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We develop an approach to efficiently grow neural networks, within which parameterization and optimization strategies are designed by considering their effects on the training dynamics. Unlike existing growing methods, which follow simple replication heuristics or utilize auxiliary gradient-based local optimization, we craft a parameterization scheme which dynamically stabilizes weight, activation, and gradient scaling as the architecture evolves, and maintains the inference functionality of the network. To address the optimization difficulty resulting from imbalanced training effort distributed to subnetworks fading in at different growth phases, we propose a learning rate adaption mechanism that rebalances the gradient contribution of these separate subcomponents. Experimental results show that our method achieves comparable or better accuracy than training large fixed-size models, while saving a substantial portion of the original computation budget for training. We demonstrate that these gains translate into real wall-clock training speedups.

Exoplanet detection by direct imaging is a difficult task: the faint signals from the objects of interest are buried under a spatially structured nuisance component induced by the host star. The exoplanet signals can only be identified when combining several observations with dedicated detection algorithms. In contrast to most of existing methods, we propose to learn a model of the spatial, temporal and spectral characteristics of the nuisance, directly from the observations. In a pre-processing step, a statistical model of their correlations is built locally, and the data are centered and whitened to improve both their stationarity and signal-to-noise ratio (SNR). A convolutional neural network (CNN) is then trained in a supervised fashion to detect the residual signature of synthetic sources in the pre-processed images. Our method leads to a better trade-off between precision and recall than standard approaches in the field. It also outperforms a state-of-the-art algorithm based solely on a statistical framework. Besides, the exploitation of the spectral diversity improves the performance compared to a similar model built solely from spatio-temporal data.

Data extraction algorithms on data hypercubes, or datacubes, are traditionally only capable of cutting boxes of data along the datacube axes. For many use cases however, this is not a sufficient approach and returns more data than users might actually need. This not only forces users to apply post-processing after extraction, but more importantly this consumes more I/O resources than is necessary. When considering very large datacubes from which users only want to extract small non-rectangular subsets, the box approach does not scale well. Indeed, with this traditional approach, I/O systems quickly reach capacity, trying to read and return unwanted data to users. In this paper, we propose a novel technique, based on computational geometry concepts, which instead carefully pre-selects the precise bytes of data which the user needs in order to then only read those from the datacube. As we discuss later on, this novel extraction method will considerably help scale access to large petabyte size data hypercubes in a variety of scientific fields.

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information, and is weighted by a regularization parameter. Selection of an appropriate regularization parameter is critical, with various choices leading to very different reconstructions. Existing strategies such as the discrepancy principle and L-curve can be used to determine a suitable parameter value, but in recent years a supervised machine learning approach called bilevel learning has been employed. Bilevel learning is a powerful framework to determine optimal parameters, and involves solving a nested optimisation problem. While previous strategies enjoy various theoretical results, the well-posedness of bilevel learning in this setting is still a developing field. One necessary property is positivity of the determined regularization parameter. In this work, we provide a new condition that better characterises positivity of optimal regularization parameters than the existing theory. Numerical results verify and explore this new condition for both small and large dimensional problems.

We establish globally optimal solutions to a class of fractional optimization problems on a class of constraint sets, whose key characteristics are as follows: 1) The numerator and the denominator of the objective function are both convex, semi-algebraic, Lipschitz continuous and differentiable with Lipschitz continuous gradients on the constraint set. 2) The constraint set is closed, convex and semi-algebraic. Compared with Dinkelbach's approach, our novelty falls into the following aspects: 1) Dinkelbach's has to solve a concave maximization problem in each iteration, which is nontrivial to obtain a solution, while ours only needs to conduct one proximity gradient operation in each iteration. 2) Dinkelbach's requires at least one nonnegative point for the numerator to proceed the algorithm, but ours does not, which is available to a much wider class of situations. 3) Dinkelbach's requires a closed and bounded constraint set, while ours only needs the closedness but not necessarily the boundedness. Therefore, our approach is viable for many more practical models, like optimizing the Sharpe ratio (SR) or the Information ratio in mathematical finance. Numerical experiments show that our approach achieves the ground-truth solutions in two simple examples. For real-world financial data, it outperforms several existing approaches for SR maximization.

In a number of tomographic applications, data cannot be fully acquired, resulting in a severely underdetermined image reconstruction. In such cases, conventional methods lead to reconstructions with significant artifacts. To overcome these artifacts, regularization methods are applied that incorporate additional information. An important example is TV reconstruction, which is known to be efficient at compensating for missing data and reducing reconstruction artifacts. At the same time, however, tomographic data is also contaminated by noise, which poses an additional challenge. The use of a single regularizer must therefore account for both the missing data and the noise. However, a particular regularizer may not be ideal for both tasks. For example, the TV regularizer is a poor choice for noise reduction across multiple scales, in which case $\ell^1$ curvelet regularization methods are well suited. To address this issue, in this paper we introduce a novel variational regularization framework that combines the advantages of different regularizers. The basic idea of our framework is to perform reconstruction in two stages, where the first stage mainly aims at accurate reconstruction in the presence of noise, and the second stage aims at artifact reduction. Both reconstruction stages are connected by a data proximity condition. The proposed method is implemented and tested for limited-view CT using a combined curvelet-TV approach. We define and implement a curvelet transform adapted to the limited-view problem and illustrate the advantages of our approach in numerical experiments.

The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain. We also propose a generalization of the depthwise separable convolution framework for graph convolutional networks, what allows to decrease the total number of trainable parameters by keeping the capacity of the model. To the best of our knowledge, such a framework has never been used in the GNNs literature. Our proposals are evaluated on both transductive and inductive graph learning problems. Obtained results show the relevance of the proposed method and provide one of the first experimental evidence of transferability of spectral filter coefficients from one graph to another. Our source codes are publicly available at: //github.com/balcilar/Spectral-Designed-Graph-Convolutions

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 .