Xuyang Guo

Yang Cao, Yubin Chen, Xuyang Guo et al.

The rapid advancement of large language models (LLMs) has led to significant breakthroughs in automated mathematical reasoning and scientific discovery. Georgiev, G${ó}$mez-Serrano, Tao, and Wagner [GGSTW+25] demonstrate that AI systems can explore new constructions and improve existing bounds, illustrating the growing potential of LLMs to accelerate mathematical discovery. Similarly, Bubeck et al. [BCE+25] show that GPT-5 can meaningfully contribute to scientific workflows, from proposing hypotheses to generating proofs and analyses. Despite these advances, a rigorous evaluation of these models on canonical, graduate-level mathematical theory remains necessary to understand their baseline reasoning capabilities. In this paper, we present a comprehensive benchmark of four frontier models: GPT-5-Thinking, Gemini-3-Pro, Claude-Sonnet-4.5-Thinking, and Grok-4 against the classic curriculum of Randomized Algorithms by Motwani and Raghavan [MR95]. We tasked each model with generating formal LaTeX proofs for a series of lemmas and exercises spanning the textbook. We find that while the top-tier models (Gemini, and Claude) achieve a high accuracy rate (approx. 66%), demonstrating a robust grasp of probabilistic method and formal logic, other models lag significantly in consistency (approx. 40%). We provide a qualitative analysis of the generated proofs, highlighting differences in conciseness, hallucination rates, and logical structure. Our results suggest that while frontier models have reached a threshold of proficiency suitable for graduate-level pedagogical assistance and formalization, significant variance exists in their reliability for rigorous mathematical derivation. The code and the full set of LLM-generated responses are open-sourced and publicly available at https://github.com/magiclinux/math_benchmark_probability.

Xuyang Guo, Zekai Huang, Jiayan Huo et al.

Generative models have driven significant progress in a variety of AI tasks, including text-to-video generation, where models like Video LDM and Stable Video Diffusion can produce realistic, movie-level videos from textual instructions. Despite these advances, current text-to-video models still face fundamental challenges in reliably following human commands, particularly in adhering to simple numerical constraints. In this work, we present T2VCountBench, a specialized benchmark aiming at evaluating the counting capability of SOTA text-to-video models as of 2025. Our benchmark employs rigorous human evaluations to measure the number of generated objects and covers a diverse range of generators, covering both open-source and commercial models. Extensive experiments reveal that all existing models struggle with basic numerical tasks, almost always failing to generate videos with an object count of 9 or fewer. Furthermore, our comprehensive ablation studies explore how factors like video style, temporal dynamics, and multilingual inputs may influence counting performance. We also explore prompt refinement techniques and demonstrate that decomposing the task into smaller subtasks does not easily alleviate these limitations. Our findings highlight important challenges in current text-to-video generation and provide insights for future research aimed at improving adherence to basic numerical constraints.

Xuyang Guo, Jiayan Huo, Zhenmei Shi et al.

Thanks to recent advancements in scalable deep architectures and large-scale pretraining, text-to-video generation has achieved unprecedented capabilities in producing high-fidelity, instruction-following content across a wide range of styles, enabling applications in advertising, entertainment, and education. However, these models' ability to render precise on-screen text, such as captions or mathematical formulas, remains largely untested, posing significant challenges for applications requiring exact textual accuracy. In this work, we introduce T2VTextBench, the first human-evaluation benchmark dedicated to evaluating on-screen text fidelity and temporal consistency in text-to-video models. Our suite of prompts integrates complex text strings with dynamic scene changes, testing each model's ability to maintain detailed instructions across frames. We evaluate ten state-of-the-art systems, ranging from open-source solutions to commercial offerings, and find that most struggle to generate legible, consistent text. These results highlight a critical gap in current video generators and provide a clear direction for future research aimed at enhancing textual manipulation in video synthesis.

Yubin Chen, Xuyang Guo, Zhenmei Shi et al.

Text-to-video (T2V) models have shown remarkable performance in generating visually reasonable scenes, while their capability to leverage world knowledge for ensuring semantic consistency and factual accuracy remains largely understudied. In response to this challenge, we propose T2VWorldBench, the first systematic evaluation framework for evaluating the world knowledge generation abilities of text-to-video models, covering 6 major categories, 60 subcategories, and 1,200 prompts across a wide range of domains, including physics, nature, activity, culture, causality, and object. To address both human preference and scalable evaluation, our benchmark incorporates both human evaluation and automated evaluation using vision-language models (VLMs). We evaluated the 10 most advanced text-to-video models currently available, ranging from open source to commercial models, and found that most models are unable to understand world knowledge and generate truly correct videos. These findings point out a critical gap in the capability of current text-to-video models to leverage world knowledge, providing valuable research opportunities and entry points for constructing models with robust capabilities for commonsense reasoning and factual generation.

Yifang Chen, Xuyang Guo, Xiaoyu Li et al.

Recently, Large Language Models (LLMs) have achieved remarkable success. A key factor behind this success is the scaling law observed by OpenAI. Specifically, for models with Transformer architecture, the test loss exhibits a power-law relationship with model size, dataset size, and the amount of computation used in training, demonstrating trends that span more than seven orders of magnitude. This scaling law challenges traditional machine learning wisdom, notably the Oscar Scissors principle, which suggests that an overparametrized algorithm will overfit the training datasets, resulting in poor test performance. Recent research has also identified the scaling law in simpler machine learning contexts, such as linear regression. However, fully explaining the scaling law in large practical models remains an elusive goal. In this work, we advance our understanding by demonstrating that the scaling law phenomenon extends to multiple regression and kernel regression settings, which are significantly more expressive and powerful than linear methods. Our analysis provides deeper insights into the scaling law, potentially enhancing our understanding of LLMs.

Xuyang Guo, Zekai Huang, Zhenmei Shi et al.

Vision-Language Models (VLMs) have become a central focus of today's AI community, owing to their impressive abilities gained from training on large-scale vision-language data from the Web. These models have demonstrated strong performance across diverse tasks, including image understanding, video understanding, complex visual reasoning, and embodied AI. Despite these noteworthy successes, a fundamental question remains: Can VLMs count objects correctly? In this paper, we introduce a simple yet effective benchmark, VLMCountBench, designed under a minimalist setting with only basic geometric shapes (e.g., triangles, circles) and their compositions, focusing exclusively on counting tasks without interference from other factors. We adopt strict independent variable control and systematically study the effects of simple properties such as color, size, and prompt refinement in a controlled ablation. Our empirical results reveal that while VLMs can count reliably when only one shape type is present, they exhibit substantial failures when multiple shape types are combined (i.e., compositional counting). This highlights a fundamental empirical limitation of current VLMs and motivates important directions for future research.