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Register a new userImproved Learning of One-hidden-layer Convolutional Neural Networks with Overlaps
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Added by
Simon Du
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other complex models.
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Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a theoretically-grounded generalizability analysis of GNNs with one hidden layer for both regression and binary classification problems. Under the assumption that there exists a ground-truth GNN model (with zero generalization error), the objective of GNN learning is to estimate the ground-truth GNN parameters from the training data. To achieve this objective, we propose a learning algorithm that is built on tensor initialization and accelerated gradient descent. We then show that the proposed learning algorithm converges to the ground-truth GNN model for the regression problem, and to a model sufficiently close to the ground-truth for the binary classification problem. Moreover, for both cases, the convergence rate of the proposed learning algorithm is proven to be linear and faster than the vanilla gradient descent algorithm. We further explore the relationship between the sample complexity of GNNs and their underlying graph properties. Lastly, we provide numerical experiments to demonstrate the validity of our analysis and the effectiveness of the proposed learning algorithm for GNNs.
Transfer learning has emerged as a powerful technique for improving the performance of machine learning models on new domains where labeled training data may be scarce. In this approach a model trained for a source task, where plenty of labeled training data is available, is used as a starting point for training a model on a related target task with only few labeled training data. Despite recent empirical success of transfer learning approaches, the benefits and fundamental limits of transfer learning are poorly understood. In this paper we develop a statistical minimax framework to characterize the fundamental limits of transfer learning in the context of regression with linear and one-hidden layer neural network models. Specifically, we derive a lower-bound for the target generalization error achievable by any algorithm as a function of the number of labeled source and target data as well as appropriate notions of similarity between the source and target tasks. Our lower bound provides new insights into the benefits and limitations of transfer learning. We further corroborate our theoretical finding with various experiments.
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.
Prior work has shown Convolutional Neural Networks (CNNs) trained on surrogate Computer Aided Design (CAD) models are able to detect and classify real-world artefacts from photographs. The applications of which support twinning of digital and physical assets in design, including rapid extraction of part geometry from model repositories, information search & retrieval and identifying components in the field for maintenance, repair, and recording. The performance of CNNs in classification tasks have been shown dependent on training data set size and number of classes. Where prior works have used relatively small surrogate model data sets ($<100$ models), the question remains as to the ability of a CNN to differentiate between models in increasingly large model repositories. This paper presents a method for generating synthetic image data sets from online CAD model repositories, and further investigates the capacity of an off-the-shelf CNN architecture trained on synthetic data to classify models as class size increases. 1,000 CAD models were curated and processed to generate large scale surrogate data sets, featuring model coverage at steps of 10$^{circ}$, 30$^{circ}$, 60$^{circ}$, and 120$^{circ}$ degrees. The findings demonstrate the capability of computer vision algorithms to classify artefacts in model repositories of up to 200, beyond this point the CNNs performance is observed to deteriorate significantly, limiting its present ability for automated twinning of physical to digital artefacts. Although, a match is more often found in the top-5 results showing potential for information search and retrieval on large repositories of surrogate models.
We present a novel global compression framework for deep neural networks that automatically analyzes each layer to identify the optimal per-layer compression ratio, while simultaneously achieving the desired overall compression. Our algorithm hinges on the idea of compressing each convolutional (or fully-connected) layer by slicing its channels into multiple groups and decomposing each group via low-rank decomposition. At the core of our algorithm is the derivation of layer-wise error bounds from the Eckart Young Mirsky theorem. We then leverage these bounds to frame the compression problem as an optimization problem where we wish to minimize the maximum compression error across layers and propose an efficient algorithm towards a solution. Our experiments indicate that our method outperforms existing low-rank compression approaches across a wide range of networks and data sets. We believe that our results open up new avenues for future research into the global performance-size trade-offs of modern neural networks. Our code is available at https://github.com/lucaslie/torchprune.
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