arXiv subjects

Jiahao Su

Publications and source records attributed to Jiahao Su.

24 records · Page 2Linked to original sources

arXiv2021

Scaling-up Diverse Orthogonal Convolutional Networks with a Paraunitary Framework

Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heuristic, and the orthogonality of convolutional layers is not systematically studied: some of these designs are not exactly orthogonal, while others only consider standard convolutional layers and propose specific classes of their realizations. To address this problem, we propose a theoretical framework for orthogonal convolutional layers, which establishes the equivalence between various orthogonal convolutional layers in the spatial domain and the paraunitary systems in the spectral domain. Since there exists a complete spectral factorization of paraunitary systems, any orthogonal convolution layer can be parameterized as convolutions of spatial filters. Our framework endows high expressive power to various convolutional layers while maintaining their exact orthogonality. Furthermore, our layers are memory and computationally efficient for deep networks compared to previous designs. Our versatile framework, for the first time, enables the study of architecture designs for deep orthogonal networks, such as choices of skip connection, initialization, stride, and dilation. Consequently, we scale up orthogonal networks to deep architectures, including ResNet, WideResNet, and ShuffleNet, substantially increasing the performance over the traditional shallow orthogonal networks.

cs.LG↗

arXiv2020

Convolutional Tensor-Train LSTM for Spatio-temporal Learning

Learning from spatio-temporal data has numerous applications such as human-behavior analysis, object tracking, video compression, and physics simulation.However, existing methods still perform poorly on challenging video tasks such as long-term forecasting. This is because these kinds of challenging tasks require learning long-term spatio-temporal correlations in the video sequence. In this paper, we propose a higher-order convolutional LSTM model that can efficiently learn these correlations, along with a succinct representations of the history. This is accomplished through a novel tensor train module that performs prediction by combining convolutional features across time. To make this feasible in terms of computation and memory requirements, we propose a novel convolutional tensor-train decomposition of the higher-order model. This decomposition reduces the model complexity by jointly approximating a sequence of convolutional kernels asa low-rank tensor-train factorization. As a result, our model outperforms existing approaches, but uses only a fraction of parameters, including the baseline models.Our results achieve state-of-the-art performance in a wide range of applications and datasets, including the multi-steps video prediction on the Moving-MNIST-2and KTH action datasets as well as early activity recognition on the Something-Something V2 dataset.

cs.LG↗

arXiv2020

ARMA Nets: Expanding Receptive Field for Dense Prediction

Global information is essential for dense prediction problems, whose goal is to compute a discrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image classification, are restrictive in these problems since the filter size limits their receptive fields. In this work, we propose to replace any traditional convolutional layer with an autoregressive moving-average (ARMA) layer, a novel module with an adjustable receptive field controlled by the learnable autoregressive coefficients. Compared with traditional convolutional layers, our ARMA layer enables explicit interconnections of the output neurons and learns its receptive field by adapting the autoregressive coefficients of the interconnections. ARMA layer is adjustable to different types of tasks: for tasks where global information is crucial, it is capable of learning relatively large autoregressive coefficients to allow for an output neuron's receptive field covering the entire input; for tasks where only local information is required, it can learn small or near zero autoregressive coefficients and automatically reduces to a traditional convolutional layer. We show both theoretically and empirically that the effective receptive field of networks with ARMA layers (named as ARMA networks) expands with larger autoregressive coefficients. We also provably solve the instability problem of learning and prediction in the ARMA layer through a re-parameterization mechanism. Additionally, we demonstrate that ARMA networks substantially improve their baselines on challenging dense prediction tasks including video prediction and semantic segmentation.

cs.CV↗

arXiv2020

Understanding Generalization in Deep Learning via Tensor Methods

Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in neural networks from perspectives of PAC-Bayes, robustness, overparametrization, compression and so on. In this work, we advance the understanding of the relations between the network's architecture and its generalizability from the compression perspective. Using tensor analysis, we propose a series of intuitive, data-dependent and easily-measurable properties that tightly characterize the compressibility and generalizability of neural networks; thus, in practice, our generalization bound outperforms the previous compression-based ones, especially for neural networks using tensors as their weight kernels (e.g. CNNs). Moreover, these intuitive measurements provide further insights into designing neural network architectures with properties favorable for better/guaranteed generalizability. Our experimental results demonstrate that through the proposed measurable properties, our generalization error bound matches the trend of the test error well. Our theoretical analysis further provides justifications for the empirical success and limitations of some widely-used tensor-based compression approaches. We also discover the improvements to the compressibility and robustness of current neural networks when incorporating tensor operations via our proposed layer-wise structure.

cs.LG↗

arXiv2019

Sampling-Free Learning of Bayesian Quantized Neural Networks

Bayesian learning of model parameters in neural networks is important in scenarios where estimates with well-calibrated uncertainty are important. In this paper, we propose Bayesian quantized networks (BQNs), quantized neural networks (QNNs) for which we learn a posterior distribution over their discrete parameters. We provide a set of efficient algorithms for learning and prediction in BQNs without the need to sample from their parameters or activations, which not only allows for differentiable learning in QNNs, but also reduces the variance in gradients. We evaluate BQNs on MNIST, Fashion-MNIST, KMNIST and CIFAR10 image classification datasets, compared against bootstrap ensemble of QNNs (E-QNN). We demonstrate BQNs achieve both lower predictive errors and better-calibrated uncertainties than E-QNN (with less than 20% of the negative log-likelihood).

cs.LG↗

arXiv2018

Tensorial Neural Networks: Generalization of Neural Networks and Application to Model Compression

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds to hierarchical nonlinear tensor decomposition. We propose to solve the learning problem using stochastic gradient descent by deriving nontrivial backpropagation rules in generalized tensor algebra we introduce. Our proposed TNNs has three advantages over existing neural networks: (1) TNNs naturally apply to high order input object and thus preserve the multi-dimensional structure in the input, as there is no need to flatten the data. (2) TNNs interpret designs of existing neural network architectures. (3) Mapping a neural network to TNNs with the same expressive power results in a TNN of fewer parameters. TNN based compression of neural network improves existing low-rank approximation based compression methods as TNNs exploit two other types of invariant structures, periodicity and modulation, in addition to the low rankness. Experiments on LeNet-5 (MNIST), ResNet-32 (CIFAR10) and ResNet-50 (ImageNet) demonstrate that our TNN based compression outperforms (5% test accuracy improvement universally on CIFAR10) the state-of-the-art low-rank approximation based compression methods under the same compression rate, besides achieving orders of magnitude faster convergence rates due to the efficiency of TNNs.

stat.ML↗