Pedro M. Q. Aguiar

João F. C. Mota, João M. F. Xavier, Pedro M. Q. Aguiar et al. · eth-zurich

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time. We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes. Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms.

Lourenço V. Pato, Renato Negrinho, Pedro M. Q. Aguiar

The majority of current object detectors lack context: class predictions are made independently from other detections. We propose to incorporate context in object detection by post-processing the output of an arbitrary detector to rescore the confidences of its detections. Rescoring is done by conditioning on contextual information from the entire set of detections: their confidences, predicted classes, and positions. We show that AP can be improved by simply reassigning the detection confidence values such that true positives that survive longer (i.e., those with the correct class and large IoU) are scored higher than false positives or detections with small IoU. In this setting, we use a bidirectional RNN with attention for contextual rescoring and introduce a training target that uses the IoU with ground truth to maximize AP for the given set of detections. The fact that our approach does not require access to visual features makes it computationally inexpensive and agnostic to the detection architecture. In spite of this simplicity, our model consistently improves AP over strong pre-trained baselines (Cascade R-CNN and Faster R-CNN with several backbones), particularly by reducing the confidence of duplicate detections (a learned form of non-maximum suppression) and removing out-of-context objects by conditioning on the confidences, classes, positions, and sizes of the co-occurrent detections. Code is available at https://github.com/LourencoVazPato/seeing-without-looking/

Manuel Madeira, Renato Negrinho, João Xavier et al.

First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common approaches, which rarely leverage global models of the objective function, we exploit convexity and L-smoothness to improve the noisy estimates outputted by the stochastic gradient oracle. Our method, named COCO denoiser, is the joint maximum likelihood estimator of multiple function gradients from their noisy observations, subject to co-coercivity constraints between them. The resulting estimate is the solution of a convex Quadratically Constrained Quadratic Problem. Although this problem is expensive to solve by interior point methods, we exploit its structure to apply an accelerated first-order algorithm, the Fast Dual Proximal Gradient method. Besides analytically characterizing the proposed estimator, we show empirically that increasing the number and proximity of the queried points leads to better gradient estimates. We also apply COCO in stochastic settings by plugging it in existing algorithms, such as SGD, Adam or STRSAGA, outperforming their vanilla versions, even in scenarios where our modelling assumptions are mismatched.

André F. T. Martins, Marcos Treviso, António Farinhas et al.

Exponential families are widely used in machine learning, including many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions in each of these families have fixed support. In contrast, for finite domains, recent work on sparse alternatives to softmax (e.g., sparsemax, $α$-entmax, and fusedmax), has led to distributions with varying support. This paper develops sparse alternatives to continuous distributions, based on several technical contributions: First, we define $Ω$-regularized prediction maps and Fenchel-Young losses for arbitrary domains (possibly countably infinite or continuous). For linearly parametrized families, we show that minimization of Fenchel-Young losses is equivalent to moment matching of the statistics, generalizing a fundamental property of exponential families. When $Ω$ is a Tsallis negentropy with parameter $α$, we obtain ``deformed exponential families,'' which include $α$-entmax and sparsemax ($α=2$) as particular cases. For quadratic energy functions, the resulting densities are $β$-Gaussians, an instance of elliptical distributions that contain as particular cases the Gaussian, biweight, triweight, and Epanechnikov densities, and for which we derive closed-form expressions for the variance, Tsallis entropy, and Fenchel-Young loss. When $Ω$ is a total variation or Sobolev regularizer, we obtain a continuous version of the fusedmax. Finally, we introduce continuous-domain attention mechanisms, deriving efficient gradient backpropagation algorithms for $α\in \{1, 4/3, 3/2, 2\}$. Using these algorithms, we demonstrate our sparse continuous distributions for attention-based audio classification and visual question answering, showing that they allow attending to time intervals and compact regions.

António Farinhas, André F. T. Martins, Pedro M. Q. Aguiar

Visual attention mechanisms are a key component of neural network models for computer vision. By focusing on a discrete set of objects or image regions, these mechanisms identify the most relevant features and use them to build more powerful representations. Recently, continuous-domain alternatives to discrete attention models have been proposed, which exploit the continuity of images. These approaches model attention as simple unimodal densities (e.g. a Gaussian), making them less suitable to deal with images whose region of interest has a complex shape or is composed of multiple non-contiguous patches. In this paper, we introduce a new continuous attention mechanism that produces multimodal densities, in the form of mixtures of Gaussians. We use the EM algorithm to obtain a clustering of relevant regions in the image, and a description length penalty to select the number of components in the mixture. Our densities decompose as a linear combination of unimodal attention mechanisms, enabling closed-form Jacobians for the backpropagation step. Experiments on visual question answering in the VQA-v2 dataset show competitive accuracies and a selection of regions that mimics human attention more closely in VQA-HAT. We present several examples that suggest how multimodal attention maps are naturally more interpretable than their unimodal counterparts, showing the ability of our model to automatically segregate objects from ground in complex scenes.

André F. T. Martins, António Farinhas, Marcos Treviso et al.

Exponential families are widely used in machine learning; they include many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions in each of these families have fixed support. In contrast, for finite domains, there has been recent work on sparse alternatives to softmax (e.g. sparsemax and alpha-entmax), which have varying support, being able to assign zero probability to irrelevant categories. This paper expands that work in two directions: first, we extend alpha-entmax to continuous domains, revealing a link with Tsallis statistics and deformed exponential families. Second, we introduce continuous-domain attention mechanisms, deriving efficient gradient backpropagation algorithms for alpha in {1,2}. Experiments on attention-based text classification, machine translation, and visual question answering illustrate the use of continuous attention in 1D and 2D, showing that it allows attending to time intervals and compact regions.

Rui F. C. Guerreiro, Pedro M. Q. Aguiar

The Discrete Cosine Transform (DCT) is widely used in lossy image and video compression schemes, e.g., JPEG and MPEG. In this paper, we show that the compression efficiency of the DCT is dependent on the edge directions within a block. In particular, higher compression ratios are achieved when edges are aligned with the image axes. To maximize compression for general images, we propose a rotated block DCT method. It consists of rotating each block, before applying the DCT, by an angle that aligns the edges, and rotating back the block in the decompression stage. We show how to compute the rotation angle and analyze two alternative block rotation approaches. Our experiments show that our method enables both a perceptual improvement and a PSNR increase of up to 2dB, compared with the standard DCT, for low and medium bit rates.