Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (i.i.d.). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of structured data. This has motivated different research areas such as data poisoning, model improvement, and explanation of machine learning models. In this work, we study the influence of a sample on determining the intrinsic topological features of its underlying manifold. We propose the Shapley homology framework, which provides a quantitative metric for the influence of a sample of the homology of a simplicial complex. Our proposed framework consists of two main parts: homology analysis, where we compute the Betti number of the target topological space, and Shapley value calculation, where we decompose the topological features of a complex built from data points to individual points. By interpreting the influence as a probability measure, we further define an entropy that reflects the complexity of the data manifold. Furthermore, we provide a preliminary discussion of the connection of the Shapley homology to the Vapnik-Chervonenkis dimension. Empirical studies show that when the zero-dimensional Shapley homology is used on neighboring graphs, samples with higher influence scores have a greater impact on the accuracy of neural networks that determine graph connectivity and on several regular grammars whose higher entropy values imply greater difficulty in being learned.

It has been recently shown that deep neural networks (DNNs) are susceptible to a particular type of attack that exploits a fundamental flaw in their design. This attack consists of generating particular synthetic examples referred to as adversarial samples. These samples are constructed by slightly manipulating real data-points that change "fool" the original DNN model, forcing it to misclassify previously correctly classified samples with high confidence. Many believe addressing this flaw is essential for DNNs to be used in critical applications such as cyber security. Previous work has shown that learning algorithms that enhance the robustness of DNN models all use the tactic of "security through obscurity". This means that security can be guaranteed only if one can obscure the learning algorithms from adversaries. Once the learning technique is disclosed, DNNs protected by these defense mechanisms are still susceptible to adversarial samples. In this work, we investigate by examining how previous research dealt with this and propose a generic approach to enhance a DNN's resistance to adversarial samples. More specifically, our approach integrates a data transformation module with a DNN, making it robust even if we reveal the underlying learning algorithm. To demonstrate the generality of our proposed approach and its potential for handling cyber security applications, we evaluate our method and several other existing solutions on datasets publicly available, such as a large scale malware dataset and MNIST and IMDB datasets. Our results indicate that our approach typically provides superior classification performance and robustness to attacks compared with state-of-art solutions.

Rule extraction from black box models is critical in domains that require model validation before implementation, as can be the case in credit scoring and medical diagnosis. Though already a challenging problem in statistical learning in general, the difficulty is even greater when highly nonlinear, recursive models, such as recurrent neural networks (RNNs), are fit to data. Here, we study the extraction of rules from second-order RNNs trained to recognize the Tomita grammars. We show that production rules can be stably extracted from trained RNNs and that in certain cases, the rules outperform the trained RNNs.

Outside the highly publicized victories in the game of Go, there have been numerous successful applications of deep learning in the fields of information retrieval, computer vision, and speech recognition. In cybersecurity, an increasing number of companies have begun exploring the use of deep learning (DL) in a variety of security tasks with malware detection among the more popular. These companies claim that deep neural networks (DNNs) could help turn the tide in the war against malware infection. However, DNNs are vulnerable to adversarial samples, a shortcoming that plagues most, if not all, statistical and machine learning models. Recent research has demonstrated that those with malicious intent can easily circumvent deep learning-powered malware detection by exploiting this weakness.