Knowledge Transfer with Jacobian Matching

Classical distillation methods transfer representations from a "teacher" neural network to a "student" network by matching their output activations. Recent methods also match the Jacobians, or the gradient of output activations with the input. However, this involves making some ad hoc decisions, in particular, the choice of the loss function. In this paper, we first establish an equivalence between Jacobian matching and distillation with input noise, from which we derive appropriate loss functions for Jacobian matching. We then rely on this analysis to apply Jacobian matching to transfer learning by establishing equivalence of a recent transfer learning procedure to distillation. We then show experimentally on standard image datasets that Jacobian-based penalties improve distillation, robustness to noisy inputs, and transfer learning

Data-free parameter pruning for Deep Neural Networks

Deep Neural nets (NNs) with millions of parameters are at the heart of many state-of-the-art computer vision systems today. However, recent works have shown that much smaller models can achieve similar levels of performance. In this work, we address the problem of pruning parameters in a trained NN model. Instead of removing individual weights one at a time as done in previous works, we remove one neuron at a time. We show how similar neurons are redundant, and propose a systematic way to remove them. Our experiments in pruning the densely connected layers show that we can remove upto 85\% of the total parameters in an MNIST-trained network, and about 35\% for AlexNet without significantly affecting performance. Our method can be applied on top of most networks with a fully connected layer to give a smaller network.Comment: BMVC 201

Compensating for Large In-Plane Rotations in Natural Images

Rotation invariance has been studied in the computer vision community primarily in the context of small in-plane rotations. This is usually achieved by building invariant image features. However, the problem of achieving invariance for large rotation angles remains largely unexplored. In this work, we tackle this problem by directly compensating for large rotations, as opposed to building invariant features. This is inspired by the neuro-scientific concept of mental rotation, which humans use to compare pairs of rotated objects. Our contributions here are three-fold. First, we train a Convolutional Neural Network (CNN) to detect image rotations. We find that generic CNN architectures are not suitable for this purpose. To this end, we introduce a convolutional template layer, which learns representations for canonical 'unrotated' images. Second, we use Bayesian Optimization to quickly sift through a large number of candidate images to find the canonical 'unrotated' image. Third, we use this method to achieve robustness to large angles in an image retrieval scenario. Our method is task-agnostic, and can be used as a pre-processing step in any computer vision system.Comment: Accepted at Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP) 201

A Taxonomy of Deep Convolutional Neural Nets for Computer Vision

Traditional architectures for solving computer vision problems and the degree of success they enjoyed have been heavily reliant on hand-crafted features. However, of late, deep learning techniques have offered a compelling alternative -- that of automatically learning problem-specific features. With this new paradigm, every problem in computer vision is now being re-examined from a deep learning perspective. Therefore, it has become important to understand what kind of deep networks are suitable for a given problem. Although general surveys of this fast-moving paradigm (i.e. deep-networks) exist, a survey specific to computer vision is missing. We specifically consider one form of deep networks widely used in computer vision - convolutional neural networks (CNNs). We start with "AlexNet" as our base CNN and then examine the broad variations proposed over time to suit different applications. We hope that our recipe-style survey will serve as a guide, particularly for novice practitioners intending to use deep-learning techniques for computer vision.Comment: Published in Frontiers in Robotics and AI (http://goo.gl/6691Bm

Efficient Estimation of the Local Robustness of Machine Learning Models

Machine learning models often need to be robust to noisy input data. Real-world noise (such as measurement noise) is often random and the effect of such noise on model predictions is captured by a model's local robustness, i.e., the consistency of model predictions in a local region around an input. Local robustness is therefore an important characterization of real-world model behavior and can be useful for debugging models and establishing user trust. However, the na\"ive approach to computing local robustness based on Monte-Carlo sampling is statistically inefficient, especially for high-dimensional data, leading to prohibitive computational costs for large-scale applications. In this work, we develop the first analytical estimators to efficiently compute local robustness of multi-class discriminative models. These estimators linearize models in the local region around an input and compute the model's local robustness using the multivariate Normal cumulative distribution function. Through the derivation of these estimators, we show how local robustness is connected to such concepts as randomized smoothing and softmax probability. In addition, we show empirically that these estimators efficiently compute the local robustness of standard deep learning models and demonstrate these estimators' usefulness for various tasks involving local robustness, such as measuring robustness bias and identifying examples that are vulnerable to noise perturbation in a dataset. To our knowledge, this work is the first to investigate local robustness in a multi-class setting and develop efficient analytical estimators for local robustness. In doing so, this work not only advances the conceptual understanding of local robustness, but also makes its computation practical, enabling the use of local robustness in critical downstream applications

Which Models have Perceptually-Aligned Gradients? An Explanation via Off-Manifold Robustness

One of the remarkable properties of robust computer vision models is that their input-gradients are often aligned with human perception, referred to in the literature as perceptually-aligned gradients (PAGs). Despite only being trained for classification, PAGs cause robust models to have rudimentary generative capabilities, including image generation, denoising, and in-painting. However, the underlying mechanisms behind these phenomena remain unknown. In this work, we provide a first explanation of PAGs via \emph{off-manifold robustness}, which states that models must be more robust off- the data manifold than they are on-manifold. We first demonstrate theoretically that off-manifold robustness leads input gradients to lie approximately on the data manifold, explaining their perceptual alignment. We then show that Bayes optimal models satisfy off-manifold robustness, and confirm the same empirically for robust models trained via gradient norm regularization, noise augmentation, and randomized smoothing. Quantifying the perceptual alignment of model gradients via their similarity with the gradients of generative models, we show that off-manifold robustness correlates well with perceptual alignment. Finally, based on the levels of on- and off-manifold robustness, we identify three different regimes of robustness that affect both perceptual alignment and model accuracy: weak robustness, bayes-aligned robustness, and excessive robustness