arXiv subjects

Anima Anandkumar

Publications and source records attributed to Anima Anandkumar.

At least 271 records · Page 15Linked to original sources

arXiv2019

Long-term Forecasting using Higher Order Tensor RNNs

We present Higher-Order Tensor RNN (HOT-RNN), a novel family of neural sequence architectures for multivariate forecasting in environments with nonlinear dynamics. Long-term forecasting in such systems is highly challenging, since there exist long-term temporal dependencies, higher-order correlations and sensitivity to error propagation. Our proposed recurrent architecture addresses these issues by learning the nonlinear dynamics directly using higher-order moments and higher-order state transition functions. Furthermore, we decompose the higher-order structure using the tensor-train decomposition to reduce the number of parameters while preserving the model performance. We theoretically establish the approximation guarantees and the variance bound for HOT-RNN for general sequence inputs. We also demonstrate 5% ~ 12% improvements for long-term prediction over general RNN and LSTM architectures on a range of simulated environments with nonlinear dynamics, as well on real-world time series data.

cs.LG↗

arXiv2019

Out-of-Distribution Detection Using Neural Rendering Generative Models

Out-of-distribution (OoD) detection is a natural downstream task for deep generative models, due to their ability to learn the input probability distribution. There are mainly two classes of approaches for OoD detection using deep generative models, viz., based on likelihood measure and the reconstruction loss. However, both approaches are unable to carry out OoD detection effectively, especially when the OoD samples have smaller variance than the training samples. For instance, both flow based and VAE models assign higher likelihood to images from SVHN when trained on CIFAR-10 images. We use a recently proposed generative model known as neural rendering model (NRM) and derive metrics for OoD. We show that NRM unifies both approaches since it provides a likelihood estimate and also carries out reconstruction in each layer of the neural network. Among various measures, we found the joint likelihood of latent variables to be the most effective one for OoD detection. Our results show that when trained on CIFAR-10, lower likelihood (of latent variables) is assigned to SVHN images. Additionally, we show that this metric is consistent across other OoD datasets. To the best of our knowledge, this is the first work to show consistently lower likelihood for OoD data with smaller variance with deep generative models.

cs.LG↗

arXiv2019

Active Learning with Partial Feedback

While many active learning papers assume that the learner can simply ask for a label and receive it, real annotation often presents a mismatch between the form of a label (say, one among many classes), and the form of an annotation (typically yes/no binary feedback). To annotate examples corpora for multiclass classification, we might need to ask multiple yes/no questions, exploiting a label hierarchy if one is available. To address this more realistic setting, we propose active learning with partial feedback (ALPF), where the learner must actively choose both which example to label and which binary question to ask. At each step, the learner selects an example, asking if it belongs to a chosen (possibly composite) class. Each answer eliminates some classes, leaving the learner with a partial label. The learner may then either ask more questions about the same example (until an exact label is uncovered) or move on immediately, leaving the first example partially labeled. Active learning with partial labels requires (i) a sampling strategy to choose (example, class) pairs, and (ii) learning from partial labels between rounds. Experiments on Tiny ImageNet demonstrate that our most effective method improves 26% (relative) in top-1 classification accuracy compared to i.i.d. baselines and standard active learners given 30% of the annotation budget that would be required (naively) to annotate the dataset. Moreover, ALPF-learners fully annotate TinyImageNet at 42% lower cost. Surprisingly, we observe that accounting for per-example annotation costs can alter the conventional wisdom that active learners should solicit labels for hard examples.

cs.LG↗

arXiv2019

Directivity Modes of Earthquake Populations with Unsupervised Learning

We present a novel approach for resolving modes of rupture directivity in large populations of earthquakes. A seismic spectral decomposition technique is used to first produce relative measurements of radiated energy for earthquakes in a spatially-compact cluster. The azimuthal distribution of energy for each earthquake is then assumed to result from one of several distinct modes of rupture propagation. Rather than fitting a kinematic rupture model to determine the most likely mode of rupture propagation, we instead treat the modes as latent variables and learn them with a Gaussian mixture model. The mixture model simultaneously determines the number of events that best identify with each mode. The technique is demonstrated on four datasets in California with several thousand earthquakes. We show that the datasets naturally decompose into distinct rupture propagation modes that correspond to different rupture directions, and the fault plane is unambiguously identified for all cases. We find that these small earthquakes exhibit unilateral ruptures 53-74% of the time on average. The results provide important observational constraints on the physics of earthquakes and faults.

physics.geo-ph↗

arXiv2019

Open Vocabulary Learning on Source Code with a Graph-Structured Cache

Machine learning models that take computer program source code as input typically use Natural Language Processing (NLP) techniques. However, a major challenge is that code is written using an open, rapidly changing vocabulary due to, e.g., the coinage of new variable and method names. Reasoning over such a vocabulary is not something for which most NLP methods are designed. We introduce a Graph-Structured Cache to address this problem; this cache contains a node for each new word the model encounters with edges connecting each word to its occurrences in the code. We find that combining this graph-structured cache strategy with recent Graph-Neural-Network-based models for supervised learning on code improves the models' performance on a code completion task and a variable naming task --- with over $100\%$ relative improvement on the latter --- at the cost of a moderate increase in computation time.

cs.LG↗

arXiv2019

signSGD with Majority Vote is Communication Efficient And Fault Tolerant

Training neural networks on large datasets can be accelerated by distributing the workload over a network of machines. As datasets grow ever larger, networks of hundreds or thousands of machines become economically viable. The time cost of communicating gradients limits the effectiveness of using such large machine counts, as may the increased chance of network faults. We explore a particularly simple algorithm for robust, communication-efficient learning---signSGD. Workers transmit only the sign of their gradient vector to a server, and the overall update is decided by a majority vote. This algorithm uses $32\times$ less communication per iteration than full-precision, distributed SGD. Under natural conditions verified by experiment, we prove that signSGD converges in the large and mini-batch settings, establishing convergence for a parameter regime of Adam as a byproduct. Aggregating sign gradients by majority vote means that no individual worker has too much power. We prove that unlike SGD, majority vote is robust when up to 50% of workers behave adversarially. The class of adversaries we consider includes as special cases those that invert or randomise their gradient estimate. On the practical side, we built our distributed training system in Pytorch. Benchmarking against the state of the art collective communications library (NCCL), our framework---with the parameter server housed entirely on one machine---led to a 25% reduction in time for training resnet50 on Imagenet when using 15 AWS p3.2xlarge machines.

cs.DC↗

arXiv2019

Stochastic Linear Bandits with Hidden Low Rank Structure

High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures like sparsity are not valid anymore. Subspace recovery methods, such as Principle Component Analysis (PCA) can find the underlying low-rank structures in the feature space and reduce the complexity of the learning tasks. In this work, we propose Projected Stochastic Linear Bandit (PSLB), an algorithm for high dimensional stochastic linear bandits (SLB) when the representation of actions has an underlying low-dimensional subspace structure. PSLB deploys PCA based projection to iteratively find the low rank structure in SLBs. We show that deploying projection methods assures dimensionality reduction and results in a tighter regret upper bound that is in terms of the dimensionality of the subspace and its properties, rather than the dimensionality of the ambient space. We modify the image classification task into the SLB setting and empirically show that, when a pre-trained DNN provides the high dimensional feature representations, deploying PSLB results in significant reduction of regret and faster convergence to an accurate model compared to state-of-art algorithm.

cs.LG↗

arXiv2018

signSGD: Compressed Optimisation for Non-Convex Problems

Training large neural networks requires distributing learning across multiple workers, where the cost of communicating gradients can be a significant bottleneck. signSGD alleviates this problem by transmitting just the sign of each minibatch stochastic gradient. We prove that it can get the best of both worlds: compressed gradients and SGD-level convergence rate. The relative $\ell_1/\ell_2$ geometry of gradients, noise and curvature informs whether signSGD or SGD is theoretically better suited to a particular problem. On the practical side we find that the momentum counterpart of signSGD is able to match the accuracy and convergence speed of Adam on deep Imagenet models. We extend our theory to the distributed setting, where the parameter server uses majority vote to aggregate gradient signs from each worker enabling 1-bit compression of worker-server communication in both directions. Using a theorem by Gauss we prove that majority vote can achieve the same reduction in variance as full precision distributed SGD. Thus, there is great promise for sign-based optimisation schemes to achieve fast communication and fast convergence. Code to reproduce experiments is to be found at https://github.com/jxbz/signSGD .

cs.LG↗

arXiv2018

Born Again Neural Networks

Knowledge Distillation (KD) consists of transferring â€œknowledgeâ€ from one machine learning model (the teacher) to another (the student). Commonly, the teacher is a high-capacity model with formidable performance, while the student is more compact. By transferring knowledge, one hopes to benefit from the studentâ€™s compactness, without sacrificing too much performance. We study KD from a new perspective: rather than compressing models, we train students parameterized identically to their teachers. Surprisingly, these Born-Again Networks (BANs), outperform their teachers significantly, both on computer vision and language modeling tasks. Our experiments with BANs based on DenseNets demonstrate state-of-the-art performance on the CIFAR-10 (3.5%) and CIFAR-100 (15.5%) datasets, by validation error. Additional experiments explore two distillation objectives: (i) Confidence-Weighted by Teacher Max (CWTM) and (ii) Dark Knowledge with Permuted Predictions (DKPP). Both methods elucidate the essential components of KD, demonstrating the effect of the teacher outputs on both predicted and non-predicted classes.

stat.ML↗

arXiv2018

StrassenNets: Deep Learning with a Multiplication Budget

A large fraction of the arithmetic operations required to evaluate deep neural networks (DNNs) consists of matrix multiplications, in both convolution and fully connected layers. We perform end-to-end learning of low-cost approximations of matrix multiplications in DNN layers by casting matrix multiplications as 2-layer sum-product networks (SPNs) (arithmetic circuits) and learning their (ternary) edge weights from data. The SPNs disentangle multiplication and addition operations and enable us to impose a budget on the number of multiplication operations. Combining our method with knowledge distillation and applying it to image classification DNNs (trained on ImageNet) and language modeling DNNs (using LSTMs), we obtain a first-of-a-kind reduction in number of multiplications (over 99.5%) while maintaining the predictive performance of the full-precision models. Finally, we demonstrate that the proposed framework is able to rediscover Strassen's matrix multiplication algorithm, learning to multiply $2 \times 2$ matrices using only 7 multiplications instead of 8.

cs.LG↗

arXiv2018

Probabilistic FastText for Multi-Sense Word Embeddings

We introduce Probabilistic FastText, a new model for word embeddings that can capture multiple word senses, sub-word structure, and uncertainty information. In particular, we represent each word with a Gaussian mixture density, where the mean of a mixture component is given by the sum of n-grams. This representation allows the model to share statistical strength across sub-word structures (e.g. Latin roots), producing accurate representations of rare, misspelt, or even unseen words. Moreover, each component of the mixture can capture a different word sense. Probabilistic FastText outperforms both FastText, which has no probabilistic model, and dictionary-level probabilistic embeddings, which do not incorporate subword structures, on several word-similarity benchmarks, including English RareWord and foreign language datasets. We also achieve state-of-art performance on benchmarks that measure ability to discern different meanings. Thus, the proposed model is the first to achieve multi-sense representations while having enriched semantics on rare words.

cs.CL↗

arXiv2018

Learning From Noisy Singly-labeled Data

Supervised learning depends on annotated examples, which are taken to be the \emph{ground truth}. But these labels often come from noisy crowdsourcing platforms, like Amazon Mechanical Turk. Practitioners typically collect multiple labels per example and aggregate the results to mitigate noise (the classic crowdsourcing problem). Given a fixed annotation budget and unlimited unlabeled data, redundant annotation comes at the expense of fewer labeled examples. This raises two fundamental questions: (1) How can we best learn from noisy workers? (2) How should we allocate our labeling budget to maximize the performance of a classifier? We propose a new algorithm for jointly modeling labels and worker quality from noisy crowd-sourced data. The alternating minimization proceeds in rounds, estimating worker quality from disagreement with the current model and then updating the model by optimizing a loss function that accounts for the current estimate of worker quality. Unlike previous approaches, even with only one annotation per example, our algorithm can estimate worker quality. We establish a generalization error bound for models learned with our algorithm and establish theoretically that it's better to label many examples once (vs less multiply) when worker quality is above a threshold. Experiments conducted on both ImageNet (with simulated noisy workers) and MS-COCO (using the real crowdsourced labels) confirm our algorithm's benefits.

cs.LG↗

arXiv2018

TensorLy: Tensor Learning in Python

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scientific community, and seamlessly integrates with them. Its BSD license makes it suitable for both academic and commercial applications. TensorLy's backend system allows users to perform computations with NumPy, MXNet, PyTorch, TensorFlow and CuPy. They can be scaled on multiple CPU or GPU machines. In addition, using the deep-learning frameworks as backend allows users to easily design and train deep tensorized neural networks. TensorLy is available at https://github.com/tensorly/tensorly

cs.LG↗

arXiv2018

Stochastic Activation Pruning for Robust Adversarial Defense

Neural networks are known to be vulnerable to adversarial examples. Carefully chosen perturbations to real images, while imperceptible to humans, induce misclassification and threaten the reliability of deep learning systems in the wild. To guard against adversarial examples, we take inspiration from game theory and cast the problem as a minimax zero-sum game between the adversary and the model. In general, for such games, the optimal strategy for both players requires a stochastic policy, also known as a mixed strategy. In this light, we propose Stochastic Activation Pruning (SAP), a mixed strategy for adversarial defense. SAP prunes a random subset of activations (preferentially pruning those with smaller magnitude) and scales up the survivors to compensate. We can apply SAP to pretrained networks, including adversarially trained models, without fine-tuning, providing robustness against adversarial examples. Experiments demonstrate that SAP confers robustness against attacks, increasing accuracy and preserving calibration.

cs.LG↗

arXiv2017

Compact Tensor Pooling for Visual Question Answering

Performing high level cognitive tasks requires the integration of feature maps with drastically different structure. In Visual Question Answering (VQA) image descriptors have spatial structures, while lexical inputs inherently follow a temporal sequence. The recently proposed Multimodal Compact Bilinear pooling (MCB) forms the outer products, via count-sketch approximation, of the visual and textual representation at each spatial location. While this procedure preserves spatial information locally, outer-products are taken independently for each fiber of the activation tensor, and therefore do not include spatial context. In this work, we introduce multi-dimensional sketch ({MD-sketch}), a novel extension of count-sketch to tensors. Using this new formulation, we propose Multimodal Compact Tensor Pooling (MCT) to fully exploit the global spatial context during bilinear pooling operations. Contrarily to MCB, our approach preserves spatial context by directly convolving the MD-sketch from the visual tensor features with the text vector feature using higher order FFT. Furthermore we apply MCT incrementally at each step of the question embedding and accumulate the multi-modal vectors with a second LSTM layer before the final answer is chosen.

cs.CV↗

arXiv2017

Homotopy Analysis for Tensor PCA

Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze the class of homotopy or continuation methods for global optimization of nonconvex functions. These methods start from an objective function that is efficient to optimize (e.g. convex), and progressively modify it to obtain the required objective, and the solutions are passed along the homotopy path. For the challenging problem of tensor PCA, we prove global convergence of the homotopy method in the "high noise" regime. The signal-to-noise requirement for our algorithm is tight in the sense that it matches the recovery guarantee for the best degree-4 sum-of-squares algorithm. In addition, we prove a phase transition along the homotopy path for tensor PCA. This allows to simplify the homotopy method to a local search algorithm, viz., tensor power iterations, with a specific initialization and a noise injection procedure, while retaining the theoretical guarantees.

stat.ML↗

arXiv2017

Tensor Contraction Layers for Parsimonious Deep Nets

Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels. Tensor methods are noted for their ability to discover multi-dimensional dependencies, and tensor decompositions in particular, have been used to produce compact low-rank approximations of data. In this paper, we explore the use of tensor contractions as neural network layers and investigate several ways to apply them to activation tensors. Specifically, we propose the Tensor Contraction Layer (TCL), the first attempt to incorporate tensor contractions as end-to-end trainable neural network layers. Applied to existing networks, TCLs reduce the dimensionality of the activation tensors and thus the number of model parameters. We evaluate the TCL on the task of image recognition, augmenting two popular networks (AlexNet, VGG). The resulting models are trainable end-to-end. Applying the TCL to the task of image recognition, using the CIFAR100 and ImageNet datasets, we evaluate the effect of parameter reduction via tensor contraction on performance. We demonstrate significant model compression without significant impact on the accuracy and, in some cases, improved performance.

cs.LG↗

arXiv2016

Training Input-Output Recurrent Neural Networks through Spectral Methods

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score functions. We guarantee consistent learning with polynomial sample and computational complexity under transparent conditions such as non-degeneracy of model parameters, polynomial activations for the neurons, and a Markovian evolution of the input sequence. We also extend our results to Bidirectional RNN which uses both previous and future information to output the label at each time point, and is employed in many NLP tasks such as POS tagging.

cs.LG↗