arXiv subjects

Thalaiyasingam Ajanthan

Publications and source records attributed to Thalaiyasingam Ajanthan.

40 records · Page 3Linked to original sources

arXiv2018

Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence

Incremental learning (IL) has received a lot of attention recently, however, the literature lacks a precise problem definition, proper evaluation settings, and metrics tailored specifically for the IL problem. One of the main objectives of this work is to fill these gaps so as to provide a common ground for better understanding of IL. The main challenge for an IL algorithm is to update the classifier whilst preserving existing knowledge. We observe that, in addition to forgetting, a known issue while preserving knowledge, IL also suffers from a problem we call intransigence, inability of a model to update its knowledge. We introduce two metrics to quantify forgetting and intransigence that allow us to understand, analyse, and gain better insights into the behaviour of IL algorithms. We present RWalk, a generalization of EWC++ (our efficient version of EWC [Kirkpatrick2016EWC]) and Path Integral [Zenke2017Continual] with a theoretically grounded KL-divergence based perspective. We provide a thorough analysis of various IL algorithms on MNIST and CIFAR-100 datasets. In these experiments, RWalk obtains superior results in terms of accuracy, and also provides a better trade-off between forgetting and intransigence.

cs.CV↗

arXiv2017

Memory Efficient Max Flow for Multi-label Submodular MRFs

Multi-label submodular Markov Random Fields (MRFs) have been shown to be solvable using max-flow based on an encoding of the labels proposed by Ishikawa, in which each variable $X_i$ is represented by $\ell$ nodes (where $\ell$ is the number of labels) arranged in a column. However, this method in general requires $2\,\ell^2$ edges for each pair of neighbouring variables. This makes it inapplicable to realistic problems with many variables and labels, due to excessive memory requirement. In this paper, we introduce a variant of the max-flow algorithm that requires much less storage. Consequently, our algorithm makes it possible to optimally solve multi-label submodular problems involving large numbers of variables and labels on a standard computer.

cs.DS↗

arXiv2017

Efficient Linear Programming for Dense CRFs

The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear programming (LP) relaxation, the state-of-the-art algorithm is too slow to be useful in practice. To alleviate this deficiency, we introduce an efficient LP minimization algorithm for dense CRFs. To this end, we develop a proximal minimization framework, where the dual of each proximal problem is optimized via block coordinate descent. We show that each block of variables can be efficiently optimized. Specifically, for one block, the problem decomposes into significantly smaller subproblems, each of which is defined over a single pixel. For the other block, the problem is optimized via conditional gradient descent. This has two advantages: 1) the conditional gradient can be computed in a time linear in the number of pixels and labels; and 2) the optimal step size can be computed analytically. Our experiments on standard datasets provide compelling evidence that our approach outperforms all existing baselines including the previous LP based approach for dense CRFs.

cs.CV↗

arXiv2014

Iteratively Reweighted Graph Cut for Multi-label MRFs with Non-convex Priors

While widely acknowledged as highly effective in computer vision, multi-label MRFs with non-convex priors are difficult to optimize. To tackle this, we introduce an algorithm that iteratively approximates the original energy with an appropriately weighted surrogate energy that is easier to minimize. Our algorithm guarantees that the original energy decreases at each iteration. In particular, we consider the scenario where the global minimizer of the weighted surrogate energy can be obtained by a multi-label graph cut algorithm, and show that our algorithm then lets us handle of large variety of non-convex priors. We demonstrate the benefits of our method over state-of-the-art MRF energy minimization techniques on stereo and inpainting problems.

cs.CV↗