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Yuchen Wu

Yuchen Wu contributes to research discovery and scholarly infrastructure.

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Computer Vision Machine Learning math.ST Artificial Intelligence Computation Computation and Language cs.CY Statistics Theory

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preprint2026arXiv

Encyclo-K: Evaluating LLMs with Dynamically Composed Knowledge Statements

Benchmarks play a crucial role in tracking the rapid advancement of large language models (LLMs) and identifying their capability boundaries. However, existing benchmarks predominantly curate questions at the question level, suffering from three fundamental limitations: vulnerability to data contamination, restriction to single-knowledge-point assessment, and reliance on costly domain expert annotation. We propose Encyclo-K, a statement-based benchmark that rethinks benchmark construction from the ground up. Our key insight is that knowledge statements, not questions, can serve as the unit of curation, and questions can then be constructed from them. We extract standalone knowledge statements from authoritative textbooks and dynamically compose them into evaluation questions through random sampling at test time. This design directly addresses all three limitations: the combinatorial space is too vast to memorize, and model rankings remain stable across dynamically generated question sets, enabling reliable periodic dataset refresh; each question aggregates 8-10 statements for comprehensive multi-knowledge assessment; annotators only verify formatting compliance without requiring domain expertise, substantially reducing annotation costs. Experiments on over 50 LLMs demonstrate that Encyclo-K poses substantial challenges with strong discriminative power. Even the top-performing OpenAI-GPT-5.1 achieves only 62.07% accuracy, and model performance displays a clear gradient distribution--reasoning models span from 16.04% to 62.07%, while chat models range from 9.71% to 50.40%. These results validate the challenges introduced by dynamic evaluation and multi-statement comprehensive understanding. These findings establish Encyclo-K as a scalable framework for dynamic evaluation of LLMs' comprehensive understanding over multiple fine-grained disciplinary knowledge statements.

preprint2026arXiv

FoundationSLAM: Unleashing the Power of Depth Foundation Models for End-to-End Dense Visual SLAM

We present FoundationSLAM, a learning-based monocular dense SLAM system that addresses the absence of geometric consistency in previous flow-based approaches for accurate and robust tracking and mapping. Our core idea is to bridge flow estimation with geometric reasoning by leveraging the guidance from foundation depth models. To this end, we first develop a Hybrid Flow Network that produces geometry-aware correspondences, enabling consistent depth and pose inference across diverse keyframes. To enforce global consistency, we propose a Bi-Consistent Bundle Adjustment Layer that jointly optimizes keyframe pose and depth under multi-view constraints. Furthermore, we introduce a Reliability-Aware Refinement mechanism that dynamically adapts the flow update process by distinguishing between reliable and uncertain regions, forming a closed feedback loop between matching and optimization. Extensive experiments demonstrate that FoundationSLAM achieves superior trajectory accuracy and dense reconstruction quality across multiple challenging datasets, while running in real-time at 18 FPS, demonstrating strong generalization to various scenarios and practical applicability of our method.

preprint2026arXiv

On the Robustness of Distribution Support under Diffusion Guidance

Diffusion guidance is a powerful technique that enables controllable and high-fidelity sample generation with diffusion models. At a high level, it modifies the score function by incorporating a guidance term that steers the generative process toward a desired condition. Despite its empirical success, the theoretical properties of diffusion guidance remain largely unexplored, and it is not well understood why it consistently produces high-quality samples. In this work, we explain the effectiveness of diffusion guidance by establishing a \emph{robustness of support} property. Specifically, we show that, given exact access to the score functions, guided diffusion processes almost always generate samples that remain close to the target support. This property is particularly desirable, as samples that lie off the support are often structurally implausible and may adversely affect downstream tasks. Our analysis covers both Denoising Diffusion Implicit Models (DDIM) and Denoising Diffusion Probabilistic Models (DDPM), and applies to a wide range of discretization schemes induced by exponential integrators. Our results provide a rigorous foundation for understanding why diffusion guidance produces physically meaningful and structurally plausible samples.

preprint2026arXiv

Personalized Safety in LLMs: A Benchmark and A Planning-Based Agent Approach

Large language models (LLMs) typically generate identical or similar responses for all users given the same prompt, posing serious safety risks in high-stakes applications where user vulnerabilities differ widely. Existing safety evaluations primarily rely on context-independent metrics - such as factuality, bias, or toxicity - overlooking the fact that the same response may carry divergent risks depending on the user's background or condition. We introduce personalized safety to fill this gap and present PENGUIN - a benchmark comprising 14,000 scenarios across seven sensitive domains with both context-rich and context-free variants. Evaluating six leading LLMs, we demonstrate that personalized user information significantly improves safety scores by 43.2%, confirming the effectiveness of personalization in safety alignment. However, not all context attributes contribute equally to safety enhancement. To address this, we develop RAISE - a training-free, two-stage agent framework that strategically acquires user-specific background. RAISE improves safety scores by up to 31.6% over six vanilla LLMs, while maintaining a low interaction cost of just 2.7 user queries on average. Our findings highlight the importance of selective information gathering in safety-critical domains and offer a practical solution for personalizing LLM responses without model retraining. This work establishes a foundation for safety research that adapts to individual user contexts rather than assuming a universal harm standard.

preprint2026arXiv

SCE-SLAM: Scale-Consistent Monocular SLAM via Scene Coordinate Embeddings

Monocular visual SLAM enables 3D reconstruction from internet video and autonomous navigation on resource-constrained platforms, yet suffers from scale drift, i.e., the gradual divergence of estimated scale over long sequences. Existing frame-to-frame methods achieve real-time performance through local optimization but accumulate scale drift due to the lack of global constraints among independent windows. To address this, we propose SCE-SLAM, an end-to-end SLAM system that maintains scale consistency through scene coordinate embeddings, which are learned patch-level representations encoding 3D geometric relationships under a canonical scale reference. The framework consists of two key modules: geometry-guided aggregation that leverages 3D spatial proximity to propagate scale information from historical observations through geometry-modulated attention, and scene coordinate bundle adjustment that anchors current estimates to the reference scale through explicit 3D coordinate constraints decoded from the scene coordinate embeddings. Experiments on KITTI, Waymo, and vKITTI demonstrate substantial improvements: our method reduces absolute trajectory error by 8.36m on KITTI compared to the best prior approach, while maintaining 36 FPS and achieving scale consistency across large-scale scenes.

preprint2026arXiv

When Does Model Collapse Occur in Structured Interactive Learning?

The proliferation of generative artificial intelligence has given rise to an interactive learning environment, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning, and (2) model training processes become inherently correlated, as models interact with one another through repeated exposure to each other's synthetic outputs in a potentially complex manner. Establishing reliable statistical inference in such structured interactive learning environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations. Prior work on model collapse primarily focuses on a single model trained on its own output, failing to capture model performance in multi-model interactive settings. In this work, we fill this gap by investigating the performance of generative models in an interactive learning environment with general interaction patterns. In particular, we formalize model interactions using directed graphs and show that the occurrence of model collapse depends critically on the topology of the interaction graph. We further derive an explicit necessary and sufficient condition characterizing when model collapse occurs, and establish finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We support our theoretical findings through extensive numerical experiments.

preprint2023arXiv

Distribution Aligned Feature Clustering for Zero-Shot Sketch-Based Image Retrieval

Zero-Shot Sketch-Based Image Retrieval (ZS-SBIR) is a challenging cross-modal retrieval task. In prior arts, the retrieval is conducted by sorting the distance between the query sketch and each image in the gallery. However, the domain gap and the zero-shot setting make neural networks hard to generalize. This paper tackles the challenges from a new perspective: utilizing gallery image features. We propose a Cluster-then-Retrieve (ClusterRetri) method that performs clustering on the gallery images and uses the cluster centroids as proxies for retrieval. Furthermore, a distribution alignment loss is proposed to align the image and sketch features with a common Gaussian distribution, reducing the domain gap. Despite its simplicity, our proposed method outperforms the state-of-the-art methods by a large margin on popular datasets, e.g., up to 31% and 39% relative improvement of mAP@all on the Sketchy and TU-Berlin datasets.

preprint2022arXiv

Statistically Optimal First Order Algorithms: A Proof via Orthogonalization

We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ (and possibly some labels ${\boldsymbol y}\in{\mathbb R}^n$) and would like to estimate a coefficient vector ${\boldsymbol θ}\in{\mathbb R}^d$ (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g., sparse regression). First order methods proceed by iteratively multiplying current estimates by ${\boldsymbol X}$ or its transpose. Examples include gradient descent or its accelerated variants. Celentano, Montanari, Wu proved that for any constant number of iterations (matrix vector multiplications), the optimal first order algorithm is a specific approximate message passing algorithm (known as `Bayes AMP'). The error of this estimator can be characterized in the high-dimensional asymptotics $n,d\to\infty$, $n/d\toδ$, and provides a lower bound to the estimation error of any first order algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of first order algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof technique does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications.

preprint2020arXiv

The estimation error of general first order methods

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are the fundamental limits to these approaches? This question is well understood from an optimization viewpoint when the underlying objective is convex. Work in this area characterizes the gap to global optimality as a function of the number of iterations. However, these results have only indirect implications in terms of the gap to statistical optimality. Here we consider two families of high-dimensional estimation problems: high-dimensional regression and low-rank matrix estimation, and introduce a class of `general first order methods' that aim at efficiently estimating the underlying parameters. This class of algorithms is broad enough to include classical first order optimization (for convex and non-convex objectives), but also other types of algorithms. Under a random design assumption, we derive lower bounds on the estimation error that hold in the high-dimensional asymptotics in which both the number of observations and the number of parameters diverge. These lower bounds are optimal in the sense that there exist algorithms whose estimation error matches the lower bounds up to asymptotically negligible terms. We illustrate our general results through applications to sparse phase retrieval and sparse principal component analysis.

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