Larger and deeper neural network architectures deliver improved accuracy on a variety of tasks, but also require a large amount of memory for training to store intermediate activations for back-propagation. We introduce an approximation strategy to significantly reduce this memory footprint, with minimal effect on training performance and negligible computational cost. Our method replaces intermediate activations with lower-precision approximations to free up memory, after the full-precision versions have been used for computation in subsequent layers in the forward pass. Only these approximate activations are retained for use in the backward pass. Compared to naive low-precision computation, our approach limits the accumulation of errors across layers and allows the use of much lower-precision approximations without affecting training accuracy. Experiments on CIFAR and ImageNet show that our method yields performance comparable to full-precision training, while storing activations at a fraction of the memory cost with 8- and even 4-bit fixed-point precision.

Active search is a learning paradigm for actively identifying as many members of a given class as possible. A critical target scenario is high-throughput screening for scientific discovery, such as drug or materials discovery. In these settings, specialized instruments can often evaluate \emph{multiple} points simultaneously; however, all existing work on active search focuses on sequential acquisition. We bridge this gap, addressing batch active search from both the theoretical and practical perspective. We first derive the Bayesian optimal policy for this problem, then prove a lower bound on the performance gap between sequential and batch optimal policies: the ``cost of parallelization.'' We also propose novel, efficient batch policies inspired by state-of-the-art sequential policies, and develop an aggressive pruning technique that can dramatically speed up computation. We conduct thorough experiments on data from three application domains: a citation network, material science, and drug discovery, testing all proposed policies (14 total) with a wide range of batch sizes. Our results demonstrate that the empirical performance gap matches our theoretical bound, that nonmyopic policies usually significantly outperform myopic alternatives, and that diversity is an important consideration for batch policy design.

Active search is a learning paradigm for actively identifying as many members of a given class as possible. A critical target scenario is high-throughput screening for scientific discovery, such as drug or materials discovery. In these settings, specialized instruments can often evaluate \emph{multiple} points simultaneously; however, all existing work on active search focuses on sequential acquisition. We bridge this gap, addressing batch active search from both the theoretical and practical perspective. We first derive the Bayesian optimal policy for this problem, then prove a lower bound on the performance gap between sequential and batch optimal policies: the ``cost of parallelization.'' We also propose novel, efficient batch policies inspired by state-of-the-art sequential policies, and develop an aggressive pruning technique that can dramatically speed up computation. We conduct thorough experiments on data from three application domains: a citation network, material science, and drug discovery, testing all proposed policies (14 total) with a wide range of batch sizes. Our results demonstrate that the empirical performance gap matches our theoretical bound, that nonmyopic policies usually significantly outperform myopic alternatives, and that diversity is an important consideration for batch policy design.

Active search is a learning paradigm for actively identifying as many members of a given class as possible. A critical target scenario is high-throughput screening for scientific discovery, such as drug or materials discovery. In this paper, we approach this problem in Bayesian decision framework. We first derive the Bayesian optimal policy under a natural utility, and establish a theoretical hardness of active search, proving that the optimal policy can not be approximated for any constant ratio. We also study the batch setting for the first time, where a batch of $b>1$ points can be queried at each iteration. We give an asymptotic lower bound, linear in batch size, on the adaptivity gap: how much we could lose if we query $b$ points at a time for $t$ iterations, instead of one point at a time for $bt$ iterations. We then introduce a novel approach to nonmyopic approximations of the optimal policy that admits efficient computation. Our proposed policy can automatically trade off exploration and exploitation, without relying on any tuning parameters. We also generalize our policy to batch setting, and propose two approaches to tackle the combinatorial search challenge. We evaluate our proposed policies on a large database of drug discovery and materials science. Results demonstrate the superior performance of our proposed policy in both sequential and batch setting; the nonmyopic behavior is also illustrated in various aspects.

Hierarchical clustering is a data analysis method that has been used for decades. Despite its widespread use, the method has an underdeveloped analytical foundation. Having a well understood foundation would both support the currently used methods and help guide future improvements. The goal of this paper is to give an analytic framework to better understand observations seen in practice. This paper considers the dual of a problem framework for hierarchical clustering introduced by Dasgupta. The main result is that one of the most popular algorithms used in practice, average linkage agglomerative clustering, has a small constant approximation ratio for this objective. Furthermore, this paper establishes that using bisecting k-means divisive clustering has a very poor lower bound on its approximation ratio for the same objective. However, we show that there are divisive algorithms that perform well with respect to this objective by giving two constant approximation algorithms. This paper is some of the first work to establish guarantees on widely used hierarchical algorithms for a natural objective function. This objective and analysis give insight into what these popular algorithms are optimizing and when they will perform well.

Clustering large data is a fundamental problem with a vast number of applications. Due to the increasing size of data, practitioners interested in clustering have turned to distributed computation methods. In this work, we consider the widely used k-center clustering problem and its variant used to handle noisy data, k-center with outliers. In the noise-free setting we demonstrate how a previously-proposed distributed method is actually an O(1)-approximation algorithm, which accurately explains its strong empirical performance. Additionally, in the noisy setting, we develop a novel distributed algorithm that is also an O(1)-approximation. These algorithms are highly parallel and lend themselves to virtually any distributed computing framework. We compare both empirically against the best known noisy sequential clustering methods and show that both distributed algorithms are consistently close to their sequential versions. The algorithms are all one can hope for in distributed settings: they are fast, memory efficient and they match their sequential counterparts.