A semi-supervised learning framework using the feedforward-designed convolutional neural networks (FF-CNNs) is proposed for image classification in this work. One unique property of FF-CNNs is that no backpropagation is used in model parameters determination. Since unlabeled data may not always enhance semi-supervised learning, we define an effective quality score and use it to select a subset of unlabeled data in the training process. We conduct experiments on the MNIST, SVHN, and CIFAR-10 datasets, and show that the proposed semi-supervised FF-CNN solution outperforms the CNN trained by backpropagation (BP-CNN) when the amount of labeled data is reduced. Furthermore, we develop an ensemble system that combines the output decision vectors of different semi-supervised FF-CNNs to boost classification accuracy. The ensemble systems can achieve further performance gains on all three benchmarking datasets.
The construction of FC layers is achieved by the cascade of multiple rectified linear least-squared regressors (LSRs) @cite_19 . Let the input and output dimensions of a FC layer be @math and @math (with @math ), respectively. To construct an FC layer, we cluster input samples of dimension @math into @math clusters, and assign pseudo-labels based on clustering results. Next, all samples are transformed into a vector space of dimension @math via LSR, where the index of the output space dimension defines a pseudo-label. In this way, we obtain a supervised LSR building module to serve as one FC layer. It accommodates intra-class variability while enhancing discriminability gradually.
@cite_19
2949474319
The model parameters of convolutional neural networks (CNNs) are determined by backpropagation (BP). In this work, we propose an interpretable feedforward (FF) design without any BP as a reference. The FF design adopts a data-centric approach. It derives network parameters of the current layer based on data statistics from the output of the previous layer in a one-pass manner. To construct convolutional layers, we develop a new signal transform, called the Saab (Subspace Approximation with Adjusted Bias) transform. It is a variant of the principal component analysis (PCA) with an added bias vector to annihilate activation's nonlinearity. Multiple Saab transforms in cascade yield multiple convolutional layers. As to fully-connected (FC) layers, we construct them using a cascade of multi-stage linear least squared regressors (LSRs). The classification and robustness (against adversarial attacks) performances of BP- and FF-designed CNNs applied to the MNIST and the CIFAR-10 datasets are compared. Finally, we comment on the relationship between BP and FF designs. We establish @math and @math error bounds for functions of many variables that are approximated by linear combinations of ReLU (rectified linear unit) and squared ReLU ridge functions with @math and @math controls on their inner and outer parameters. With the squared ReLU ridge function, we show that the @math approximation error is inversely proportional to the inner layer @math sparsity and it need only be sublinear in the outer layer @math sparsity. Our constructions are obtained using a variant of the Jones-Barron probabilistic method, which can be interpreted as either stratified sampling with proportionate allocation or two-stage cluster sampling. We also provide companion error lower bounds that reveal near optimality of our constructions. Despite the sparsity assumptions, we showcase the richness and flexibility of these ridge combinations by defining a large family of functions, in terms of certain spectral conditions, that are particularly well approximated by them. In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to @math in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation functions satisfy the distilled properties, including rectified linear units (ReLUs), leaky ReLUs, squared ReLUs and sigmoids. For activation functions that are also smooth, we show @math guarantees of gradient descent under a resampling rule. For homogeneous activations, we show tensor methods are able to initialize the parameters to fall into the local strong convexity region. As a result, tensor initialization followed by gradient descent is guaranteed to recover the ground truth with sample complexity @math and computational complexity @math for smooth homogeneous activations with high probability, where @math is the dimension of the input, @math ( @math ) is the number of hidden nodes, @math is a conditioning property of the ground-truth parameter matrix between the input layer and the hidden layer, @math is the targeted precision and @math is the number of samples. To the best of our knowledge, this is the first work that provides recovery guarantees for 1NNs with both sample complexity and computational complexity @math in the input dimension and @math in the precision. We present new approximation algorithms for the @math -median and @math -means clustering problems. To this end, we obtain small coresets for @math -median and @math -means clustering in general metric spaces and in Euclidean spaces. In @math , these coresets are of size with polynomial dependency on the dimension @math . This leads to @math -approximation algorithms to the optimal @math -median and @math -means clustering in @math , with running time @math , where @math is the number of points. This improves over previous results. We use those coresets to maintain a @math -approximate @math -median and @math -means clustering of a stream of points in @math , using @math space. These are the first streaming algorithms, for those problems, that have space complexity with polynomial dependency on the dimension.