Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network models for classical machine learning. In this work, we combine the ideas of matrix product state (MPS), the simplest tensor network structure, and residual neural network and propose the residual matrix product state (ResMPS). The ResMPS can be treated as a network where its layers map the "hidden" features to the outputs (e.g., classifications), and the variational parameters of the layers are the functions of the features of the samples (e.g., pixels of images). This is different from neural network, where the layers map feed-forwardly the features to the output. The ResMPS can equip with the non-linear activations and dropout layers, and outperforms the state-of-the-art tensor network models in terms of efficiency, stability, and expression power. Besides, ResMPS is interpretable from the perspective of polynomial expansion, where the factorization and exponential machines naturally emerge. Our work contributes to connecting and hybridizing neural and tensor networks, which is crucial to further enhance our understand of the working mechanisms and improve the performance of both models.
相關內容
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte Carlo estimators based on random Rademacher, sparse Rademacher, normalized and unnormalized Gaussian vectors, and to vectors with bounded fourth moments. The novel use of matrix concentration inequalities in our proofs represents a systematic model for future analyses. Our bounds mostly do not depend on the matrix dimension, target different error measures than existing work, and imply that the accuracy of the estimators increases with the diagonal dominance of the matrix. An application to derivative-based global sensitivity metrics corroborates this, as do numerical experiments on synthetic test matrices. We recommend against the use in practice of sparse Rademacher vectors, which are the basis for many randomized sketching and sampling algorithms, because they tend to deliver barely a digit of accuracy even under large sampling amounts.
To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as surrogate models obtained via a machine learning approach. Thanks to its physics-based structure, ensured by the use of a Galerkin projection of the full order model (FOM) onto a linear low-dimensional subspace, RB methods yield approximations that fulfill the physical problem at hand. However, to make the assembling of a ROM independent of the FOM dimension, intrusive and expensive hyper-reduction stages are usually required, such as the discrete empirical interpolation method (DEIM), thus making this strategy less feasible for problems characterized by (high-order polynomial or nonpolynomial) nonlinearities. To overcome this bottleneck, we propose a novel strategy for learning nonlinear ROM operators using deep neural networks (DNNs). The resulting hyper-reduced order model enhanced by deep neural networks, to which we refer to as Deep-HyROMnet, is then a physics-based model, still relying on the RB method approach, however employing a DNN architecture to approximate reduced residual vectors and Jacobian matrices once a Galerkin projection has been performed. Numerical results dealing with fast simulations in nonlinear structural mechanics show that Deep-HyROMnets are orders of magnitude faster than POD-Galerkin-DEIM ROMs, keeping the same level of accuracy.
Contrastive learning has seen increasing success in the fields of computer vision and information retrieval in recent years. This poster is the first work that applies contrastive learning to the task of product matching in e-commerce using product offers from different e-shops. More specifically, we employ a supervised contrastive learning technique to pre-train a Transformer encoder which is afterwards fine-tuned for the matching problem using pair-wise training data. We further propose a source-aware sampling strategy which enables contrastive learning to be applied for use cases in which the training data does not contain product idenifiers. We show that applying supervised contrastive pre-training in combination with source-aware sampling significantly improves the state-of-the art performance on several widely used benchmark datasets: For Abt-Buy, we reach an F1 of 94.29 (+3.24 compared to the previous state-of-the-art), for Amazon-Google 79.28 (+ 3.7). For WDC Computers datasets, we reach improvements between +0.8 and +8.84 F1 depending on the training set size. Further experiments with data augmentation and self-supervised contrastive pre-training show, that the former can be helpful for smaller training sets while the latter leads to a significant decline in performance due to inherent label-noise. We thus conclude that contrastive pre-training has a high potential for product matching use cases in which explicit supervision is available.
Convolutional neural networks typically contain several downsampling operators, such as strided convolutions or pooling layers, that progressively reduce the resolution of intermediate representations. This provides some shift-invariance while reducing the computational complexity of the whole architecture. A critical hyperparameter of such layers is their stride: the integer factor of downsampling. As strides are not differentiable, finding the best configuration either requires cross-validation or discrete optimization (e.g. architecture search), which rapidly become prohibitive as the search space grows exponentially with the number of downsampling layers. Hence, exploring this search space by gradient descent would allow finding better configurations at a lower computational cost. This work introduces DiffStride, the first downsampling layer with learnable strides. Our layer learns the size of a cropping mask in the Fourier domain, that effectively performs resizing in a differentiable way. Experiments on audio and image classification show the generality and effectiveness of our solution: we use DiffStride as a drop-in replacement to standard downsampling layers and outperform them. In particular, we show that introducing our layer into a ResNet-18 architecture allows keeping consistent high performance on CIFAR10, CIFAR100 and ImageNet even when training starts from poor random stride configurations. Moreover, formulating strides as learnable variables allows us to introduce a regularization term that controls the computational complexity of the architecture. We show how this regularization allows trading off accuracy for efficiency on ImageNet.
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, very much in the spirit of classical numerical analysis and statistical physics. We demonstrate that conventional machine learning models and algorithms, such as the random feature model, the shallow neural network model and the residual neural network model, can all be recovered as particular discretizations of different continuous formulations. We also present examples of new models, such as the flow-based random feature model, and new algorithms, such as the smoothed particle method and spectral method, that arise naturally from this continuous formulation. We discuss how the issues of generalization error and implicit regularization can be studied under this framework.
For many computer vision applications such as image captioning, visual question answering, and person search, learning discriminative feature representations at both image and text level is an essential yet challenging problem. Its challenges originate from the large word variance in the text domain as well as the difficulty of accurately measuring the distance between the features of the two modalities. Most prior work focuses on the latter challenge, by introducing loss functions that help the network learn better feature representations but fail to account for the complexity of the textual input. With that in mind, we introduce TIMAM: a Text-Image Modality Adversarial Matching approach that learns modality-invariant feature representations using adversarial and cross-modal matching objectives. In addition, we demonstrate that BERT, a publicly-available language model that extracts word embeddings, can successfully be applied in the text-to-image matching domain. The proposed approach achieves state-of-the-art cross-modal matching performance on four widely-used publicly-available datasets resulting in absolute improvements ranging from 2% to 5% in terms of rank-1 accuracy.
We present Residual Policy Learning (RPL): a simple method for improving nondifferentiable policies using model-free deep reinforcement learning. RPL thrives in complex robotic manipulation tasks where good but imperfect controllers are available. In these tasks, reinforcement learning from scratch remains data-inefficient or intractable, but learning a residual on top of the initial controller can yield substantial improvement. We study RPL in five challenging MuJoCo tasks involving partial observability, sensor noise, model misspecification, and controller miscalibration. By combining learning with control algorithms, RPL can perform long-horizon, sparse-reward tasks for which reinforcement learning alone fails. Moreover, we find that RPL consistently and substantially improves on the initial controllers. We argue that RPL is a promising approach for combining the complementary strengths of deep reinforcement learning and robotic control, pushing the boundaries of what either can achieve independently.
Asynchronous distributed machine learning solutions have proven very effective so far, but always assuming perfectly functioning workers. In practice, some of the workers can however exhibit Byzantine behavior, caused by hardware failures, software bugs, corrupt data, or even malicious attacks. We introduce \emph{Kardam}, the first distributed asynchronous stochastic gradient descent (SGD) algorithm that copes with Byzantine workers. Kardam consists of two complementary components: a filtering and a dampening component. The first is scalar-based and ensures resilience against $\frac{1}{3}$ Byzantine workers. Essentially, this filter leverages the Lipschitzness of cost functions and acts as a self-stabilizer against Byzantine workers that would attempt to corrupt the progress of SGD. The dampening component bounds the convergence rate by adjusting to stale information through a generic gradient weighting scheme. We prove that Kardam guarantees almost sure convergence in the presence of asynchrony and Byzantine behavior, and we derive its convergence rate. We evaluate Kardam on the CIFAR-100 and EMNIST datasets and measure its overhead with respect to non Byzantine-resilient solutions. We empirically show that Kardam does not introduce additional noise to the learning procedure but does induce a slowdown (the cost of Byzantine resilience) that we both theoretically and empirically show to be less than $f/n$, where $f$ is the number of Byzantine failures tolerated and $n$ the total number of workers. Interestingly, we also empirically observe that the dampening component is interesting in its own right for it enables to build an SGD algorithm that outperforms alternative staleness-aware asynchronous competitors in environments with honest workers.
Interest point descriptors have fueled progress on almost every problem in computer vision. Recent advances in deep neural networks have enabled task-specific learned descriptors that outperform hand-crafted descriptors on many problems. We demonstrate that commonly used metric learning approaches do not optimally leverage the feature hierarchies learned in a Convolutional Neural Network (CNN), especially when applied to the task of geometric feature matching. While a metric loss applied to the deepest layer of a CNN, is often expected to yield ideal features irrespective of the task, in fact the growing receptive field as well as striding effects cause shallower features to be better at high precision matching tasks. We leverage this insight together with explicit supervision at multiple levels of the feature hierarchy for better regularization, to learn more effective descriptors in the context of geometric matching tasks. Further, we propose to use activation maps at different layers of a CNN, as an effective and principled replacement for the multi-resolution image pyramids often used for matching tasks. We propose concrete CNN architectures employing these ideas, and evaluate them on multiple datasets for 2D and 3D geometric matching as well as optical flow, demonstrating state-of-the-art results and generalization across datasets.
Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to maximize the translation performance. The models proposed recently for neural machine translation often belong to a family of encoder-decoders and consists of an encoder that encodes a source sentence into a fixed-length vector from which a decoder generates a translation. In this paper, we conjecture that the use of a fixed-length vector is a bottleneck in improving the performance of this basic encoder-decoder architecture, and propose to extend this by allowing a model to automatically (soft-)search for parts of a source sentence that are relevant to predicting a target word, without having to form these parts as a hard segment explicitly. With this new approach, we achieve a translation performance comparable to the existing state-of-the-art phrase-based system on the task of English-to-French translation. Furthermore, qualitative analysis reveals that the (soft-)alignments found by the model agree well with our intuition.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191