Error accumulation is an essential component of the Top-$k$ sparsification method in distributed gradient descent. It implicitly scales the learning rate and prevents the slow-down of lateral movement, but it can also deteriorate convergence. This paper proposes a novel sparsification algorithm called regularized Top-$k$ (RegTop-$k$) that controls the learning rate scaling of error accumulation. The algorithm is developed by looking at the gradient sparsification as an inference problem and determining a Bayesian optimal sparsification mask via maximum-a-posteriori estimation. It utilizes past aggregated gradients to evaluate posterior statistics, based on which it prioritizes the local gradient entries. Numerical experiments with ResNet-18 on CIFAR-10 show that at $0.1\%$ sparsification, RegTop-$k$ achieves about $8\%$ higher accuracy than standard Top-$k$.
National Research University Higher School of Economics（国立研究型大学高等经济学院）；Samsung AI Center（三星人工智能中心）
Bayesian methods have been successfully applied to sparsify weights of neural networks and to remove structure units from the networks, e. g. neurons. We apply and further develop this approach for gated recurrent architectures. Specifically, in addition to sparsification of individual weights and neurons, we propose to sparsify preactivations of gates and information flow in LSTM. It makes some gates and information flow components constant, speeds up forward pass and improves compression. Moreover, the resulting structure of gate sparsity is interpretable and depends on the task. Code is ava…
Bayesian sparsification for deep neural networks with Bayesian model reduction
Technische Universität Dresden（德累斯顿工业大学）；University College London（伦敦大学学院）；Wellcome Centre for Human Neuroimaging（惠康人类神经成像中心）；Queen Square Institute of Neurology（皇后广场神经病学研究所）；VERSES AI Research Lab（VERSES AI研究实验室）；Centre for Tactile Internet with Human-in-the-Loop (CeTI)（以人为中心的触觉互联网中心）
National Research University Higher School of Economics（国立研究大学高等经济学院）；Kaspersky Lab（卡巴斯基实验室）；Lomonosov Moscow State University（莫斯科国立大学）；Yandex
Recurrent neural networks show state-of-the-art results in many text analysis tasks but often require a lot of memory to store their weights. Recently proposed Sparse Variational Dropout eliminates the majority of the weights in a feed-forward neural network without significant loss of quality. We apply this technique to sparsify recurrent neural networks. To account for recurrent specifics we also rely on Binary Variational Dropout for RNN. We report 99.5% sparsity level on sentiment analysis task without a quality drop and up to 87% sparsity level on language modeling task with slight loss o…
With continual miniaturization ever more applications of deep learning can be found in embedded systems, where it is common to encounter data with natural complex domain representation. To this end we extend Sparse Variational Dropout to complex-valued neural networks and verify the proposed Bayesian technique by conducting a large numerical study of the performance-compression trade-off of C-valued networks on two tasks: image recognition on MNIST-like and CIFAR10 datasets and music transcription on MusicNet. We replicate the state-of-the-art result by Trabelsi et al. [2018] on MusicNet with …
Shapley-Value-Based Graph Sparsification for GNN Inference
Department of Intelligent Systems Engineering Indiana University Bloomington Bloomington Indiana USA；Department of Computer Science \& Engineering Texas A\&M University College Station Texas USA；Indiana University Bloomington；Texas A\&M University
Shaving Weights with Occam's Razor: Bayesian Sparsification for Neural Networks Using the Marginal Likelihood
Technical University of Munich（慕尼黑工业大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；ETH Zürich（苏黎世联邦理工学院）；Max Planck Institute for Intelligent Systems, Tübingen（马克斯·普朗克智能系统研究所（蒂宾根））；Pruna AI（Pruna AI公司）；Helmholtz AI, Munich（亥姆霍兹人工智能研究所（慕尼黑））
National Research University Higher School of Economics（国立研究型大学高等经济学院）；Samsung AI Center（三星人工智能中心）
In natural language processing, a lot of the tasks are successfully solved with recurrent neural networks, but such models have a huge number of parameters. The majority of these parameters are often concentrated in the embedding layer, which size grows proportionally to the vocabulary length. We propose a Bayesian sparsification technique for RNNs which allows compressing the RNN dozens or hundreds of times without time-consuming hyperparameters tuning. We also generalize the model for vocabulary sparsification to filter out unnecessary words and compress the RNN even further. We show that th…
Georgia Institute of Technology（佐治亚理工学院）；IQVIA（艾昆纬）；University of Illinois, Urbana-Champagne（伊利诺伊大学厄巴纳-香槟分校）
The attention mechanism has demonstrated superior performance for inference over nodes in graph neural networks (GNNs), however, they result in a high computational burden during both training and inference. We propose FastGAT, a method to make attention based GNNs lightweight by using spectral sparsification to generate an optimal pruning of the input graph. This results in a per-epoch time that is almost linear in the number of graph nodes as opposed to quadratic. We theoretically prove that spectral sparsification preserves the features computed by the GAT model, thereby justifying our algo…
Training deep neural networks with an $L_0$ regularization is one of the prominent approaches for network pruning or sparsification. The method prunes the network during training by encouraging weights to become exactly zero. However, recent work of Gale et al. reveals that although this method yields high compression rates on smaller datasets, it performs inconsistently on large-scale learning tasks, such as ResNet50 on ImageNet. We analyze this phenomenon through the lens of variational inference and find that it is likely due to the independent modeling of binary gates, the mean-field appro…
Motivating Next-Gen Accelerators with Flexible (N:M) Activation Sparsity via Benchmarking Lightweight Post-Training Sparsification Approaches
Applied AI（应用人工智能）；Artificial Intelligence Research Institute（人工智能研究所）；HSE University（俄罗斯高等经济大学）；Sb AI Lab（Sb人工智能实验室）；MWS AI（MWS人工智能）；Yandex；Independent Researcher（独立研究者）
The Hong Kong University of Science and Technology（香港科技大学）
Weight pruning is an effective technique to reduce the model size and inference time for deep neural networks in real-world deployments. However, since magnitudes and relative importance of weights are very different for different layers of a neural network, existing methods rely on either manual tuning or handcrafted heuristic rules to find appropriate pruning rates individually for each layer. This approach generally leads to suboptimal performance. In this paper, by directly working on the probability space, we propose an effective network sparsification method called {\it probabilistic mas…
Northeastern University（东北大学）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）；Princeton University（普林斯顿大学）；Dalian University of Technology（大连理工大学）
Deep neural networks (DNNs) are effective in solving many real-world problems. Larger DNN models usually exhibit better quality (e.g., accuracy) but their excessive computation results in long inference time. Model sparsification can reduce the computation and memory cost while maintaining model quality. Most existing sparsification algorithms unidirectionally remove weights, while others randomly or greedily explore a small subset of weights in each layer for pruning. The limitations of these algorithms reduce the level of achievable sparsity. In addition, many algorithms still require pre-tr…
Wellcome Centre for Human Neuroimaging, University College London（伦敦大学学院威康人类神经影像中心）；Department of Mathematics, Imperial College London（伦敦帝国理工学院数学系）
Active inference, a corollary of the free energy principle, is a formal way of describing the behavior of certain kinds of random dynamical systems that have the appearance of sentience. In this chapter, we describe how active inference combines Bayesian decision theory and optimal Bayesian design principles under a single imperative to minimize expected free energy. It is this aspect of active inference that allows for the natural emergence of information-seeking behavior. When removing prior outcomes preferences from expected free energy, active inference reduces to optimal Bayesian design, …
The notion of Craig interpolant, used as a form of explanation in automated reasoning, is adapted from logical inference to statistical inference and used to explain inferences made by neural networks. The method produces explanations that are at the same time concise, understandable and precise.
Modern deep neural network models suffer from adversarial examples, i.e. confidently misclassified points in the input space. It has been shown that Bayesian neural networks are a promising approach for detecting adversarial points, but careful analysis is problematic due to the complexity of these models. Recently Gilmer et al. (2018) introduced adversarial spheres, a toy set-up that simplifies both practical and theoretical analysis of the problem. In this work, we use the adversarial sphere set-up to understand the properties of approximate Bayesian inference methods for a linear model in a…
University College of London（伦敦大学学院）；Athens University of Economics and Business（雅典经济与商业大学）；The Alan Turing Institute（艾伦·图灵研究所）
We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states and the static parameters of the model. We build up on recent advances in computational statistics that combine variational methods with sequential Monte Carlo sampling and we demonstrate the advantages of performing full Bayesian inference over the static parameters rather than just performing variational EM approximations. We illustrate how our approach e…
We propose a Bayesian approach for both medical inquiry and disease inference, the two major phases in differential diagnosis. Unlike previous work that simulates data from given probabilities and uses ML algorithms on them, we directly use the Quick Medical Reference (QMR) belief network, and apply Bayesian inference in the inference phase and Bayesian experimental design in the inquiry phase. Moreover, we improve the inquiry phase by extending the Bayesian experimental design framework from one-step search to multi-step search. Our approach has some practical advantages as it is interpretabl…
University of Cambridge（剑桥大学）；IT University of Copenhagen（哥本哈根信息技术大学）
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synt…
Balliol College（贝利奥尔学院）；University of Oxford（牛津大学）
Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They create a binary split in which all approximate inference is equally 'irrational'. Instead, we should ask ourselves how to define a spectrum of more- and less-rational reasoning that explains why we might prefer one Bayesian approximation to another. I explore approximate inference in Bayesian neural networks and consider the unintended interactions between th…
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and utilizes the expected improvement idea from Bayesian global optimization. We adaptively construct training designs by maximizing the expected improvement in fit of the Gaussian process model to the noisy observational data. Numerical experiments on model problems with synthetic data demonstrate the effectiveness of the obtained adaptive designs compared to the…
We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies demonstrate that the proposed density estimates have excellent comparative performance and scale well to very large sample sizes due to a binning strategy. Moreover, the approach is fully Bayesian and all estimates are accompanied by pointwise credible intervals. An accompanying package in the R language facilitates easy use of the new density estimates.
Harvard University（哈佛大学）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive uncertainty estimates for 10 common inference methods on both regression and classification tasks. Our experiments demonstrate that commonly used metrics (e.g. test log-likelihood) can be misleading. Our experiments also indicate that inference innovations designed to capture structure in the posterior do not necessarily produce high quality posterior approxi…
In this work, we use a combination of Bayesian inference, Markov chain Monte Carlo and deep learning in the form of LSTM autoencoders to build and test a framework to provide robust estimates of injection rate from ground surface data in coupled flow and geomechanics problems. We use LSTM autoencoders to reconstruct the displacement time series for grid points on the top surface of a faulting due to water injection problem. We then deploy this LSTM autoencoder based model instead of the high fidelity model in the Bayesian inference framework to estimate injection rate from displacement input.
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be utilised during inference. This paper thus introduces a method for transforming between a gamma distributed precision parameter and the distribution of the associated standard deviation. The proposed method is based on numerical optimisation and shows adequate results for a wide range of scenarios.
INRIA Paris - École Normale Supérieure（法国国家信息与自动化研究所巴黎分部 - 巴黎高等师范学院）；Google（谷歌）
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanation to the Bayesian Occam's razor criteria, under the assumption that the data is generated by an i.i.d distribution. Moreover, as the negative log-likelihood is an unbounded loss function, we motivate and propose a PAC-Bayesian theorem tailored for the sub-gamma loss family, and w…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；University of Helsinki（赫尔辛基大学）
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to incorrect posterior predictive distributions. We present a novel approach that corrects for inaccuracies in posterior inference by altering the decision-making process. We train a separate model to make optimal decisions under the approximate posterior, combining interpretable Bayesian modeling with optimization of direct predictive accuracy in a principled fas…
Davidson College（戴维森学院）；University of Maryland（马里兰大学）；Florida State University（佛罗里达州立大学）
TensorBNN is a new package based on TensorFlow that implements Bayesian inference for modern neural network models. The posterior density of neural network model parameters is represented as a point cloud sampled using Hamiltonian Monte Carlo. The TensorBNN package leverages TensorFlow's architecture and training features as well as its ability to use modern graphics processing units (GPU) in both the training and prediction stages.
University of Sydney（悉尼大学）；University of Science and Technology of China（中国科学技术大学）
The right to be forgotten has been legislated in many countries but the enforcement in machine learning would cause unbearable costs: companies may need to delete whole models learned from massive resources due to single individual requests. Existing works propose to remove the knowledge learned from the requested data via its influence function which is no longer naturally well-defined in Bayesian inference. This paper proposes a {\it Bayesian inference forgetting} (BIF) framework to realize the right to be forgotten in Bayesian inference. In the BIF framework, we develop forgetting algorithm…
College of Information and Computer Sciences（信息与计算机科学学院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly accounts for noise introduced by the privacy mechanism. It is efficient because it works only with sufficient statistics and not individual data. Unlike other methods, it gives properly calibrated posterior beliefs in the non-asymptotic data regime.
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large scale approximate Bayesian inference algorithm for linear models with non-factorial (latent tree-structured) scale mixture priors. Experimental results on a range of denoising and inpainting problems demonstrate substantially improved performance compared to MAP estimation or to …
The University of Melbourne（墨尔本大学）；Univ-Lille-3（里尔第三大学）；Chalmers University of Technology（查尔姆斯理工大学）
We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesian updates, either directly to the posterior parameters, or to their Fourier transform so as to preserve update consistency. We also utilise a recently introduced posterior sampling mechanism, for which we prove bounds for the specific but general case of discrete Bayesian network…
