Jiahao Zhang

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.

Chengyi Liu, Jiahao Zhang, Shijie Wang et al.

With the prevalence of social networks on online platforms, social recommendation has become a vital technique for enhancing personalized recommendations. The effectiveness of social recommendations largely relies on the social homophily assumption, which presumes that individuals with social connections often share similar preferences. However, this foundational premise has been recently challenged due to the inherent complexity and noise present in real-world social networks. In this paper, we tackle the low social homophily challenge from an innovative generative perspective, directly generating optimal user social representations that maximize consistency with collaborative signals. Specifically, we propose the Score-based Generative Model for Social Recommendation (SGSR), which effectively adapts the Stochastic Differential Equation (SDE)-based diffusion models for social recommendations. To better fit the recommendation context, SGSR employs a joint curriculum training strategy to mitigate challenges related to missing supervision signals and leverages self-supervised learning techniques to align knowledge across social and collaborative domains. Extensive experiments on real-world datasets demonstrate the effectiveness of our approach in filtering redundant social information and improving recommendation performance.

Yang Cao, Yubin Chen, Zhao Song et al.

Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient single-step sampling. In this work, we introduce a theoretical study on Second-Order MeanFlow, a novel extension that incorporates average acceleration fields into the MeanFlow objective. We first establish the feasibility of our approach by proving that the average acceleration satisfies a generalized consistency condition analogous to first-order MeanFlow, thereby supporting stable, one-step sampling and tractable loss functions. We then characterize its expressivity via circuit complexity analysis, showing that under mild assumptions, the Second-Order MeanFlow sampling process can be implemented by uniform threshold circuits within the $\mathsf{TC}^0$ class. Finally, we derive provably efficient criteria for scalable implementation by leveraging fast approximate attention computations: we prove that attention operations within the Second-Order MeanFlow architecture can be approximated to within $1/\mathrm{poly}(n)$ error in time $n^{2+o(1)}$. Together, these results lay the theoretical foundation for high-order flow matching models that combine rich dynamics with practical sampling efficiency.