Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing procedures for statistical networks based on the principle of maximum entropy (MaxEnt). Our approach formulates a constrained entropy-maximization problem on the space of networks, subject to prescribed structural constraints. The resulting test statistics are defined through the Lagrange multipliers associated with the constrained optimization problem, which, to our knowledge, is novel in the statistical networks literature. We establish consistency in the classical regime where the number of vertices is fixed. We then consider asymptotic regimes in which the graph size grows with the sample size, developing tests for both dense and sparse settings. In the dense case, we analyze exponential random graph models (ERGM) (including the Erdös-Rènyi models), while in the sparse regime our theory applies to Erd{ö}s-R{è}nyi graphs. Our analysis leverages recent advances in nonlinear large deviation theory for random graphs. We further show that the proposed Lagrange-multiplier framework connects naturally to classical score tests for constrained maximum likelihood estimation. The results provide a unified entropy-based framework for network model assessment across diverse growth regimes.

We study learning problems on correlated stochastic block models with two balanced communities.

Autonomous driving technology is spearheading a transformation in the global automotive industries, and its safe and reliable implementation is the core prerequisite for large-scale adoption (Ren et al., 2025). Comprehensive testing and evaluation of autonomous driving systems (ADSs) are essential to ensuring their safety, in which the identification and generation of safety-critical scenarios represent a core challenge (Yang et al., 2025). "Safety-critical scenarios" specifically refer to rare driving situations with potentially high risks (Ding et al., 2023). Conducting tests under such scenarios enables effective evaluation of the ADSs' safety performance, as well as the clarification and iterative refinement of its Operational Design Domain (ODD). However, due to the rarity of safety-critical scenarios in naturalistic driving environments (Feng et al., 2023), real-world road testing is inefficient and cost-prohibitive, making it unsuitable for large-scale testing of high-level ADSs. As a more efficient and practical solution, simulation-based testing has garnered significant industrial and scholarly attention (Sun et al., 2022). In recent years, engineers in enterprises generally extract safety-critical testing scenarios by directly replaying vehicle-collected data in simulation environments (Liu et al., 2024), while some researchers achieve accelerated sampling of safety-critical scenarios through optimization-based search within a predefined scenario parameter space (Wu et al., 2024, 2026). However, the background vehicles (BVs) in the safety-critical testing scenarios generated by the aforementioned methods exhibit fixed behaviors and cannot dynamically respond to the actions of the vehicle under test (VUT). As a remedy, some other studies have introduced reinforcement learning to train adversarial BV driver models, thereby constructing naturalistic adversarial driving environments (NADE) (Feng et al., 2021) or evolving scenarios (Ma et al., 2024; Wu et al., 2025).

We study the computational task of detecting and estimating correlated signals in a pair of spiked Wigner matrices. Our model consists of observations $$ X = \tfracλ{\sqrt{n}} xx^{\top} + W \,, \quad Y = \tfracμ{\sqrt{n}} yy^{\top} + Z \,. $$ where $x,y \in \mathbb R^n$ are signal vectors with norm $\|x\|,\|y\| \approx\sqrt{n}$ and correlation $\langle x,y \rangle \approx ρ\|x\|\|y\|$, while $W,Z$ are independent Gaussian Wigner matrices. We propose an efficient algorithm that succeeds whenever $F(λ,μ,ρ)>1$, where $$ F(λ,μ,ρ)=\max\Big\{ λ,μ, \frac{ λ^2 ρ^2 }{ 1-λ^2+λ^2 ρ^2 } + \frac{ μ^2 ρ^2 }{ 1-μ^2+μ^2 ρ^2 } \Big\} \,. $$ Our result shows that an algorithm can leverage the correlation between the spikes to detect and estimate the signals even in regimes where efficiently recovering either $x$ from $X$ alone or $y$ from $Y$ alone is believed to be computationally infeasible. We complement our algorithmic result with evidence for a matching computational lower bound. In particular, we prove that when $F(λ,μ,ρ)<1$, all algorithms based on {\em low-degree polynomials} fails to distinguish $(X,Y)$ with two independent Wigner matrices. This low-degree analysis strongly suggests that $F(λ,μ,ρ)=1$ is the precise computation threshold for this problem.

We propose an efficient algorithm for tensor PCA based on counting a specific family of weighted hypergraphs. For the order-$p$ tensor PCA problem where $p \geq 3$ is a fixed integer, we show that when the signal-to-noise ratio is $λn^{-\frac{p}{4}}$ where $λ=Ω(1)$, our algorithm succeeds and runs in time $n^{C+o(1)}$ where $C=C(λ)$ is a constant depending on $λ$. This algorithm improves a poly-logarithmic factor compared to previous algorithms based on the Sum-of-Squares hierarchy \cite{HSS15} or based on the Kikuchi hierarchy in statistical physics \cite{WEM19}. Furthermore, our result shows a smooth tradeoff between the signal-to-noise ratio and the computational cost in this problem, thereby confirming a conjecture posed in \cite{KWB22}.

Low-degree polynomials have emerged as a powerful paradigm for providing evidence of statistical-computational gaps across a variety of high-dimensional statistical models [Wein25]. For detection problems -- where the goal is to test a planted distribution $\mathbb{P}'$ against a null distribution $\mathbb{P}$ with independent components -- the standard approach is to bound the advantage using an $\mathbb{L}^2(\mathbb{P})$-orthonormal family of polynomials. However, this method breaks down for estimation tasks or more complex testing problems where $\mathbb{P}$ has some planted structures, so that no simple $\mathbb{L}^2(\mathbb{P})$-orthogonal polynomial family is available. To address this challenge, several technical workarounds have been proposed [SW22,SW25], though their implementation can be delicate. In this work, we propose a more direct proof strategy. Focusing on random graph models, we construct a basis of polynomials that is almost orthonormal under $\mathbb{P}$, in precisely those regimes where statistical-computational gaps arise. This almost orthonormal basis not only yields a direct route to establishing low-degree lower bounds, but also allows us to explicitly identify the polynomials that optimize the low-degree criterion. This, in turn, provides insights into the design of optimal polynomial-time algorithms. We illustrate the effectiveness of our approach by recovering known low-degree lower bounds, and establishing new ones for problems such as hidden subcliques, stochastic block models, and seriation models.

Generative Flow Networks (GFlowNets) offer a powerful framework for sampling graphs in proportion to their rewards. However, existing approaches suffer from systematic biases due to inaccuracies in state transition probability computations. These biases, rooted in the inherent symmetries of graphs, impact both atom-based and fragment-based generation schemes. To address this challenge, we introduce Symmetry-Aware GFlowNets (SA-GFN), a method that incorporates symmetry corrections into the learning process through reward scaling. By integrating bias correction directly into the reward structure, SA-GFN eliminates the need for explicit state transition computations. Empirical results show that SA-GFN enables unbiased sampling while enhancing diversity and consistently generating high-reward graphs that closely match the target distribution.

Following the widespread adoption of ChatGPT in early 2023, numerous studies reported that large language models (LLMs) can match or even surpass human performance in creative tasks. However, it remains unclear whether LLMs have become more creative over time, and how consistent their creative output is. In this study, we evaluated 14 widely used LLMs -- including GPT-4, Claude, Llama, Grok, Mistral, and DeepSeek -- across two validated creativity assessments: the Divergent Association Task (DAT) and the Alternative Uses Task (AUT). Contrary to expectations, we found no evidence of increased creative performance over the past 18-24 months, with GPT-4 performing worse than in previous studies. For the more widely used AUT, all models performed on average better than the average human, with GPT-4o and o3-mini performing best. However, only 0.28% of LLM-generated responses reached the top 10% of human creativity benchmarks. Beyond inter-model differences, we document substantial intra-model variability: the same LLM, given the same prompt, can produce outputs ranging from below-average to original. This variability has important implications for both creativity research and practical applications. Ignoring such variability risks misjudging the creative potential of LLMs, either inflating or underestimating their capabilities. The choice of prompts affected LLMs differently. Our findings underscore the need for more nuanced evaluation frameworks and highlight the importance of model selection, prompt design, and repeated assessment when using Generative AI (GenAI) tools in creative contexts.