arXiv subjects

Stefano Soatto

Publications and source records attributed to Stefano Soatto.

At least 199 records · Page 11Linked to original sources

arXiv2017

Classification regions of deep neural networks

The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. Through a systematic empirical investigation, we show that state-of-the-art deep nets learn connected classification regions, and that the decision boundary in the vicinity of datapoints is flat along most directions. We further draw an essential connection between two seemingly unrelated properties of deep networks: their sensitivity to additive perturbations in the inputs, and the curvature of their decision boundary. The directions where the decision boundary is curved in fact remarkably characterize the directions to which the classifier is the most vulnerable. We finally leverage a fundamental asymmetry in the curvature of the decision boundary of deep nets, and propose a method to discriminate between original images, and images perturbed with small adversarial examples. We show the effectiveness of this purely geometric approach for detecting small adversarial perturbations in images, and for recovering the labels of perturbed images.

cs.CV↗

arXiv2017

Adaptive Regularization of Some Inverse Problems in Image Analysis

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce the use of a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.

cs.CV↗

arXiv2017

On the energy landscape of deep networks

We introduce "AnnealSGD", a regularized stochastic gradient descent algorithm motivated by an analysis of the energy landscape of a particular class of deep networks with sparse random weights. The loss function of such networks can be approximated by the Hamiltonian of a spherical spin glass with Gaussian coupling. While different from currently-popular architectures such as convolutional ones, spin glasses are amenable to analysis, which provides insights on the topology of the loss function and motivates algorithms to minimize it. Specifically, we show that a regularization term akin to a magnetic field can be modulated with a single scalar parameter to transition the loss function from a complex, non-convex landscape with exponentially many local minima, to a phase with a polynomial number of minima, all the way down to a trivial landscape with a unique minimum. AnnealSGD starts training in the relaxed polynomial regime and gradually tightens the regularization parameter to steer the energy towards the original exponential regime. Even for convolutional neural networks, which are quite unlike sparse random networks, we empirically show that AnnealSGD improves the generalization error using competitive baselines on MNIST and CIFAR-10.

cs.LG↗

arXiv2017

Entropy-SGD: Biasing Gradient Descent Into Wide Valleys

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

cs.LG↗

arXiv2017

Visual-Inertial-Semantic Scene Representation for 3-D Object Detection

We describe a system to detect objects in three-dimensional space using video and inertial sensors (accelerometer and gyrometer), ubiquitous in modern mobile platforms from phones to drones. Inertials afford the ability to impose class-specific scale priors for objects, and provide a global orientation reference. A minimal sufficient representation, the posterior of semantic (identity) and syntactic (pose) attributes of objects in space, can be decomposed into a geometric term, which can be maintained by a localization-and-mapping filter, and a likelihood function, which can be approximated by a discriminatively-trained convolutional neural network. The resulting system can process the video stream causally in real time, and provides a representation of objects in the scene that is persistent: Confidence in the presence of objects grows with evidence, and objects previously seen are kept in memory even when temporarily occluded, with their return into view automatically predicted to prime re-detection.

cs.CV↗

arXiv2017

Multi-Label Segmentation via Residual-Driven Adaptive Regularization

We present a variational multi-label segmentation algorithm based on a robust Huber loss for both the data and the regularizer, minimized within a convex optimization framework. We introduce a novel constraint on the common areas, to bias the solution towards mutually exclusive regions. We also propose a regularization scheme that is adapted to the spatial statistics of the residual at each iteration, resulting in a varying degree of regularization being applied as the algorithm proceeds: the effect of the regularizer is strongest at initialization, and wanes as the solution increasingly fits the data. This minimizes the bias induced by the regularizer at convergence. We design an efficient convex optimization algorithm based on the alternating direction method of multipliers using the equivalent relation between the Huber function and the proximal operator of the one-norm. We empirically validate our proposed algorithm on synthetic and real images and offer an information-theoretic derivation of the cost-function that highlights the modeling choices made.

cs.CV↗

arXiv2017

Information Dropout: Learning Optimal Representations Through Noisy Computation

The cross-entropy loss commonly used in deep learning is closely related to the defining properties of optimal representations, but does not enforce some of the key properties. We show that this can be solved by adding a regularization term, which is in turn related to injecting multiplicative noise in the activations of a Deep Neural Network, a special case of which is the common practice of dropout. We show that our regularized loss function can be efficiently minimized using Information Dropout, a generalization of dropout rooted in information theoretic principles that automatically adapts to the data and can better exploit architectures of limited capacity. When the task is the reconstruction of the input, we show that our loss function yields a Variational Autoencoder as a special case, thus providing a link between representation learning, information theory and variational inference. Finally, we prove that we can promote the creation of disentangled representations simply by enforcing a factorized prior, a fact that has been observed empirically in recent work. Our experiments validate the theoretical intuitions behind our method, and we find that information dropout achieves a comparable or better generalization performance than binary dropout, especially on smaller models, since it can automatically adapt the noise to the structure of the network, as well as to the test sample.

stat.ML↗

arXiv2016

ShapeFit and ShapeKick for Robust, Scalable Structure from Motion

We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth.

cs.CV↗

arXiv2016

An Empirical Evaluation of Current Convolutional Architectures' Ability to Manage Nuisance Location and Scale Variability

We conduct an empirical study to test the ability of Convolutional Neural Networks (CNNs) to reduce the effects of nuisance transformations of the input data, such as location, scale and aspect ratio. We isolate factors by adopting a common convolutional architecture either deployed globally on the image to compute class posterior distributions, or restricted locally to compute class conditional distributions given location, scale and aspect ratios of bounding boxes determined by proposal heuristics. In theory, averaging the latter should yield inferior performance compared to proper marginalization. Yet empirical evidence suggests the converse, leading us to conclude that - at the current level of complexity of convolutional architectures and scale of the data sets used to train them - CNNs are not very effective at marginalizing nuisance variability. We also quantify the effects of context on the overall classification task and its impact on the performance of CNNs, and propose improved sampling techniques for heuristic proposal schemes that improve end-to-end performance to state-of-the-art levels. We test our hypothesis on a classification task using the ImageNet Challenge benchmark and on a wide-baseline matching task using the Oxford and Fischer's datasets.

cs.CV↗

arXiv2016

Visual Representations: Defining Properties and Deep Approximations

Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of raw data with smallest complexity and no performance loss on the task at hand. Invariance guarantees that the statistic is constant with respect to uninformative transformations of the data. We derive analytical expressions for such representations and show they are related to feature descriptors commonly used in computer vision, as well as to convolutional neural networks. This link highlights the assumptions and approximations tacitly assumed by these methods and explains empirical practices such as clamping, pooling and joint normalization.

cs.CV↗

arXiv2016

A Theory of Local Matching: SIFT and Beyond

Why has SIFT been so successful? Why its extension, DSP-SIFT, can further improve SIFT? Is there a theory that can explain both? How can such theory benefit real applications? Can it suggest new algorithms with reduced computational complexity or new descriptors with better accuracy for matching? We construct a general theory of local descriptors for visual matching. Our theory relies on concepts in energy minimization and heat diffusion. We show that SIFT and DSP-SIFT approximate the solution the theory suggests. In particular, DSP-SIFT gives a better approximation to the theoretical solution; justifying why DSP-SIFT outperforms SIFT. Using the developed theory, we derive new descriptors that have fewer parameters and are potentially better in handling affine deformations.

cs.CV↗

arXiv2015

Domain-Size Pooling in Local Descriptors: DSP-SIFT

We introduce a simple modification of local image descriptors, such as SIFT, based on pooling gradient orientations across different domain sizes, in addition to spatial locations. The resulting descriptor, which we call DSP-SIFT, outperforms other methods in wide-baseline matching benchmarks, including those based on convolutional neural networks, despite having the same dimension of SIFT and requiring no training.

cs.CV↗

arXiv2015

Observability, Identifiability and Sensitivity of Vision-Aided Navigation

We analyze the observability of motion estimates from the fusion of visual and inertial sensors. Because the model contains unknown parameters, such as sensor biases, the problem is usually cast as a mixed identification/filtering, and the resulting observability analysis provides a necessary condition for any algorithm to converge to a unique point estimate. Unfortunately, most models treat sensor bias rates as noise, independent of other states including biases themselves, an assumption that is patently violated in practice. When this assumption is lifted, the resulting model is not observable, and therefore past analyses cannot be used to conclude that the set of states that are indistinguishable from the measurements is a singleton. In other words, the resulting model is not observable. We therefore re-cast the analysis as one of sensitivity: Rather than attempting to prove that the indistinguishable set is a singleton, which is not the case, we derive bounds on its volume, as a function of characteristics of the input and its sufficient excitation. This provides an explicit characterization of the indistinguishable set that can be used for analysis and validation purposes.

cs.RO↗

arXiv2015

Visual Scene Representations: Contrast, Scaling and Occlusion

We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical expressions for such representations and show that, under certain restrictive assumptions, they are related to features commonly in use in the computer vision community. This link highlights the condition tacitly assumed by these descriptors, and also suggests ways to improve and generalize them. This new interpretation draws connections to the classical theories of sampling, hypothesis testing and group invariance.

cs.CV↗

arXiv2015

Boosting Convolutional Features for Robust Object Proposals

Deep Convolutional Neural Networks (CNNs) have demonstrated excellent performance in image classification, but still show room for improvement in object-detection tasks with many categories, in particular for cluttered scenes and occlusion. Modern detection algorithms like Regions with CNNs (Girshick et al., 2014) rely on Selective Search (Uijlings et al., 2013) to propose regions which with high probability represent objects, where in turn CNNs are deployed for classification. Selective Search represents a family of sophisticated algorithms that are engineered with multiple segmentation, appearance and saliency cues, typically coming with a significant run-time overhead. Furthermore, (Hosang et al., 2014) have shown that most methods suffer from low reproducibility due to unstable superpixels, even for slight image perturbations. Although CNNs are subsequently used for classification in top-performing object-detection pipelines, current proposal methods are agnostic to how these models parse objects and their rich learned representations. As a result they may propose regions which may not resemble high-level objects or totally miss some of them. To overcome these drawbacks we propose a boosting approach which directly takes advantage of hierarchical CNN features for detecting regions of interest fast. We demonstrate its performance on ImageNet 2013 detection benchmark and compare it with state-of-the-art methods.

cs.CV↗

arXiv2014

Robust Inference for Visual-Inertial Sensor Fusion

Inference of three-dimensional motion from the fusion of inertial and visual sensory data has to contend with the preponderance of outliers in the latter. Robust filtering deals with the joint inference and classification task of selecting which data fits the model, and estimating its state. We derive the optimal discriminant and propose several approximations, some used in the literature, others new. We compare them analytically, by pointing to the assumptions underlying their approximations, and empirically. We show that the best performing method improves the performance of state-of-the-art visual-inertial sensor fusion systems, while retaining the same computational complexity.

cs.RO↗

arXiv2014

Cavlectometry: Towards Holistic Reconstruction of Large Mirror Objects

We introduce a method based on the deflectometry principle for the reconstruction of specular objects exhibiting significant size and geometric complexity. A key feature of our approach is the deployment of an Automatic Virtual Environment (CAVE) as pattern generator. To unfold the full power of this extraordinary experimental setup, an optical encoding scheme is developed which accounts for the distinctive topology of the CAVE. Furthermore, we devise an algorithm for detecting the object of interest in raw deflectometric images. The segmented foreground is used for single-view reconstruction, the background for estimation of the camera pose, necessary for calibrating the sensor system. Experiments suggest a significant gain of coverage in single measurements compared to previous methods. To facilitate research on specular surface reconstruction, we will make our data set publicly available.

cs.CV↗

arXiv2013

On the Design and Analysis of Multiple View Descriptors

We propose an extension of popular descriptors based on gradient orientation histograms (HOG, computed in a single image) to multiple views. It hinges on interpreting HOG as a conditional density in the space of sampled images, where the effects of nuisance factors such as viewpoint and illumination are marginalized. However, such marginalization is performed with respect to a very coarse approximation of the underlying distribution. Our extension leverages on the fact that multiple views of the same scene allow separating intrinsic from nuisance variability, and thus afford better marginalization of the latter. The result is a descriptor that has the same complexity of single-view HOG, and can be compared in the same manner, but exploits multiple views to better trade off insensitivity to nuisance variability with specificity to intrinsic variability. We also introduce a novel multi-view wide-baseline matching dataset, consisting of a mixture of real and synthetic objects with ground truthed camera motion and dense three-dimensional geometry.

cs.CV↗