The main advantages of deep neural networks (DNNs) are their architectural simplicity and automatic feature learning. The latter is crucial for working with unstructured data as developers don't need to design features by hand. However, giving away the control over features leads to black box models - DNNs tend to learn hardly interpretable "shortcut" correlations [17] that leak from train to test [20], hampering alignment and out-of-distribution performance. In particular, this gives rise to adversarial attacks [35] - semantically negligible perturbations of data that arbitrarily change model's predictions. Adversarial vulnerability is a widespread phenomenon (vision [35], segmentation/detection [39], speech recognition [9], tabular data [10], RL [19], NLP [41]) and largely contributes to the general lack of trust in DNNs, substantially limiting their adoption in high-stakes applications such as healthcare, military, autonomous vehicles or cybersecurity. Conversely, the main advantage of hand-designed features is the fine-grained control over model's performance; however, such systems quickly become infeasibly complex. This paper aims to address those issues by reconciling Deep Learning with feature engineering - with the help of locality engineering. Specifically, semantic features are introduced as a general conceptual machinery for controlled dimensionality reduction inside a neural network layer. Figure 1 presents the core idea behind the notion and the rigorous definition is given in Section 4. Implementing a semantic feature predominantly involves encoding appropriate invariants (i.e.

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on large data sets, due to their discrete parameters and structures. Ensemble methods and fuzzy/soft rules are commonly used to improve performance, but they sacrifice the model interpretability. To obtain both good scalability and interpretability, we propose a new classifier, named Rule-based Representation Learner (RRL), that automatically learns interpretable non-fuzzy rules for data representation and classification. To train the non-differentiable RRL effectively, we project it to a continuous space and propose a novel training method, called Gradient Grafting, that can directly optimize the discrete model using gradient descent. A novel design of logical activation functions is also devised to increase the scalability of RRL and enable it to discretize the continuous features end-to-end. Exhaustive experiments on ten small and four large data sets show that RRL outperforms the competitive interpretable approaches and can be easily adjusted to obtain a trade-off between classification accuracy and model complexity for different scenarios. Our code is available at: https://github.com/12wang3/rrl.

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on large data sets, due to their discrete parameters and structures. Ensemble methods and fuzzy/soft rules are commonly used to improve performance, but they sacrifice the model interpretability. To obtain both good scalability and interpretability, we propose a new classifier, named Rule-based Representation Learner (RRL), that automatically learns interpretable non-fuzzy rules for data representation and classification. To train the non-differentiable RRL effectively, we project it to a continuous space and propose a novel training method, called Gradient Grafting, that can directly optimize the discrete model using gradient descent. An improved design of logical activation functions is also devised to increase the scalability of RRL and enable it to discretize the continuous features end-to-end. Exhaustive experiments on nine small and four large data sets show that RRL outperforms the competitive interpretable approaches and can be easily adjusted to obtain a trade-off between classification accuracy and model complexity for different scenarios. Our code is available at: https://github.com/12wang3/rrl.