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Arthur Szlam

Publications and source records attributed to Arthur Szlam.

At least 91 records · Page 5Linked to original sources
arXiv2016

MazeBase: A Sandbox for Learning from Games

This paper introduces MazeBase: an environment for simple 2D games, designed as a sandbox for machine learning approaches to reasoning and planning. Within it, we create 10 simple games embodying a range of algorithmic tasks (e.g. if-then statements or set negation). A variety of neural models (fully connected, convolutional network, memory network) are deployed via reinforcement learning on these games, with and without a procedurally generated curriculum. Despite the tasks' simplicity, the performance of the models is far from optimal, suggesting directions for future development. We also demonstrate the versatility of MazeBase by using it to emulate small combat scenarios from StarCraft. Models trained on the MazeBase version can be directly applied to StarCraft, where they consistently beat the in-game AI.

cs.LG↗
arXiv2015

Simple Baseline for Visual Question Answering

We describe a very simple bag-of-words baseline for visual question answering. This baseline concatenates the word features from the question and CNN features from the image to predict the answer. When evaluated on the challenging VQA dataset [2], it shows comparable performance to many recent approaches using recurrent neural networks. To explore the strength and weakness of the trained model, we also provide an interactive web demo and open-source code. .

cs.CV↗
arXiv2015

A mathematical motivation for complex-valued convolutional networks

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as "data-driven multiscale windowed power spectra," "data-driven multiscale windowed absolute spectra," "data-driven multiwavelet absolute values," or (in their most general configuration) "data-driven nonlinear multiwavelet packets." Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (for example, logistic or tanh) nonlinearities, max. pooling, etc., do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

cs.LG↗
arXiv2015

End-To-End Memory Networks

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

cs.NE↗
arXiv2015

Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks

In this paper we introduce a generative parametric model capable of producing high quality samples of natural images. Our approach uses a cascade of convolutional networks within a Laplacian pyramid framework to generate images in a coarse-to-fine fashion. At each level of the pyramid, a separate generative convnet model is trained using the Generative Adversarial Nets (GAN) approach (Goodfellow et al.). Samples drawn from our model are of significantly higher quality than alternate approaches. In a quantitative assessment by human evaluators, our CIFAR10 samples were mistaken for real images around 40% of the time, compared to 10% for samples drawn from a GAN baseline model. We also show samples from models trained on the higher resolution images of the LSUN scene dataset.

cs.CV↗
arXiv2014

An implementation of a randomized algorithm for principal component analysis

Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present paper presents an essentially black-box, fool-proof implementation for Mathworks' MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical techniques (such as Lanczos iterations) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms, and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces).

stat.CO↗
arXiv2014

An Incremental Reseeding Strategy for Clustering

In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then randomly reseeding the thresholded clusters. We demonstrate experimentally that the proper combination of these ingredients leads to an algorithm that achieves state-of-the-art performance in terms of cluster purity on standard benchmarks datasets. Moreover, the algorithm runs an order of magnitude faster than the other algorithms that achieve comparable results in terms of accuracy. We also describe a coarsen, cluster and refine approach similar to GRACLUS and METIS that removes an additional order of magnitude from the runtime of our algorithm while still maintaining competitive accuracy.

stat.ML↗
arXiv2014

Spectral Networks and Locally Connected Networks on Graphs

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.

cs.LG↗
arXiv2014

Better Feature Tracking Through Subspace Constraints

Feature tracking in video is a crucial task in computer vision. Usually, the tracking problem is handled one feature at a time, using a single-feature tracker like the Kanade-Lucas-Tomasi algorithm, or one of its derivatives. While this approach works quite well when dealing with high-quality video and "strong" features, it often falters when faced with dark and noisy video containing low-quality features. We present a framework for jointly tracking a set of features, which enables sharing information between the different features in the scene. We show that our method can be employed to track features for both rigid and nonrigid motions (possibly of few moving bodies) even when some features are occluded. Furthermore, it can be used to significantly improve tracking results in poorly-lit scenes (where there is a mix of good and bad features). Our approach does not require direct modeling of the structure or the motion of the scene, and runs in real time on a single CPU core.

cs.CV↗
arXiv2014

Signal Recovery from Pooling Representations

In this work we compute lower Lipschitz bounds of $\ell_p$ pooling operators for $p=1, 2, \infty$ as well as $\ell_p$ pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.

stat.ML↗
arXiv2013

Unsupervised Feature Learning by Deep Sparse Coding

In this paper, we propose a new unsupervised feature learning framework, namely Deep Sparse Coding (DeepSC), that extends sparse coding to a multi-layer architecture for visual object recognition tasks. The main innovation of the framework is that it connects the sparse-encoders from different layers by a sparse-to-dense module. The sparse-to-dense module is a composition of a local spatial pooling step and a low-dimensional embedding process, which takes advantage of the spatial smoothness information in the image. As a result, the new method is able to learn several levels of sparse representation of the image which capture features at a variety of abstraction levels and simultaneously preserve the spatial smoothness between the neighboring image patches. Combining the feature representations from multiple layers, DeepSC achieves the state-of-the-art performance on multiple object recognition tasks.

cs.LG↗
arXiv2013

Learning Stable Group Invariant Representations with Convolutional Networks

Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing mathematical properties, where convolutions, together with pooling operators, bring stability to additive and geometric perturbations of the input. Whereas physical transformation groups are ubiquitous in image and audio applications, they do not account for all the variability of complex signal classes. We show that the invariance properties built by deep convolutional networks can be cast as a form of stable group invariance. The network wiring architecture determines the invariance group, while the trainable filter coefficients characterize the group action. We give explanatory examples which illustrate how the network architecture controls the resulting invariance group. We also explore the principle by which additional convolutional layers induce a group factorization enabling more abstract, powerful invariant representations.

cs.AI↗
arXiv2012

Hybrid Linear Modeling via Local Best-fit Flats

We present a simple and fast geometric method for modeling data by a union of affine subspaces. The method begins by forming a collection of local best-fit affine subspaces, i.e., subspaces approximating the data in local neighborhoods. The correct sizes of the local neighborhoods are determined automatically by the Jones' $β_2$ numbers (we prove under certain geometric conditions that our method finds the optimal local neighborhoods). The collection of subspaces is further processed by a greedy selection procedure or a spectral method to generate the final model. We discuss applications to tracking-based motion segmentation and clustering of faces under different illuminating conditions. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the suggested algorithms on these problems and also on synthetic hybrid linear data as well as the MNIST handwritten digits data; and we demonstrate how to use our algorithms for fast determination of the number of affine subspaces.

cs.CV↗
arXiv2012

Fast approximations to structured sparse coding and applications to object classification

We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We store a lookup table with the assignments and the pseudoinverses for each node, allowing for very fast inference. We give an algorithm for learning the tree, the dictionary and the dictionary element assignment, and In the process of describing this algorithm, we discuss the more general problem of learning the groups in group structured sparse modelling. We show that our method creates good sparse representations by using it in the object recognition framework of \cite{lazebnik06,yang-cvpr-09}. Implementing our own fast version of the SIFT descriptor the whole system runs at 20 frames per second on $321 \times 481$ sized images on a laptop with a quad-core cpu, while sacrificing very little accuracy on the Caltech 101 and 15 scenes benchmarks.

cs.CV↗
arXiv2010

Randomized hybrid linear modeling by local best-fit flats

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global l1 error measure. The size of the local neighborhoods is determined automatically by the Jones' l2 beta numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.

cs.CV↗
arXiv2009

Median K-flats for hybrid linear modeling with many outliers

We describe the Median K-Flats (MKF) algorithm, a simple online method for hybrid linear modeling, i.e., for approximating data by a mixture of flats. This algorithm simultaneously partitions the data into clusters while finding their corresponding best approximating l1 d-flats, so that the cumulative l1 error is minimized. The current implementation restricts d-flats to be d-dimensional linear subspaces. It requires a negligible amount of storage, and its complexity, when modeling data consisting of N points in D-dimensional Euclidean space with K d-dimensional linear subspaces, is of order O(n K d D+n d^2 D), where n is the number of iterations required for convergence (empirically on the order of 10^4). Since it is an online algorithm, data can be supplied to it incrementally and it can incrementally produce the corresponding output. The performance of the algorithm is carefully evaluated using synthetic and real data.

cs.CV↗