Convolution with even-sized kernels and symmetric padding

Compact convolutional neural networks gain efficiency mainly through depthwise convolutions, expanded channels and complex topologies, which contrarily aggravate the training process. Besides, 3x3 kernels dominate the spatial representation in these models, whereas even-sized kernels (2x2, 4x4) are rarely adopted. In this work, we quantify the shift problem occurs in even-sized kernel convolutions by an information erosion hypothesis, and eliminate it by proposing symmetric padding on four sides of the feature maps (C2sp, C4sp). Symmetric padding releases the generalization capabilities of even-sized kernels at little computational cost, making them outperform 3x3 kernels in image classification and generation tasks. Moreover, C2sp obtains comparable accuracy to emerging compact models with much less memory and time consumption during training. Symmetric padding coupled with even-sized convolutions can be neatly implemented into existing frameworks, providing effective elements for architecture designs, especially on online and continual learning occasions where training efforts are emphasized.Comment: 12 pages, 4 figures, 4 table

A Computationally Efficient Neural Network Invariant to the Action of Symmetry Subgroups

We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element of the proposed network architecture is a new $G$-invariant transformation module, which produces a $G$-invariant latent representation of the input data. This latent representation is then processed with a multi-layer perceptron in the network. We prove the universality of the proposed architecture, discuss its properties and highlight its computational and memory efficiency. Theoretical considerations are supported by numerical experiments involving different network configurations, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other $G$-invariant neural networks

On the Expressive Power of Deep Learning: A Tensor Analysis

It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast empirical evidence supporting this belief, theoretical justifications to date are limited. In particular, they do not account for the locality, sharing and pooling constructs of convolutional networks, the most successful deep learning architecture to date. In this work we derive a deep network architecture based on arithmetic circuits that inherently employs locality, sharing and pooling. An equivalence between the networks and hierarchical tensor factorizations is established. We show that a shallow network corresponds to CP (rank-1) decomposition, whereas a deep network corresponds to Hierarchical Tucker decomposition. Using tools from measure theory and matrix algebra, we prove that besides a negligible set, all functions that can be implemented by a deep network of polynomial size, require exponential size in order to be realized (or even approximated) by a shallow network. Since log-space computation transforms our networks into SimNets, the result applies directly to a deep learning architecture demonstrating promising empirical performance. The construction and theory developed in this paper shed new light on various practices and ideas employed by the deep learning community

S-Net: A Scalable Convolutional Neural Network for JPEG Compression Artifact Reduction

Recent studies have used deep residual convolutional neural networks (CNNs) for JPEG compression artifact reduction. This study proposes a scalable CNN called S-Net. Our approach effectively adjusts the network scale dynamically in a multitask system for real-time operation with little performance loss. It offers a simple and direct technique to evaluate the performance gains obtained with increasing network depth, and it is helpful for removing redundant network layers to maximize the network efficiency. We implement our architecture using the Keras framework with the TensorFlow backend on an NVIDIA K80 GPU server. We train our models on the DIV2K dataset and evaluate their performance on public benchmark datasets. To validate the generality and universality of the proposed method, we created and utilized a new dataset, called WIN143, for over-processed images evaluation. Experimental results indicate that our proposed approach outperforms other CNN-based methods and achieves state-of-the-art performance.Comment: accepted by Journal of Electronic Imagin

PZnet: Efficient 3D ConvNet Inference on Manycore CPUs

Convolutional nets have been shown to achieve state-of-the-art accuracy in many biomedical image analysis tasks. Many tasks within biomedical analysis domain involve analyzing volumetric (3D) data acquired by CT, MRI and Microscopy acquisition methods. To deploy convolutional nets in practical working systems, it is important to solve the efficient inference problem. Namely, one should be able to apply an already-trained convolutional network to many large images using limited computational resources. In this paper we present PZnet, a CPU-only engine that can be used to perform inference for a variety of 3D convolutional net architectures. PZNet outperforms MKL-based CPU implementations of PyTorch and Tensorflow by more than 3.5x for the popular U-net architecture. Moreover, for 3D convolutions with low featuremap numbers, cloud CPU inference with PZnet outperfroms cloud GPU inference in terms of cost efficiency

Bootstrapping Deep Neural Networks from Approximate Image Processing Pipelines

Complex image processing and computer vision systems often consist of a processing pipeline of functional modules. We intend to replace parts or all of a target pipeline with deep neural networks to achieve benefits such as increased accuracy or reduced computational requirement. To acquire a large amount of labeled data necessary to train the deep neural network, we propose a workflow that leverages the target pipeline to create a significantly larger labeled training set automatically, without prior domain knowledge of the target pipeline. We show experimentally that despite the noise introduced by automated labeling and only using a very small initially labeled data set, the trained deep neural networks can achieve similar or even better performance than the components they replace, while in some cases also reducing computational requirements.Comment: 6 pages, 5 figure

Solving Many-Electron Schr\"odinger Equation Using Deep Neural Networks

We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schr\"odinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the ground-states of the tested systems, including He, H2, Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schr\"odinger equation

A theoretical basis for efficient computations with noisy spiking neurons

Network of neurons in the brain apply - unlike processors in our current generation of computer hardware - an event-based processing strategy, where short pulses (spikes) are emitted sparsely by neurons to signal the occurrence of an event at a particular point in time. Such spike-based computations promise to be substantially more power-efficient than traditional clocked processing schemes. However it turned out to be surprisingly difficult to design networks of spiking neurons that are able to carry out demanding computations. We present here a new theoretical framework for organizing computations of networks of spiking neurons. In particular, we show that a suitable design enables them to solve hard constraint satisfaction problems from the domains of planning - optimization and verification - logical inference. The underlying design principles employ noise as a computational resource. Nevertheless the timing of spikes (rather than just spike rates) plays an essential role in the resulting computations. Furthermore, one can demonstrate for the Traveling Salesman Problem a surprising computational advantage of networks of spiking neurons compared with traditional artificial neural networks and Gibbs sampling. The identification of such advantage has been a well-known open problem.Comment: main paper: 21 pages, 5 figures supplemental paper: 11 pages, no figure

Chaotic Simulated Annealing by A Neural Network Model with Transient Chaos

We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks. Unlike conventional neural networks only with point attractors, the proposed neural network has richer and more flexible dynamics, so that it can be expected to have higher ability of searching for globally optimal or near-optimal solutions. A significant property of this model is that the chaotic neurodynamics is temporarily generated for searching and self-organizing, and eventually vanishes with autonomous decreasing of a bifurcation parameter corresponding to the "temperature" in usual annealing process. Therefore, the neural network gradually approaches, through the transient chaos, to dynamical structure similar to such conventional models as the Hopfield neural network which converges to a stable equilibrium point. Since the optimization process of the transiently chaotic neural network is similar to simulated annealing, not in a stochastic way but in a deterministically chaotic way, the new method is regarded as chaotic simulated annealing (CSA). Fundamental characteristics of the transiently chaotic neurodynamics are numerically investigated with examples of a single neuron model and the Traveling Salesman Problem (TSP). Moreover, a maintenance scheduling problem for generators in a practical power system is also analysed to verify practical efficiency of this new method.Comment: the theoretical results related to this paper should be referred to "Chaos and Asymptotical Stability in Discrete-time Neural Networks" by L.Chen and K.Aihara, Physica D (in press). Journal ref.: Neural Networks, Vol.8, No.6, pp.915-930, 199

Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement

The purpose of this paper is to study the problem of computing unitary eigenvalues (U-eigenvalues) of non-symmetric complex tensors. By means of symmetric embedding of complex tensors, the relationship between U-eigenpairs of a non-symmetric complex tensor and unitary symmetric eigenpairs (US-eigenpairs) of its symmetric embedding tensor is established. An algorithm (Algorithm \ref{algo:1}) is given to compute the U-eigenvalues of non-symmetric complex tensors by means of symmetric embedding. Another algorithm, Algorithm \ref{algo:2}, is proposed to directly compute the U-eigenvalues of non-symmetric complex tensors, without the aid of symmetric embedding. Finally, a tensor version of the well-known Gauss-Seidel method is developed. Efficiency of these three algorithms are compared by means of various numerical examples. These algorithms are applied to compute the geometric measure of entanglement of quantum multipartite non-symmetric pure states.Comment: 19 pages; submitted for publication; comments are welcom