### Universal Supervised Learning for Individual Data

Universal supervised learning is considered from an information theoretic point of view following the universal prediction approach, see Merhav and Feder (1998). We consider the standard supervised "batch" learning where prediction is done on a test sample once the entire training data is observed, and the individual setting where the features and labels, both in the training and test, are specific individual quantities. The information theoretic approach naturally uses the self-information loss or log-loss. Our results provide universal learning schemes that compete with a "genie" (or reference) that knows the true test label. In particular, it is demonstrated that the main proposed scheme, termed Predictive Normalized Maximum Likelihood (pNML), is a robust learning solution that outperforms the current leading approach based on Empirical Risk Minimization (ERM). Furthermore, the pNML construction provides a pointwise indication for the learnability of the specific test challenge with the given training examples

### A New Look at an Old Problem: A Universal Learning Approach to Linear Regression

Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a linear combination of the feature vector $x^T\theta$ where $x\in {\cal R}^M$, within a Gaussian error. The Predictive Normalized Maximum Likelihood (pNML) solution for universal learning of individual data can be expressed analytically in this case, as well as its associated learnability measure. Interestingly, the situation where the number of parameters $M$ may even be larger than the number of training samples $N$ can be examined. As expected, in this case learnability cannot be attained in every situation; nevertheless, if the test vector resides mostly in a subspace spanned by the eigenvectors associated with the large eigenvalues of the empirical correlation matrix of the training data, linear regression can generalize despite the fact that it uses an over-parametrized'' model. We demonstrate the results with a simulation of fitting a polynomial to data with a possibly large polynomial degree.

### An Explainable Adversarial Robustness Metric for Deep Learning Neural Networks

Deep Neural Networks(DNN) have excessively advanced the field of computer vision by achieving state of the art performance in various vision tasks. These results are not limited to the field of vision but can also be seen in speech recognition and machine translation tasks. Recently, DNNs are found to poorly fail when tested with samples that are crafted by making imperceptible changes to the original input images. This causes a gap between the validation and adversarial performance of a DNN. An effective and generalizable robustness metric for evaluating the performance of DNN on these adversarial inputs is still missing from the literature. In this paper, we propose Noise Sensitivity Score (NSS), a metric that quantifies the performance of a DNN on a specific input under different forms of fix-directional attacks. An insightful mathematical explanation is provided for deeply understanding the proposed metric. By leveraging the NSS, we also proposed a skewness based dataset robustness metric for evaluating a DNN's adversarial performance on a given dataset. Extensive experiments using widely used state of the art architectures along with popular classification datasets, such as MNIST, CIFAR-10, CIFAR-100, and ImageNet, are used to validate the effectiveness and generalization of our proposed metrics. Instead of simply measuring a DNN's adversarial robustness in the input domain, as previous works, the proposed NSS is built on top of insightful mathematical understanding of the adversarial attack and gives a more explicit explanation of the robustness.

### Out-of-Distribution Detection using Multiple Semantic Label Representations

Deep Neural Networks are powerful models that attained remarkable results on a variety of tasks. These models are shown to be extremely efficient when training and test data are drawn from the same distribution. However, it is not clear how a network will act when it is fed with an out-of-distribution example. In this work, we consider the problem of out-of-distribution detection in neural networks. We propose to use multiple semantic dense representations instead of sparse representation as the target label. Specifically, we propose to use several word representations obtained from different corpora or architectures as target labels. We evaluated the proposed model on computer vision, and speech commands detection tasks and compared it to previous methods. Results suggest that our method compares favorably with previous work. Besides, we present the efficiency of our approach for detecting wrongly classified and adversarial examples.

### Controlling Over-generalization and its Effect on Adversarial Examples Generation and Detection

Convolutional Neural Networks (CNNs) allowed improving the state-of-the-art for many vision applications. However, naive CNNs suffer from two serious issues: vulnerability to adversarial examples and making incorrect but confident predictions for out-distribution samples. In this paper, we draw a connection between these two issues of CNNs through over-generalization. We reveal an augmented CNN (an extra output class added) as a simple yet effective end-to-end approach has the capacity for controlling over-generalization. We demonstrate training an augmented CNN on only a properly selected natural out-distribution dataset and interpolated samples empowers it to classify a wide range of unseen out-distribution samples as dustbin. Meanwhile, its misclassification rates on a broad spectrum of well-known black-box adversaries drop drastically as it classifies a portion of adversaries as dustbin class (rejection option) while correctly classifies some of the remaining. However, such an augmented CNN is never trained with any types of adversaries. Finally, generation of white-box adversarial attacks using augmented CNNs can be harder as the attack algorithms have to avoid dustbin regions for generating actual adversaries.