Raymond K. W. Wong

Peiman Mohseni, Nick Duffield, Raymond K. W. Wong

Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering. Neural processes (NPs), a family of probabilistic functional models, are promising solutions -- especially when endowed with domain-specific symmetries like translation equivariance, which improve sample efficiency and generalization. Yet existing translation-equivariant NPs face two limitations: (i) they stack generic components with non-linearities, obscuring the induced function class and limiting interpretability; and (ii) convolutional designs rely on kernels with local receptive fields and require dense uniform input grids, while attention-based methods avoid these issues but scale quadratically with the number of observations. We address both with two contributions. First, using the Volterra expansion, we characterize continuous translation-equivariant operators as sums of higher-order convolutions, yielding analytical transparency while admitting efficient approximation by first-order convolutions. Second, we introduce set Fourier convolutions (SFConvs), a frequency-domain parameterization that operates directly on irregularly sampled points, achieves approximately global receptive fields, and scales linearly in the number of observations. Building on these ideas, we propose two conditional NPs (CNPs): SFConvCNPs, which stack SFConv blocks with non-linearities, and SFVConvCNPs, which integrate the Volterra formulation. Experiments on synthetic and real-world datasets demonstrate our methods' efficacy against state-of-the-art baselines.

Jiayi Wang, Raymond K. W. Wong

We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar. In this setting, only a subset of matrix entries is observed, and even for observed entries, the underlying distributions are not directly accessible; instead, we observe finitely many samples drawn from them. To represent distributional entries, we employ kernel mean embeddings and introduce a notion of Tucker rank for distribution-valued matrices to capture their low-rank structure. The infinite-dimensional nature of kernel embeddings poses significant methodological challenges. To address this, we introduce functional unfolding operators that link the proposed distributional low-rank structure to the classical Tucker rank for finite-dimensional tensors. Based on this framework, we propose a novel estimator for distributional matrix completion. We establish non-asymptotic error bounds that characterize the statistical performance of the estimator. Extensive experiments on synthetic data and a real-world application demonstrate the effectiveness of the proposed method.

Qiyuan Wang, Yao Li, Raymond K. W. Wong

Despite recent progress in backdoor attacks, existing methods remain susceptible to post-training defenses that erase the backdoor through fine-tuning or pruning. We revisit the core objectives of backdoor attacks and derive principled criteria characterizing optimal sample-specific trigger construction under a Bayes-optimal model of the victim's training. Our analysis reveals that both attack success and clean-accuracy preservation are simultaneously optimized when triggered samples are steered into low-density regions of the clean data distribution, a distributional condition that controls all moments of the poisoned distribution at once rather than a handful of input-space summary statistics. We introduce a bilevel optimization framework that estimates density ratios via conditional time-score matching and optimizes a mixture-model objective to place triggered samples in these sparse regions. Extensive evaluations on MNIST, CIFAR-10, GTSRB, and TinyImageNet demonstrate that our method achieves above 99\% attack success rate before defense and retains 50--85 percentage points higher post-defense ASR than the strongest baselines under fine-tuning defenses. Against neuron-pruning defenses, the method exhibits complete immunity, with zero neurons identified for removal across all pruning thresholds. These results expose a fundamental gap in current defense paradigms and underscore the need for defenses that operate beyond the support of the clean distribution.

Sungee Hong, Jiayi Wang, Zhengling Qi et al.

In reinforcement learning, distributional off-policy evaluation (OPE) focuses on estimating the return distribution of a target policy using offline data collected under a different policy. This work focuses on extending the widely used fitted Q-evaluation -- developed for expectation-based reinforcement learning -- to the distributional OPE setting. We refer to this extension as fitted distributional evaluation (FDE). While only a few related approaches exist, there remains no unified framework for designing FDE methods. To fill this gap, we present a set of guiding principles for constructing theoretically grounded FDE methods. Building on these principles, we develop several new FDE methods with convergence analysis and provide theoretical justification for existing methods, even in non-tabular environments. Extensive experiments, including simulations on linear quadratic regulators and Atari games, demonstrate the superior performance of the FDE methods.

Ya Zhou, Raymond K. W. Wong, Kejun He

Tensor linear regression is an important and useful tool for analyzing tensor data. To deal with high dimensionality, CANDECOMP/PARAFAC (CP) low-rank constraints are often imposed on the coefficient tensor parameter in the (penalized) $M$-estimation. However, we show that the corresponding optimization may not be attainable, and when this happens, the estimator is not well-defined. This is closely related to a phenomenon, called CP degeneracy, in low-rank tensor approximation problems. In this article, we provide useful results of CP degeneracy in tensor regression problems. In addition, we provide a general penalized strategy as a solution to overcome CP degeneracy. The asymptotic properties of the resulting estimation are also studied. Numerical experiments are conducted to illustrate our findings.