Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the similarity constraints, and initially ignoring the features, we are able to learn target vectors for each instance using one of several appropriately designed loss functions. A regression model can then be constructed that maps novel feature vectors to the same target vector space, resulting in a feature extractor that computes vectors for which a predefined metric is a meaningful measure of similarity. We present results on both multiclass and multi-label classification datasets that demonstrate considerably faster convergence, as well as higher accuracy on the majority of the intrinsic evaluation tasks and all extrinsic evaluation tasks.
There is also an extension of NCA to nonlinear transformations of the input data @cite_16 . This method can be viewed as a probabilistic variant of Siamese networks. The nonlinear transformation models used in the original exposition of this method were stacked Restricted Boltzmann Machines, initialised using unsupervised pretraining and subsequently fine-tuned using the NCA loss function.
@cite_16
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Nowadays model based techniques play very important role in solving measurement and control problems. Recently for representing nonlinear systems fuzzy and neural network (NN) models became very popular. For evaluating measurement data and for controller design also the inverse models are of considerable interest. In this paper, different observer based techniques to perform fuzzy and neural network model inversion are presented. The methods are based on solving a nonlinear equation derived from the multiple-input single-output (MISO) forward fuzzy model simple by interchanging the role of the output and one of the inputs. The utilization of the inverse model can be either a direct compensation of some measurement nonlinearities or a controller mechanism for nonlinear plants. For discrete-time inputs the technique provides good performance if the iterative inversion is fast enough compared to system variations, i.e., the iteration is convergent within the sampling period applied. The proposed method can be considered also as a simple nonlinear state observer which reconstructs the selected input of the forward (fuzzy or NN) model from its output using an appropriate strategy and a copy of the fuzzy or neural network model itself. Improved performance can be obtained by introducing genetic algorithms in the prediction-correction mechanism. Although, the overall performance of the suggested technique is highly influenced by the nature of the non-linearity and the actual prediction-correction mechanism applied, it can also be shown that using this observer concept completely inverted models can be derived. The inversion can be extended towards anytime modes of operation, as well, providing short response time and flexibility during temporal loss of computational power and or time. The model parameters of convolutional neural networks (CNNs) are determined by backpropagation (BP). In this work, we propose an interpretable feedforward (FF) design without any BP as a reference. The FF design adopts a data-centric approach. It derives network parameters of the current layer based on data statistics from the output of the previous layer in a one-pass manner. To construct convolutional layers, we develop a new signal transform, called the Saab (Subspace Approximation with Adjusted Bias) transform. It is a variant of the principal component analysis (PCA) with an added bias vector to annihilate activation's nonlinearity. Multiple Saab transforms in cascade yield multiple convolutional layers. As to fully-connected (FC) layers, we construct them using a cascade of multi-stage linear least squared regressors (LSRs). The classification and robustness (against adversarial attacks) performances of BP- and FF-designed CNNs applied to the MNIST and the CIFAR-10 datasets are compared. Finally, we comment on the relationship between BP and FF designs. In this paper, we make two contributions to unsupervised domain adaptation (UDA) using the convolutional neural network (CNN). First, our approach transfers knowledge in all the convolutional layers through attention alignment. Most previous methods align high-level representations, e.g., activations of the fully connected (FC) layers. In these methods, however, the convolutional layers which underpin critical low-level domain knowledge cannot be updated directly towards reducing domain discrepancy. Specifically, we assume that the discriminative regions in an image are relatively invariant to image style changes. Based on this assumption, we propose an attention alignment scheme on all the target convolutional layers to uncover the knowledge shared by the source domain. Second, we estimate the posterior label distribution of the unlabeled data for target network training. Previous methods, which iteratively update the pseudo labels by the target network and refine the target network by the updated pseudo labels, are vulnerable to label estimation errors. Instead, our approach uses category distribution to calculate the cross-entropy loss for training, thereby ameliorating the error accumulation of the estimated labels. The two contributions allow our approach to outperform the state-of-the-art methods by +2.6 on the Office-31 dataset. Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Frechet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark. This paper aims to accelerate the test-time computation of convolutional neural networks (CNNs), especially very deep CNNs [1] that have substantially impacted the computer vision community. Unlike previous methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into account. We develop an effective solution to the resulting nonlinear optimization problem without the need of stochastic gradient descent (SGD). More importantly, while previous methods mainly focus on optimizing one or two layers, our nonlinear method enables an asymmetric reconstruction that reduces the rapidly accumulated error when multiple (e.g., @math 10) layers are approximated. For the widely used very deep VGG-16 model [1] , our method achieves a whole-model speedup of 4 @math with merely a 0.3 percent increase of top-5 error in ImageNet classification. Our 4 @math accelerated VGG-16 model also shows a graceful accuracy degradation for object detection when plugged into the Fast R-CNN detector [2] . Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the Frechet Inception Distance'' (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method. We propose a novel method called deep convolutional decision jungle (CDJ) and its learning algorithm for image classification. The CDJ maintains the structure of standard convolutional neural networks (CNNs), i.e. multiple layers of multiple response maps fully connected. Each response map-or node-in both the convolutional and fully-connected layers selectively respond to class labels s.t. each data sample travels via a specific soft route of those activated nodes. The proposed method CDJ automatically learns features, whereas decision forests and jungles require pre-defined feature sets. Compared to CNNs, the method embeds the benefits of using data-dependent discriminative functions, which better handles multi-modal heterogeneous data; further,the method offers more diverse sparse network responses, which in turn can be used for cost-effective learning classification. The network is learnt by combining conventional softmax and proposed entropy losses in each layer. The entropy loss,as used in decision tree growing, measures the purity of data activation according to the class label distribution. The back-propagation rule for the proposed loss function is derived from stochastic gradient descent (SGD) optimization of CNNs. We show that our proposed method outperforms state-of-the-art methods on three public image classification benchmarks and one face verification dataset. We also demonstrate the use of auxiliary data labels, when available, which helps our method to learn more discriminative routing and representations and leads to improved classification. Training energy-based probabilistic models is confronted with apparently intractable sums, whose Monte Carlo estimation requires sampling from the estimated probability distribution in the inner loop of training. This can be approximately achieved by Markov chain Monte Carlo methods, but may still face a formidable obstacle that is the difficulty of mixing between modes with sharp concentrations of probability. Whereas an MCMC process is usually derived from a given energy function based on mathematical considerations and requires an arbitrarily long time to obtain good and varied samples, we propose to train a deep directed generative model (not a Markov chain) so that its sampling distribution approximately matches the energy function that is being trained. Inspired by generative adversarial networks, the proposed framework involves training of two models that represent dual views of the estimated probability distribution: the energy function (mapping an input configuration to a scalar energy value) and the generator (mapping a noise vector to a generated configuration), both represented by deep neural networks. We develop a novel modeling framework for Boltzmann machines, augmenting each hidden unit with a latent transformation assignment variable which describes the selection of the transformed view of the canonical connection weights associated with the unit. This enables the inferences of the model to transform in response to transformed input data in a stable and predictable way, and avoids learning multiple features differing only with respect to the set of transformations. Extending prior work on translation equivariant (convolutional) models, we develop translation and rotation equivariant restricted Boltzmann machines (RBMs) and deep belief nets (DBNs), and demonstrate their effectiveness in learning frequently occurring statistical structure from artificial and natural images. This paper introduces a novel approach to the task of data association within the context of pedestrian tracking, by introducing a two-stage learning scheme to match pairs of detections. First, a Siamese convolutional neural network (CNN) is trained to learn descriptors encoding local spatio-temporal structures between the two input image patches, aggregating pixel values and optical flow information. Second, a set of contextual features derived from the position and size of the compared input patches are combined with the CNN output by means of a gradient boosting classifier to generate the final matching probability. This learning approach is validated by using a linear programming based multi-person tracker showing that even a simple and efficient tracker may outperform much more complex models when fed with our learned matching probabilities. Results on publicly available sequences show that our method meets state-of-the-art standards in multiple people tracking. This paper introduces a novel approach to the task of data association within the context of pedestrian tracking, by introducing a two-stage learning scheme to match pairs of detections. First, a Siamese convolutional neural network (CNN) is trained to learn descriptors encoding local spatio-temporal structures between the two input image patches, aggregating pixel values and optical flow information. Second, a set of contextual features derived from the position and size of the compared input patches are combined with the CNN output by means of a gradient boosting classifier to generate the final matching probability. This learning approach is validated by using a linear programming based multi-person tracker showing that even a simple and efficient tracker may outperform much more complex models when fed with our learned matching probabilities. Results on publicly available sequences show that our method meets state-of-the-art standards in multiple people tracking. Abstract The ability to make decisions based on quantities of interest that depend on variables inferred from measurement finds application in different fields of mechanics and physics. The evaluation of the inferred variables, and hence the quantities of interest, from the measurement typically requires the solution of an inverse problem. For example, in medical imaging the elastic heterogeneity of a tumor and its nonlinear elastic response can be used to distinguish benign tumors from their malignant counterparts. These images of linear and nonlinear elastic parameters of tissue are typically obtained by using a measured displacement field and solving a complex inverse elasticity problem. In this paper we consider circumventing the solution of the inverse problem by using measured displacements as input to a deep convolutional neural network (CNN) and training it to classify tumors on the basis of their elastic heterogeneity and nonlinearity. For a simple, 5-layer CNN trained with 8,000 samples for heterogeneity, and a 4-layer CNN trained with 4,000 samples for nonlinear elasticity we report classification accuracies in the range of 99 . 7 − 99 . 9 . The training and testing data are both obtained from the forward solution of finite element models of samples. We also analyze the weights of the trained model to understand the process through which the network extracts features of elastic moduli from the input displacement images. Finally, we apply the nonlinear elasticity classifier, which is trained entirely using simulated data, to displacement images obtained from ten patients with breast lesions and note that it correctly classifies eight out of ten cases. This application illustrates how data from physics-based models can be used in improving the performance of a data-driven algorithm in data-sparse scenarios. In this paper, we propose a novel method for image inpainting based on a Deep Convolutional Generative Adversarial Network (DCGAN). We define a loss function consisting of two parts: (1) a contextual loss that preserves similarity between the input corrupted image and the recovered image, and (2) a perceptual loss that ensures a perceptually realistic output image. Given a corrupted image with missing values, we use back-propagation on this loss to map the corrupted image to a smaller latent space. The mapped vector is then passed through the generative model to predict the missing content. The proposed framework is evaluated on the CelebA and SVHN datasets for two challenging inpainting tasks with random 80 corruption and large blocky corruption. Experiments show that our method can successfully predict semantic information in the missing region and achieve pixel-level photorealism, which is impossible by almost all existing methods. In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equivariance under translations and rotations by design. The proposed architecture employs steerable filters to efficiently compute orientation dependent responses for many orientations without suffering interpolation artifacts from filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize He's weight initialization scheme to filters which are defined as a linear combination of a system of atomic filters. Numerical experiments show a substantial enhancement of the sample complexity with a growing number of sampled filter orientations and confirm that the network generalizes learned patterns over orientations. The proposed approach achieves state-of-the-art on the rotated MNIST benchmark and on the ISBI 2012 2D EM segmentation challenge. Learning Convolutional Neural Networks (CNN) is commonly carried out by plain supervised gradient descent. With sufficient training data, this leads to very competitive results for visual recognition tasks when starting from a random initialization. When the amount of labeled data is limited, CNNs reveal their strong dependence on large amounts of training data. However, recent results have shown that a well chosen optimization starting point can be beneficial for convergence to a good generalizing minimum. This starting point was mostly found using unsupervised feature learning techniques such as sparse coding or transfer learning from related recognition tasks. In this work, we compare these two approaches against a simple patch based initialization scheme and a random initialization of the weights. We show that pre-training helps to train CNNs from few samples and that the correct choice of the initialization scheme can push the network's performance by up to 41 compared to random initialization. We present an approach to learn a dense pixel-wise labeling from image-level tags. Each image-level tag imposes constraints on the output labeling of a Convolutional Neural Network (CNN) classifier. We propose Constrained CNN (CCNN), a method which uses a novel loss function to optimize for any set of linear constraints on the output space (i.e. predicted label distribution) of a CNN. Our loss formulation is easy to optimize and can be incorporated directly into standard stochastic gradient descent optimization. The key idea is to phrase the training objective as a biconvex optimization for linear models, which we then relax to nonlinear deep networks. Extensive experiments demonstrate the generality of our new learning framework. The constrained loss yields state-of-the-art results on weakly supervised semantic image segmentation. We further demonstrate that adding slightly more supervision can greatly improve the performance of the learning algorithm. We present an approach to learn a dense pixel-wise labeling from image-level tags. Each image-level tag imposes constraints on the output labeling of a Convolutional Neural Network (CNN) classifier. We propose Constrained CNN (CCNN), a method which uses a novel loss function to optimize for any set of linear constraints on the output space (i.e. predicted label distribution) of a CNN. Our loss formulation is easy to optimize and can be incorporated directly into standard stochastic gradient descent optimization. The key idea is to phrase the training objective as a biconvex optimization for linear models, which we then relax to nonlinear deep networks. Extensive experiments demonstrate the generality of our new learning framework. The constrained loss yields state-of-the-art results on weakly supervised semantic image segmentation. We further demonstrate that adding slightly more supervision can greatly improve the performance of the learning algorithm. We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. The transition distribution of the Markov chain is conditional on the previous state, generally involving a small move, so this conditional distribution has fewer dominant modes, being unimodal in the limit of small moves. Thus, it is easier to learn because it is easier to approximate its partition function, more like learning to perform supervised function approximation, with gradients that can be obtained by backprop. We provide theorems that generalize recent work on the probabilistic interpretation of denoising autoencoders and obtain along the way an interesting justification for dependency networks and generalized pseudolikelihood, along with a definition of an appropriate joint distribution and sampling mechanism even when the conditionals are not consistent. GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. We validate these theoretical results with experiments on two image datasets using an architecture that mimics the Deep Boltzmann Machine Gibbs sampler but allows training to proceed with simple backprop, without the need for layerwise pretraining. In this paper, we use dynamical system to analyze the nonlinear weight dynamics of two-layered bias-free networks in the form of @math , where @math is ReLU nonlinearity. We assume that the input @math follow Gaussian distribution. The network is trained using gradient descent to mimic the output of a teacher network of the same size with fixed parameters @math using @math loss. We first show that when @math , the nonlinear dynamics can be written in close form, and converges to @math with at least @math probability, if random weight initializations of proper standard derivation ( @math ) is used, verifying empirical practice. For networks with many ReLU nodes ( @math ), we apply our close form dynamics and prove that when the teacher parameters @math forms orthonormal bases, (1) a symmetric weight initialization yields a convergence to a saddle point and (2) a certain symmetry-breaking weight initialization yields global convergence to @math without local minima. To our knowledge, this is the first proof that shows global convergence in nonlinear neural network without unrealistic assumptions on the independence of ReLU activations. In addition, we also give a concise gradient update formulation for a multilayer ReLU network when it follows a teacher of the same size with @math loss. Simulations verify our theoretical analysis.