Deep networks have shown remarkable results in the task of object detection. However, their performance suffers critical drops when they are subsequently trained on novel classes without any sample from the base classes originally used to train the model. This phenomenon is known as catastrophic forgetting. Recently, several incremental learning methods are proposed to mitigate catastrophic forgetting for object detection. Despite the effectiveness, these methods require co-occurrence of the unlabeled base classes in the training data of the novelclasses. This requirement isimpractical in manyreal-world settings since the base classes do not necessarily co-occur with the novel classes.

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In this setting, neural operators trained to minimize squared error losses, while capable of accurate short-term forecasts, often fail to reproduce statistical or structural properties of the dynamics over longer time horizons and can yield degenerate results.

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Ensemble methodsand fuzzy/soft rules are commonly used to improve performance, but they sacrifice the model interpretability.

We show that the proposed algorithms converge to the (regularized) global optimal solution, andmoreover,theirratesofconvergence areofpolynomial orderinthe online setting and exponential order inthe finite sample setting, respectively.