We introduce a simple and efficient method, called Auxiliary Tuning, for adapting a pre-trained Language Model to a novel task; we demonstrate this approach on the task of conditional text generation. Our approach supplements the original pre-trained model with an auxiliary model that shifts the output distribution according to the target task. The auxiliary model is trained by adding its logits to the pre-trained model logits and maximizing the likelihood of the target task output. Our method imposes no constraints on the auxiliary architecture. In particular, the auxiliary model can ingest additional input relevant to the target task, independently from the pre-trained model's input. Furthermore, mixing the models at the logits level provides a natural probabilistic interpretation of the method. Our method achieved similar results to training from scratch for several different tasks, while using significantly fewer resources for training; we share a specific example of text generation conditioned on keywords.

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study the distributed kernel regression via the divide and conquer approach. This approach has been proved asymptotically minimax optimal if the kernel is perfectly selected so that the true regression function lies in the associated reproducing kernel Hilbert space. However, this is usually, if not always, impractical because kernels that can only be selected via prior knowledge or a tuning process are hardly perfect. Instead it is more common that the kernel is good enough but imperfect in the sense that the true regression can be well approximated by but does not lie exactly in the kernel space. We show distributed kernel regression can still achieves capacity independent optimal rate in this case. To this end, we first establish a general framework that allows to analyze distributed regression with response weighted base algorithms by bounding the error of such algorithms on a single data set, provided that the error bounds has factored the impact of the unexplained variance of the response variable. Then we perform a leave one out analysis of the kernel ridge regression and bias corrected kernel ridge regression, which in combination with the aforementioned framework allows us to derive sharp error bounds and capacity independent optimal rates for the associated distributed kernel regression algorithms. As a byproduct of the thorough analysis, we also prove the kernel ridge regression can achieve rates faster than $N^{-1}$ (where $N$ is the sample size) in the noise free setting which, to our best knowledge, are first observed and novel in regression learning.

The design process of complex systems such as new configurations of aircraft or launch vehicles is usually decomposed in different phases which are characterized for instance by the depth of the analyses in terms of number of design variables and fidelity of the physical models. At each phase, the designers have to compose with accurate but computationally intensive models as well as cheap but inaccurate models. Multi-fidelity modeling is a way to merge different fidelity models to provide engineers with accurate results with a limited computational cost. Within the context of multi-fidelity modeling, approaches relying on Gaussian Processes emerge as popular techniques to fuse information between the different fidelity models. The relationship between the fidelity models is a key aspect in multi-fidelity modeling. This paper provides an overview of Gaussian process-based multi-fidelity modeling techniques for variable relationship between the fidelity models (e.g., linearity, non-linearity, variable correlation). Each technique is described within a unified framework and the links between the different techniques are highlighted. All the approaches are numerically compared on a series of analytical test cases and four aerospace related engineering problems in order to assess their benefits and disadvantages with respect to the problem characteristics.

The use of quantum computing in graph community detection and regularity checking related to Szemeredi's Regularity Lemma (SRL) are demonstrated with D-Wave Systems' quantum annealer and simulations. We demonstrate the capability of quantum computing in solving hard problems relevant to big data. A new community detection algorithm based on SRL is also introduced and tested. In worst case scenario of regularity check we use Grover's algorithm and quantum phase estimation algorithm, in order to speed-up computations using a quantum gate computers.

This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that allow for integrating robustness and skewness into a single unified cluster analysis framework. Non-symmetrically distributed and heavy-tailed data clusters have been reported in a variety of real-world applications. Robustness is essential because a few outlying observations can severely obscure the cluster structure. The RESK distributions are a generalization of the Real Elliptically Symmetric (RES) distributions. To estimate the cluster parameters and memberships, we derive an expectation maximization (EM) algorithm for arbitrary RESK distributions. Special attention is given to a new robust skew-Huber M-estimator, which is also the maximum likelihood estimator (MLE) for the skew-Huber distribution that belongs to the RESK class. Numerical experiments on simulated and real-world data confirm the usefulness of the proposed methods for skewed and heavy-tailed data sets.

Neural network scaling has been critical for improving the model quality in many real-world machine learning applications with vast amounts of training data and compute. Although this trend of scaling is affirmed to be a sure-fire approach for better model quality, there are challenges on the path such as the computation cost, ease of programming, and efficient implementation on parallel devices. GShard is a module composed of a set of lightweight annotation APIs and an extension to the XLA compiler. It provides an elegant way to express a wide range of parallel computation patterns with minimal changes to the existing model code. GShard enabled us to scale up multilingual neural machine translation Transformer model with Sparsely-Gated Mixture-of-Experts beyond 600 billion parameters using automatic sharding. We demonstrate that such a giant model can efficiently be trained on 2048 TPU v3 accelerators in 4 days to achieve far superior quality for translation from 100 languages to English compared to the prior art.

We present an explicit deep neural network construction that transforms uniformly distributed one-dimensional noise into an arbitrarily close approximation of any two-dimensional Lipschitz-continuous target distribution. The key ingredient of our design is a generalization of the "space-filling" property of sawtooth functions discovered in (Bailey & Telgarsky, 2018). We elicit the importance of depth - in our neural network construction - in driving the Wasserstein distance between the target distribution and the approximation realized by the network to zero. An extension to output distributions of arbitrary dimension is outlined. Finally, we show that the proposed construction does not incur a cost - in terms of error measured in Wasserstein-distance - relative to generating $d$-dimensional target distributions from $d$ independent random variables.

Name & Citation Appendix Metropolis-Hastings (Hastings, 1970) B.1 Markov Chain Monte Carlo (MCMC) is a computational Mixture Proposal (Habib & Barber, 2018) B.2 approach to fundamental problems such Multiple-Try Metropolis (Liu et al., 2000) B.3 as inference, integration, optimization, and simulation. Sample-Adaptive MCMC (Zhu, 2019) B.4 The field has developed a broad spectrum Reversible-Jump MCMC (Green, 1995) B.5 of algorithms, varying in the way they are motivated, Hybrid Monte Carlo (Duane et al., 1987) B.6 the way they are applied and how efficiently RMHMC (Girolami & Calderhead, 2011) B.7 they sample. Despite all the differences, many of NeuTra (Hoffman et al., 2019) B.8 them share the same core principle, which we A-NICE-MC (Song et al., 2017) B.9 unify as the Involutive MCMC (iMCMC) framework. L2HMC (Levy et al., 2017) B.10 Building upon this, we describe a wide Persistent HMC (Horowitz, 1991) B.11 range of MCMC algorithms in terms of iMCMC, Gibbs (Geman & Geman, 1984) B.12 and formulate a number of "tricks" which one Look Ahead (Sohl-Dickstein et al., 2014) B.13 can use as design principles for developing new NRJ (Gagnon & Doucet, 2019) B.14 MCMC algorithms. Thus, iMCMC provides a Lifted MH (Turitsyn et al., 2011) B.15 unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. Table 1: List of algorithms that we describe by the Involutive We demonstrate the latter with two MCMC framework. See their descriptions and formulations examples where we transform known reversible in terms of iMCMC in corresponding appendices.

We present some novel, straightforward methods for training the connection graph of a randomly initialized neural network without training the weights. These methods do not use hyperparameters defining cutoff thresholds and therefore remove the need for iteratively searching optimal values of such hyperparameters. We can achieve similar or higher performances than in the case of training all weights, with a similar computational cost as for standard training techniques. Besides switching connections on and off, we introduce a novel way of training a network by flipping the signs of the weights. If we try to minimize the number of changed connections, by changing less than 10\% of the total it is already possible to reach more than 90\% of the accuracy achieved by standard training. We obtain good results even with weights of constant magnitude or even when weights are drawn from highly asymmetric distributions. These results shed light on the over-parameterization of neural networks and on how they may be reduced to their effective size.

Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics. We apply some of the latest techniques in data science such as supervised and unsupervised machine-learning and topological data analysis to the Wolfram database of some 8000 finite graphs in light of studying these correspondences. Encouragingly, we find that neural classifiers, regressors and networks can perform, with high efficiently and accuracy, a multitude of tasks ranging from recognizing graph Ricci-flatness, to predicting the spectral gap, to detecting the presence of Hamiltonian cycles, etc.