Continual learning aims to create artificial neural networks capable of accumulating knowledge and skills through incremental training on a sequence of tasks. The main challenge of continual learning is catastrophic interference, wherein new knowledge overrides or interferes with past knowledge, leading to forgetting. An associated issue is the problem of learning "cross-task knowledge," where models fail to acquire and retain knowledge that helps differentiate classes across task boundaries. A common solution to both problems is "replay," where a limited buffer of past instances is utilized to learn cross-task knowledge and mitigate catastrophic interference. However, a notable drawback of these methods is their tendency to overfit the limited replay buffer. In contrast, our proposed solution, SurpriseNet, addresses catastrophic interference by employing a parameter isolation method and learning cross-task knowledge using an auto-encoder inspired by anomaly detection. SurpriseNet is applicable to both structured and unstructured data, as it does not rely on image-specific inductive biases. We have conducted empirical experiments demonstrating the strengths of SurpriseNet on various traditional vision continual-learning benchmarks, as well as on structured data datasets. Source code made available at https://doi.org/10.5281/zenodo.8247906 and https://github.com/tachyonicClock/SurpriseNet-CIKM-23