skip to main content

Explore Research Products in the NSF-PAR

Title: Diving into the shallows: a computational perspective on large-scale shallow learning
Remarkable recent success of deep neural networks has not been easy to analyze theoretically. It has been particularly hard to disentangle relative significance of architecture and optimization in achieving accurate classification on large datasets. On the flip side, shallow methods (such as kernel methods) have encountered obstacles in scaling to large data, despite excellent performance on smaller datasets, and extensive theoretical analysis. Practical methods, such as variants of gradient descent used so successfully in deep learning, seem to perform below par when applied to kernel methods. This difficulty has sometimes been attributed to the limitations of shallow architecture. In this paper we identify a basic limitation in gradient descent-based optimization methods when used in conjunctions with smooth kernels. Our analysis demonstrates that only a vanishingly small fraction of the function space is reachable after a polynomial number of gradient descent iterations. That drastically limits the approximating power of gradient descent leading to over-regularization. The issue is purely algorithmic, persisting even in the limit of infinite data. To address this shortcoming in practice, we introduce EigenPro iteration, a simple and direct preconditioning scheme using a small number of approximately computed eigenvectors. It can also be viewed as learning a kernel optimized for gradient descent. Injecting this small, computationally inexpensive and SGD-compatible, amount of approximate second-order information leads to major improvements in convergence. For large data, this leads to a significant performance boost over the state-of-the-art kernel methods. In particular, we are able to match or improve the results reported in the literature at a small fraction of their computational budget.  more » « less
Award ID(s):
1837827
NSF-PAR ID:
10073226
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Advances in neural information processing systems
Volume:
30
ISSN:
1049-5258
Page Range / eLocation ID:
3778-3787
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ( , International Conference on Machine Learning)
    null (Ed.)
    Neural Architecture Search (NAS) is a popular method for automatically designing optimized architectures for high-performance deep learning. In this approach, it is common to use bilevel optimization where one optimizes the model weights over the training data (lower-level problem) and various hyperparameters such as the configuration of the architecture over the validation data (upper-level problem). This paper explores the statistical aspects of such problems with train-validation splits. In practice, the lower-level problem is often overparameterized and can easily achieve zero loss. Thus, a-priori it seems impossible to distinguish the right hyperparameters based on training loss alone which motivates a better understanding of the role of train-validation split. To this aim this work establishes the following results: • We show that refined properties of the validation loss such as risk and hyper-gradients are indicative of those of the true test loss. This reveals that the upper-level problem helps select the most generalizable model and prevent overfitting with a near-minimal validation sample size. Importantly, this is established for continuous spaces – which are highly relevant for popular differentiable search schemes. • We establish generalization bounds for NAS problems with an emphasis on an activation search problem. When optimized with gradient-descent, we show that the train-validation procedure returns the best (model, architecture) pair even if all architectures can perfectly fit the training data to achieve zero error. • Finally, we highlight rigorous connections between NAS, multiple kernel learning, and low-rank matrix learning. The latter leads to novel algorithmic insights where the solution of the upper problem can be accurately learned via efficient spectral methods to achieve near-minimal risk. 
    more » « less
  2. ; ; ( , ICML 2021)
    Neural Architecture Search (NAS) is a popular method for automatically designing optimized architectures for high-performance deep learning. In this approach, it is common to use bilevel optimization where one optimizes the model weights over the training data (lower-level problem) and various hyperparameters such as the configuration of the architecture over the validation data (upper-level problem). This paper explores the statistical aspects of such problems with train-validation splits. In practice, the lower-level problem is often overparameterized and can easily achieve zero loss. Thus, a-priori it seems impossible to distinguish the right hyperparameters based on training loss alone which motivates a better understanding of the role of train-validation split. To this aim this work establishes the following results: • We show that refined properties of the validation loss such as risk and hyper-gradients are indicative of those of the true test loss. This reveals that the upper-level problem helps select the most generalizable model and prevent overfitting with a near-minimal validation sample size. Importantly, this is established for continuous spaces – which are highly relevant for popular differentiable search schemes. • We establish generalization bounds for NAS problems with an emphasis on an activation search problem. When optimized with gradient-descent, we show that the train-validation procedure returns the best (model, architecture) pair even if all architectures can perfectly fit the training data to achieve zero error. • Finally, we highlight rigorous connections between NAS, multiple kernel learning, and low-rank matrix learning. The latter leads to novel algorithmic insights where the solution of the upper problem can be accurately learned via efficient spectral methods to achieve near-minimal risk. 
    more » « less
  3. ; ; ; ; ; ; ( , International Conference on Learning Representations)
    null (Ed.)
    A broad class of unsupervised deep learning methods such as Generative Adversarial Networks (GANs) involve training of overparameterized models where the number of parameters of the model exceeds a certain threshold. Indeed, most successful GANs used in practice are trained using overparameterized generator and discriminator networks, both in terms of depth and width. A large body of work in supervised learning have shown the importance of model overparameterization in the convergence of the gradient descent (GD) to globally optimal solutions. In contrast, the unsupervised setting and GANs in particular involve non-convex concave mini-max optimization problems that are often trained using Gradient Descent/Ascent (GDA). The role and benefits of model overparameterization in the convergence of GDA to a global saddle point in non-convex concave problems is far less understood. In this work, we present a comprehensive analysis of the importance of model overparameterization in GANs both theoretically and empirically. We theoretically show that in an overparameterized GAN model with a 1-layer neural network generator and a linear discriminator, GDA converges to a global saddle point of the underlying non-convex concave min-max problem. To the best of our knowledge, this is the first result for global convergence of GDA in such settings. Our theory is based on a more general result that holds for a broader class of nonlinear generators and discriminators that obey certain assumptions (including deeper generators and random feature discriminators). Our theory utilizes and builds upon a novel connection with the convergence analysis of linear timevarying dynamical systems which may have broader implications for understanding the convergence behavior of GDA for non-convex concave problems involving overparameterized models. We also empirically study the role of model overparameterization in GANs using several large-scale experiments on CIFAR-10 and Celeb-A datasets. Our experiments show that overparameterization improves the quality of generated samples across various model architectures and datasets. Remarkably, we observe that overparameterization leads to faster and more stable convergence behavior of GDA across the board. 
    more » « less
  4. ; ; ; ; ( , 2020 25th International Conference on Pattern Recognition (ICPR))
    In recent years, deep neural networks have achieved state-of-the-art performance in a variety of recognition and segmentation tasks in medical imaging including brain tumor segmentation. We investigate that segmenting a brain tumor is facing to the imbalanced data problem where the number of pixels belonging to the background class (non tumor pixel) is much larger than the number of pixels belonging to the foreground class (tumor pixel). To address this problem, we propose a multitask network which is formed as a cascaded structure. Our model consists of two targets, i.e., (i) effectively differentiate the brain tumor regions and (ii) estimate the brain tumor mask. The first objective is performed by our proposed contextual brain tumor detection network, which plays a role of an attention gate and focuses on the region around brain tumor only while ignoring the far neighbor background which is less correlated to the tumor. Different from other existing object detection networks which process every pixel, our contextual brain tumor detection network only processes contextual regions around ground-truth instances and this strategy aims at producing meaningful regions proposals. The second objective is built upon a 3D atrous residual network and under an encode-decode network in order to effectively segment both large and small objects (brain tumor). Our 3D atrous residual network is designed with a skip connection to enables the gradient from the deep layers to be directly propagated to shallow layers, thus, features of different depths are preserved and used for refining each other. In order to incorporate larger contextual information from volume MRI data, our network utilizes the 3D atrous convolution with various kernel sizes, which enlarges the receptive field of filters. Our proposed network has been evaluated on various datasets including BRATS2015, BRATS2017 and BRATS2018 datasets with both validation set and testing set. Our performance has been benchmarked by both regionbased metrics and surface-based metrics. We also have conducted comparisons against state-of-the-art approaches 
    more » « less
  5. ; ; ; ( , ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))
    While deep neural networks (DNNs) have achieved state-of-the-art results in many fields, they are typically over-parameterized. Parameter redundancy, in turn, leads to inefficiency. Sparse signal recovery (SSR) techniques, on the other hand, find compact solutions to over-complete linear problems. Therefore, a logical step is to draw the connection between SSR and DNNs. In this paper, we explore the application of iterative reweighting methods popular in SSR to learning efficient DNNs. By efficient, we mean sparse networks that require less computation and storage than the original, dense network. We propose a reweighting framework to learn sparse connections within a given architecture without biasing the optimization process, by utilizing the affine scaling transformation strategy. The resulting algorithm, referred to as Sparsity-promoting Stochastic Gradient Descent (SSGD), has simple gradient-based updates which can be easily implemented in existing deep learning libraries. We demonstrate the sparsification ability of SSGD on image classification tasks and show that it outperforms existing methods on the MNIST and CIFAR-10 datasets. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email