The learning dynamics of modern neural networks remain an open problem in deep learning. The Neural Tangent Kernel (NTK) offers an elegant description of training dynamics in the infinite‑width limit, yet its classical formulation assumes a static data set. Modern model training practice departs from this strong assumption through the use of on‑the‑fly data augmentations (e.g. additive noise). In this work, we conduct an NTK-driven analysis of how data transformations affect a neural net's evolution in the function space. Our theoretical contributions characterize how repeated Gaussian perturbations from NTK-derived covariances can steer neural-net optimizations toward user‑specified behavior. These theoretical insights are empirically validated by controlled experiments. Taken together, our results lay the foundation for a promising future research direction that transforms the NTK from a descriptive to a prescriptive tool, enabling control of neural net training trajectories and behavior of inference generalization with grounded interventions.

Developments in deep neural nets have trended towards increasingly larger overparameterized architectures, resulting in lengthy training sessions with ever more elusive training dynamics. Thus, ensuring these models learn accurate generalizable representations of data efficiently is challenging. Previous works have developed specialized techniques from data-pruning, architecture selection, pseudo-label generation, bias identification, or label refurbishment to improve downstream training. Problematically, most methods require prohibitively expensive iterative model training. In this paper, we demonstrate that we can exploit the recent neural tangent kernel (NTK) theory for understanding and improving model training behavior before ever training a model. First, we show a powerful signal derived from the NTK theory can be computed remarkably fast. We then leverage this signal for the design of a unified suite of surprisingly effective tools for the four important tasks of architecture selection, pseudo-label verification, bias identification, and label refurbishment, all requiring zero model training.

Due to the scarcity of reliable anomaly labels, recent anomaly detection methods leveraging noisy auto-generated labels either select clean samples or refurbish noisy labels. However, both approaches struggle due to the unique properties of anomalies. Sample selection often fails to separate sufficiently many clean anomaly samples from noisy ones, while label refurbishment erroneously refurbishes marginal clean samples. To overcome these limitations, we design Unity, the first learning from noisy labels (LNL) approach for anomaly detection that elegantly leverages the merits of both sample selection and label refurbishment to iteratively prepare a diverse clean sample set for network training. Unity uses a pair of deep anomaly networks to collaboratively select samples with clean labels based on prediction agreement, followed by a disagreement resolution mechanism to capture marginal samples with clean labels. Thereafter, Unity utilizes unique properties of anomalies to design an anomaly-centric contrastive learning strategy that accurately refurbishes the remaining noisy labels. The resulting set, composed of selected and refurbished clean samples, will be used to train the anomaly networks in the next training round. Our experimental study on 10 real-world benchmark datasets demonstrates that Unity consistently outperforms state-of-the-art LNL techniques by up to 0.31 in F-1 Score (0.52 \rightarrow 0.83).

Generative Adversarial Networks (GANs) are a generative framework with a notorious reputation for instability. Despite significant work in attempting to improve stability, training remains extremely difficult in practice. Nearly all GAN optimization methods are built on either simultaneous (Sim-GDA) or alternating (Alt-GDA) gradient descent-ascent, where the generator and discriminator are updated either at the same time iteratively or in a fixed pattern. Unfortunately, neither Sim-GDA nor Alt-GDA have any strongly convergent properties, nor are they Lyapunov-stable. In this paper, we prove for simple GANs, for which training had been proven non-convergent under Sim-GDA and Alt-GDA, that our newly introduced training method is Lyapunov-stable. We then design a novel oracle-guided GDA training strategy called Dynamic-GDA that leverages generalized analogs of the properties exhibited in the simple case. We also prove that in contrast to Sim/Alt-GDA, GANs with Dynamic-GDA achieve Lyapunov-stable training with non-infinitesimal learning rates. Empirically, we show Dynamic-GDA improves convergence orthogonally to common stabilizing techniques on 8 classes of GAN models and 7 different data sets.

Human activity recognition (HAR) is the process of using mobile sensor data to determine the physical activities performed by individuals. HAR is the backbone of many mobile healthcare applications, such as passive health monitoring systems, early diagnosing systems, and fall detection systems. Effective HAR models rely on deep learning architectures and big data in order to accurately classify activities. Unfortunately, HAR datasets are expensive to collect, are often mislabeled, and have large class imbalances. State-of-the-art approaches to address these challenges utilize Generative Adversarial Networks (GANs) for generating additional synthetic data along with their labels. Problematically, these HAR GANs only synthesize continuous features — features that are represented by real numbers — recorded from gyroscopes, accelerometers, and other sensors that produce continuous data. This is limiting since mobile sensor data commonly has discrete features that provide additional context such as device location and the time-of-day, which have been shown to substantially improve HAR classification. Hence, we studied Conditional Tabular Generative Adversarial Networks (CTGANs) for data generation to synthesize mobile sensor data containing both continuous and discrete features, a task never been done by state-of-the-art approaches. We show HAR-CTGANs generate data with greater realism resulting in allowing better downstream performance in HAR models, and when state-of-the-art models were modified with HAR-CTGAN characteristics, downstream performance also improves.

Human activity recognition (HAR), the task of predicting the activities performed by an individual using mobile sensor data, is an active and important area of research. Unfortunately, it is very costly to collect the data required to train robust HAR classifiers. To tackle this issue, there has been an increasing focus on generating synthetic HAR data for augmentation purposes. The state-of-the-art generative HAR approaches utilize Generative Adversarial Networks (GANs) to produce realistic synthetic HAR data. However, these solutions can not generate personalized data that matches the behavior of particular users, limiting their potential use cases. This is particularly problematic in the mobile health domain, where the target users are often elderly or disabled and are thus likely to have activity signals that are unique from the general population. To overcome this drawback, we propose a novel controllable GAN solution Control-HAR-GAN. Our approach learns user and activity signals independently, and when generating synthetic instances, practitioners can specify both the activity to be generated as well as the user the data should match. This has the added benefit in that our model supports novel user-activity pairs by generating examples that match the data that would have been recorded by a particular user if they had performed the target activity, even if the user never performed that activity during the data collection process. We show that our model outperforms the existing HAR GAN approach in generating observed user-activity pairs by up to 10%. Additionally, our approach can also perform the task of novel user-activity pair generation, which is impossible for existing approaches.