Learning Compact Features via In-Training Representation Alignment

Deep neural networks (DNNs) for supervised learning can be viewed as a pipeline of the feature extractor (i.e., last hidden layer) and a linear classifier (i.e., output layer) that are trained jointly with stochastic gradient descent (SGD) on the loss function (e.g., cross-entropy). In each epoch, the true gradient of the loss function is estimated using a mini-batch sampled from the training set and model parameters are then updated with the mini-batch gradients. Although the latter provides an unbiased estimation of the former, they are subject to substantial variances derived from the size and number of sampled mini-batches, leading to noisy and jumpy updates. To stabilize such undesirable variance in estimating the true gradients, we propose In-Training Representation Alignment (ITRA) that explicitly aligns feature distributions of two different mini-batches with a matching loss in the SGD training process. We also provide a rigorous analysis of the desirable effects of the matching loss on feature representation learning: (1) extracting compact feature representation; (2) reducing over-adaption on mini-batches via an adaptive weighting mechanism; and (3) accommodating to multi-modalities. Finally, we conduct large-scale experiments on both image and text classifications to demonstrate its superior performance to the strong baselines.Comment: 11 pages, 4 figures, 6 tables. Accepted for publication by AAAI-23. arXiv admin note: text overlap with arXiv:2002.0991

Cascade Subspace Clustering for Outlier Detection

Many methods based on sparse and low-rank representation been developed along with guarantees of correct outlier detection. Self-representation states that a point in a subspace can always be expressed as a linear combination of other points in the subspace. A suitable Markov Chain can be defined on the self-representation and it allows us to recognize the difference between inliers and outliers. However, the reconstruction error of self-representation that is still informative to detect outlier detection, is neglected.Inspired by the gradient boosting, in this paper, we propose a new outlier detection framework that combines a series of weak "outlier detectors" into a single strong one in an iterative fashion by constructing multi-pass self-representation. At each stage, we construct a self-representation based on elastic-net and define a suitable Markov Chain on it to detect outliers. The residual of the self-representation is used for the next stage to learn the next weaker outlier detector. Such a stage will repeat many times. And the final decision of outliers is generated by the previous all results. Experimental results on image and speaker datasets demonstrate its superiority with respect to state-of-the-art sparse and low-rank outlier detection methods.Comment: arXiv admin note: text overlap with arXiv:1704.03925 by other author

MAGMA: Multi-level accelerated gradient mirror descent algorithm for large-scale convex composite minimization

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms for convex composite models are accelerated first order methods, however they can take a large number of iterations to compute an acceptable solution for large-scale problems. In this paper we propose to speed up first order methods by taking advantage of the structure present in many applications and in image processing in particular. Our method is based on multi-level optimization methods and exploits the fact that many applications that give rise to large scale models can be modelled using varying degrees of fidelity. We use Nesterov's acceleration techniques together with the multi-level approach to achieve $\mathcal{O}(1/\sqrt{\epsilon})$ convergence rate, where $\epsilon$ denotes the desired accuracy. The proposed method has a better convergence rate than any other existing multi-level method for convex problems, and in addition has the same rate as accelerated methods, which is known to be optimal for first-order methods. Moreover, as our numerical experiments show, on large-scale face recognition problems our algorithm is several times faster than the state of the art

Convolutional Dictionary Learning: Acceleration and Convergence

Convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared to the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large datasets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Image Processin