Zeyu He

Wenhan Cao, Shiqi Liu, Chang Liu et al.

Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is critical to state distribution inference. Previously, the conditional probability is assumed to be exactly known, which represents a measure of the occurrence probability of one event, given the second event. In this paper, we find that by adding an additional event that stipulates an inequality condition, we can transform the conditional probability into a special integration that is analogous to convolution. Based on this transformation, we show that both transition probability and output probability can be generalized to convolutional forms, resulting in a more general filtering framework that we call convolutional Bayesian filtering. This new framework encompasses standard Bayesian filtering as a special case when the distance metric of the inequality condition is selected as Dirac delta function. It also allows for a more nuanced consideration of model mismatch by choosing different types of inequality conditions. For instance, when the distance metric is defined in a distributional sense, the transition probability and output probability can be approximated by simply rescaling them into fractional powers. Under this framework, a robust version of Kalman filter can be constructed by only altering the noise covariance matrix, while maintaining the conjugate nature of Gaussian distributions. Finally, we exemplify the effectiveness of our approach by reshaping classic filtering algorithms into convolutional versions, including Kalman filter, extended Kalman filter, unscented Kalman filter and particle filter.

Zeyu He, Shuai Huang, Yuwu Lu et al.

Few-Shot Class-Incremental Learning (FSCIL) must contend with the dual challenge of learning new classes from scarce samples while preserving old class knowledge. Existing methods use the frozen feature extractor and class-averaged prototypes to mitigate against catastrophic forgetting and overfitting. However, new-class prototypes suffer significant estimation bias due to extreme data scarcity, whereas base-class prototypes benefit from sufficient data. In this work, we theoretically demonstrate that aligning the new-class priors with old-class statistics via Bayesian analysis reduces variance and improves prototype accuracy. Furthermore, we propose large-scale contrastive learning to enforce cross-category feature tightness. To further enrich feature diversity and inject prior information for new-class prototypes, we integrate momentum self-supervision and virtual categories into the Momentum Tightness and Contrast framework (MoTiC), constructing a feature space with rich representations and enhanced interclass cohesion. Experiments on three FSCIL benchmarks produce state-of-the-art performances, particularly on the fine-grained task CUB-200, validating our method's ability to reduce estimation bias and improve incremental learning robustness.