Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks. One of the most straightforward ways is to regularize the neural network with some additional objectives. L2 regularization serves as a standard regularization for neural networks. Despite its popularity, it essentially regularizes one dimension of the individual neuron, which is not strong enough to control the capacity of highly over-parameterized neural networks. Motivated by this, hyperspherical uniformity is proposed as a novel family of relational regularizations that impact the interaction among neurons. We consider several geometrically distinct ways to achieve hyperspherical uniformity. The effectiveness of hyperspherical uniformity is justified by theoretical insights and empirical evaluations.
Improving the aesthetic quality of images is challenging and eager for the public. To address this problem, most existing algorithms are based on supervised learning methods to learn an automatic photo enhancer for paired data, which consists of low-quality photos and corresponding expert-retouched versions. However, the style and characteristics of photos retouched by experts may not meet the needs or preferences of general users. In this paper, we present an unsupervised image enhancement generative adversarial network (UEGAN), which learns the corresponding image-to-image mapping from a set of images with desired characteristics in an unsupervised manner, rather than learning on a large number of paired images. The proposed model is based on single deep GAN which embeds the modulation and attention mechanisms to capture richer global and local features. Based on the proposed model, we introduce two losses to deal with the unsupervised image enhancement: (1) fidelity loss, which is defined as a L2 regularization in the feature domain of a pre-trained VGG network to ensure the content between the enhanced image and the input image is the same, and (2) quality loss that is formulated as a relativistic hinge adversarial loss to endow the input image the desired characteristics. Both quantitative and qualitative results show that the proposed model effectively improves the aesthetic quality of images. Our code is available at: https://github.com/eezkni/UEGAN.
Regularization has long been utilized to learn sparsity in deep neural network pruning. However, its role is mainly explored in the small penalty strength regime. In this work, we extend its application to a new scenario where the regularization grows large gradually to tackle two central problems of pruning: pruning schedule and weight importance scoring. (1) The former topic is newly brought up in this work, which we find critical to the pruning performance while receives little research attention. Specifically, we propose an L2 regularization variant with rising penalty factors and show it can bring significant accuracy gains compared with its one-shot counterpart, even when the same weights are removed. (2) The growing penalty scheme also brings us an approach to exploit the Hessian information for more accurate pruning without knowing their specific values, thus not bothered by the common Hessian approximation problems. Empirically, the proposed algorithms are easy to implement and scalable to large datasets and networks in both structured and unstructured pruning. Their effectiveness is demonstrated with modern deep neural networks on the CIFAR and ImageNet datasets, achieving competitive results compared to many state-of-the-art algorithms. Our code and trained models are publicly available at https://github.com/mingsuntse/regularization-pruning.
The extent to which the arbitrarily selected L2 regularization hyperparameter value affects the outcome of semantic segmentation with deep learning is demonstrated. Demonstrations rely on training U-net on small LGE-MRI datasets using the arbitrarily selected L2 regularization values. The remaining hyperparameters are to be manually adjusted or tuned only when 10 % of all epochs are reached before the training validation accuracy reaches 90%. Semantic segmentation with deep learning outcomes are objectively and subjectively evaluated against the manual ground truth segmentation.
Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some improvement in accuracy, but at the cost of extended runtime. In this paper we examine these methods for the case of data acquired as non-uniform Fourier samples. We then develop a non-iterative weighted regularization method that uses a pre-processing edge detection to find exactly where the sparsity should be in the edge domain. We show that its performance in terms of both accuracy and speed has the potential to outperform reweighted TV regularization methods.
How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the learning ability of each layer in the network is neglected. A common and tough issue that limits the capacity of the network is overfitting. To tackle this, L2 regularization is applied widely in existing deep learning frameworks. However,the effect on the generalization ability with L2 regularization is limited as it only controls large value in parameters. To make up the gap, in this paper, we propose a novel regularization term called Gram regularization which reinforces the learning ability of the network by encouraging the weight kernels to extract different information on the corresponding feature map. By forcing the variance between weight kernels to be large, the regularizer can help to extract discriminative features. The proposed Gram regularization is data independent and can converge stably and quickly without bells and whistles. Moreover, it can be easily plugged into existing off-the-shelf architectures. Extensive experimental results on the popular 3D object retrieval benchmark ModelNet demonstrate the effectiveness of our method.
Membership inference attacks are one of the simplest forms of privacy leakage for machine learning models: given a data point and model, determine whether the point was used to train the model. Existing membership inference attacks exploit models' abnormal confidence when queried on their training data. These attacks do not apply if the adversary only gets access to models' predicted labels, without a confidence measure. In this paper, we introduce label-only membership inference attacks. Instead of relying on confidence scores, our attacks evaluate the robustness of a model's predicted labels under perturbations to obtain a fine-grained membership signal. These perturbations include common data augmentations or adversarial examples. We empirically show that our label-only membership inference attacks perform on par with prior attacks that required access to model confidences. We further demonstrate that label-only attacks break multiple defenses against membership inference attacks that (implicitly or explicitly) rely on a phenomenon we call confidence masking. These defenses modify a model's confidence scores in order to thwart attacks, but leave the model's predicted labels unchanged. Our label-only attacks demonstrate that confidence-masking is not a viable defense strategy against membership inference. Finally, we investigate worst-case label-only attacks, that infer membership for a small number of outlier data points. We show that label-only attacks also match confidence-based attacks in this setting. We find that training models with differential privacy and (strong) L2 regularization are the only known defense strategies that successfully prevents all attacks. This remains true even when the differential privacy budget is too high to offer meaningful provable guarantees.
In the conventional Takagi-Sugeno-Kang (TSK)-type fuzzy models, constant or linear functions are usually utilized as the consequent parts of the fuzzy rules, but they cannot effectively describe the behavior within local regions defined by the antecedent parts. In this article, a theoretical and practical design methodology is developed to address this problem. First, the information granulation (Fuzzy C-Means) method is applied to capture the structure in the data and split the input space into subspaces, as well as form the antecedent parts. Second, the quadratic polynomials (QPs) are employed as the consequent parts. Compared with constant and linear functions, QPs can describe the input-output behavior within the local regions (subspaces) by refining the relationship between input and output variables. However, although QP can improve the approximation ability of the model, it could lead to the deterioration of the prediction ability of the model (e.g., overfitting). To handle this issue, we introduce an exponential weight approach inspired by the weight function theory encountered in harmonic analysis. More specifically, we adopt the exponential functions as the targeted penalty terms, which are equipped with l2 regularization (l2) (i.e., exponential weighted l2, ewl_2) to match the proposed reinforced second-order fuzzy rule-based model (RSFRM) properly. The advantage of el 2 compared to ordinary l2 lies in separately identifying and penalizing different types of polynomial terms in the coefficient estimation, and its results not only alleviate the overfitting and prevent the deterioration of generalization ability but also effectively release the prediction potential of the model.
DQN (Deep Q-Network) is a method to perform Q-learning for reinforcement learning using deep neural networks. DQNs require a large buffer and batch processing for an experience replay and rely on a backpropagation based iterative optimization, making them difficult to be implemented on resource-limited edge devices. In this paper, we propose a lightweight on-device reinforcement learning approach for low-cost FPGA devices. It exploits a recently proposed neural-network based on-device learning approach that does not rely on the backpropagation method but uses OS-ELM (Online Sequential Extreme Learning Machine) based training algorithm. In addition, we propose a combination of L2 regularization and spectral normalization for the on-device reinforcement learning so that output values of the neural network can be fit into a certain range and the reinforcement learning becomes stable. The proposed reinforcement learning approach is designed for PYNQ-Z1 board as a low-cost FPGA platform. The evaluation results using OpenAI Gym demonstrate that the proposed algorithm and its FPGA implementation complete a CartPole-v0 task 29.77x and 89.40x faster than a conventional DQN-based approach when the number of hidden-layer nodes is 64.
Spatial data exhibits the property that nearby points are correlated. This also holds for learnt representations across layers, but not for commonly used weight initialization methods. Our theoretical analysis quantifies the learning behavior of weights of a single spatial filter. It is thus in contrast to a large body of work that discusses statistical properties of weights. It shows that uncorrelated initialization (i) might lead to poor convergence behavior and (ii) training of (some) parameters is likely subject to slow convergence. Empirical analysis shows that these findings for a single spatial filter extend to networks with many spatial filters. The impact of (correlated) initialization depends strongly on learning rates and l2-regularization.
In large-scale classification problems, the data set always be faced with frequent updates when a part of the data is added to or removed from the original data set. In this case, conventional incremental learning, which updates an existing classifier by explicitly modeling the data modification, is more efficient than retraining a new classifier from scratch. However, sometimes, we are more interested in determining whether we should update the classifier or performing some sensitivity analysis tasks. To deal with these such tasks, we propose an algorithm to make rational inferences about the updated linear classifier without exactly updating the classifier. Specifically, the proposed algorithm can be used to estimate the upper and lower bounds of the updated classifier's coefficient matrix with a low computational complexity related to the size of the updated dataset. Both theoretical analysis and experiment results show that the proposed approach is superior to existing methods in terms of tightness of coefficients' bounds and computational complexity.
Machine Learning (ML) algorithms are vulnerable to poisoning attacks, where a fraction of the training data is manipulated to deliberately degrade the algorithms' performance. Optimal poisoning attacks, which can be formulated as bilevel optimisation problems, help to assess the robustness of learning algorithms in worst-case scenarios. However, current attacks against algorithms with hyperparameters typically assume that these hyperparameters remain constant ignoring the effect the attack has on them. We show that this approach leads to an overly pessimistic view of the robustness of the algorithms. We propose a novel optimal attack formulation that considers the effect of the attack on the hyperparameters by modelling the attack as a multiobjective bilevel optimisation problem. We apply this novel attack formulation to ML classifiers using $L_2$ regularisation and show that, in contrast to results previously reported, $L_2$ regularisation enhances the stability of the learning algorithms and helps to mitigate the attacks. Our empirical evaluation on different datasets confirms the limitations of previous strategies, evidences the benefits of using $L_2$ regularisation to dampen the effect of poisoning attacks and shows how the regularisation hyperparameter increases with the fraction of poisoning points.
The Big Data analytics are a logical analysis of very large scale datasets. The data analysis enhances an organization and improve the decision making process. In this article, we present Airline Delay Analysis and Prediction to analyze airline datasets with the combination of weather dataset. In this research work, we consider various attributes to analyze flight delay, for example, day-wise, airline-wise, cloud cover, temperature, etc. Moreover, we present rigorous experiments on various machine learning model to predict correctly the delay of a flight, namely, logistic regression with L2 regularization, Gaussian Naive Bayes, K-Nearest Neighbors, Decision Tree classifier and Random forest model. The accuracy of the Random Forest model is 82% with a delay threshold of 15 minutes of flight delay. The analysis is carried out using dataset from 1987 to 2008, the training is conducted with dataset from 2000 to 2007 and validated prediction result using 2008 data. Moreover, we have got recall 99% in the Random Forest model.
Machine learning (ML) models have been shown to be vulnerable to Membership Inference Attacks (MIA), which infer the membership of a given data point in the target dataset by observing the prediction output of the ML model. While the key factors for the success of MIA have not yet been fully understood, existing defense mechanisms such as using L2 regularization \cite{10shokri2017membership} and dropout layers \cite{salem2018ml} take only the model's overfitting property into consideration. In this paper, we provide an empirical analysis of the impact of both the data and ML model properties on the vulnerability of ML techniques to MIA. Our results reveal the relationship between MIA accuracy and properties of the dataset and training model in use. In particular, we show that the size of shadow dataset, the class and feature balance and the entropy of the target dataset, the configurations and fairness of the training model are the most influential factors. Based on those experimental findings, we conclude that along with model overfitting, multiple properties jointly contribute to MIA success instead of any single property. Building on our experimental findings, we propose using those data and model properties as regularizers to protect ML models against MIA. Our results show that the proposed defense mechanisms can reduce the MIA accuracy by up to 25\% without sacrificing the ML model prediction utility.
Knowledge distillation introduced in the deep learning context is a method to transfer knowledge from one architecture to another. In particular, when the architectures are identical, this is called self-distillation. The idea is to feed in predictions of the trained model as new target values for retraining (and iterate this loop possibly a few times). It has been empirically observed that the self-distilled model often achieves higher accuracy on held out data. Why this happens, however, has been a mystery: the self-distillation dynamics does not receive any new information about the task and solely evolves by looping over training. To the best of our knowledge, there is no rigorous understanding of this phenomenon. This work provides the first theoretical analysis of self-distillation. We focus on fitting a nonlinear function to training data, where the model space is Hilbert space and fitting is subject to $\ell_2$ regularization in this function space. We show that self-distillation iterations modify regularization by progressively limiting the number of basis functions that can be used to represent the solution. This implies (as we also verify empirically) that while a few rounds of self-distillation may reduce over-fitting, further rounds may lead to under-fitting and thus worse performance.
In this study, a predictive model using Multi-layer Perceptron of Artificial Neural Network architecture was developed to predict customer churn in a financial institution. Previous researches have used supervised machine learning classifiers such as Logistic Regression, Decision Tree, Support Vector Machine, K-Nearest Neighbors, and Random Forest. These classifiers require human effort to perform feature engineering which leads to over-specified and incomplete feature selection. Therefore, this research developed a model to eliminate manual feature engineering in data preprocessing stage. Fifty thousand customers? data were extracted from the database of one of the leading financial institution in Nigeria for the study. The multi-layer perceptron model was built with python programming language and used two overfitting techniques (Dropout and L2 regularization). The implementation done in python was compared with another model in Neuro solution infinity software. The results showed that the Artificial Neural Network software development (Python) had comparable performance with that obtained from the Neuro Solution Infinity software. The accuracy rates are 97.53% and 97.4% while ROC (Receiver Operating Characteristic) curve graphs are 0.89 and 0.85 respectively.
There has recently been an increasing desire to evaluate neural networks locally on computationally-limited devices in order to exploit their recent effectiveness for several applications; such effectiveness has nevertheless come together with a considerable increase in the size of modern neural networks, which constitute a major downside in several of the aforementioned computationally-limited settings. There has thus been a demand of compression techniques for neural networks. Several proposal in this direction have been made, which famously include hashing-based methods and pruning-based ones. However, the evaluation of the efficacy of these techniques has so far been heterogeneous, with no clear evidence in favor of any of them over the others. The goal of this work is to address this latter issue by providing a comparative study. While most previous studies test the capability of a technique in reducing the number of parameters of state-of-the-art networks , we follow [CWT + 15] in evaluating their performance on basic ar-chitectures on the MNIST dataset and variants of it, which allows for a clearer analysis of some aspects of their behavior. To the best of our knowledge, we are the first to directly compare famous approaches such as HashedNet, Optimal Brain Damage (OBD), and magnitude-based pruning with L1 and L2 regularization among them and against equivalent-size feed-forward neural networks with simple (fully-connected) and structural (convolutional) neural networks. Rather surprisingly, our experiments show that (iterative) pruning-based methods are substantially better than the HashedNet architecture, whose compression doesn't appear advantageous to a carefully chosen convolutional network. We also show that, when the compression level is high, the famous OBD pruning heuristics deteriorates to the point of being less efficient than simple magnitude-based techniques.
We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse regularization. In particular, we consider the L1 norm on the coefficients, its sorted Slope version, and the Group L1-L2 extension. We propose a new theoretical framework that uses common assumptions in the literature to simultaneously derive new high-dimensional L2 estimation upper bounds for all three regularization schemes. %, and to improve over existing results. For L1 and Slope regularizations, our bounds scale as $(k^*/n) \log(p/k^*)$ -- $n\times p$ is the size of the design matrix and $k^*$ the dimension of the theoretical loss minimizer $\B{\beta}^*$ -- and match the optimal minimax rate achieved for the least-squares case. For Group L1-L2 regularization, our bounds scale as $(s^*/n) \log\left( G / s^* \right) + m^* / n$ -- $G$ is the total number of groups and $m^*$ the number of coefficients in the $s^*$ groups which contain $\B{\beta}^*$ -- and improve over the least-squares case. We show that, when the signal is strongly group-sparse, Group L1-L2 is superior to L1 and Slope. In addition, we adapt our approach to the sub-Gaussian linear regression framework and reach the optimal minimax rate for Lasso, and an improved rate for Group-Lasso. Finally, we release an accelerated proximal algorithm that computes the nine main convex estimators of interest when the number of variables is of the order of $100,000s$.
Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the function space and provide simple yet effective methods to stabilize GANs' training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, where CLC is implemented as a squared $L2$ regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.
Hand-crafting effective and efficient structures for recurrent neural networks (RNNs) is a difficult, expensive, and time-consuming process. To address this challenge, we propose a novel neuro-evolution algorithm based on ant colony optimization (ACO), called ant swarm neuro-evolution (ASNE), for directly optimizing RNN topologies. The procedure selects from multiple modern recurrent cell types such as Delta-RNN, GRU, LSTM, MGU and UGRNN cells, as well as recurrent connections which may span multiple layers and/or steps of time. In order to introduce an inductive bias that encourages the formation of sparser synaptic connectivity patterns, we investigate several variations of the core algorithm. We do so primarily by formulating different functions that drive the underlying pheromone simulation process (which mimic L1 and L2 regularization in standard machine learning) as well as by introducing ant agents with specialized roles (inspired by how real ant colonies operate), i.e., explorer ants that construct the initial feed forward structure and social ants which select nodes from the feed forward connections to subsequently craft recurrent memory structures. We also incorporate a Lamarckian strategy for weight initialization which reduces the number of backpropagation epochs required to locally train candidate RNNs, speeding up the neuro-evolution process. Our results demonstrate that the sparser RNNs evolved by ASNE significantly outperform traditional one and two layer architectures consisting of modern memory cells, as well as the well-known NEAT algorithm. Furthermore, we improve upon prior state-of-the-art results on the time series dataset utilized in our experiments.