Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. A possible starting point suggests that deep learning performs a sophisticated coarse graining. Coarse graining is the foundation of the renormalization group (RG), which provides a systematic construction of the theory of large scales starting from an underlying microscopic theory. In this way RG can be interpreted as providing a mechanism to explain the emergence of large scale structure, which is directly relevant to deep learning. We pursue the possibility that RG may provide a useful framework within which to pursue a theoretical explanation of deep learning. A statistical mechanics model for a magnet, the Ising model, is used to train an unsupervised RBM. The patterns generated by the trained RBM are compared to the configurations generated through a RG treatment of the Ising model. We argue that correlation functions between hidden and visible neurons are capable of diagnosing RG-like coarse graining. Numerical experiments show the presence of RG-like patterns in correlators computed using the trained RBMs. The observables we consider are also able to exhibit important differences between RG and deep learning.

Recent advances in semi-supervised learning methods rely on estimating the categories of unlabeled data using a model trained on the labeled data (pseudo-labeling) and using the unlabeled data for various consistency-based regularization. In this work, we propose to explicitly leverage the structure of the data manifold based on a Manifold Graph constructed over the image instances within the feature space. Specifically, we propose an architecture based on graph networks that jointly optimizes feature extraction, graph connectivity, and feature propagation and aggregation to unlabeled data in an end-to-end manner. Further, we present a novel Prototype Generator for producing a diverse set of prototypes that compactly represent each category, which supports feature propagation. To evaluate our method, we first contribute a strong baseline that combines two consistency-based regularizers that already achieves state-of-the-art results especially with fewer labels. We then show that when combined with these regularizers, the proposed method facilitates the propagation of information from generated prototypes to image data to further improve results. We provide extensive qualitative and quantitative experimental results on semi-supervised benchmarks demonstrating the improvements arising from our design and show that our method achieves state-of-the-art performance when compared with existing methods using a single model and comparable with ensemble methods. Specifically, we achieve error rates of 3.35% on SVHN, 8.27% on CIFAR-10, and 33.83% on CIFAR-100. With much fewer labels, we surpass the state of the arts by significant margins of 41% relative error decrease on average.

As a result of the growing size of Deep Neural Networks (DNNs), the gap to hardware capabilities in terms of memory and compute increases. To effectively compress DNNs, quantization and connection pruning are usually considered. However, unconstrained pruning usually leads to unstructured parallelism, which maps poorly to massively parallel processors, and substantially reduces the efficiency of general-purpose processors. Similar applies to quantization, which often requires dedicated hardware. We propose Parameterized Structured Pruning (PSP), a novel method to dynamically learn the shape of DNNs through structured sparsity. PSP parameterizes structures (e.g. channel- or layer-wise) in a weight tensor and leverages weight decay to learn a clear distinction between important and unimportant structures. As a result, PSP maintains prediction performance, creates a substantial amount of sparsity that is structured and, thus, easy and efficient to map to a variety of massively parallel processors, which are mandatory for utmost compute power and energy efficiency. PSP is experimentally validated on the popular CIFAR10/100 and ILSVRC2012 datasets using ResNet and DenseNet architectures, respectively.

We present an artificial neural network (ANN) approach to value financial derivatives. Atypically to standard ANN applications, practitioners equally use option pricing models to validate market prices and to infer unobserved prices. Importantly, models need to generate realistic arbitrage-free prices, meaning that no option portfolio can lead to risk-free profits. The absence of arbitrage opportunities is guaranteed by penalizing the loss using soft constraints on an extended grid of input values. ANNs can be pre-trained by first calibrating a standard option pricing model, and then training an ANN to a larger synthetic dataset generated from the calibrated model. The parameters transfer as well as the non-arbitrage constraints appear to be particularly useful when only sparse or erroneous data are available. We also explore how deeper ANNs improve over shallower ones, as well as other properties of the network architecture. We benchmark our method against standard option pricing models, such as Heston with and without jumps. We validate our method both on training sets, and testing sets, namely, highlighting both their capacity to reproduce observed prices and predict new ones.

ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of shallow (one hidden-layer) networks. For example, in the task of memorizing a random sample of size $m$ and dimension $d$, the best theoretical result requires the size of the network to be $\tilde{\Omega}(\frac{m^2}{d})$, while empirically a network of size slightly larger than $\frac{m}{d}$ is sufficient. To bridge this gap, we turn to study a simplified model for ReLU networks. We observe that a ReLU neuron is a product of a linear function with a gate (the latter determines whether the neuron is active or not), where both share a jointly trained weight vector. In this spirit, we introduce the Gated Linear Unit (GaLU), which simply decouples the linearity from the gating by assigning different vectors for each role. We show that GaLU networks allow us to get optimization and generalization results that are much stronger than those available for ReLU networks. Specifically, we show a memorization result for networks of size $\tilde{\Omega}(\frac{m}{d})$, and improved generalization bounds. Finally, we show that in some scenarios, GaLU networks behave similarly to ReLU networks, hence proving to be a good choice of a simplified model.

Recently, deep learning models play more and more important roles in contents recommender systems. However, although the performance of recommendations is greatly improved, the "Matthew effect" becomes increasingly evident. While the head contents get more and more popular, many competitive long-tail contents are difficult to achieve timely exposure because of lacking behavior features. This issue has badly impacted the quality and diversity of recommendations. To solve this problem, look-alike algorithm is a good choice to extend audience for high quality long-tail contents. But the traditional look-alike models which widely used in online advertising are not suitable for recommender systems because of the strict requirement of both real-time and effectiveness. This paper introduces a real-time attention based look-alike model (RALM) for recommender systems, which tackles the challenge of conflict between real-time and effectiveness. RALM realizes real-time look-alike audience extension benefiting from seeds-to-user similarity prediction and improves the effectiveness through optimizing user representation learning and look-alike learning modeling. For user representation learning, we propose a novel neural network structure named attention merge layer to replace the concatenation layer, which significantly improves the expressive ability of multi-fields feature learning. On the other hand, considering the various members of seeds, we design global attention unit and local attention unit to learn robust and adaptive seeds representation with respect to a certain target user. At last, we introduce seeds clustering mechanism which not only reduces the time complexity of attention units prediction but also minimizes the loss of seeds information at the same time. According to our experiments, RALM shows superior effectiveness and performance than popular look-alike models.

Consider a device that is connected to an edge processor via a communication channel. The device holds local data that is to be offloaded to the edge processor so as to train a machine learning model, e.g., for regression or classification. Transmission of the data to the learning processor, as well as training based on Stochastic Gradient Descent (SGD), must be both completed within a time limit. Assuming that communication and computation can be pipelined, this letter investigates the optimal choice for the packet payload size, given the overhead of each data packet transmission and the ratio between the computation and the communication rates. This amounts to a tradeoff between bias and variance, since communicating the entire data set first reduces the bias of the training process but it may not leave sufficient time for learning. Analytical bounds on the expected optimality gap are derived so as to enable an effective optimization, which is validated in numerical results.

Stochastic Gradient Langevin Dynamics infuses isotropic gradient noise to SGD to help navigate pathological curvature in the loss landscape for deep networks. Isotropic nature of the noise leads to poor scaling, and adaptive methods based on higher order curvature information such as Fisher Scoring have been proposed to precondition the noise in order to achieve better convergence. In this paper, we describe an adaptive method to estimate the parameters of the noise and conduct experiments on well-known model architectures to show that the adaptively preconditioned SGLD method achieves convergence with the speed of adaptive first order methods such as Adam, AdaGrad etc. and achieves generalization equivalent of SGD in the test set.

Environmental stresses such as drought and heat can cause substantial yield loss in agriculture. As such, hybrid crops which are tolerant to drought and heat stress would produce more consistent yields compared to the hybrids which are not tolerant to these stresses. In the 2019 Syngenta Crop Challenge, Syngenta released several large datasets that recorded the yield performances of 2,452 corn hybrids planted in 1,560 locations between 2008 and 2017 and asked participants to classify the corn hybrids as either tolerant or susceptible to drought stress, heat stress, and combined drought and heat stress. As one of the winning teams, we designed a two-step approach to solve this problem in an unsupervised way since no data was provided that classified any set of hybrids as tolerant or susceptible to any type of stress. First, we designed a deep convolutional neural network (CNN) that took advantage of state-of-the-art modeling and solution techniques to extract stress metrics for each type of stress. Our CNN model was found to successfully distinguish between the low and high stress environments due to considering multiple factors such as planting/harvest dates, daily weather, and soil conditions. Then, we conducted a linear regression of the yield of hybrid against each stress metric, and classified the hybrid based on the slope of the regression line, since the slope of the regression line showed how sensitive a hybrid was to a specific environmental stress. Our results suggested that only 14 % of the corn hybrids were tolerant to at least one type of stress.

Conversational machine reading systems help users answer high-level questions (e.g. determine if they qualify for particular government benefits) when they do not know the exact rules by which the determination is made(e.g. whether they need certain income levels or veteran status). The key challenge is that these rules are only provided in the form of a procedural text (e.g. guidelines from government website) which the system must read to figure out what to ask the user. We present a new conversational machine reading model that jointly extracts a set of decision rules from the procedural text while reasoning about which are entailed by the conversational history and which still need to be edited to create questions for the user. On the recently introduced ShARC conversational machine reading dataset, our Entailment-driven Extract and Edit network (E3) achieves a new state-of-the-art, outperforming existing systems as well as a new BERT-based baseline. In addition, by explicitly highlighting which information still needs to be gathered, E3 provides a more explainable alternative to prior work. We release source code for our models and experiments at https://github.com/vzhong/e3.