arXiv subjects

Sewoong Oh

Publications and source records attributed to Sewoong Oh.

At least 109 records · Page 6Linked to original sources

arXiv2020

Learning in Gated Neural Networks

Gating is a key feature in modern neural networks including LSTMs, GRUs and sparsely-gated deep neural networks. The backbone of such gated networks is a mixture-of-experts layer, where several experts make regression decisions and gating controls how to weigh the decisions in an input-dependent manner. Despite having such a prominent role in both modern and classical machine learning, very little is understood about parameter recovery of mixture-of-experts since gradient descent and EM algorithms are known to be stuck in local optima in such models. In this paper, we perform a careful analysis of the optimization landscape and show that with appropriately designed loss functions, gradient descent can indeed learn the parameters accurately. A key idea underpinning our results is the design of two {\em distinct} loss functions, one for recovering the expert parameters and another for recovering the gating parameters. We demonstrate the first sample complexity results for parameter recovery in this model for any algorithm and demonstrate significant performance gains over standard loss functions in numerical experiments.

cs.LG↗

arXiv2020

Optimal transport mapping via input convex neural networks

In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel minimax optimization. Building upon recent advances in the field of input convex neural networks, we propose a new framework where the gradient of one convex function represents the optimal transport mapping. Numerical experiments confirm that we learn the optimal transport mapping. This approach ensures that the transport mapping we find is optimal independent of how we initialize the neural networks. Further, target distributions from a discontinuous support can be easily captured, as gradient of a convex function naturally models a {\em discontinuous} transport mapping.

cs.LG↗

arXiv2020

Proof-of-Stake Longest Chain Protocols: Security vs Predictability

The Nakamoto longest chain protocol is remarkably simple and has been proven to provide security against any adversary with less than 50% of the total hashing power. Proof-of-stake (PoS) protocols are an energy efficient alternative; however existing protocols adopting Nakamoto's longest chain design achieve provable security only by allowing long-term predictability (which have serious security implications). In this paper, we prove that a natural longest chain PoS protocol with similar predictability as Nakamoto's PoW protocol can achieve security against any adversary with less than 1/(1+e) fraction of the total stake. Moreover we propose a new family of longest chain PoS protocols that achieve security against a 50% adversary, while only requiring short-term predictability. Our proofs present a new approach to analyzing the formal security of blockchains, based on a notion of adversary-proof convergence.

cs.CR↗

arXiv2020

Meta-learning for mixed linear regression

In modern supervised learning, there are a large number of tasks, but many of them are associated with only a small amount of labeled data. These include data from medical image processing and robotic interaction. Even though each individual task cannot be meaningfully trained in isolation, one seeks to meta-learn across the tasks from past experiences by exploiting some similarities. We study a fundamental question of interest: When can abundant tasks with small data compensate for lack of tasks with big data? We focus on a canonical scenario where each task is drawn from a mixture of $k$ linear regressions, and identify sufficient conditions for such a graceful exchange to hold; The total number of examples necessary with only small data tasks scales similarly as when big data tasks are available. To this end, we introduce a novel spectral approach and show that we can efficiently utilize small data tasks with the help of $\tildeΩ(k^{3/2})$ medium data tasks each with $\tildeΩ(k^{1/2})$ examples.

cs.LG↗

arXiv2019

Turbo Autoencoder: Deep learning based channel codes for point-to-point communication channels

Designing codes that combat the noise in a communication medium has remained a significant area of research in information theory as well as wireless communications. Asymptotically optimal channel codes have been developed by mathematicians for communicating under canonical models after over 60 years of research. On the other hand, in many non-canonical channel settings, optimal codes do not exist and the codes designed for canonical models are adapted via heuristics to these channels and are thus not guaranteed to be optimal. In this work, we make significant progress on this problem by designing a fully end-to-end jointly trained neural encoder and decoder, namely, Turbo Autoencoder (TurboAE), with the following contributions: ($a$) under moderate block lengths, TurboAE approaches state-of-the-art performance under canonical channels; ($b$) moreover, TurboAE outperforms the state-of-the-art codes under non-canonical settings in terms of reliability. TurboAE shows that the development of channel coding design can be automated via deep learning, with near-optimal performance.

cs.IT↗

arXiv2019

Barracuda: The Power of $\ell$-polling in Proof-of-Stake Blockchains

A blockchain is a database of sequential events that is maintained by a distributed group of nodes. A key consensus problem in blockchains is that of determining the next block (data element) in the sequence. Many blockchains address this by electing a new node to propose each new block. The new block is (typically) appended to the tip of the proposer's local blockchain, and subsequently broadcast to the rest of the network. Without network delay (or adversarial behavior), this procedure would give a perfect chain, since each proposer would have the same view of the blockchain. A major challenge in practice is forking. Due to network delays, a proposer may not yet have the most recent block, and may, therefore, create a side chain that branches from the middle of the main chain. Forking reduces throughput, since only one a single main chain can survive, and all other blocks are discarded. We propose a new P2P protocol for blockchains called Barracuda, in which each proposer, prior to proposing a block, polls $\ell$ other nodes for their local blocktree information. Under a stochastic network model, we prove that this lightweight primitive improves throughput as if the entire network were a factor of $\ell$ faster. We provide guidelines on how to implement Barracuda in practice, guaranteeing robustness against several real-world factors.

cs.CR↗

arXiv2019

Efficient Algorithms for Smooth Minimax Optimization

This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings -- strongly convex and nonconvex -- and improve upon the best known rates in both. For strongly-convex $g(\cdot, y),\ \forall y$, we propose a new algorithm combining Mirror-Prox and Nesterov's AGD, and show that it can find global optimum in $\tilde{O}(1/k^2)$ iterations, improving over current state-of-the-art rate of $O(1/k)$. We use this result along with an inexact proximal point method to provide $\tilde{O}(1/k^{1/3})$ rate for finding stationary points in the nonconvex setting where $g(\cdot, y)$ can be nonconvex. This improves over current best-known rate of $O(1/k^{1/5})$. Finally, we instantiate our result for finite nonconvex minimax problems, i.e., $\min_x \max_{1\leq i\leq m} f_i(x)$, with nonconvex $f_i(\cdot)$, to obtain convergence rate of $O(m(\log m)^{3/2}/k^{1/3})$ total gradient evaluations for finding a stationary point.

math.OC↗

arXiv2019

Robust conditional GANs under missing or uncertain labels

Matching the performance of conditional Generative Adversarial Networks with little supervision is an important task, especially in venturing into new domains. We design a new training algorithm, which is robust to missing or ambiguous labels. The main idea is to intentionally corrupt the labels of generated examples to match the statistics of the real data, and have a discriminator process the real and generated examples with corrupted labels. We showcase the robustness of this proposed approach both theoretically and empirically. We show that minimizing the proposed loss is equivalent to minimizing true divergence between real and generated data up to a multiplicative factor, and characterize this multiplicative factor as a function of the statistics of the uncertain labels. Experiments on MNIST dataset demonstrates that proposed architecture is able to achieve high accuracy in generating examples faithful to the class even with only a few examples per class.

stat.ML↗

arXiv2019

Breaking the gridlock in Mixture-of-Experts: Consistent and Efficient Algorithms

Mixture-of-Experts (MoE) is a widely popular model for ensemble learning and is a basic building block of highly successful modern neural networks as well as a component in Gated Recurrent Units (GRU) and Attention networks. However, present algorithms for learning MoE including the EM algorithm, and gradient descent are known to get stuck in local optima. From a theoretical viewpoint, finding an efficient and provably consistent algorithm to learn the parameters remains a long standing open problem for more than two decades. In this paper, we introduce the first algorithm that learns the true parameters of a MoE model for a wide class of non-linearities with global consistency guarantees. While existing algorithms jointly or iteratively estimate the expert parameters and the gating paramters in the MoE, we propose a novel algorithm that breaks the deadlock and can directly estimate the expert parameters by sensing its echo in a carefully designed cross-moment tensor between the inputs and the output. Once the experts are known, the recovery of gating parameters still requires an EM algorithm; however, we show that the EM algorithm for this simplified problem, unlike the joint EM algorithm, converges to the true parameters. We empirically validate our algorithm on both the synthetic and real data sets in a variety of settings, and show superior performance to standard baselines.

cs.LG↗

arXiv2019

Minimax Rates of Estimating Approximate Differential Privacy

Differential privacy has become a widely accepted notion of privacy, leading to the introduction and deployment of numerous privatization mechanisms. However, ensuring the privacy guarantee is an error-prone process, both in designing mechanisms and in implementing those mechanisms. Both types of errors will be greatly reduced, if we have a data-driven approach to verify privacy guarantees, from a black-box access to a mechanism. We pose it as a property estimation problem, and study the fundamental trade-offs involved in the accuracy in estimated privacy guarantees and the number of samples required. We introduce a novel estimator that uses polynomial approximation of a carefully chosen degree to optimally trade-off bias and variance. With $n$ samples, we show that this estimator achieves performance of a straightforward plug-in estimator with $n \ln n$ samples, a phenomenon referred to as effective sample size amplification. The minimax optimality of the proposed estimator is proved by comparing it to a matching fundamental lower bound.

cs.IT↗

arXiv2019

DeepTurbo: Deep Turbo Decoder

Present-day communication systems routinely use codes that approach the channel capacity when coupled with a computationally efficient decoder. However, the decoder is typically designed for the Gaussian noise channel and is known to be sub-optimal for non-Gaussian noise distribution. Deep learning methods offer a new approach for designing decoders that can be trained and tailored for arbitrary channel statistics. We focus on Turbo codes and propose DeepTurbo, a novel deep learning based architecture for Turbo decoding. The standard Turbo decoder (Turbo) iteratively applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm with an interleaver in the middle. A neural architecture for Turbo decoding termed (NeuralBCJR), was proposed recently. There, the key idea is to create a module that imitates the BCJR algorithm using supervised learning, and to use the interleaver architecture along with this module, which is then fine-tuned using end-to-end training. However, knowledge of the BCJR algorithm is required to design such an architecture, which also constrains the resulting learned decoder. Here we remedy this requirement and propose a fully end-to-end trained neural decoder - Deep Turbo Decoder (DeepTurbo). With novel learnable decoder structure and training methodology, DeepTurbo reveals superior performance under both AWGN and non-AWGN settings as compared to the other two decoders - Turbo and NeuralBCJR. Furthermore, among all the three, DeepTurbo exhibits the lowest error floor.

eess.SP↗

arXiv2019

Learning One-hidden-layer Neural Networks under General Input Distributions

Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a restrictive assumption: the training data is drawn from a Gaussian distribution. In this paper, we provide a novel unified framework to design loss functions with desirable landscape properties for a wide range of general input distributions. On these loss functions, remarkably, stochastic gradient descent theoretically recovers the true parameters with global initializations and empirically outperforms the existing approaches. Our loss function design bridges the notion of score functions with the topic of neural network optimization. Central to our approach is the task of estimating the score function from samples, which is of basic and independent interest to theoretical statistics. Traditional estimation methods (example: kernel based) fail right at the outset; we bring statistical methods of local likelihood to design a novel estimator of score functions, that provably adapts to the local geometry of the unknown density.

cs.LG↗

arXiv2019

Rate Distortion For Model Compression: From Theory To Practice

The enormous size of modern deep neural networks makes it challenging to deploy those models in memory and communication limited scenarios. Thus, compressing a trained model without a significant loss in performance has become an increasingly important task. Tremendous advances has been made recently, where the main technical building blocks are parameter pruning, parameter sharing (quantization), and low-rank factorization. In this paper, we propose principled approaches to improve upon the common heuristics used in those building blocks, namely pruning and quantization. We first study the fundamental limit for model compression via the rate distortion theory. We bring the rate distortion function from data compression to model compression to quantify this fundamental limit. We prove a lower bound for the rate distortion function and prove its achievability for linear models. Although this achievable compression scheme is intractable in practice, this analysis motivates a novel model compression framework. This framework provides a new objective function in model compression, which can be applied together with other classes of model compressor such as pruning or quantization. Theoretically, we prove that the proposed scheme is optimal for compressing one-hidden-layer ReLU neural networks. Empirically, we show that the proposed scheme improves upon the baseline in the compression-accuracy tradeoff.

cs.IT↗

arXiv2018

Learning from Comparisons and Choices

When tracking user-specific online activities, each user's preference is revealed in the form of choices and comparisons. For example, a user's purchase history is a record of her choices, i.e. which item was chosen among a subset of offerings. A user's preferences can be observed either explicitly as in movie ratings or implicitly as in viewing times of news articles. Given such individualized ordinal data in the form of comparisons and choices, we address the problem of collaboratively learning representations of the users and the items. The learned features can be used to predict a user's preference of an unseen item to be used in recommendation systems. This also allows one to compute similarities among users and items to be used for categorization and search. Motivated by the empirical successes of the MultiNomial Logit (MNL) model in marketing and transportation, and also more recent successes in word embedding and crowdsourced image embedding, we pose this problem as learning the MNL model parameters that best explain the data. We propose a convex relaxation for learning the MNL model, and show that it is minimax optimal up to a logarithmic factor by comparing its performance to a fundamental lower bound. This characterizes the minimax sample complexity of the problem, and proves that the proposed estimator cannot be improved upon other than by a logarithmic factor. Further, the analysis identifies how the accuracy depends on the topology of sampling via the spectrum of the sampling graph. This provides a guideline for designing surveys when one can choose which items are to be compared. This is accompanied by numerical simulations on synthetic and real data sets, confirming our theoretical predictions.

stat.ML↗

arXiv2018

Number of Connected Components in a Graph: Estimation via Counting Patterns

Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that have been surveyed. Inferring a global property of the original graph from such a sampled subgraph is of a fundamental interest. In this work, we focus on estimating the number of connected components. It is a challenging problem and, for general graphs, little is known about the connection between the observed subgraph and the number of connected components of the original graph. In order to make this connection, we propose a highly redundant and large-dimensional representation of the subgraph, which at first glance seems counter-intuitive. A subgraph is represented by the counts of patterns, known as network motifs. This representation is crucial in introducing a novel estimator for the number of connected components for general graphs, under the knowledge of the spectral gap of the original graph. The connection is made precise via the Schatten $k$-norms of the graph Laplacian and the spectral representation of the number of connected components. We provide a guarantee on the resulting mean squared error that characterizes the bias variance tradeoff. Experiments on synthetic and real-world graphs suggest that we improve upon competing algorithms for graphs with spectral gaps bounded away from zero.

cs.LG↗

arXiv2018

Robustness of Conditional GANs to Noisy Labels

We study the problem of learning conditional generators from noisy labeled samples, where the labels are corrupted by random noise. A standard training of conditional GANs will not only produce samples with wrong labels, but also generate poor quality samples. We consider two scenarios, depending on whether the noise model is known or not. When the distribution of the noise is known, we introduce a novel architecture which we call Robust Conditional GAN (RCGAN). The main idea is to corrupt the label of the generated sample before feeding to the adversarial discriminator, forcing the generator to produce samples with clean labels. This approach of passing through a matching noisy channel is justified by corresponding multiplicative approximation bounds between the loss of the RCGAN and the distance between the clean real distribution and the generator distribution. This shows that the proposed approach is robust, when used with a carefully chosen discriminator architecture, known as projection discriminator. When the distribution of the noise is not known, we provide an extension of our architecture, which we call RCGAN-U, that learns the noise model simultaneously while training the generator. We show experimentally on MNIST and CIFAR-10 datasets that both the approaches consistently improve upon baseline approaches, and RCGAN-U closely matches the performance of RCGAN.

stat.ML↗

arXiv2018

PacGAN: The power of two samples in generative adversarial networks

Generative adversarial networks (GANs) are innovative techniques for learning generative models of complex data distributions from samples. Despite remarkable recent improvements in generating realistic images, one of their major shortcomings is the fact that in practice, they tend to produce samples with little diversity, even when trained on diverse datasets. This phenomenon, known as mode collapse, has been the main focus of several recent advances in GANs. Yet there is little understanding of why mode collapse happens and why existing approaches are able to mitigate mode collapse. We propose a principled approach to handling mode collapse, which we call packing. The main idea is to modify the discriminator to make decisions based on multiple samples from the same class, either real or artificially generated. We borrow analysis tools from binary hypothesis testing---in particular the seminal result of Blackwell [Bla53]---to prove a fundamental connection between packing and mode collapse. We show that packing naturally penalizes generators with mode collapse, thereby favoring generator distributions with less mode collapse during the training process. Numerical experiments on benchmark datasets suggests that packing provides significant improvements in practice as well.

cs.LG↗

arXiv2018

Compounding of Wealth in Proof-of-Stake Cryptocurrencies

Proof-of-stake (PoS) is a promising approach for designing efficient blockchains, where block proposers are randomly chosen with probability proportional to their stake. A primary concern with PoS systems is the "rich getting richer" phenomenon, whereby wealthier nodes are more likely to get elected, and hence reap the block reward, making them even wealthier. In this paper, we introduce the notion of equitability, which quantifies how much a proposer can amplify her stake compared to her initial investment. Even with everyone following protocol (i.e., honest behavior), we show that existing methods of allocating block rewards lead to poor equitability, as does initializing systems with small stake pools and/or large rewards relative to the stake pool. We identify a \emph{geometric} reward function, which we prove is maximally equitable over all choices of reward functions under honest behavior and bound the deviation for strategic actions; the proofs involve the study of optimization problems and stochastic dominances of Polya urn processes, and are of independent mathematical interest. These results allow us to provide a systematic framework to choose the parameters of a practical incentive system for PoS cryptocurrencies.

cs.CR↗