Neural networks trained with stochastic gradient descent exhibit an inductive bias towards simpler decision boundaries, typically converging to a narrow family of functions, and often fail to capture more complex features. This phenomenon raises concerns about the capacity of deep models to adequately learn and represent real-world datasets. Traditional approaches such as explicit regularization, data augmentation, architectural modifications, etc., have largely proven ineffective in encouraging the models to learn diverse features. In this work, we investigate the impact of pre-training models with noisy labels on the dynamics of SGD across various architectures and datasets. We show that pretraining promotes learning complex functions and diverse features in the presence of noise. Our experiments demonstrate that pre-training with noisy labels encourages gradient descent to find alternate minima that do not solely depend upon simple features, rather learns more complex and broader set of features, without hurting performance.

It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently adaptive iterative techniques were analyzed from a theoretical point of view. In the present paper we introduce new adaptive algorithms endowed with momentum terms for stochastic non-convex optimization problems. Our purpose is to show a deep connection between accelerated methods endowed with different inertial steps and AMSGrad-type momentum methods. Our methodology is based on the framework of stochastic and possibly non-convex objective mappings, along with some assumptions that are often used in the investigation of adaptive algorithms. In addition to discussing the finite-time horizon analysis in relation to a certain final iteration and the almost sure convergence to stationary points, we shall also look at the worst-case iteration complexity. This will be followed by an estimate for the expectation of the squared Euclidean norm of the gradient. Various computational simulations for the training of neural networks are being used to support the theoretical analysis. For future research we emphasize that there are multiple possible extensions to our work, from which we mention the investigation regarding non-smooth objective functions and the theoretical analysis of a more general formulation that encompass our adaptive optimizers in a stochastic framework.

Graph Neural Networks (GNNs) have emerged in recent years as a powerful tool to learn tasks across a wide range of graph domains in a data-driven fashion; based on a message passing mechanism, GNNs have gained increasing popularity due to their intuitive formulation, closely linked with the Weisfeiler-Lehman (WL) test for graph isomorphism, to which they have proven equivalent. From a theoretical point of view, GNNs have been shown to be universal approximators, and their generalization capability (namely, bounds on the Vapnik Chervonekis (VC) dimension) has recently been investigated for GNNs with piecewise polynomial activation functions. The aim of our work is to extend this analysis on the VC dimension of GNNs to other commonly used activation functions, such as sigmoid and hyperbolic tangent, using the framework of Pfaffian function theory. Bounds are provided with respect to architecture parameters (depth, number of neurons, input size) as well as with respect to the number of colors resulting from the 1-WL test applied on the graph domain. The theoretical analysis is supported by a preliminary experimental study.

Neural network compression has been an increasingly important subject, due to its practical implications in terms of reducing the computational requirements and its theoretical implications, as there is an explicit connection between compressibility and the generalization error. Recent studies have shown that the choice of the hyperparameters of stochastic gradient descent (SGD) can have an effect on the compressibility of the learned parameter vector. Even though these results have shed some light on the role of the training dynamics over compressibility, they relied on unverifiable assumptions and the resulting theory does not provide a practical guideline due to its implicitness. In this study, we propose a simple modification for SGD, such that the outputs of the algorithm will be provably compressible without making any nontrivial assumptions. We consider a one-hidden-layer neural network trained with SGD and we inject additive heavy-tailed noise to the iterates at each iteration. We then show that, for any compression rate, there exists a level of overparametrization (i.e., the number of hidden units), such that the output of the algorithm will be compressible with high probability. To achieve this result, we make two main technical contributions: (i) we build on a recent study on stochastic analysis and prove a 'propagation of chaos' result with improved rates for a class of heavy-tailed stochastic differential equations, and (ii) we derive strong-error estimates for their Euler discretization. We finally illustrate our approach on experiments, where the results suggest that the proposed approach achieves compressibility with a slight compromise from the training and test error.

Leveraging privileged information (PI), or features available during training but not at test time, has recently been shown to be an effective method for addressing label noise. However, the reasons for its effectiveness are not well understood. In this study, we investigate the role played by different properties of the PI in explaining away label noise. Through experiments on multiple datasets with real PI (CIFAR-N/H) and a new large-scale benchmark ImageNet-PI, we find that PI is most helpful when it allows networks to easily distinguish clean from noisy data, while enabling a learning shortcut to memorize the noisy examples. Interestingly, when PI becomes too predictive of the target label, PI methods often perform worse than their no-PI baselines. Based on these findings, we propose several enhancements to the state-of-the-art PI methods and demonstrate the potential of PI as a means of tackling label noise. Finally, we show how we can easily combine the resulting PI approaches with existing no-PI techniques designed to deal with label noise.

For tabular data generated from IIoT devices, traditional machine learning (ML) techniques based on the decision tree algorithm have been employed. However, these methods have limitations in processing tabular data where real number attributes dominate. To address this issue, DeepInsight, REFINED, and IGTD were proposed to convert tabular data into images for utilizing convolutional neural networks (CNNs). They gather similar features in some specific spots of an image to make the converted image look like an actual image. Gathering similar features contrasts with traditional ML techniques for tabular data, which drops some highly correlated attributes to avoid overfitting. Also, previous converting methods fixed the image size, and there are wasted or insufficient pixels according to the number of attributes of tabular data. Therefore, this paper proposes a new converting method, Vortex Feature Positioning (VFP). VFP considers the correlation of features and places similar features far away from each. Features are positioned in the vortex shape from the center of an image, and the number of attributes determines the image size. VFP shows better test performance than traditional ML techniques for tabular data and previous converting methods in five datasets: Iris, Wine, Dry Bean, Epileptic Seizure, and SECOM, which have differences in the number of attributes.

Among attempts at giving a theoretical account of the success of deep neural networks, a recent line of work has identified a so-called'lazy' training regime in which the network can be well approximated by its linearization around initialization. Here we investigate the comparative effect of the lazy (linear) and feature learning (non-linear) regimes on subgroups of examples based on their difficulty. Specifically, we show that easier examples are given more weight in feature learning mode, resulting in faster training compared to more difficult ones. In other words, the non-linear dynamics tends to sequentialize the learning of examples of increasing difficulty. We illustrate this phenomenon across different ways to quantify example difficulty, including c-score, label noise, and in the presence of easy-to-learn spurious correlations. Our results reveal a new understanding of how deep networks prioritize resources across example difficulty.

Out-of-distribution generalization is a core challenge in machine learning. We introduce and propose a solution to a new type of out-of-distribution evaluation, which we call close category generalization. This task specifies how a classifier should extrapolate to unseen classes by considering a bi-criteria objective: (i) on in-distribution examples, output the correct label, and (ii) on out-of-distribution examples, output the label of the nearest neighbor in the training set. In addition to formalizing this problem, we present a new training algorithm to improve the close category generalization of neural networks. We compare to many baselines, including robust algorithms and out-of-distribution detection methods, and we show that our method has better or comparable close category generalization. Then, we investigate a related representation learning task, and we find that performing well on close category generalization correlates with learning a good representation of an unseen class and with finding a good initialization for few-shot learning. Code available at https://github.com/yangarbiter/close-category-generalization

This technical report records the experiments of applying multiple machine learning algorithms for predicting eating and food purchasing behaviors of free-living individuals. Data was collected with accelerometer, global positioning system (GPS), and body-worn cameras called SenseCam over a one week period in 81 individuals from a variety of ages and demographic backgrounds. These data were turned into minute-level features from sensors as well as engineered features that included time (e.g., time since last eating) and environmental context (e.g., distance to nearest grocery store). Algorithms include Logistic Regression, RBF-SVM, Random Forest, and Gradient Boosting. Our results show that the Gradient Boosting model has the highest mean accuracy score (0.7289) for predicting eating events before 0 to 4 minutes. For predicting food purchasing events, the RBF-SVM model (0.7395) outperforms others. For both prediction models, temporal and spatial features were important contributors to predicting eating and food purchasing events.