Probabilistic Invariant Learning with Randomized Linear Classifiers

Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage randomness and design models that are both expressive and invariant but use less resources. Inspired by randomized algorithms, our key insight is that accepting probabilistic notions of universal approximation and invariance can reduce our resource requirements. More specifically, we propose a class of binary classification models called Randomized Linear Classifiers (RLCs). We give parameter and sample size conditions in which RLCs can, with high probability, approximate any (smooth) function while preserving invariance to compact group transformations. Leveraging this result, we design three RLCs that are provably probabilistic invariant for classification tasks over sets, graphs, and spherical data. We show how these models can achieve probabilistic invariance and universality using less resources than (deterministic) neural networks and their invariant counterparts. Finally, we empirically demonstrate the benefits of this new class of models on invariant tasks where deterministic invariant neural networks are known to struggle.

FOSI: Hybrid First and Second Order Optimization

Though second-order optimization methods are highly effective, popular approaches in machine learning such as SGD and Adam use only first-order information due to the difficulty of computing curvature in high dimensions. We present FOSI, a novel meta-algorithm that improves the performance of any first-order optimizer by efficiently incorporating second-order information during the optimization process. In each iteration, FOSI implicitly splits the function into two quadratic functions defined on orthogonal subspaces, then uses a second-order method to minimize the first, and the base optimizer to minimize the other. Our analysis of FOSI's preconditioner and effective Hessian proves that FOSI improves the condition number for a large family of optimizers. Our empirical evaluation demonstrates that FOSI improves the convergence rate and optimization time of GD, Heavy-Ball, and Adam when applied to several deep neural networks training tasks such as audio classification, transfer learning, and object classification and when applied to convex functions.

Unsupervised Frequent Pattern Mining for CEP

Complex Event Processing (CEP) is a set of methods that allow efficient knowledge extraction from massive data streams using complex and highly descriptive patterns. Numerous applications, such as online finance, healthcare monitoring and fraud detection use CEP technologies to capture critical alerts, potential threats, or vital notifications in real time. As of today, in many fields, patterns are manually defined by human experts. However, desired patterns often contain convoluted relations that are difficult for humans to detect, and human expertise is scarce in many domains. We present REDEEMER (REinforcement baseD cEp pattErn MinER), a novel reinforcement and active learning approach aimed at mining CEP patterns that allow expansion of the knowledge extracted while reducing the human effort required. This approach includes a novel policy gradient method for vast multivariate spaces and a new way to combine reinforcement and active learning for CEP rule learning while minimizing the number of labels needed for training. REDEEMER aims to enable CEP integration in domains that could not utilize it before. To the best of our knowledge, REDEEMER is the first system that suggests new CEP rules that were not observed beforehand, and is the first method aimed for increasing pattern knowledge in fields where experts do not possess sufficient information required for CEP tools. Our experiments on diverse data-sets demonstrate that REDEEMER is able to extend pattern knowledge while outperforming several state-of-the-art reinforcement learning methods for pattern mining.

Coin Flipping Neural Networks

We show that neural networks with access to randomness can outperform deterministic networks by using amplification. We call such networks Coin-Flipping Neural Networks, or CFNNs. We show that a CFNN can approximate the indicator of a $d$-dimensional ball to arbitrary accuracy with only 2 layers and $\mathcal{O}(1)$ neurons, where a 2-layer deterministic network was shown to require $\Omega(e^d)$ neurons, an exponential improvement (arXiv:1610.09887). We prove a highly non-trivial result, that for almost any classification problem, there exists a trivially simple network that solves it given a sufficiently powerful generator for the network's weights. Combining these results we conjecture that for most classification problems, there is a CFNN which solves them with higher accuracy or fewer neurons than any deterministic network. Finally, we verify our proofs experimentally using novel CFNN architectures on CIFAR10 and CIFAR100, reaching an improvement of 9.25\% from the baseline.

Learning Under Delayed Feedback: Implicitly Adapting to Gradient Delays

We consider stochastic convex optimization problems, where several machines act asynchronously in parallel while sharing a common memory. We propose a robust training method for the constrained setting and derive non asymptotic convergence guarantees that do not depend on prior knowledge of update delays, objective smoothness, and gradient variance. Conversely, existing methods for this setting crucially rely on this prior knowledge, which render them unsuitable for essentially all shared-resources computational environments, such as clouds and data centers. Concretely, existing approaches are unable to accommodate changes in the delays which result from dynamic allocation of the machines, while our method implicitly adapts to such changes.

It's Not What Machines Can Learn, It's What We Cannot Teach

Can deep neural networks learn to solve any task, and in particular problems of high complexity? This question attracts a lot of interest, with recent works tackling computationally hard tasks such as the traveling salesman problem and satisfiability. In this work we offer a different perspective on this question. Given the common assumption that $\textit{NP} \neq \textit{coNP}$ we prove that any polynomial-time sample generator for an $\textit{NP}$-hard problem samples, in fact, from an easier sub-problem. We empirically explore a case study, Conjunctive Query Containment, and show how common data generation techniques generate biased datasets that lead practitioners to over-estimate model accuracy. Our results suggest that machine learning approaches that require training on a dense uniform sampling from the target distribution cannot be used to solve computationally hard problems, the reason being the difficulty of generating sufficiently large and unbiased training sets.

Adaptive Communication Bounds for Distributed Online Learning

We consider distributed online learning protocols that control the exchange of information between local learners in a round-based learning scenario. The learning performance of such a protocol is intuitively optimal if approximately the same loss is incurred as in a hypothetical serial setting. If a protocol accomplishes this, it is inherently impossible to achieve a strong communication bound at the same time. In the worst case, every input is essential for the learning performance, even for the serial setting, and thus needs to be exchanged between the local learners. However, it is reasonable to demand a bound that scales well with the hardness of the serialized prediction problem, as measured by the loss received by a serial online learning algorithm. We provide formal criteria based on this intuition and show that they hold for a simplified version of a previously published protocol.

Gap Aware Mitigation of Gradient Staleness

Cloud computing is becoming increasingly popular as a platform for distributed training of deep neural networks. Synchronous stochastic gradient descent (SSGD) suffers from substantial slowdowns due to stragglers if the environment is non-dedicated, as is common in cloud computing. Asynchronous SGD (ASGD) methods are immune to these slowdowns but are scarcely used due to gradient staleness, which encumbers the convergence process. Recent techniques have had limited success mitigating the gradient staleness when scaling up to many workers (computing nodes). In this paper we define the Gap as a measure of gradient staleness and propose Gap-Aware (GA), a novel asynchronous-distributed method that penalizes stale gradients linearly to the Gap and performs well even when scaling to large numbers of workers. Our evaluation on the CIFAR, ImageNet, and WikiText-103 datasets shows that GA outperforms the currently acceptable gradient penalization method, in final test accuracy. We also provide convergence rate proof for GA. Despite prior beliefs, we show that if GA is applied, momentum becomes beneficial in asynchronous environments, even when the number of workers scales up.

Taming Momentum in a Distributed Asynchronous Environment

Although distributed computing can significantly reduce the training time of deep neural networks, scaling the training process while maintaining high efficiency and final accuracy is challenging. Distributed asynchronous training enjoys near-linear speedup, but asynchrony causes gradient staleness, the main difficulty in scaling stochastic gradient descent to large clusters. Momentum, which is often used to accelerate convergence and escape local minima, exacerbates the gradient staleness, thereby hindering convergence. We propose DANA: a novel asynchronous distributed technique which is based on a new gradient staleness measure that we call the gap. By minimizing the gap, DANA mitigates the gradient staleness, despite using momentum, and therefore scales to large clusters while maintaining high final accuracy and fast convergence. DANA adapts Nesterov's Accelerated Gradient to a distributed setting, computing the gradient on an estimated future position of the model's parameters. In turn, we show that DANA's estimation of the future position amplifies the use of a Taylor expansion, which relies on a fast Hessian approximation, making it much more effective and accurate. Our evaluation on the CIFAR and ImageNet datasets shows that DANA outperforms existing methods, in both final accuracy and convergence speed.