Deep neural networks (DNNs) have played a key role in a wide range of machine learning applications. However, DNN classifiers are vulnerable to human-imperceptible adversarial perturbations, which can cause them to misclassify inputs with high confidence. Thus, creating robust DNNs which can defend against malicious examples is critical in applications where security plays a major role. In this paper, we study the effect of intrinsic dataset properties on the performance of adversarial attack and defense methods, testing on five popular image classification datasets - MNIST, Fashion-MNIST, CIFAR10/CIFAR100, and ImageNet. We find that input size and image contrast play key roles in attack and defense success. Our discoveries highlight that dataset design and data preprocessing steps are important to boost the adversarial robustness of DNNs. To our best knowledge, this is the first comprehensive work that studies the effect of intrinsic dataset properties on adversarial machine learning.

Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different distributions (denoted as $\mu$ and $\mu'$, respectively). In this work, we give an information-theoretic analysis on the generalization error and the excess risk of transfer learning algorithms, following a line of work initiated by Russo and Zhou. Our results suggest, perhaps as expected, that the Kullback-Leibler (KL) divergence $D(mu||mu')$ plays an important role in characterizing the generalization error in the settings of domain adaptation. Specifically, we provide generalization error upper bounds for general transfer learning algorithms and extend the results to a specific empirical risk minimization (ERM) algorithm where data from both distributions are available in the training phase. We further apply the method to iterative, noisy gradient descent algorithms, and obtain upper bounds which can be easily calculated, only using parameters from the learning algorithms. A few illustrative examples are provided to demonstrate the usefulness of the results. In particular, our bound is tighter in specific classification problems than the bound derived using Rademacher complexity.

Gradient tree boosting (e.g. XGB) is one of the most widely usedmachine learning models in practice. How to build a secure XGB inface of data isolation problem becomes a hot research topic. However, existing works tend to leak intermediate information and thusraise potential privacy risk. In this paper, we propose a novel framework for two parties to build secure XGB with vertically partitioneddata. Specifically, we associate Homomorphic Encryption (HE) domain with Secret Sharing (SS) domain by providing the two-waytransformation primitives. The framework generally promotes theefficiency for privacy preserving machine learning and offers theflexibility to implement other machine learning models. Then weelaborate two secure XGB training algorithms as well as a corresponding prediction algorithm under the hybrid security domains.Next, we compare our proposed two training algorithms throughboth complexity analysis and experiments. Finally, we verify themodel performance on benchmark dataset and further apply ourwork to a real-world scenario.

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no mechanism for adjusting the trajectory based on subsequent observations. Here, we demonstrate how this may be resolved through the well-understood mathematics of \emph{controlled differential equations}. The resulting \emph{neural controlled differential equation} model is directly applicable to the general setting of partially-observed irregularly-sampled multivariate time series, and (unlike previous work on this problem) it may utilise memory-efficient adjoint-based backpropagation even across observations. We demonstrate that our model achieves state-of-the-art performance against similar (ODE or RNN based) models in empirical studies on a range of datasets. Finally we provide theoretical results demonstrating universal approximation, and that our model subsumes alternative ODE models.

Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat partitions of the sub-string set induced by the documents as Bernoulli random variables. The mean value of each random variable is an estimate of the classifier's precision when presented with a document inducing that partition. These means can be compared, using standard statistical tests, to a desired or expected classifier precision. A set of binary classifiers can be combined into a single, multi-label classifier by an application of the Dempster-Shafer theory of evidence. The utility of this approach is demonstrated with a benchmark problem.

AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics -- a MathZero. MathZero would require a formal foundation and an objective. We propose the foundation of set-theoretic dependent type theory and an objective defined in terms of the classification problem -- the problem of classifying concept instances up to isomorphism. The natural numbers arise as the solution to the classification problem for finite sets. Here we generalize classical Bourbaki set-theoretic isomorphism to set-theoretic dependent type theory. To our knowledge we give the first isomorphism inference rules for set-theoretic dependent type theory with propositional set-theoretic equality. The presentation is intended to be accessible to mathematicians with no prior exposure to type theory.

Collision detection is one of the most challenging tasks for Unmanned Aerial Vehicles (UAVs), especially for small or micro UAVs with limited computational power. In nature, fly insects with compact and simple visual systems demonstrate the amazing ability to navigating and avoid collision in a complex environment. A good example of this is locusts. Locusts avoid collision in a dense swarm relying on an identified vision neuron called Lobula Giant Movement Detector (LGMD) which has been modelled and applied on ground robots and vehicles. LGMD as a fly insect's visual neuron, is an ideal model for UAV collision detection. However, the existing models are inadequate in coping with complex visual challenges unique for UAVs. In this paper, we proposed a new LGMD model for flying robots considering distributed spatial-temporal computing for both excitation and inhibition to enhance the looming selectivity in flying scenes. The proposed model integrated recent discovered presynaptic connection types in biological LGMD neuron into a spatial-temporal filter with linear distributed interconnection. Systematic experiments containing quadcopter's first person view (FPV) flight videos demonstrated that the proposed distributed presynaptic structure can dramatically enhance LGMD's looming selectivity especially in complex flying UAV applications.

The goal of knowledge tracing is to track the state of a student's knowledge as it evolves over time. This plays a fundamental role in understanding the learning process and is a key task in the development of an intelligent tutoring system. In this paper we propose a novel approach to knowledge tracing that combines techniques from matrix factorization with recent progress in recurrent neural networks (RNNs) to effectively track the state of a student's knowledge. The proposed \emph{DynEmb} framework enables the tracking of student knowledge even without the concept/skill tag information that other knowledge tracing models require while simultaneously achieving superior performance. We provide experimental evaluations demonstrating that DynEmb achieves improved performance compared to baselines and illustrating the robustness and effectiveness of the proposed framework. We also evaluate our approach using several real-world datasets showing that the proposed model outperforms the previous state-of-the-art. These results suggest that combining embedding models with sequential models such as RNNs is a promising new direction for knowledge tracing.

Numerical reasoning is often important to accurately understand the world. Recently, several format-specific datasets have been proposed, such as numerical reasoning in the settings of Natural Language Inference (NLI), Reading Comprehension (RC), and Question Answering (QA). Several format-specific models and architectures in response to those datasets have also been proposed. However, there exists a strong need for a benchmark which can evaluate the abilities of models, in performing question format independent numerical reasoning, as (i) the numerical reasoning capabilities we want to teach are not controlled by question formats, (ii) for numerical reasoning technology to have the best possible application, it must be able to process language and reason in a way that is not exclusive to a single format, task, dataset or domain. In pursuit of this goal, we introduce NUMBERGAME, a multifaceted benchmark to evaluate model performance across numerical reasoning tasks of eight diverse formats. We add four existing question types in our compilation. Two of the new types we add are about questions that require external numerical knowledge, commonsense knowledge and domain knowledge. For building a more practical numerical reasoning system, NUMBERGAME demands four capabilities beyond numerical reasoning: (i) detecting question format directly from data (ii) finding intermediate common format to which every format can be converted (iii) incorporating commonsense knowledge (iv) handling data imbalance across formats. We build several baselines, including a new model based on knowledge hunting using a cheatsheet. However, all baselines perform poorly in contrast to the human baselines, indicating the hardness of our benchmark. Our work takes forward the recent progress in generic system development, demonstrating the scope of these under-explored tasks.

In some complicated datasets, due to the presence of noisy data points and outliers, cluster validity indices can give conflicting results in determining the optimal number of clusters. This paper presents a new validity index for fuzzy-possibilistic c-means clustering called Fuzzy-Possibilistic)FP (index, which works well in the presence of clusters that vary in shape and density. Moreover, FPCM like most of the clustering algorithms is susceptible to some initial parameters. In this regard, in addition to the number of clusters, FPCM requires a priori selection of the degree of fuzziness (m) and the degree of typicality (η). Therefore, we presented an efficient procedure for determining an optimal value for and. The proposed approach has been evaluated using several synthetic and real-world datasets. Final computational results demonstrate the capabilities and reliability of the proposed approach compared with several well-known fuzzy validity indices in the literature. Furthermore, to clarify the ability of the proposed method in real applications, the proposed method is implemented in microarray gene expression data clustering and medical image segmentation.