Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that are computable by a given network. We study real infinitely differentiable (smooth) hierarchical functions implemented by feedforward neural networks via composing simpler functions in two cases: 1) each constituent function of the composition has fewer inputs than the resulting function; 2) constituent functions are in the more specific yet prevalent form of a non-linear univariate function (e.g. tanh) applied to a linear multivariate function. We establish that in each of these regimes there exist non-trivial algebraic partial differential equations (PDEs), which are satisfied by the computed functions. These PDEs are purely in terms of the partial derivatives and are dependent only on the topology of the network. For compositions of polynomial functions, the algebraic PDEs yield non-trivial equations (of degrees dependent only on the architecture) in the ambient polynomial space that are satisfied on the associated functional varieties. Conversely, we conjecture that such PDE constraints, once accompanied by appropriate non-singularity conditions and perhaps certain inequalities involving partial derivatives, guarantee that the smooth function under consideration can be represented by the network. The conjecture is verified in numerous examples including the case of tree architectures which are of neuroscientific interest. Our approach is a step toward formulating an algebraic description of functional spaces associated with specific neural networks, and may provide new, useful tools for constructing neural networks.

Machine learning shows remarkable success for recognizing patterns in data. Here we apply the machine learning (ML) for the diagnosis of early stage diabetes, which is known as a challenging task in medicine. Blood glucose levels are tightly regulated by two counter-regulatory hormones, insulin and glucagon, and the failure of the glucose homeostasis leads to the common metabolic disease, diabetes mellitus. It is a chronic disease that has a long latent period the complicates detection of the disease at an early stage. The vast majority of diabetics result from that diminished effectiveness of insulin action. The insulin resistance must modify the temporal profile of blood glucose. Thus we propose to use ML to detect the subtle change in the temporal pattern of glucose concentration. Time series data of blood glucose with sufficient resolution is currently unavailable, so we confirm the proposal using synthetic data of glucose profiles produced by a biophysical model that considers the glucose regulation and hormone action. Multi-layered perceptrons, convolutional neural networks, and recurrent neural networks all identified the degree of insulin resistance with high accuracy above $85\%$.

In this paper we demonstrate methods for reliable and efficient training of discrete representation using Vector-Quantized Variational Auto-Encoder models (VQ-VAEs). Discrete latent variable models have been shown to learn nontrivial representations of speech, applicable to unsupervised voice conversion and reaching state-of-the-art performance on unit discovery tasks. For unsupervised representation learning, they became viable alternatives to continuous latent variable models such as the Variational Auto-Encoder (VAE). However, training deep discrete variable models is challenging, due to the inherent non-differentiability of the discretization operation. In this paper we focus on VQ-VAE, a state-of-the-art discrete bottleneck model shown to perform on par with its continuous counterparts. It quantizes encoder outputs with on-line $k$-means clustering. We show that the codebook learning can suffer from poor initialization and non-stationarity of clustered encoder outputs. We demonstrate that these can be successfully overcome by increasing the learning rate for the codebook and periodic date-dependent codeword re-initialization. As a result, we achieve more robust training across different tasks, and significantly increase the usage of latent codewords even for large codebooks. This has practical benefit, for instance, in unsupervised representation learning, where large codebooks may lead to disentanglement of latent representations.

Previous researches of sketches often considered sketches in pixel format and leveraged CNN based models in the sketch understanding. Fundamentally, a sketch is stored as a sequence of data points, a vector format representation, rather than the photo-realistic image of pixels. SketchRNN studied a generative neural representation for sketches of vector format by Long Short Term Memory networks (LSTM). Unfortunately, the representation learned by SketchRNN is primarily for the generation tasks, rather than the other tasks of recognition and retrieval of sketches. To this end and inspired by the recent BERT model, we present a model of learning Sketch Bidirectional Encoder Representation from Transformer (Sketch-BERT). We generalize BERT to sketch domain, with the novel proposed components and pre-training algorithms, including the newly designed sketch embedding networks, and the self-supervised learning of sketch gestalt. Particularly, towards the pre-training task, we present a novel Sketch Gestalt Model (SGM) to help train the Sketch-BERT. Experimentally, we show that the learned representation of Sketch-BERT can help and improve the performance of the downstream tasks of sketch recognition, sketch retrieval, and sketch gestalt.

Murdoch and Szlam Understanding and explaining decisions of complex (2017) explain long short term memory networks models such as neural networks has recently (LSTMs) (Hochreiter and Schmidhuber, 1997) by gained a lot of attention for engendering trust in means of ngram rules, but their rules are limited these models, improving them, and understanding to presence of single ngrams and do not capture them better (Montavon et al., 2018; Alishahi et al., interaction between ngrams in text. To learn explanation 2019; Belinkov and Glass, 2019). Several previous rules for RNNs while overcoming the studies developing interpretability techniques provide limitations of the previous approaches, we have the a set of input features or segments that are the following contributions in the paper: most salient for the model output. Approaches such as input perturbation and gradient computation are 1. We induce explanation rules over important popular for this purpose (Ancona et al., 2018; Arras skipgrams in text, while ensuring that these et al., 2019). A drawback of these approaches rules generalize to unseen data. To this end, is the lack of information about interaction between we quantify skipgram importance in LSTMs different features. While heatmaps (Li et al., by first pooling gradients across embedding 2016b,a; Arras et al., 2017) and partial dependence dimensions to compute word importance, and plots (Lundberg and Lee, 2017) are popularly used, thereby aggregating them into skipgram importance. Research conducted while at CLiPS.

In this paper, we explore strategies to detect and evaluate counterfactual sentences. Since causal insight is an inherent characteristic of a counterfactual, is it possible to use this information in order to locate antecedent and consequent fragments in counterfactual statements? We thus propose to compare and evaluate models to correctly identify and chunk counterfactual sentences. In our experiments, we attempt to answer the following questions: First, can a learned model discern counterfactual statements reasonably well? Second, is it possible to clearly identify antecedent and consequent parts of counterfactual sentences?

Objectives: With the technological advancements in the field of tele-health monitoring, it is now possible to gather huge amounts of electro-physiological signals such as electrocardiogram (ECG). It is therefore necessary to develop models/algorithms that are capable of analysing these massive amounts of data in real-time. This paper proposes a deep learning model for real-time segmentation of heartbeats. Methods: The proposed algorithm, named as the DENS-ECG algorithm, combines convolutional neural network (CNN) and long short-term memory (LSTM) model to detect onset, peak, and offset of different heartbeat waveforms such as the P-wave, QRS complex, T-wave, and No wave (NW). Using ECG as the inputs, the model learns to extract high level features through the training process, which, unlike other classical machine learning based methods, eliminates the feature engineering step. Results: The proposed DENS-ECG model was trained and validated on a dataset with 105 ECGs of length 15 minutes each and achieved an average sensitivity and precision of 97.95% and 95.68%, respectively, using a 5-fold cross validation. Additionally, the model was evaluated on an unseen dataset to examine its robustness in QRS detection, which resulted in a sensitivity of 99.61% and precision of 99.52%. Conclusion: The empirical results show the flexibility and accuracy of the combined CNN-LSTM model for ECG signal delineation. Significance: This paper proposes an efficient and easy to use approach using deep learning for heartbeat segmentation, which could potentially be used in real-time tele-health monitoring systems.

Deep learning models are known to be vulnerable not only to input-dependent adversarial attacks but also to input-agnostic or universal adversarial attacks. Dezfooli et al. \cite{Dezfooli17,Dezfooli17anal} construct universal adversarial attack on a given model by looking at a large number of training data points and the geometry of the decision boundary near them. Subsequent work \cite{Khrulkov18} constructs universal attack by looking only at test examples and intermediate layers of the given model. In this paper, we propose a simple universalization technique to take any input-dependent adversarial attack and construct a universal attack by only looking at very few adversarial test examples. We do not require details of the given model and have negligible computational overhead for universalization. We theoretically justify our universalization technique by a spectral property common to many input-dependent adversarial perturbations, e.g., gradients, Fast Gradient Sign Method (FGSM) and DeepFool. Using matrix concentration inequalities and spectral perturbation bounds, we show that the top singular vector of input-dependent adversarial directions on a small test sample gives an effective and simple universal adversarial attack. For VGG16 and VGG19 models trained on ImageNet, our simple universalization of Gradient, FGSM, and DeepFool perturbations using a test sample of 64 images gives fooling rates comparable to state-of-the-art universal attacks \cite{Dezfooli17,Khrulkov18} for reasonable norms of perturbation.

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.

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.