Learning Layer-wise Equivariances Automatically using Gradients

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and can not be adapted. Our goal is to allow flexible symmetry constraints that can automatically be learned from data using gradients. Learning symmetry and associated weight connectivity structures from scratch is difficult for two reasons. First, it requires efficient and flexible parameterisations of layer-wise equivariances. Secondly, symmetries act as constraints and are therefore not encouraged by training losses measuring data fit. To overcome these challenges, we improve parameterisations of soft equivariance and learn the amount of equivariance in layers by optimising the marginal likelihood, estimated using differentiable Laplace approximations. The objective balances data fit and model complexity enabling layer-wise symmetry discovery in deep networks. We demonstrate the ability to automatically learn layer-wise equivariances on image classification tasks, achieving equivalent or improved performance over baselines with hard-coded symmetry

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Hierarchical learning : theory with applications in speech and vision

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 123-132).Over the past two decades several hierarchical learning models have been developed and applied to a diverse range of practical tasks with much success. Little is known, however, as to why such models work as well as they do. Indeed, most are difficult to analyze, and cannot be easily characterized using the established tools from statistical learning theory. In this thesis, we study hierarchical learning architectures from two complementary perspectives: one theoretical and the other empirical. The theoretical component of the thesis centers on a mathematical framework describing a general family of hierarchical learning architectures. The primary object of interest is a recursively defined feature map, and its associated kernel. The class of models we consider exploit the fact that data in a wide variety of problems satisfy a decomposability property. Paralleling the primate visual cortex, hierarchies are assembled from alternating filtering and pooling stages that build progressively invariant representations which are simultaneously selective for increasingly complex stimuli. A goal of central importance in the study of hierarchical architectures and the cortex alike, is that of understanding quantitatively the tradeoff between invariance and selectivity, and how invariance and selectivity contribute towards providing an improved representation useful for learning from data. A reasonable expectation is that an unsupervised hierarchical representation will positively impact the sample complexity of a corresponding supervised learning task.(cont.) We therefore analyze invariance and discrimination properties that emerge in particular instances of layered models described within our framework. A group-theoretic analysis leads to a concise set of conditions which must be met to establish invariance, as well as a constructive prescription for meeting those conditions. An information-theoretic analysis is then undertaken and seen as a means by which to characterize a model's discrimination properties. The empirical component of the thesis experimentally evaluates key assumptions built into the mathematical framework. In the case of images, we present simulations which support the hypothesis that layered architectures can reduce the sample complexity of a non-trivial learning problem. In the domain of speech, we describe a 3 localized analysis technique that leads to a noise-robust representation. The resulting biologically-motivated features are found to outperform traditional methods on a standard phonetic classification task in both clean and noisy conditions.by Jacob V. Bouvrie.Ph.D

Principles of Neural Network Architecture Design - Invertibility and Domain Knowledge

Neural networks architectures allow a tremendous variety of design choices. In this work, we study two principles underlying these architectures: First, the design and application of invertible neural networks (INNs). Second, the incorporation of domain knowledge into neural network architectures. After introducing the mathematical foundations of deep learning, we address the invertibility of standard feedforward neural networks from a mathematical perspective. These results serve as a motivation for our proposed invertible residual networks (i-ResNets). This architecture class is then studied in two scenarios: First, we propose ways to use i-ResNets as a normalizing flow and demonstrate the applicability for high-dimensional generative modeling. Second, we study the excessive invariance of common deep image classifiers and discuss consequences for adversarial robustness. We finish with a study of convolutional neural networks for tumor classification based on imaging mass spectrometry (IMS) data. For this application, we propose an adapted architecture guided by our knowledge of the domain of IMS data and show its superior performance on two challenging tumor classification datasets

ScatterNet Hybrid Frameworks for Deep Learning

Image understanding is the task of interpreting images by effectively solving the individual tasks of object recognition and semantic image segmentation. An image understanding system must have the capacity to distinguish between similar looking image regions while being invariant in its response to regions that have been altered by the appearance-altering transformation. The fundamental challenge for any such system lies within this simultaneous requirement for both invariance and specificity. Many image understanding systems have been proposed that capture geometric properties such as shapes, textures, motion and 3D perspective projections using filtering, non-linear modulus, and pooling operations. Deep learning networks ignore these geometric considerations and compute descriptors having suitable invariance and stability to geometric transformations using (end-to-end) learned multi-layered network filters. These deep learning networks in recent years have come to dominate the previously separate fields of research in machine learning, computer vision, natural language understanding and speech recognition. Despite the success of these deep networks, there remains a fundamental lack of understanding in the design and optimization of these networks which makes it difficult to develop them. Also, training of these networks requires large labeled datasets which in numerous applications may not be available. In this dissertation, we propose the ScatterNet Hybrid Framework for Deep Learning that is inspired by the circuitry of the visual cortex. The framework uses a hand-crafted front-end, an unsupervised learning based middle-section, and a supervised back-end to rapidly learn hierarchical features from unlabelled data. Each layer in the proposed framework is automatically optimized to produce the desired computationally efficient architecture. The term `Hybrid' is coined because the framework uses both unsupervised as well as supervised learning. We propose two hand-crafted front-ends that can extract locally invariant features from the input signals. Next, two ScatterNet Hybrid Deep Learning (SHDL) networks (a generative and a deterministic) were introduced by combining the proposed front-ends with two unsupervised learning modules which learn hierarchical features. These hierarchical features were finally used by a supervised learning module to solve the task of either object recognition or semantic image segmentation. The proposed front-ends have also been shown to improve the performance and learning of current Deep Supervised Learning Networks (VGG, NIN, ResNet) with reduced computing overhead

画像認識における物体の空間共起性及び回転特性に基づく特徴抽出

筑波大学 (University of Tsukuba)201

Local Binary Pattern based algorithms for the discrimination and detection of crops and weeds with similar morphologies

In cultivated agricultural fields, weeds are unwanted species that compete with the crop plants for nutrients, water, sunlight and soil, thus constraining their growth. Applying new real-time weed detection and spraying technologies to agriculture would enhance current farming practices, leading to higher crop yields and lower production costs. Various weed detection methods have been developed for Site-Specific Weed Management (SSWM) aimed at maximising the crop yield through efficient control of weeds. Blanket application of herbicide chemicals is currently the most popular weed eradication practice in weed management and weed invasion. However, the excessive use of herbicides has a detrimental impact on the human health, economy and environment. Before weeds are resistant to herbicides and respond better to weed control strategies, it is necessary to control them in the fallow, pre-sowing, early post-emergent and in pasture phases. Moreover, the development of herbicide resistance in weeds is the driving force for inventing precision and automation weed treatments. Various weed detection techniques have been developed to identify weed species in crop fields, aimed at improving the crop quality, reducing herbicide and water usage and minimising environmental impacts. In this thesis, Local Binary Pattern (LBP)-based algorithms are developed and tested experimentally, which are based on extracting dominant plant features from camera images to precisely detecting weeds from crops in real time. Based on the efficient computation and robustness of the first LBP method, an improved LBP-based method is developed based on using three different LBP operators for plant feature extraction in conjunction with a Support Vector Machine (SVM) method for multiclass plant classification. A 24,000-image dataset, collected using a testing facility under simulated field conditions (Testbed system), is used for algorithm training, validation and testing. The dataset, which is published online under the name “bccr-segset”, consists of four subclasses: background, Canola (Brassica napus), Corn (Zea mays), and Wild radish (Raphanus raphanistrum). In addition, the dataset comprises plant images collected at four crop growth stages, for each subclass. The computer-controlled Testbed is designed to rapidly label plant images and generate the “bccr-segset” dataset. Experimental results show that the classification accuracy of the improved LBP-based algorithm is 91.85%, for the four classes. Due to the similarity of the morphologies of the canola (crop) and wild radish (weed) leaves, the conventional LBP-based method has limited ability to discriminate broadleaf crops from weeds. To overcome this limitation and complex field conditions (illumination variation, poses, viewpoints, and occlusions), a novel LBP-based method (denoted k-FLBPCM) is developed to enhance the classification accuracy of crops and weeds with similar morphologies. Our contributions include (i) the use of opening and closing morphological operators in pre-processing of plant images, (ii) the development of the k-FLBPCM method by combining two methods, namely, the filtered local binary pattern (LBP) method and the contour-based masking method with a coefficient k, and (iii) the optimal use of SVM with the radial basis function (RBF) kernel to precisely identify broadleaf plants based on their distinctive features. The high performance of this k-FLBPCM method is demonstrated by experimentally attaining up to 98.63% classification accuracy at four different growth stages for all classes of the “bccr-segset” dataset. To evaluate performance of the k-FLBPCM algorithm in real-time, a comparison analysis between our novel method (k-FLBPCM) and deep convolutional neural networks (DCNNs) is conducted on morphologically similar crops and weeds. Various DCNN models, namely VGG-16, VGG-19, ResNet50 and InceptionV3, are optimised, by fine-tuning their hyper-parameters, and tested. Based on the experimental results on the “bccr-segset” dataset collected from the laboratory and the “fieldtrip_can_weeds” dataset collected from the field under practical environments, the classification accuracies of the DCNN models and the k-FLBPCM method are almost similar. Another experiment is conducted by training the algorithms with plant images obtained at mature stages and testing them at early stages. In this case, the new k-FLBPCM method outperformed the state-of-the-art CNN models in identifying small leaf shapes of canola-radish (crop-weed) at early growth stages, with an order of magnitude lower error rates in comparison with DCNN models. Furthermore, the execution time of the k-FLBPCM method during the training and test phases was faster than the DCNN counterparts, with an identification time difference of approximately 0.224ms per image for the laboratory dataset and 0.346ms per image for the field dataset. These results demonstrate the ability of the k-FLBPCM method to rapidly detect weeds from crops of similar appearance in real time with less data, and generalize to different size plants better than the CNN-based methods