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Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

We revisit the problem of designing scalable protocols for private statistics and private federated learning when each device holds its private data. Locally differentially private algorithms require little trust but are (provably) limited in their utility. Centrally differentially private algorithms can allow significantly better utility but require a trusted curator. This gap has led to significant interest in the design and implementation of simple cryptographic primitives, that can allow central-like utility guarantees without having to trust a central server. Our first contribution is to propose a new primitive that allows for efficient implementation of several commonly used algorithms, and allows for privacy accounting that is close to that in the central setting without requiring the strong trust assumptions it entails. {\em Shuffling} and {\em aggregation} primitives that have been proposed in earlier works enable this for some algorithms, but have significant limitations as primitives. We propose a {\em Samplable Anonymous Aggregation} primitive, which computes an aggregate over a random subset of the inputs and show that it leads to better privacy-utility trade-offs for various fundamental tasks. Secondly, we propose a system architecture that implements this primitive and perform a security analysis of the proposed system. Our design combines additive secret-sharing with anonymization and authentication infrastructures., Comment: 34 pages

Privately learning statistics of events on devices can enable improved user experience. Differentially private algorithms for such problems can benefit significantly from interactivity. We argue that an aggregation protocol can enable an interactive private federated statistics system where user's devices maintain control of the privacy assurance. We describe the architecture of such a system, and analyze its security properties.

Despite recent advances in neural text generation, encoding the rich diversity in human language remains elusive. We argue that the sub-optimal text generation is mainly attributable to the imbalanced token distribution, which particularly misdirects the learning model when trained with the maximum-likelihood objective. As a simple yet effective remedy, we propose two novel methods, F^2-Softmax and MefMax, for a balanced training even with the skewed frequency distribution. MefMax assigns tokens uniquely to frequency classes, trying to group tokens with similar frequencies and equalize frequency mass between the classes. F^2-Softmax then decomposes a probability distribution of the target token into a product of two conditional probabilities of (i) frequency class, and (ii) token from the target frequency class. Models learn more uniform probability distributions because they are confined to subsets of vocabularies. Significant performance gains on seven relevant metrics suggest the supremacy of our approach in improving not only the diversity but also the quality of generated texts., Comment: EMNLP 2020

Recently, image-to-image translation has obtained significant attention. Among many, those approaches based on an exemplar image that contains the target style information has been actively studied, due to its capability to handle multimodality as well as its applicability in practical use. However, two intrinsic problems exist in the existing methods: what and where to transfer. First, those methods extract style from an entire exemplar which includes noisy information, which impedes a translation model from properly extracting the intended style of the exemplar. That is, we need to carefully determine what to transfer from the exemplar. Second, the extracted style is applied to the entire input image, which causes unnecessary distortion in irrelevant image regions. In response, we need to decide where to transfer the extracted style. In this paper, we propose a novel approach that extracts out a local mask from the exemplar that determines what style to transfer, and another local mask from the input image that determines where to transfer the extracted style. The main novelty of this paper lies in (1) the highway adaptive instance normalization technique and (2) an end-to-end translation framework which achieves an outstanding performance in reflecting a style of an exemplar. We demonstrate the quantitative and qualitative evaluation results to confirm the advantages of our proposed approach.

Recently, unsupervised exemplar-based image-to-image translation, conditioned on a given exemplar without the paired data, has accomplished substantial advancements. In order to transfer the information from an exemplar to an input image, existing methods often use a normalization technique, e.g., adaptive instance normalization, that controls the channel-wise statistics of an input activation map at a particular layer, such as the mean and the variance. Meanwhile, style transfer approaches similar task to image translation by nature, demonstrated superior performance by using the higher-order statistics such as covariance among channels in representing a style. In detail, it works via whitening (given a zero-mean input feature, transforming its covariance matrix into the identity). followed by coloring (changing the covariance matrix of the whitened feature to those of the style feature). However, applying this approach in image translation is computationally intensive and error-prone due to the expensive time complexity and its non-trivial backpropagation. In response, this paper proposes an end-to-end approach tailored for image translation that efficiently approximates this transformation with our novel regularization methods. We further extend our approach to a group-wise form for memory and time efficiency as well as image quality. Extensive qualitative and quantitative experiments demonstrate that our proposed method is fast, both in training and inference, and highly effective in reflecting the style of an exemplar. Finally, our code is available at https://github.com/WonwoongCho/GDWCT., Comment: CVPR 2019 (oral)

Questions convey information about the questioner, namely what one does not know. In this paper, we propose a novel approach to allow a learning agent to ask what it considers as tricky to predict, in the course of producing a final output. By analyzing when and what it asks, we can make our model more transparent and interpretable. We first develop this idea to propose a general framework of deep neural networks that can ask questions, which we call asking networks. A specific architecture and training process for an asking network is proposed for the task of colorization, which is an exemplar one-to-many task and thus a task where asking questions is helpful in performing the task accurately. Our results show that the model learns to generate meaningful questions, asks difficult questions first, and utilizes the provided hint more efficiently than baseline models. We conclude that the proposed asking framework makes the learning agent reveal its weaknesses, which poses a promising new direction in developing interpretable and interactive models., Comment: 10 pages

Machine comprehension question answering, which finds an answer to the question given a passage, involves high-level reasoning processes of understanding and tracking the relevant contents across various semantic units such as words, phrases, and sentences in a document. This paper proposes the novel question-aware sentence gating networks that directly incorporate the sentence-level information into word-level encoding processes. To this end, our model first learns question-aware sentence representations and then dynamically combines them with word-level representations, resulting in semantically meaningful word representations for QA tasks. Experimental results demonstrate that our approach consistently improves the accuracy over existing baseline approaches on various QA datasets and bears the wide applicability to other neural network-based QA models.

Recently, generative adversarial networks (GANs) have shown promising performance in generating realistic images. However, they often struggle in learning complex underlying modalities in a given dataset, resulting in poor-quality generated images. To mitigate this problem, we present a novel approach called mixture of experts GAN (MEGAN), an ensemble approach of multiple generator networks. Each generator network in MEGAN specializes in generating images with a particular subset of modalities, e.g., an image class. Instead of incorporating a separate step of handcrafted clustering of multiple modalities, our proposed model is trained through an end-to-end learning of multiple generators via gating networks, which is responsible for choosing the appropriate generator network for a given condition. We adopt the categorical reparameterization trick for a categorical decision to be made in selecting a generator while maintaining the flow of the gradients. We demonstrate that individual generators learn different and salient subparts of the data and achieve a multiscale structural similarity (MS-SSIM) score of 0.2470 for CelebA and a competitive unsupervised inception score of 8.33 in CIFAR-10., Comment: 27th International Joint Conference on Artificial Intelligence (IJCAI 2018)

This paper proposes a novel approach to generate multiple color palettes that reflect the semantics of input text and then colorize a given grayscale image according to the generated color palette. In contrast to existing approaches, our model can understand rich text, whether it is a single word, a phrase, or a sentence, and generate multiple possible palettes from it. For this task, we introduce our manually curated dataset called Palette-and-Text (PAT). Our proposed model called Text2Colors consists of two conditional generative adversarial networks: the text-to-palette generation networks and the palette-based colorization networks. The former captures the semantics of the text input and produce relevant color palettes. The latter colorizes a grayscale image using the generated color palette. Our evaluation results show that people preferred our generated palettes over ground truth palettes and that our model can effectively reflect the given palette when colorizing an image., Comment: 25 pages, 22 figures