Recent works on implicit regularization have shown that gradient descent converges to the max-margin direction for logistic regression with one-layer or multi-layer linear networks. In this paper, we generalize this result to homogeneous neural networks, including fully-connected and convolutional neural networks with ReLU or LeakyReLU activations. In particular, we study the gradient flow (gradient descent with infinitesimal step size) optimizing the logistic loss or cross-entropy loss of any homogeneous model (possibly non-smooth), and show that if the training loss decreases below a certain threshold, then we can define a smoothed version of the normalized margin which increases over time. We also formulate a natural constrained optimization problem related to margin maximization, and prove that both the normalized margin and its smoothed version converge to the objective value at a KKT point of the optimization problem. Furthermore, we extend the above results to a large family of loss functions. We conduct several experiments to justify our theoretical finding on MNIST and CIFAR-10 datasets. For gradient descent with constant learning rate, we observe that the normalized margin indeed keeps increasing after the dataset is fitted, but the speed is very slow. However, if we schedule the learning rate more carefully, we can observe a more rapid growth of the normalized margin. Finally, as margin is closely related to robustness, we discuss potential benefits of training longer for improving the robustness of the model.

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on factorisations of the variational posterior. As we demonstrate in our experiments, the factorisation between latent system states and transition function can lead to a miscalibrated posterior and to learning unnecessarily large noise terms. We eliminate this factorisation by explicitly modelling the dependence between state trajectories and the Gaussian process posterior. Samples of the latent states can then be tractably generated by conditioning on this representation. The method we obtain (VCDT: variationally coupled dynamics and trajectories) gives better predictive performance and more calibrated estimates of the transition function, yet maintains the same time and space complexities as mean-field methods. Code is available at: github.com/ialong/GPt.

Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a generic nonlinear system, as they have proven to be very effective in approximating complex highly nonlinear functions. In this work, we propose low-rank tensor completion as an appealing alternative for modeling and learning complex nonlinear systems. We model the interactions between the $N$ input variables and the scalar output of a system by a single N-way tensor, and setup a weighted low-rank tensor completion problem with smoothness regularization which we tackle using a block coordinate descent algorithm. We extend our method to the multi-output setting and the case of partially observed data, which cannot be readily handled by neural networks. Finally, we demonstrate the effectiveness of the approach using several regression tasks including some standard benchmarks and a challenging student grade prediction task.

This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile loss poses new challenges to high-dimensional distributed estimation in both computation and theoretical development. To address the challenge, we transform the response variable and establish a new connection between quantile regression and ordinary linear regression. Then, we provide a distributed estimator that is both computationally and communicationally efficient, where only the gradient information is communicated at each iteration. Theoretically, we show that, after a constant number of iterations, the proposed estimator achieves a near-oracle convergence rate without any restriction on the number of machines. Moreover, we establish the theoretical guarantee for the support recovery. The simulation analysis is provided to demonstrate the effectiveness of our method.

The emulation task of a nonlinear autoregressive moving average model, i.e., the NARMA10 task, has been widely used as a benchmark task for recurrent neural networks, especially in reservoir computing. However, the type and quantity of computational capabilities required to emulate the NARMA10 model remain unclear, and, to date, the NARMA10 task has been utilized blindly. Therefore, in this study, we have investigated the properties of the NARMA10 model from a dynamical system perspective. We revealed its bifurcation structure and basin of attraction, as well as the system's Lyapunov spectra. Furthermore, we have analyzed the computational capabilities required to emulate the NARMA10 model by decomposing it into multiple combinations of orthogonal nonlinear polynomials using Legendre polynomials, and we directly evaluated its information processing capacity together with its dependences on some system parameters. The result demonstrates that the NARMA10 model contains an unstable region in the phase space that makes the system diverge according to the selection of the input range and initial conditions. Furthermore, the information processing capacity of the model varies according to the input range. These properties prevent safe application of this model and fair comparisons among experiments, which are unfavorable for a benchmark task. As a result, we propose a benchmark model that can clearly evaluate equivalent computational capacity using NARMA10. Compared to the original NARMA10 model, the proposed model is highly stable and robust against the input range settings.

The reliance on deep learning algorithms has grown significantly in recent years. Yet, these models are highly vulnerable to adversarial attacks, which introduce visually imperceptible perturbations into testing data to induce misclassifications. The literature has proposed several methods to combat such adversarial attacks, but each method either fails at high perturbation values, requires excessive computing power, or both. This letter proposes a computationally efficient method for defending the Fast Gradient Sign (FGS) adversarial attack by simultaneously denoising and compressing data. Specifically, our proposed defense relies on training a fully connected multi-layer Denoising Autoencoder (DAE) and using its encoder as a defense against the adversarial attack. Our results show that using this dimensionality reduction scheme is not only highly effective in mitigating the effect of the FGS attack in multiple threat models, but it also provides a 2.43x speedup in comparison to defense strategies providing similar robustness against the same attack.

Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models by letting them either output a prediction set or abstain when the uncertainty is high. We propose training these selective prediction-set models using an uncertainty-aware loss minimization framework, which unifies ideas from decision theory and robust maximum likelihood. Moreover, since black-box methods are not guaranteed to output well-calibrated prediction sets, we show how to calculate point estimates and confidence intervals for the true coverage of any selective prediction-set model, as well as a uniform mixture of K set models obtained from K-fold sample-splitting. When applied to predicting in-hospital mortality and length-of-stay for ICU patients, our model outperforms existing approaches on both in-sample and out-of-sample age groups, and our recalibration method provides accurate inference for prediction set coverage.

Swarm-based optimizers like Particle Swarm Optimization or Imperialistic Competitive Algorithm that act under influences of cooperation or competition among groups, are unable to search in multiple volumes of locality or globality and do not have nested localities. As hybrid optimizers, they may not give satisfactory results as initializers in Gradient Descent approximators used in plenty of multimodal problems like nonlinear subspace learning and neural network training, which have hierarchies of convex spaces due to nonlinearity and multi-layer nature of these models. To search in various levels of scale in a homogenous way, a framework is proposed to equip PSO and ICA a multi-scale search capability. Then, the resulted optimizers are evaluated in single and GD-hybridized mode. Hybrid evaluation as GD randomizer is implemented with the help of a nonlinear subspace filtering objective function over EEG data and optimization loss and validation data accuracy is compared with other hybrids containing GD. A single evaluation is also taken place between the proposed ones, PSO, ICA, CLPSO, and CICA, which are used more in hybrid learning-based approaches. Evaluations were with respect to solution error. Before concluding the paper, it is shown and analyzed that proposed optimizers outperform algorithms of related context both in single and hybrid-GD mode.

Fuzzing has played an important role in improving software development and testing over the course of several decades. Recent research in fuzzing has focused on applications of machine learning (ML), offering useful tools to overcome challenges in the fuzzing process. This review surveys the current research in applying ML to fuzzing. Specifically, this review discusses successful applications of ML to fuzzing, briefly explores challenges encountered, and motivates future research to address fuzzing bottlenecks.

The recent application of Deep Learning in various areas of medical image analysis has brought excellent performance gain. The application of deep learning technologies in medical image registration successfully outperformed traditional optimization based registration algorithms both in registration time and accuracy. In this paper, we present a densely connected convolutional architecture for deformable image registration. The training of the network is unsupervised and does not require ground-truth deformation or any synthetic deformation as a label. The proposed architecture is trained and tested on two different version of tissue cleared data, 10\% and 25\% resolution of high resolution dataset respectively and demonstrated comparable registration performance with the state-of-the-art ANTS registration method. The proposed method is also compared with the deep-learning based Voxelmorph registration method. Due to the memory limitation, original voxelmorph can work at most 15\% resolution of Tissue cleared data. For rigorous experimental comparison we developed a patch-based version of Voxelmorph network, and trained it on 10\% and 25\% resolution. In both resolution, proposed DenseDeformation network outperformed Voxelmorph in registration accuracy.