In particular, it aggregates multiple sub-models called experts based on a gating network. Here, experts can be formulated as neural networks, and they specialize in different aspects of the data.

However, the problem of provably editing a DNN to satisfy a property remains challenging.

Our PMs are continuous and path-independent, overcoming the deficiencyofpreviousworks[47]. Moreover, there is still room for improvement in our approach and related works. This paper mainly focuses on adversarial robustness regarding white-box attacks generated by the first-order gradient-based methods. When employing our MAIL in real-world applications, it may lead to over-confidence regarding many other attacks, e.g., provable attacks [5], black-box attacks [6], and physical attacks [25]. For data assigned with larger weights, the resulting model would be more robust when encounters similar dataduring thetest. This unfairness problem seems inevitable forareweighted learning framework, which will interest our further study.

One-class learning or classification has many applications. For example, in information retrieval, one has a set of documents of interest and wants to identify more such documents [55].

We then apply this approach totheproblem ofmaking good decisions inthebranch-and-cut framework for mixed-integer optimization (e.g., which cut to add?). In other words, the neural network will take as input a mixed-integer optimization instance and output a decision that will result in a small branch-and-cut tree for that instance.