We solve a long-standing open problem about the optimal codebook structure of codes in $n$-dimensional Euclidean space that consist of $n+1$ codewords subject to a codeword energy constraint, in terms of minimizing the average decoding error probability. The conjecture states that optimal codebooks are formed by the $n+1$ vertices of a regular simplex (the $n$-dimensional generalization of a regular tetrahedron) inscribed in the unit sphere. A self-contained proof of this conjecture is provided that hinges on symmetry arguments and leverages a relaxation approach that consists in jointly optimizing the codebook and the decision regions, rather than the codeword locations alone.
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Watermarking of language model outputs enables statistical detection of model-generated text, which has many applications in the responsible deployment of language models. Existing watermarking strategies operate by altering the decoder of an existing language model, and the ability for a language model to directly learn to generate the watermark would have significant implications for the real-world deployment of watermarks. First, learned watermarks could be used to build open models that naturally generate watermarked text, allowing for open models to benefit from watermarking. Second, if watermarking is used to determine the provenance of generated text, an adversary can hurt the reputation of a victim model by spoofing its watermark and generating damaging watermarked text. To investigate the learnability of watermarks, we propose watermark distillation, which trains a student model to behave like a teacher model that uses decoding-based watermarking. We test our approach on three distinct decoding-based watermarking strategies and various hyperparameter settings, finding that models can learn to generate watermarked text with high detectability. We also find limitations to learnability, including the loss of watermarking capabilities under fine-tuning on normal text and high sample complexity when learning low-distortion watermarks.
In the arena of privacy-preserving machine learning, differentially private stochastic gradient descent (DP-SGD) has outstripped the objective perturbation mechanism in popularity and interest. Though unrivaled in versatility, DP-SGD requires a non-trivial privacy overhead (for privately tuning the model's hyperparameters) and a computational complexity which might be extravagant for simple models such as linear and logistic regression. This paper revamps the objective perturbation mechanism with tighter privacy analyses and new computational tools that boost it to perform competitively with DP-SGD on unconstrained convex generalized linear problems.
In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the problem is assembling $t$ from the dictionary. The second version is the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). In this case, $t$ is not given, and we should construct the shortest string (we call it superstring) that contains each string from the given sequence as a substring. These problems are connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. For both problems, we suggest new quantum algorithms that work better than their classical counterparts. In the first case, we present a quantum algorithm with $O(m+\log m\sqrt{nL})$ running time. In the case of SSP, we present a quantum algorithm with running time $O(n^3 1.728^n +L +\sqrt{L}n^{1.5}+\sqrt{L}n\log^2L\log^2n)$.
We develop a post-selection inference method for the Cox proportional hazards model with interval-censored data, which provides asymptotically valid p-values and confidence intervals conditional on the model selected by lasso. The method is based on a pivotal quantity that is shown to converge to a uniform distribution under local alternatives. The proof can be adapted to many other regression models, which is illustrated by the extension to generalized linear models and the Cox model with right-censored data. Our method involves estimation of the efficient information matrix, for which several approaches are proposed with proof of their consistency. Thorough simulation studies show that our method has satisfactory performance in samples of modest sizes. The utility of the method is illustrated via an application to an Alzheimer's disease study.
We study the following combinatorial problem. Given a set of $n$ y-monotone curves, which we call wires, a tangle determines the order of the wires on a number of horizontal layers such that any two consecutive layers differ only in swaps of neighboring wires. Given a multiset $L$ of swaps (that is, unordered pairs of wires) and an initial order of the wires, a tangle realizes $L$ if each pair of wires changes its order exactly as many times as specified by $L$. Deciding whether a given multiset of swaps admits a realizing tangle is known to be NP-hard [Yamanaka et al., CCCG 2018]. We prove that this problem remains NP-hard if every pair of wires swaps only a constant number of times. On the positive side, we improve the runtime of a previous exponential-time algorithm. We also show that the problem is in NP and fixed-parameter tractable with respect to the number of wires.
Elixir is a dynamically-typed functional language running on the Erlang Virtual Machine, designed for building scalable and maintainable applications. Its characteristics have earned it a surging adoption by hundreds of industrial actors and tens of thousands of developers. Static typing seems nowadays to be the most important request coming from the Elixir community. We present a gradual type system we plan to include in the Elixir compiler, outline its characteristics and design principles, and show by some short examples how to use it in practice. Developing a static type system suitable for Erlang's family of languages has been an open research problem for almost two decades. Our system transposes to this family of languages a polymorphic type system with set-theoretic types and semantic subtyping. To do that, we had to improve and extend both semantic subtyping and the typing techniques thereof, to account for several characteristics of these languages -- and of Elixir in particular -- such as the arity of functions, the use of guards, a uniform treatment of records and dictionaries, the need for a new sound gradual typing discipline that does not rely on the insertion at compile time of specific run-time type-tests but, rather, takes into account both the type tests performed by the virtual machine and those explicitly added by the programmer. The system presented here is "gradually" being implemented and integrated in Elixir, but a prototype implementation is already available. The aim of this work is to serve as a longstanding reference that will be used to introduce types to Elixir programmers, as well as to hint at some future directions and possible evolutions of the Elixir language.
Neural machine translation (NMT) is a deep learning based approach for machine translation, which yields the state-of-the-art translation performance in scenarios where large-scale parallel corpora are available. Although the high-quality and domain-specific translation is crucial in the real world, domain-specific corpora are usually scarce or nonexistent, and thus vanilla NMT performs poorly in such scenarios. Domain adaptation that leverages both out-of-domain parallel corpora as well as monolingual corpora for in-domain translation, is very important for domain-specific translation. In this paper, we give a comprehensive survey of the state-of-the-art domain adaptation techniques for NMT.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
Deep Convolutional Neural Networks have pushed the state-of-the art for semantic segmentation provided that a large amount of images together with pixel-wise annotations is available. Data collection is expensive and a solution to alleviate it is to use transfer learning. This reduces the amount of annotated data required for the network training but it does not get rid of this heavy processing step. We propose a method of transfer learning without annotations on the target task for datasets with redundant content and distinct pixel distributions. Our method takes advantage of the approximate content alignment of the images between two datasets when the approximation error prevents the reuse of annotation from one dataset to another. Given the annotations for only one dataset, we train a first network in a supervised manner. This network autonomously learns to generate deep data representations relevant to the semantic segmentation. Then the images in the new dataset, we train a new network to generate a deep data representation that matches the one from the first network on the previous dataset. The training consists in a regression between feature maps and does not require any annotations on the new dataset. We show that this method reaches performances similar to a classic transfer learning on the PASCAL VOC dataset with synthetic transformations.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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