Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLabel-Based Diversity Measure Among Hidden Units of Deep Neural Networks: A Regularization Method
92
0
0.0
(
0
)
Added by
Chenguang Zhang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Although the deep structure guarantees the powerful expressivity of deep networks (DNNs), it also triggers serious overfitting problem. To improve the generalization capacity of DNNs, many strategies were developed to improve the diversity among hidden units. However, most of these strategies are empirical and heuristic in absence of either a theoretical derivation of the diversity measure or a clear connection from the diversity to the generalization capacity. In this paper, from an information theoretic perspective, we introduce a new definition of redundancy to describe the diversity of hidden units under supervised learning settings by formalizing the effect of hidden layers on the generalization capacity as the mutual information. We prove an opposite relationship existing between the defined redundancy and the generalization capacity, i.e., the decrease of redundancy generally improving the generalization capacity. The experiments show that the DNNs using the redundancy as the regularizer can effectively reduce the overfitting and decrease the generalization error, which well supports above points.
rate research
Read More
Deep Learning (DL) is considered the state-of-the-art in computer vision, speech recognition and natural language processing. Until recently, it was also widely accepted that DL is irrelevant for learning tasks on tabular data, especially in the small sample regime where ensemble methods are acknowledged as the gold standard. We present a new end-to-end differentiable method to train a standard FFNN. Our method, textbf{Muddling labels for Regularization} (texttt{MLR}), penalizes memorization through the generation of uninformative labels and the application of a differentiable close-form regularization scheme on the last hidden layer during training. texttt{MLR} outperforms classical NN and the gold standard (GBDT, RF) for regression and classification tasks on several datasets from the UCI database and Kaggle covering a large range of sample sizes and feature to sample ratios. Researchers and practitioners can use texttt{MLR} on its own as an off-the-shelf DL{} solution or integrate it into the most advanced ML pipelines.
In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime polynomial in the data size albeit exponential in the input dimension. Further, we improve on the known lower bounds on size (from exponential to super exponential) for approximating a ReLU deep net function by a shallower ReLU net. Our gap theorems hold for smoothly parametrized families of hard functions, contrary to countable, discrete families known in the literature. An example consequence of our gap theorems is the following: for every natural number $k$ there exists a function representable by a ReLU DNN with $k^2$ hidden layers and total size $k^3$, such that any ReLU DNN with at most $k$ hidden layers will require at least $frac{1}{2}k^{k+1}-1$ total nodes. Finally, for the family of $mathbb{R}^nto mathbb{R}$ DNNs with ReLU activations, we show a new lowerbound on the number of affine pieces, which is larger than previous constructions in certain regimes of the network architecture and most distinctively our lowerbound is demonstrated by an explicit construction of a *smoothly parameterized* family of functions attaining this scaling. Our construction utilizes the theory of zonotopes from polyhedral theory.
The past few years have witnessed the fast development of different regularization methods for deep learning models such as fully-connected deep neural networks (DNNs) and Convolutional Neural Networks (CNNs). Most of previous methods mainly consider to drop features from input data and hidden layers, such as Dropout, Cutout and DropBlocks. DropConnect select to drop connections between fully-connected layers. By randomly discard some features or connections, the above mentioned methods control the overfitting problem and improve the performance of neural networks. In this paper, we proposed two novel regularization methods, namely DropFilter and DropFilter-PLUS, for the learning of CNNs. Different from the previous methods, DropFilter and DropFilter-PLUS selects to modify the convolution filters. For DropFilter-PLUS, we find a suitable way to accelerate the learning process based on theoretical analysis. Experimental results on MNIST show that using DropFilter and DropFilter-PLUS may improve performance on image classification tasks.
Despite the improved accuracy of deep neural networks, the discovery of adversarial examples has raised serious safety concerns. In this paper, we study two variants of pointwise robustness, the maximum safe radius problem, which for a given input sample computes the minimum distance to an adversarial example, and the feature robustness problem, which aims to quantify the robustness of individual features to adversarial perturbations. We demonstrate that, under the assumption of Lipschitz continuity, both problems can be approximated using finite optimisation by discretising the input space, and the approximation has provable guarantees, i.e., the error is bounded. We then show that the resulting optimisation problems can be reduced to the solution of two-player turn-based games, where the first player selects features and the second perturbs the image within the feature. While the second player aims to minimise the distance to an adversarial example, depending on the optimisation objective the first player can be cooperative or competitive. We employ an anytime approach to solve the games, in the sense of approximating the value of a game by monotonically improving its upper and lower bounds. The Monte Carlo tree search algorithm is applied to compute upper bounds for both games, and the Admissible A* and the Alpha-Beta Pruning algorithms are, respectively, used to compute lower bounds for the maximum safety radius and feature robustness games. When working on the upper bound of the maximum safe radius problem, our tool demonstrates competitive performance against existing adversarial example crafting algorithms. Furthermore, we show how our framework can be deployed to evaluate pointwise robustness of neural networks in safety-critical applications such as traffic sign recognition in self-driving cars.
Filter is the key component in modern convolutional neural networks (CNNs). However, since CNNs are usually over-parameterized, a pre-trained network always contain some invalid (unimportant) filters. These filters have relatively small $l_{1}$ norm and contribute little to the output (textbf{Reason}). While filter pruning removes these invalid filters for efficiency consideration, we tend to reactivate them to improve the representation capability of CNNs. In this paper, we introduce filter grafting (textbf{Method}) to achieve this goal. The activation is processed by grafting external information (weights) into invalid filters. To better perform the grafting, we develop a novel criterion to measure the information of filters and an adaptive weighting strategy to balance the grafted information among networks. After the grafting operation, the network has fewer invalid filters compared with its initial state, enpowering the model with more representation capacity. Meanwhile, since grafting is operated reciprocally on all networks involved, we find that grafting may lose the information of valid filters when improving invalid filters. To gain a universal improvement on both valid and invalid filters, we compensate grafting with distillation (textbf{Cultivation}) to overcome the drawback of grafting . Extensive experiments are performed on the classification and recognition tasks to show the superiority of our method. Code is available at textcolor{black}{emph{https://github.com/fxmeng/filter-grafting}}.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
