowledge than GPT-3.5. This work highlights the challenges and opportunities of LLMs for MT, which we hope can inspire the future design and evaluation of LLMs.We release our data and annotations at https://github.com/longyuewangdcu/Document-MT-LLM.

Conventional Transformer-based Video Question Answering (VideoQA) approaches generally encode frames independently through one or more image encoders followed by interaction between frames and question. However, such schema would incur significant memory use and inevitably slow down the training and inference speed. In this work, we present a highly efficient approach for VideoQA based on existing vision-language pre-trained models where we concatenate video frames to a $n\times n$ matrix and then convert it to one image. By doing so, we reduce the use of the image encoder from $n^{2}$ to $1$ while maintaining the temporal structure of the original video. Experimental results on MSRVTT and TrafficQA show that our proposed approach achieves state-of-the-art performance with nearly $4\times$ faster speed and only 30% memory use. We show that by integrating our approach into VideoQA systems we can achieve comparable, even superior, performance with a significant speed up for training and inference. We believe the proposed approach can facilitate VideoQA-related research by reducing the computational requirements for those who have limited access to budgets and resources. Our code will be made publicly available for research use.

Event-Level Video Question Answering (EVQA) requires complex reasoning across video events to obtain the visual information needed to provide optimal answers. However, despite significant progress in model performance, few studies have focused on using the explicit semantic connections between the question and visual information especially at the event level. There is need for using such semantic connections to facilitate complex reasoning across video frames. Therefore, we propose a semantic-aware dynamic retrospective-prospective reasoning approach for video-based question answering. Specifically, we explicitly use the Semantic Role Labeling (SRL) structure of the question in the dynamic reasoning process where we decide to move to the next frame based on which part of the SRL structure (agent, verb, patient, etc.) of the question is being focused on. We conduct experiments on a benchmark EVQA dataset - TrafficQA. Results show that our proposed approach achieves superior performance compared to previous state-of-the-art models. Our code will be made publicly available for research use.

Question Generation (QG) aims to automate the task of composing questions for a passage with a set of chosen answers found within the passage. In recent years, the introduction of neural generation models has resulted in substantial improvements of automatically generated questions in terms of quality, especially compared to traditional approaches that employ manually crafted heuristics. However, the metrics commonly applied in QG evaluations have been criticized for their low agreement with human judgement. We therefore propose a new reference-free evaluation metric that has the potential to provide a better mechanism for evaluating QG systems, called QAScore. Instead of fine-tuning a language model to maximize its correlation with human judgements, QAScore evaluates a question by computing the cross entropy according to the probability that the language model can correctly generate the masked words in the answer to that question. Furthermore, we conduct a new crowd-sourcing human evaluation experiment for the QG evaluation to investigate how QAScore and other metrics can correlate with human judgements. Experiments show that QAScore obtains a stronger correlation with the results of our proposed human evaluation method compared to existing traditional word-overlap-based metrics such as BLEU and ROUGE, as well as the existing pretrained-model-based metric BERTScore.