Lorenzo Luzi

Sina Alemohammad, Josue Casco-Rodriguez, Lorenzo Luzi et al.

Seismic advances in generative AI algorithms for imagery, text, and other data types has led to the temptation to use synthetic data to train next-generation models. Repeating this process creates an autophagous (self-consuming) loop whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-art generative image models of three families of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and in whether the samples from previous generation models have been biased to trade off data quality versus diversity. Our primary conclusion across all scenarios is that without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) or diversity (recall) progressively decrease. We term this condition Model Autophagy Disorder (MAD), making analogy to mad cow disease.

Lorenzo Luzi, Paul M Mayer, Josue Casco-Rodriguez et al.

The inference stage of diffusion models can be seen as running a reverse-time diffusion stochastic differential equation, where samples from a Gaussian latent distribution are transformed into samples from a target distribution that usually reside on a low-dimensional manifold, e.g., an image manifold. The intermediate values between the initial latent space and the image manifold can be interpreted as noisy images, with the amount of noise determined by the forward diffusion process noise schedule. We utilize this interpretation to present Boomerang, an approach for local sampling of image manifolds. As implied by its name, Boomerang local sampling involves adding noise to an input image, moving it closer to the latent space, and then mapping it back to the image manifold through a partial reverse diffusion process. Thus, Boomerang generates images on the manifold that are ``similar,'' but nonidentical, to the original input image. We can control the proximity of the generated images to the original by adjusting the amount of noise added. Furthermore, due to the stochastic nature of the reverse diffusion process in Boomerang, the generated images display a certain degree of stochasticity, allowing us to obtain local samples from the manifold without encountering any duplicates. Boomerang offers the flexibility to work seamlessly with any pretrained diffusion model, such as Stable Diffusion, without necessitating any adjustments to the reverse diffusion process. We present three applications for Boomerang. First, we provide a framework for constructing privacy-preserving datasets having controllable degrees of anonymity. Second, we show that using Boomerang for data augmentation increases generalization performance and outperforms state-of-the-art synthetic data augmentation. Lastly, we introduce a perceptual image enhancement framework, which enables resolution enhancement.

Yehuda Dar, Lorenzo Luzi, Richard G. Baraniuk

We study the generalization behavior of transfer learning of deep neural networks (DNNs). We adopt the overparameterization perspective -- featuring interpolation of the training data (i.e., approximately zero train error) and the double descent phenomenon -- to explain the delicate effect of the transfer learning setting on generalization performance. We study how the generalization behavior of transfer learning is affected by the dataset size in the source and target tasks, the number of transferred layers that are kept frozen in the target DNN training, and the similarity between the source and target tasks. We show that the test error evolution during the target DNN training has a more significant double descent effect when the target training dataset is sufficiently large. In addition, a larger source training dataset can yield a slower target DNN training. Moreover, we demonstrate that the number of frozen layers can determine whether the transfer learning is effectively underparameterized or overparameterized and, in turn, this may induce a freezing-wise double descent phenomenon that determines the relative success or failure of learning. Also, we show that the double descent phenomenon may make a transfer from a less related source task better than a transfer from a more related source task. We establish our results using image classification experiments with the ResNet, DenseNet and the vision transformer (ViT) architectures.

Lorenzo Luzi, Helen Jenne, Ryan Murray et al.

The rapid advancement of Generative Adversarial Networks (GANs) necessitates the need to robustly evaluate these models. Among the established evaluation criteria, the FréchetInception Distance (FID) has been widely adopted due to its conceptual simplicity, fast computation time, and strong correlation with human perception. However, FID has inherent limitations, mainly stemming from its assumption that feature embeddings follow a Gaussian distribution, and therefore can be defined by their first two moments. As this does not hold in practice, in this paper we explore the importance of third-moments in image feature data and use this information to define a new measure, which we call the Skew Inception Distance (SID). We prove that SID is a pseudometric on probability distributions, show how it extends FID, and present a practical method for its computation. Our numerical experiments support that SID either tracks with FID or, in some cases, aligns more closely with human perception when evaluating image features of ImageNet data. Our work also shows that principal component analysis can be used to speed up the computation time of both FID and SID. Although we focus on using SID on image features for GAN evaluation, SID is applicable much more generally, including for the evaluation of other generative models.

Gabriel Diaz Ramos, Lorenzo Luzi, Debshila Basu Mallick et al.

To advance Educational Data Mining (EDM) within strict privacy-protecting regulatory frameworks, researchers must develop methods that enable data-driven analysis while protecting sensitive student information. Synthetic data generation is one such approach, enabling the release of statistically generated samples instead of real student records; however, existing deep learning and parametric generators often distort marginal distributions and degrade under iterative regeneration, leading to distribution drift and progressive loss of distributional support that compromise reliability. In response, we introduce the Non-Parametric Gaussian Copula (NPGC), a plug-and-play synthesis method that replaces deep learning and parametric optimization with empirical statistical anchoring to preserve the observed marginal distributions while modeling dependencies through a copula framework. NPGC integrates Differential Privacy (DP) at both the marginal and correlation levels, supports heterogeneous variable types, and treats missing data as an explicit state to retain informative absence patterns. We evaluate NPGC against deep learning and parametric baselines on five benchmark datasets and demonstrate that it remains stable across multiple regeneration cycles and achieves competitive downstream performance at substantially lower computational cost. We further validate NPGC through deployment in a real-world online learning platform, demonstrating its practicality for privacy-preserving research.

Jake R. Patock, Nicole Catherine Lewis, Kevin McCoy et al.

State-of-the-art (SOTA) image and text generation models are multimodal models that have many similarities to large language models (LLMs). Despite achieving strong performances, leading foundational multimodal model architectures frequently lag behind the architectural sophistication of contemporary LLMs. We propose GRR-CoCa, an improved SOTA Contrastive Captioner (CoCa) model that incorporates Gaussian error gated linear units, root mean squared normalization, and rotary positional embedding into the textual decoders and the vision transformer (ViT) encoder. Each architectural modification has been shown to improve model performance in LLMs, but has yet to be adopted in CoCa. We benchmarked GRR-CoCa against Baseline CoCa, a model with the same modified textual decoders but with CoCa's original ViT encoder. We used standard pretraining and fine-tuning workflows to benchmark the models on contrastive and generative tasks. Our GRR-CoCa significantly outperformed Baseline CoCa on the pretraining dataset and three diverse fine-tuning datasets. Pretraining improvements were 27.25% in contrastive loss, 3.71% in perplexity, and 7.15% in CoCa loss. The average fine-tuning improvements were 13.66% in contrastive loss, 5.18% in perplexity, and 5.55% in CoCa loss. We show that GRR-CoCa's modified architecture improves performance and generalization across vision-language domains.

Paul Mayer, Lorenzo Luzi, Ali Siahkoohi et al.

Generative models unfairly penalize data belonging to minority classes, suffer from model autophagy disorder (MADness), and learn biased estimates of the underlying distribution parameters. Our theoretical and empirical results show that training generative models with intentionally designed hypernetworks leads to models that 1) are more fair when generating datapoints belonging to minority classes 2) are more stable in a self-consumed (i.e., MAD) setting, and 3) learn parameters that are less statistically biased. To further mitigate unfairness, MADness, and bias, we introduce a regularization term that penalizes discrepancies between a generative model's estimated weights when trained on real data versus its own synthetic data. To facilitate training existing deep generative models within our framework, we offer a scalable implementation of hypernetworks that automatically generates a hypernetwork architecture for any given generative model.

Sina Alemohammad, Hossein Babaei, CJ Barberan et al.

Deep neural networks have become essential for numerous applications due to their strong empirical performance such as vision, RL, and classification. Unfortunately, these networks are quite difficult to interpret, and this limits their applicability in settings where interpretability is important for safety, such as medical imaging. One type of deep neural network is neural tangent kernel that is similar to a kernel machine that provides some aspect of interpretability. To further contribute interpretability with respect to classification and the layers, we develop a new network as a combination of multiple neural tangent kernels, one to model each layer of the deep neural network individually as opposed to past work which attempts to represent the entire network via a single neural tangent kernel. We demonstrate the interpretability of this model on two datasets, showing that the multiple kernels model elucidates the interplay between the layers and predictions.

Lorenzo Luzi, Carlos Ortiz Marrero, Nile Wynar et al.

We develop a measure for evaluating the performance of generative networks given two sets of images. A popular performance measure currently used to do this is the Fréchet Inception Distance (FID). FID assumes that images featurized using the penultimate layer of Inception-v3 follow a Gaussian distribution, an assumption which cannot be violated if we wish to use FID as a metric. However, we show that Inception-v3 features of the ImageNet dataset are not Gaussian; in particular, every single marginal is not Gaussian. To remedy this problem, we model the featurized images using Gaussian mixture models (GMMs) and compute the 2-Wasserstein distance restricted to GMMs. We define a performance measure, which we call WaM, on two sets of images by using Inception-v3 (or another classifier) to featurize the images, estimate two GMMs, and use the restricted $2$-Wasserstein distance to compare the GMMs. We experimentally show the advantages of WaM over FID, including how FID is more sensitive than WaM to imperceptible image perturbations. By modelling the non-Gaussian features obtained from Inception-v3 as GMMs and using a GMM metric, we can more accurately evaluate generative network performance.

Lorenzo Luzi, Yehuda Dar, Richard Baraniuk

We study overparameterization in generative adversarial networks (GANs) that can interpolate the training data. We show that overparameterization can improve generalization performance and accelerate the training process. We study the generalization error as a function of latent space dimension and identify two main behaviors, depending on the learning setting. First, we show that overparameterized generative models that learn distributions by minimizing a metric or $f$-divergence do not exhibit double descent in generalization errors; specifically, all the interpolating solutions achieve the same generalization error. Second, we develop a novel pseudo-supervised learning approach for GANs where the training utilizes pairs of fabricated (noise) inputs in conjunction with real output samples. Our pseudo-supervised setting exhibits double descent (and in some cases, triple descent) of generalization errors. We combine pseudo-supervision with overparameterization (i.e., overly large latent space dimension) to accelerate training while matching or even surpassing generalization performance without pseudo-supervision. While our analysis focuses mostly on linear models, we also apply important insights for improving generalization of nonlinear, multilayer GANs.

Sina Alemohammad, Hossein Babaei, Randall Balestriero et al.

High dimensionality poses many challenges to the use of data, from visualization and interpretation, to prediction and storage for historical preservation. Techniques abound to reduce the dimensionality of fixed-length sequences, yet these methods rarely generalize to variable-length sequences. To address this gap, we extend existing methods that rely on the use of kernels to variable-length sequences via use of the Recurrent Neural Tangent Kernel (RNTK). Since a deep neural network with ReLu activation is a Max-Affine Spline Operator (MASO), we dub our approach Max-Affine Spline Kernel (MASK). We demonstrate how MASK can be used to extend principal components analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) and apply these new algorithms to separate synthetic time series data sampled from second-order differential equations.

Lorenzo Luzi, Randall Balestriero, Richard G. Baraniuk

Most current computer vision datasets are composed of disconnected sets, such as images from different classes. We prove that distributions of this type of data cannot be represented with a continuous generative network without error. They can be represented in two ways: With an ensemble of networks or with a single network with truncated latent space. We show that ensembles are more desirable than truncated distributions in practice. We construct a regularized optimization problem that establishes the relationship between a single continuous GAN, an ensemble of GANs, conditional GANs, and Gaussian Mixture GANs. This regularization can be computed efficiently, and we show empirically that our framework has a performance sweet spot which can be found with hyperparameter tuning. This ensemble framework allows better performance than a single continuous GAN or cGAN while maintaining fewer total parameters.

Yehuda Dar, Paul Mayer, Lorenzo Luzi et al.

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i.e., the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained.