To automate the generation of interactive features, recent methods are proposed to either explicitly traverse the interactive feature space or implicitly express the interactions via intermediate activations of some designed models. These two kinds of methods show that there is essentially a trade-off between feature interpretability and efficient search. To possess both of their merits, we propose a novel method named Feature Interaction Via Edge Search (FIVES), which formulates the task of interactive feature generation as searching for edges on the defined feature graph. We first present our theoretical evidence that motivates us to search for interactive features in an inductive manner. Then we instantiate this search strategy by alternatively updating the edge structure and the predictive model of a graph neural network (GNN) associated with the defined feature graph. In this way, the proposed FIVES method traverses a trimmed search space and enables explicit feature generation according to the learned adjacency tensor of the GNN. Experimental results on both benchmark and real-world datasets demonstrate the advantages of FIVES over several state-of-the-art methods.

Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable empirical success, little is known about how such constrained neural networks behave during their training via gradient descent. More importantly, even less is known about why such models sometimes fail to train at all. In this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent. Specifically, we derive the NTK of PINNs and prove that, under appropriate conditions, it converges to a deterministic kernel that stays constant during training in the infinite-width limit. This allows us to analyze the training dynamics of PINNs through the lens of their limiting NTK and find a remarkable discrepancy in the convergence rate of the different loss components contributing to the total training error. To address this fundamental pathology, we propose a novel gradient descent algorithm that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error. Finally, we perform a series of numerical experiments to verify the correctness of our theory and the practical effectiveness of the proposed algorithms. The data and code accompanying this manuscript are publicly available at \url{https://github.com/PredictiveIntelligenceLab/PINNsNTK}.

Deep Neural Networks (DNNs) with sparse input features have been widely used in recommender systems in industry. These models have large memory requirements and need a huge amount of training data. The large model size usually entails a cost, in the range of millions of dollars, for storage and communication with the inference services. In this paper, we propose a hybrid hashing method to combine frequency hashing and double hashing techniques for model size reduction, without compromising performance. We evaluate the proposed models on two product surfaces. In both cases, experiment results demonstrated that we can reduce the model size by around 90 % while keeping the performance on par with the original baselines.

Federated Learning (FL) has emerged as a promising technique for edge devices to collaboratively learn a shared prediction model, while keeping their training data on the device, thereby decoupling the ability to do machine learning from the need to store the data in the cloud. However, FL is difficult to implement and deploy in practice, considering the heterogeneity in mobile devices, e.g., different programming languages, frameworks, and hardware accelerators. Although there are a few frameworks available to simulate FL algorithms (e.g., TensorFlow Federated), they do not support implementing FL workloads on mobile devices. Furthermore, these frameworks are designed to simulate FL in a server environment and hence do not allow experimentation in distributed mobile settings for a large number of clients. In this paper, we present Flower (https://flower.dev/), a FL framework which is both agnostic towards heterogeneous client environments and also scales to a large number of clients, including mobile and embedded devices. Flower's abstractions let developers port existing mobile workloads with little overhead, regardless of the programming language or ML framework used, while also allowing researchers flexibility to experiment with novel approaches to advance the state-of-the-art. We describe the design goals and implementation considerations of Flower and show our experiences in evaluating the performance of FL across clients with heterogeneous computational and communication capabilities.

Understanding the effect of depth in deep learning is a critical problem. In this work, we utilize the Fourier analysis to empirically provide a promising mechanism to understand why deeper learning is faster. To this end, we separate a deep neural network into two parts, one is a pre-condition component and the other is a learning component, in which the output of the pre-condition one is the input of the learning one. Based on experiments of deep networks and real dataset, we propose a deep frequency principle, that is, the effective target function for a deeper hidden layer has a bias towards a function with more low frequency during the training. Therefore, the learning component effectively learns a lower frequency function if the pre-condition component has more layers. Due to the well-studied frequency principle, i.e., deep neural networks learn lower frequency functions faster, the deep frequency principle provides a reasonable explanation to why deeper learning is faster. We believe these empirical studies would be valuable for future theoretical studies of the effect of depth in deep learning.

Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional neural networks applied to approximate functions on the unit sphere $\mathbb{S}^{d-1}$ of $\mathbb{R}^d$. Our analysis presents rates of uniform approximation when the approximated function lies in the Sobolev space $W^r_\infty (\mathbb{S}^{d-1})$ with $r>0$ or takes an additive ridge form. Our work verifies theoretically the modelling and approximation ability of deep convolutional neural networks followed by downsampling and one fully connected layer or two. The key idea of our spherical analysis is to use the inner product form of the reproducing kernels of the spaces of spherical harmonics and then to apply convolutional factorizations of filters to realize the generated linear features.

Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The greedy techniques are low computational cost algorithms, which have also been modified to incorporate the non-negativity of the representations. One such modification has been proposed for Matching Pursuit (MP) based algorithms, which first chooses positive coefficients and uses a non-negative optimisation technique that guarantees the non-negativity of the coefficients. The performance of greedy algorithms, like all non-exhaustive search methods, suffer from high coherence with the linear generative model, called the dictionary. We here first reformulate the non-negative matching pursuit algorithm in the form of a deep neural network. We then show that the proposed model after training yields a significant improvement in terms of exact recovery performance, compared to other non-trained greedy algorithms, while keeping the complexity low.

Because learning sometimes involves sensitive data, machine learning algorithms have been extended to offer privacy for training data. In practice, this has been mostly an afterthought, with privacy-preserving models obtained by re-running training with a different optimizer, but using the model architectures that already performed well in a non-privacy-preserving setting. This approach leads to less than ideal privacy/utility tradeoffs, as we show here. Instead, we propose that model architectures are chosen ab initio explicitly for privacy-preserving training. To provide guarantees under the gold standard of differential privacy, one must bound as strictly as possible how individual training points can possibly affect model updates. In this paper, we are the first to observe that the choice of activation function is central to bounding the sensitivity of privacy-preserving deep learning. We demonstrate analytically and experimentally how a general family of bounded activation functions, the tempered sigmoids, consistently outperform unbounded activation functions like ReLU. Using this paradigm, we achieve new state-of-the-art accuracy on MNIST, FashionMNIST, and CIFAR10 without any modification of the learning procedure fundamentals or differential privacy analysis.

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and reliability of predictions. We answer these questions by computing reachable sets of neural networks, i.e. sets of outputs resulting from continuous sets of inputs. We provide two efficient approaches that lead to over- and under-approximations of the reachable set. This principle is highly versatile, as we show. First, we analyze and enhance the robustness properties of both classifiers and regression models. This is in contrast to existing works, which only handle classification. Specifically, we verify (non-)robustness, propose a robust training procedure, and show that our approach outperforms adversarial attacks as well as state-of-the-art methods of verifying classifiers for non-norm bound perturbations. We also provide a technique of distinguishing between reliable and non-reliable predictions for unlabeled inputs, quantify the influence of each feature on a prediction, and compute a feature ranking.

We propose a class of neural network models that universally approximate any point process intensity function. Our model can be easily applied to a wide variety of applications where the distribution of event times is of interest, such as, earthquake aftershocks, social media events, and financial transactions. Point processes have long been used to model these events, but more recently, neural network point process models have been developed to provide further flexibility. However, the theoretical foundations of these neural point processes are not well understood. We propose a neural network point process model which uses the summation of basis functions and the function composition of a transfer function to define point process intensity functions. In contrast to prior work, we prove that our model has universal approximation properties in the limit of infinite basis functions. We demonstrate how to use positive monotonic Lipschitz continuous transfer functions to shift universal approximation from the class of real valued continuous functions to the class of point process intensity functions. To this end, the Stone-Weierstrass Theorem is used to provide sufficient conditions for the sum of basis functions to achieve point process universal approximation. We further extend the notion of universal approximation mentioned in prior work for neural point processes to account for the approximation of sequences, instead of just single events. Using these insights, we design and implement a novel neural point process model that achieves strong empirical results on synthetic and real world datasets; outperforming state-of-the-art neural point process on all but one real world dataset.