arXiv subjects

Giulio Franzese

Publications and source records attributed to Giulio Franzese.

26 records · Page 2Linked to original sources

arXiv2023

One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Models

Generative Models (GMs) have attracted considerable attention due to their tremendous success in various domains, such as computer vision where they are capable to generate impressive realistic-looking images. Likelihood-based GMs are attractive due to the possibility to generate new data by a single model evaluation. However, they typically achieve lower sample quality compared to state-of-the-art score-based diffusion models (DMs). This paper provides a significant step in the direction of addressing this limitation. The idea is to borrow one of the strengths of score-based DMs, which is the ability to perform accurate density estimation in low-density regions and to address manifold overfitting by means of data mollification. We connect data mollification through the addition of Gaussian noise to Gaussian homotopy, which is a well-known technique to improve optimization. Data mollification can be implemented by adding one line of code in the optimization loop, and we demonstrate that this provides a boost in generation quality of likelihood-based GMs, without computational overheads. We report results on image data sets with popular likelihood-based GMs, including variants of variational autoencoders and normalizing flows, showing large improvements in FID score.

cs.LG↗

arXiv2023

Continuous-Time Functional Diffusion Processes

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

cs.LG↗

arXiv2023

Multi-modal Latent Diffusion

Multi-modal data-sets are ubiquitous in modern applications, and multi-modal Variational Autoencoders are a popular family of models that aim to learn a joint representation of the different modalities. However, existing approaches suffer from a coherence-quality tradeoff, where models with good generation quality lack generative coherence across modalities, and vice versa. We discuss the limitations underlying the unsatisfactory performance of existing methods, to motivate the need for a different approach. We propose a novel method that uses a set of independently trained, uni-modal, deterministic autoencoders. Individual latent variables are concatenated into a common latent space, which is fed to a masked diffusion model to enable generative modeling. We also introduce a new multi-time training method to learn the conditional score network for multi-modal diffusion. Our methodology substantially outperforms competitors in both generation quality and coherence, as shown through an extensive experimental campaign.

cs.LG↗

arXiv2022

How Much is Enough? A Study on Diffusion Times in Score-based Generative Models

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

stat.ML↗

arXiv2021

Revisiting the Effects of Stochasticity for Hamiltonian Samplers

We revisit the theoretical properties of Hamiltonian stochastic differential equations (SDES) for Bayesian posterior sampling, and we study the two types of errors that arise from numerical SDE simulation: the discretization error and the error due to noisy gradient estimates in the context of data subsampling. Our main result is a novel analysis for the effect of mini-batches through the lens of differential operator splitting, revising previous literature results. The stochastic component of a Hamiltonian SDE is decoupled from the gradient noise, for which we make no normality assumptions. This leads to the identification of a convergence bottleneck: when considering mini-batches, the best achievable error rate is $\mathcal{O}(η^2)$, with $η$ being the integrator step size. Our theoretical results are supported by an empirical study on a variety of regression and classification tasks for Bayesian neural networks.

cs.LG↗

arXiv2021

Sparsification as a Remedy for Staleness in Distributed Asynchronous SGD

Large scale machine learning is increasingly relying on distributed optimization, whereby several machines contribute to the training process of a statistical model. In this work we study the performance of asynchronous, distributed settings, when applying sparsification, a technique used to reduce communication overheads. In particular, for the first time in an asynchronous, non-convex setting, we theoretically prove that, in presence of staleness, sparsification does not harm SGD performance: the ergodic convergence rate matches the known result of standard SGD, that is $\mathcal{O} \left( 1/\sqrt{T} \right)$. We also carry out an empirical study to complement our theory, and confirm that the effects of sparsification on the convergence rate are negligible, when compared to 'vanilla' SGD, even in the challenging scenario of an asynchronous, distributed system.

cs.LG↗

arXiv2020

Isotropic SGD: a Practical Approach to Bayesian Posterior Sampling

In this work we define a unified mathematical framework to deepen our understanding of the role of stochastic gradient (SG) noise on the behavior of Markov chain Monte Carlo sampling (SGMCMC) algorithms. Our formulation unlocks the design of a novel, practical approach to posterior sampling, which makes the SG noise isotropic using a fixed learning rate that we determine analytically, and that requires weaker assumptions than existing algorithms. In contrast, the common traits of existing \sgmcmc algorithms is to approximate the isotropy condition either by drowning the gradients in additive noise (annealing the learning rate) or by making restrictive assumptions on the \sg noise covariance and the geometry of the loss landscape. Extensive experimental validations indicate that our proposal is competitive with the state-of-the-art on \sgmcmc, while being much more practical to use.

cs.LG↗

arXiv2018

Deep Information Networks

We describe a novel classifier with a tree structure, designed using information theory concepts. This Information Network is made of information nodes, that compress the input data, and multiplexers, that connect two or more input nodes to an output node. Each information node is trained, independently of the others, to minimize a local cost function that minimizes the mutual information between its input and output with the constraint of keeping a given mutual information between its output and the target (information bottleneck). We show that the system is able to provide good results in terms of accuracy, while it shows many advantages in terms of modularity and reduced complexity.

cs.LG↗