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Register a new userContinual Learning in Low-rank Orthogonal Subspaces
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Arslan Chaudhry
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In continual learning (CL), a learner is faced with a sequence of tasks, arriving one after the other, and the goal is to remember all the tasks once the continual learning experience is finished. The prior art in CL uses episodic memory, parameter regularization or extensible network structures to reduce interference among tasks, but in the end, all the approaches learn different tasks in a joint vector space. We believe this invariably leads to interference among different tasks. We propose to learn tasks in different (low-rank) vector subspaces that are kept orthogonal to each other in order to minimize interference. Further, to keep the gradients of different tasks coming from these subspaces orthogonal to each other, we learn isometric mappings by posing network training as an optimization problem over the Stiefel manifold. To the best of our understanding, we report, for the first time, strong results over experience-replay baseline with and without memory on standard classification benchmarks in continual learning. The code is made publicly available.
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The latent space of a Generative Adversarial Network (GAN) has been shown to encode rich semantics within some subspaces. To identify these subspaces, researchers typically analyze the statistical information from a collection of synthesized data, and the identified subspaces tend to control image attributes globally (i.e., manipulating an attribute causes the change of an entire image). By contrast, this work introduces low-rank subspaces that enable more precise control of GAN generation. Concretely, given an arbitrary image and a region of interest (e.g., eyes of face images), we manage to relate the latent space to the image region with the Jacobian matrix and then use low-rank factorization to discover steerable latent subspaces. There are three distinguishable strengths of our approach that can be aptly called LowRankGAN. First, compared to analytic algorithms in prior work, our low-rank factorization of Jacobians is able to find the low-dimensional representation of attribute manifold, making image editing more precise and controllable. Second, low-rank factorization naturally yields a null space of attributes such that moving the latent code within it only affects the outer region of interest. Therefore, local image editing can be simply achieved by projecting an attribute vector into the null space without relying on a spatial mask as existing methods do. Third, our method can robustly work with a local region from one image for analysis yet well generalize to other images, making it much easy to use in practice. Extensive experiments on state-of-the-art GAN models (including StyleGAN2 and BigGAN) trained on various datasets demonstrate the effectiveness of our LowRankGAN.
We introduce a learning-based algorithm for the low-rank decomposition problem: given an $n times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A$ that minimizes the approximation loss $|A-A|_F$. The algorithm uses a training set of input matrices in order to optimize its performance. Specifically, some of the most efficient approximate algorithms for computing low-rank approximations proceed by computing a projection $SA$, where $S$ is a sparse random $m times n$ sketching matrix, and then performing the singular value decomposition of $SA$. We show how to replace the random matrix $S$ with a learned matrix of the same sparsity to reduce the error. Our experiments show that, for multiple types of data sets, a learned sketch matrix can substantially reduce the approximation loss compared to a random matrix $S$, sometimes by one order of magnitude. We also study mixed matrices where only some of the rows are trained and the remaining ones are random, and show that matrices still offer improved performance while retaining worst-case guarantees. Finally, to understand the theoretical aspects of our approach, we study the special case of $m=1$. In particular, we give an approximation algorithm for minimizing the empirical loss, with approximation factor depending on the stable rank of matrices in the training set. We also show generalization bounds for the sketch matrix learning problem.
Entity linking is an important problem with many applications. Most previous solutions were designed for settings where annotated training data is available, which is, however, not the case in numerous domains. We propose a light-weight and scalable entity linking method, Eigenthemes, that relies solely on the availability of entity names and a referent knowledge base. Eigenthemes exploits the fact that the entities that are truly mentioned in a document (the gold entities) tend to form a semantically dense subset of the set of all candidate entities in the document. Geometrically speaking, when representing entities as vectors via some given embedding, the gold entities tend to lie in a low-rank subspace of the full embedding space. Eigenthemes identifies this subspace using the singular value decomposition and scores candidate entities according to their proximity to the subspace. On the empirical front, we introduce multiple strong baselines that compare favorably to the existing state of the art. Extensive experiments on benchmark datasets from a variety of real-world domains showcase the effectiveness of our approach.
Continual learning (CL) studies the problem of learning a sequence of tasks, one at a time, such that the learning of each new task does not lead to the deterioration in performance on the previously seen ones while exploiting previously learned features. This paper presents Bilevel Continual Learning (BiCL), a general framework for continual learning that fuses bilevel optimization and recent advances in meta-learning for deep neural networks. BiCL is able to train both deep discriminative and generative models under the conservative setting of the online continual learning. Experimental results show that BiCL provides competitive performance in terms of accuracy for the current task while reducing the effect of catastrophic forgetting. This is a concurrent work with [1]. We submitted it to AAAI 2020 and IJCAI 2020. Now we put it on the arxiv for record. Different from [1], we also consider continual generative model as well. At the same time, the authors are aware of a recent proposal on bilevel optimization based coreset construction for continual learning [2]. [1] Q. Pham, D. Sahoo, C. Liu, and S. C. Hoi. Bilevel continual learning. arXiv preprint arXiv:2007.15553, 2020. [2] Z. Borsos, M. Mutny, and A. Krause. Coresets via bilevel optimization for continual learning and streaming. arXiv preprint arXiv:2006.03875, 2020
Continual learning aims to learn continuously from a stream of tasks and data in an online-learning fashion, being capable of exploiting what was learned previously to improve current and future tasks while still being able to perform well on the previous tasks. One common limitation of many existing continual learning methods is that they often train a model directly on all available training data without validation due to the nature of continual learning, thus suffering poor generalization at test time. In this work, we present a novel framework of continual learning named Bilevel Continual Learning (BCL) by unifying a {it bilevel optimization} objective and a {it dual memory management} strategy comprising both episodic memory and generalization memory to achieve effective knowledge transfer to future tasks and alleviate catastrophic forgetting on old tasks simultaneously. Our extensive experiments on continual learning benchmarks demonstrate the efficacy of the proposed BCL compared to many state-of-the-art methods. Our implementation is available at https://github.com/phquang/bilevel-continual-learning.
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