Neural processes (NPs) are a promising paradigm to enable skill transfer learning across tasks with the aid of the distribution of functions. The previous NPs employ the empirical risk minimization principle in optimization. However, the fast adaption ability to different tasks can vary widely, and the worst fast adaptation can be catastrophic in risk-sensitive tasks. To achieve robust neural processes modeling, we consider the problem of training models in a risk-averse manner, which can control the worst fast adaption cases at a certain probabilistic level. By transferring the risk minimization problem to a two-level finite sum minimax optimization problem, we can easily solve it via a double-looped stochastic mirror prox algorithm with a task-aware variance reduction mechanism via sampling samples across all tasks. The mirror prox technique ensures better handling of complex constraint sets and non-Euclidean geometries, making the optimization adaptable to various tasks. The final solution, by aggregating prox points with the adaptive learning rates, enables a stable and high-quality output. The proposed learning strategy can work with various NPs flexibly and achieves less biased approximation with a theoretical guarantee. To illustrate the superiority of the proposed model, we perform experiments on both synthetic and real-world data, and the results demonstrate that our approach not only helps to achieve more accurate performance but also improves model robustness.

Existing work in physical-informed machine learning (PIML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical ordinary/partial differential equations (ODEs/PDEs) solvers. Of these, Neural Operators (NOs) have emerged as particularly promising. However, a key challenge in the field of NOs lies in developing methods that can effectively handle out-of-distribution (OOD) forecasting problems. Such problems involve the ability to adaptively learn from observations of the same dynamical system governed by ODEs/PDEs, where the underlying parameters are unknown and vary across instances. These tasks further require precise predictions even when faced with initial conditions and PDEs/ODEs parameters outside the training distribution. In this study, we consider the problem of training models in a risk-reverse manner. We introduce a risk-aware framework aimed at enhancing the OOD robustness of NOs by stochastically optimizing the conditional value-at-risk (CVAR) of a loss distribution. Through experiments on different distinct OOD tasks, our approach demonstrates a significant performance improvement over existing advanced NOs.

Neural Processes (NPs) combine the adaptability of neural networks with the efficiency of meta-learning, offering a powerful framework for modeling stochastic processes. However, existing methods focus on empirical performance while lacking a rigorous theoretical understanding of generalization. To address this, we propose an information-theoretic framework to analyze the generalization bounds of NPs, introducing dynamical stability regularization to minimize sharpness and improve optimization dynamics. Additionally, we show how noise-injected parameter updates complement this regularization. The proposed approach, applicable to a wide range of NP models, is validated through experiments on classic benchmarks, including 1D regression, image completion, Bayesian optimization, and contextual bandits. The results demonstrate tighter generalization bounds and superior predictive performance, establishing a principled foundation for advancing generalizable NP models.

Appearance-based gaze estimation has been widely studied recently with promising performance. The majority of appearance-based gaze estimation methods are developed under the deterministic frameworks. However, the deterministic gaze estimation methods suffer from large performance drop upon challenging eye images in low-resolution, darkness, partial occlusions, etc. To alleviate this problem, in this article, we alternatively reformulate the appearance-based gaze estimation problem under a generative framework. Specifically, we propose a variational inference model, that is, variational gaze estimation network (VGE-Net), to generate multiple gaze maps as complimentary candidates simultaneously supervised by the ground-truth gaze map. To achieve robust estimation, we adaptively fuse the gaze directions predicted on these candidate gaze maps by a regression network through a simple attention mechanism. Experiments on three benchmarks, that is, MPIIGaze, EYEDIAP, and Columbia, demonstrate that our VGE-Net outperforms state-of-the-art gaze estimation methods, especially on challenging cases. Comprehensive ablation studies also validate the effectiveness of our contributions. The code will be publicly released.

Mainstream lane detection methods often lack flexibility, accuracy, and efficiency in challenging scenarios, especially with occlusion and extreme lighting. To address this, we reframe lane detection as a variational inference problem. Specifically, we propose a Variational Lane Detection Network (VLD-Net) using a Conditional Variational Auto-Encoder (CVAE) as the generative network to produce multiple lane maps as candidates, supervised by the ground-truth lane map. To build a more complex, expressive probability distribution, we incorporate normalizing flows into lane map generation, enhancing realism. Additionally, we develop a Lane-Attention Fusion (LAF) module using attention mechanisms to adaptively fuse generated candidate lane maps. LAF also includes a lane local feature aggregator to enhance local lane keypoint correlation. Experimental results on TuSimple and CULane datasets show our method outperforms previous approaches in challenging scenarios.