arXiv subjects

Jinwen Xu

Publications and source records attributed to Jinwen Xu.

8 recordsLinked to original sources

arXiv2026

Online Bayesian Node Classification on Inductive Graphs under Distribution Shift

On evolving graphs, node classifiers must satisfy two key requirements: inductive generalization to newly arriving nodes under distribution shift and calibrated uncertainty for safety-sensitive applications. Standard graph neural networks (GNNs) are typically trained once and address neither requirement. We adapt the Bayesian last-layer (BLL) model by placing random last-layer parameters on top of a deterministic GNN encoder for uncertainty quantification. The categorical softmax likelihood required for classification breaks Gaussian conjugacy, so neither the training posterior nor the test-time streaming update has a closed-form solution. To address both challenges, we introduce a variational Bayesian last-layer (VBLL) objective that jointly trains the encoder and an approximate last-layer posterior by maximizing an evidence lower bound with a Monte Carlo expected log-likelihood. At test time, we freeze the encoder and apply an online Laplace update to the last-layer posterior. This update corresponds to a power-prior Bayesian model with exponential forgetting and a Kullback-Leibler anchor to the training posterior. Across five node-classification benchmarks under distribution shift, online GVBLL is the only method to achieve the best accuracy and negative log-likelihood on every dataset. It improves accuracy by up to 17 percentage points on Cora and 14 percentage points on ogbn-arxiv over the strongest non-GVBLL baseline, while remaining competitive in calibration with MC Dropout, Deep Ensembles, Temperature Scaling, and Gaussian-process classifiers.

cs.LG↗

arXiv2025

Conformalized Gaussian processes for online uncertainty quantification over graphs

Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by devising topology-aware kernel functions. However, such GP-based approaches are limited not only by the prohibitive computational complexity, but also the strict modeling assumptions that might yield poor coverage, especially with labels arriving on the fly. To effect scalability, we devise a novel graph-aware parametric GP model by leveraging the random feature (RF)-based kernel approximation, which is amenable to efficient recursive Bayesian model updates. To further allow for adaptivity, an ensemble of graph-aware RF-based scalable GPs have been leveraged, with per-GP weight adapted to data arriving incrementally. To ensure valid coverage with robustness to model mis-specification, we wed the GP-based set predictors with the online conformal prediction framework, which post-processes the prediction sets using adaptive thresholds. Experimental results the proposed method yields improved coverage and efficient prediction sets over existing baselines by adaptively ensembling the GP models and setting the key threshold parameters in CP.

cs.LG↗

arXiv2025

Fine-tuning LLMs with variational Bayesian last layer for high-dimensional Bayesian optimization

A plethora of applications entail solving black-box optimization problems with high evaluation costs, including drug discovery, material design, as well as hyperparameter tuning. Toward finding the global optimum of such black-box optimization problems with sample efficiency, Bayesian optimization (BO) is a theoretically elegant framework that relies on a probabilistic surrogate model so as to iteratively select the query point with well-balanced exploration-exploitation tradeoffs. The Gaussian process (GP), as the de-facto choice for surrogate modeling, has achieved compelling performances for vanilla BO with low-dimensional continuous variables. However, GPs fall short in coping with high-dimensional counterparts with {\it irregular} variables (e.g., categorical, ordinal, etc.). To alleviate this, neural network-based surrogates have been explored. Inspired by the powerful capabilities of LLMs, we adopt the LLM as the surrogate to model the mapping from the high-dimensional input variables to the objective function. To adapt to the current problem, we leverage the low-rank adaptation (LoRA) to fine-tune the LLM parameters together with the posterior of a linear regression head via the variational Bayesian last layer (VBLL) framework. The resulting LoRA-VBLL is not only computationally light compared to existing alternatives, but also admits recursive updates. To automate the critical selection of the LoRA rank as well as other hyperparameters, a weighted ensemble (ENS) of LoRA-VBLL surrogates has been devised, which further accommodates continual update of the per-model weight and individual LoRA-VBLL parameters via recursive Bayes. Extensive experimental results demonstrate the compelling performance of the proposed (ENS-)LoRA-VBLL approaches on various high-dimensional benchmarks and the real-world molecular optimization tasks.

cs.LG↗

arXiv2025

Adaptive Bayesian Optimization for Robust Identification of Stochastic Dynamical Systems

This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require nontrivial gradient computations and are prone to local optima. To overcome these limitations, a sample-efficient global optimization method based on Bayesian optimization (BO) is proposed, using an ensemble Gaussian process (EGP) surrogate with weighted kernels from a predefined dictionary. This ensemble enables a richer function space and improves robustness over single-kernel BO. Each objective evaluation is efficiently performed via Kalman filter recursion. Extensive experiments across parameter settings and sampling intervals show that the EGP-based BO consistently outperforms MLE via steady-state filtering and expectation-maximization (whose derivation is a side contribution) in terms of RMSE and statistical consistency. Unlike the ensemble variant, single-kernel BO does not always yield such gains, underscoring the benefits of model averaging. Notably, the BO-based estimator achieves RMSE below the classical Cramer-Rao bound, particularly for the inverse time constant, long considered difficult to estimate. This counterintuitive outcome is attributed to a data-driven prior implicitly induced by the GP surrogate in BO.

stat.ML↗

arXiv2025

Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challenges

Due to the remarkable capabilities and growing impact of large language models (LLMs), they have been deeply integrated into many aspects of society. Thus, ensuring their alignment with human values and intentions has emerged as a critical challenge. This survey provides a comprehensive overview of practical alignment techniques, training protocols, and empirical findings in LLM alignment. We analyze the development of alignment methods across diverse paradigms, characterizing the fundamental trade-offs between core alignment objectives. Our analysis shows that while supervised fine-tuning enables basic instruction-following, preference-based methods offer more flexibility for aligning with nuanced human intent. We discuss state-of-the-art techniques, including Direct Preference Optimization (DPO), Constitutional AI, brain-inspired methods, and alignment uncertainty quantification (AUQ), highlighting their approaches to balancing quality and efficiency. We review existing evaluation frameworks and benchmarking datasets, emphasizing limitations such as reward misspecification, distributional robustness, and scalable oversight. We summarize strategies adopted by leading AI labs to illustrate the current state of practice. We conclude by outlining open problems in oversight, value pluralism, robustness, and continuous alignment. This survey aims to inform both researchers and practitioners navigating the evolving landscape of LLM alignment.

cs.AI↗

arXiv2024

Online scalable Gaussian processes with conformal prediction for guaranteed coverage

The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency of the resulting uncertainty values however, hinges on the premise that the learning function conforms to the properties specified by the GP model, such as smoothness, periodicity and more, which may not be satisfied in practice, especially with data arriving on the fly. To combat against such model mis-specification, we propose to wed the GP with the prevailing conformal prediction (CP), a distribution-free post-processing framework that produces it prediction sets with a provably valid coverage under the sole assumption of data exchangeability. However, this assumption is usually violated in the online setting, where a prediction set is sought before revealing the true label. To ensure long-term coverage guarantee, we will adaptively set the key threshold parameter based on the feedback whether the true label falls inside the prediction set. Numerical results demonstrate the merits of the online GP-CP approach relative to existing alternatives in the long-term coverage performance.

cs.LG↗

arXiv2021

Conjectures on the distribution behavior of the class numbers of certain real quadratic number fields

Given a random real quadratic field from $\{ \mathbb{Q}(\sqrt{p}\,) ~|~ p \text{ primes} \}$, the conjectural probability $\mathbb{P}(h=q)$ that it has class number $q$ is given for all positive odd integers $q$. Some related conjectures of the Cohen-Lenstra heuristic are given here as corollaries. These results suggest that the set of real quadratic number fields may have some natural hierarchical structures.

math.NT↗

arXiv2019

Region crossing change on surfaces

Region crossing change is a local operation on link diagrams. The behavior of region crossing change on $S^2$ is well understood. In this paper, we study the behavior of (modified) region crossing change on higher genus surfaces.

math.GT↗