neural network

Deep Double Descent


We show that the double descent phenomenon occurs in CNNs, ResNets, and transformers: performance first improves, then gets worse, and then improves again with increasing model size, data size, or training time. This effect is often avoided through careful regularization. While this behavior appears to be fairly universal, we don't yet fully understand why it happens, and view further study of this phenomenon as an important research direction. The peak occurs predictably at a "critical regime," where the models are barely able to fit the training set. As we increase the number of parameters in a neural network, the test error initially decreases, increases, and, just as the model is able to fit the train set, undergoes a second descent.

Which Algorithmic Choices Matter at Which Batch Sizes? Insights From a Noisy Quadratic Model

Neural Information Processing Systems

Increasing the batch size is a popular way to speed up neural network training, but beyond some critical batch size, larger batch sizes yield diminishing returns. In this work, we study how the critical batch size changes based on properties of the optimization algorithm, including acceleration and preconditioning, through two different lenses: large scale experiments and analysis using a simple noisy quadratic model (NQM). We experimentally demonstrate that optimization algorithms that employ preconditioning, specifically Adam and K-FAC, result in much larger critical batch sizes than stochastic gradient descent with momentum. We also demonstrate that the NQM captures many of the essential features of real neural network training, despite being drastically simpler to work with. The NQM predicts our results with preconditioned optimizers, previous results with accelerated gradient descent, and other results around optimal learning rates and large batch training, making it a useful tool to generate testable predictions about neural network optimization.

Hamiltonian Variational Auto-Encoder

Neural Information Processing Systems

Variational Auto-Encoders (VAE) have become very popular techniques to perform inference and learning in latent variable models as they allow us to leverage the rich representational power of neural networks to obtain flexible approximations of the posterior of latent variables as well as tight evidence lower bounds (ELBO). Com- bined with stochastic variational inference, this provides a methodology scaling to large datasets. However, for this methodology to be practically efficient, it is neces- sary to obtain low-variance unbiased estimators of the ELBO and its gradients with respect to the parameters of interest. While the use of Markov chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo (HMC) has been previously suggested to achieve this [23, 26], the proposed methods require specifying reverse kernels which have a large impact on performance. Additionally, the resulting unbiased estimator of the ELBO for most MCMC kernels is typically not amenable to the reparameterization trick.

Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data

Neural Information Processing Systems

Neural networks have many successful applications, while much less theoretical understanding has been gained. Towards bridging this gap, we study the problem of learning a two-layer overparameterized ReLU neural network for multi-class classification via stochastic gradient descent (SGD) from random initialization. In the overparameterized setting, when the data comes from mixtures of well-separated distributions, we prove that SGD learns a network with a small generalization error, albeit the network has enough capacity to fit arbitrary labels. Furthermore, the analysis provides interesting insights into several aspects of learning neural networks and can be verified based on empirical studies on synthetic data and on the MNIST dataset. Papers published at the Neural Information Processing Systems Conference.

Efficient Approximation of Deep ReLU Networks for Functions on Low Dimensional Manifolds

Neural Information Processing Systems

Deep neural networks have revolutionized many real world applications, due to their flexibility in data fitting and accurate predictions for unseen data. A line of research reveals that neural networks can approximate certain classes of functions with an arbitrary accuracy, while the size of the network scales exponentially with respect to the data dimension. Empirical results, however, suggest that networks of moderate size already yield appealing performance. To explain such a gap, a common belief is that many data sets exhibit low dimensional structures, and can be modeled as samples near a low dimensional manifold. In this paper, we prove that neural networks can efficiently approximate functions supported on low dimensional manifolds.

Chirality Nets for Human Pose Regression

Neural Information Processing Systems

We propose Chirality Nets, a family of deep nets that is equivariant to the "chirality transform," i.e., the transformation to create a chiral pair. Through parameter sharing, odd and even symmetry, we propose and prove variants of standard building blocks of deep nets that satisfy the equivariance property, including fully connected layers, convolutional layers, batch-normalization, and LSTM/GRU cells. The proposed layers lead to a more data efficient representation and a reduction in computation by exploiting symmetry. We evaluate chirality nets on the task of human pose regression, which naturally exploits the left/right mirroring of the human body. We study three pose regression tasks: 3D pose estimation from video, 2D pose forecasting, and skeleton based activity recognition.

The limits of squared Euclidean distance regularization

Neural Information Processing Systems

Some of the simplest loss functions considered in Machine Learning are the square loss, the logistic loss and the hinge loss. The most common family of algorithms, including Gradient Descent (GD) with and without Weight Decay, always predict with a linear combination of the past instances. We give a random construction for sets of examples where the target linear weight vector is trivial to learn but any algorithm from the above family is drastically sub-optimal. Our lower bound on the latter algorithms holds even if the algorithms are enhanced with an arbitrary kernel function. This type of result was known for the square loss.

On Exact Computation with an Infinitely Wide Neural Net

Neural Information Processing Systems

How well does a classic deep net architecture like AlexNet or VGG19 classify on a standard dataset such as CIFAR-10 when its "width"-- namely, number of channels in convolutional layers, and number of nodes in fully-connected internal layers -- is allowed to increase to infinity? Such questions have come to the forefront in the quest to theoretically understand deep learning and its mysteries about optimization and generalization. They also connect deep learning to notions such as Gaussian processes and kernels. A recent paper [Jacot et al., 2018] introduced the Neural Tangent Kernel (NTK) which captures the behavior of fully-connected deep nets in the infinite width limit trained by gradient descent; this object was implicit in some other recent papers. An attraction of such ideas is that a pure kernel-based method is used to capture the power of a fully-trained deep net of infinite width.

A Deep Architecture for Matching Short Texts

Neural Information Processing Systems

Many machine learning problems can be interpreted as learning for matching two types of objects (e.g., images and captions, users and products, queries and documents). The matching level of two objects is usually measured as the inner product in a certain feature space, while the modeling effort focuses on mapping of objects from the original space to the feature space. This schema, although proven successful on a range of matching tasks, is insufficient for capturing the rich structure in the matching process of more complicated objects. In this paper, we propose a new deep architecture to more effectively model the complicated matching relations between two objects from heterogeneous domains. More specifically, we apply this model to matching tasks in natural language, e.g., finding sensible responses for a tweet, or relevant answers to a given question.

Stochastic Ratio Matching of RBMs for Sparse High-Dimensional Inputs

Neural Information Processing Systems

Sparse high-dimensional data vectors are common in many application domains where a very large number of rarely non-zero features can be devised. Unfortunately, this creates a computational bottleneck for unsupervised feature learning algorithms such as those based on auto-encoders and RBMs, because they involve a reconstruction step where the whole input vector is predicted from the current feature values. An algorithm was recently developed to successfully handle the case of auto-encoders, based on an importance sampling scheme stochastically selecting which input elements to actually reconstruct during training for each particular example. To generalize this idea to RBMs, we propose a stochastic ratio-matching algorithm that inherits all the computational advantages and unbiasedness of the importance sampling scheme. We show that stochastic ratio matching is a good estimator, allowing the approach to beat the state-of-the-art on two bag-of-word text classification benchmarks (20 Newsgroups and RCV1), while keeping computational cost linear in the number of non-zeros.