While recent studies have shed light on the expressivity, complexity and compositionality of convolutional networks, the real inductive bias of the family of functions reachable by gradient descent on natural data is still unknown. By exploiting symmetries in the preactivation space of convolutional layers, we present preliminary empirical evidence of regularities in the preimage of trained rectifier networks, in terms of arrangements of polytopes, and relate it to the nonlinear transformations applied by the network to its input.

This paper provides an extensive study on the availability of image representations based on convolutional networks (ConvNets) for the task of visual instance retrieval.Besides the choice of convolutional layers, we present an efficient pipeline exploiting multi-scale schemes to extract local features, in particular, by taking geometric invariancc into explicit account, i.e.positions, scales and spatial consistency.In our experiments using five standard image retrieval datasets, we demonstrate that generic ConvNet image representations can outperform other state-of-the-art methods if they are extracted appropriately. 

The preimage of the activity at a certain level of a deep network is the set of inputs that result in the same node activity. For fully connected multi layer rectifier networks we demonstrate how to compute the preimages of activities at arbitrary levels from knowledge of the parameters in a deep rectifying network. If the preimage set of a certain activity in the network contains elements from more than one class it means that these classes are irreversibly mixed. This implies that preimage sets which are piecewise linear manifolds are building blocks for describing the input manifolds specific classes, ie all preimages should ideally be from the same class. We believe that the knowledge of how to compute preimages will be valuable in understanding the efficiency displayed by deep learning networks and could potentially be used in designing more efficient training algorithms.

Evidence is mounting that Convolutional Networks (ConvNets) are the most effective representation learning method for visual recognition tasks. In the common scenario, a ConvNet is trained on a large labeled dataset (source) and the feed-forward units activation of the trained network, at a certain layer of the network, is used as a generic representation of an input image for a task with relatively smaller training set (target). Recent studies have shown this form of representation transfer to be suitable for a wide range of target visual recognition tasks. This paper introduces and investigates several factors affecting the transferability of such representations. It includes parameters for training of the source ConvNet such as its architecture, distribution of the training data, etc. and also the parameters of feature extraction such as layer of the trained ConvNet, dimensionality reduction, etc. Then, by optimizing these factors, we show that significant improvements can be achieved on various (17) visual recognition tasks. We further show that these visual recognition tasks can be categorically ordered based on their similarity to the source task such that a correlation between the performance of tasks and their similarity to the source task w.r.t. the proposed factors is observed.

This paper provides an extensive study on the availability of image representations based on convolutional networks (ConvNets) for the task of visual instance retrieval. Besides the choice of convolutional layers, we present an efficient pipeline exploiting multi-scale schemes to extract local features, in particular, by taking geometric invariance into explicit account, i.e. positions, scales and spatial consistency. In our experiments using five standard image retrieval datasets, we demonstrate that generic ConvNet image representations can outperform other state-of-the-art methods if they are extracted appropriately.

Evidence is mounting that ConvNets are the best representation learning method for recognition. In the common scenario, a ConvNet is trained on a large labeled dataset and the feed-forward units activation, at a certain layer of the network, is used as a generic representation of an input image. Recent studies have shown this form of representation to be astoundingly effective for a wide range of recognition tasks. This paper thoroughly investigates the transferability of such representations w.r.t. several factors. It includes parameters for training the network such as its architecture and parameters of feature extraction. We further show that different visual recognition tasks can be categorically ordered based on their distance from the source task. We then show interesting results indicating a clear correlation between the performance of tasks and their distance from the source task conditioned on proposed factors. Furthermore, by optimizing these factors, we achieve stateof-the-art performances on 16 visual recognition tasks.

Supervised training of a convolutional network for object classification should make explicit any information related to the class of objects and disregard any auxiliary information associated with the capture of the image or thevariation within the object class. Does this happen in practice? Although this seems to pertain to the very final layers in the network, if we look at earlier layers we find that this is not the case. Surprisingly, strong spatial information is implicit. This paper addresses this, in particular, exploiting the image representation at the first fully connected layer,i.e. the global image descriptor which has been recently shown to be most effective in a range of visual recognition tasks. We empirically demonstrate evidences for the finding in the contexts of four different tasks: 2d landmark detection, 2d object keypoints prediction, estimation of the RGB values of input image, and recovery of semantic label of each pixel. We base our investigation on a simple framework with ridge rigression commonly across these tasks,and show results which all support our insight. Such spatial information can be used for computing correspondence of landmarks to a good accuracy, but should potentially be useful for improving the training of the convolutional nets for classification purposes.

Discriminative latent variable models (LVM) are frequently applied to various visualrecognition tasks. In these systems the latent (hidden) variables provide a formalism formodeling structured variation of visual features. Conventionally, latent variables are de-fined on the variation of the foreground (positive) class. In this work we augment LVMsto includenegativelatent variables corresponding to the background class. We formalizethe scoring function of such a generalized LVM (GLVM). Then we discuss a frameworkfor learning a model based on the GLVM scoring function. We theoretically showcasehow some of the current visual recognition methods can benefit from this generalization.Finally, we experiment on a generalized form of Deformable Part Models with negativelatent variables and show significant improvements on two different detection tasks.