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Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NNs). However the intriguing approach of training NNs with MIP solvers is under-explored. State-of-the-art-methods to train NNs are typically gradient-based and require significant data, computation on GPUs, and extensive hyper-parameter tuning. In contrast, training with MIP solvers does not require GPUs or heavy hyper-parameter tuning, but currently cannot handle anything but small amounts of data. This article builds on recent advances that train binarized NNs using MIP solvers. We go beyond current work by formulating new MIP models which improve training efficiency and which can train the important class of integer-valued neural networks (INNs). We provide two novel methods to further the potential significance of using MIP to train NNs. The first method optimizes the number of neurons in the NN while training. This reduces the need for deciding on network architecture before training. The second method addresses the amount of training data which MIP can feasibly handle: we provide a batch training method that dramatically increases the amount of data that MIP solvers can use to train. We thus provide a promising step towards using much more data than before when training NNs using MIP models. Experimental results on two real-world data-limited datasets demonstrate that our approach strongly outperforms the previous state of the art in training NN with MIP, in terms of accuracy, training time and amount of data. Our methodology is proficient at training NNs when minimal training data is available, and at training with minimal memory requirements -- which is potentially valuable for deploying to low-memory devices.

Projection operations are a typical computation bottleneck in online learning. In this paper, we enable projection-free online learning within the framework of Online Convex Optimization with Memory (OCO-M) -- OCO-M captures how the history of decisions affects the current outcome by allowing the online learning loss functions to depend on both current and past decisions. Particularly, we introduce the first projection-free meta-base learning algorithm with memory that minimizes dynamic regret, i.e., that minimizes the suboptimality against any sequence of time-varying decisions. We are motivated by artificial intelligence applications where autonomous agents need to adapt to time-varying environments in real-time, accounting for how past decisions affect the present. Examples of such applications are: online control of dynamical systems; statistical arbitrage; and time series prediction. The algorithm builds on the Online Frank-Wolfe (OFW) and Hedge algorithms. We demonstrate how our algorithm can be applied to the online control of linear time-varying systems in the presence of unpredictable process noise. To this end, we develop a controller with memory and bounded dynamic regret against any optimal time-varying linear feedback control policy. We validate our algorithm in simulated scenarios of online control of linear time-invariant systems.

Average-K classification is an alternative to top-K classification in which the number of labels returned varies with the ambiguity of the input image but must average to K over all the samples. A simple method to solve this task is to threshold the softmax output of a model trained with the cross-entropy loss. This approach is theoretically proven to be asymptotically consistent, but it is not guaranteed to be optimal for a finite set of samples. In this paper, we propose a new loss function based on a multi-label classification head in addition to the classical softmax. This second head is trained using pseudo-labels generated by thresholding the softmax head while guaranteeing that K classes are returned on average. We show that this approach allows the model to better capture ambiguities between classes and, as a result, to return more consistent sets of possible classes. Experiments on two datasets from the literature demonstrate that our approach outperforms the softmax baseline, as well as several other loss functions more generally designed for weakly supervised multi-label classification. The gains are larger the higher the uncertainty, especially for classes with few samples.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.

Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.

This work addresses a novel and challenging problem of estimating the full 3D hand shape and pose from a single RGB image. Most current methods in 3D hand analysis from monocular RGB images only focus on estimating the 3D locations of hand keypoints, which cannot fully express the 3D shape of hand. In contrast, we propose a Graph Convolutional Neural Network (Graph CNN) based method to reconstruct a full 3D mesh of hand surface that contains richer information of both 3D hand shape and pose. To train networks with full supervision, we create a large-scale synthetic dataset containing both ground truth 3D meshes and 3D poses. When fine-tuning the networks on real-world datasets without 3D ground truth, we propose a weakly-supervised approach by leveraging the depth map as a weak supervision in training. Through extensive evaluations on our proposed new datasets and two public datasets, we show that our proposed method can produce accurate and reasonable 3D hand mesh, and can achieve superior 3D hand pose estimation accuracy when compared with state-of-the-art methods.

Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal agreement about what constitutes a salient object when multiple observers are queried. This implies that some objects are more likely to be judged salient than others, and implies a relative rank exists on salient objects. The solution presented in this paper solves this more general problem that considers relative rank, and we propose data and metrics suitable to measuring success in a relative objects saliency landscape. A novel deep learning solution is proposed based on a hierarchical representation of relative saliency and stage-wise refinement. We also show that the problem of salient object subitizing can be addressed with the same network, and our approach exceeds performance of any prior work across all metrics considered (both traditional and newly proposed).

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a deep learning approach to spectral clustering that overcomes the above shortcomings. Our network, which we call SpectralNet, learns a map that embeds input data points into the eigenspace of their associated graph Laplacian matrix and subsequently clusters them. We train SpectralNet using a procedure that involves constrained stochastic optimization. Stochastic optimization allows it to scale to large datasets, while the constraints, which are implemented using a special-purpose output layer, allow us to keep the network output orthogonal. Moreover, the map learned by SpectralNet naturally generalizes the spectral embedding to unseen data points. To further improve the quality of the clustering, we replace the standard pairwise Gaussian affinities with affinities leaned from unlabeled data using a Siamese network. Additional improvement can be achieved by applying the network to code representations produced, e.g., by standard autoencoders. Our end-to-end learning procedure is fully unsupervised. In addition, we apply VC dimension theory to derive a lower bound on the size of SpectralNet. State-of-the-art clustering results are reported on the Reuters dataset. Our implementation is publicly available at //github.com/kstant0725/SpectralNet .

Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.