Search Results for author: Nicholas M. Boffi

Found 14 papers, 2 papers with code

SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers

1 code implementation16 Jan 2024 Nanye Ma, Mark Goldstein, Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden, Saining Xie

We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT).

Image Generation

Stochastic interpolants with data-dependent couplings

no code implementations5 Oct 2023 Michael S. Albergo, Mark Goldstein, Nicholas M. Boffi, Rajesh Ranganath, Eric Vanden-Eijnden

In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings.


Multimarginal generative modeling with stochastic interpolants

no code implementations5 Oct 2023 Michael S. Albergo, Nicholas M. Boffi, Michael Lindsey, Eric Vanden-Eijnden

Given a set of $K$ probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals.

Fairness Style Transfer

Deep learning probability flows and entropy production rates in active matter

no code implementations22 Sep 2023 Nicholas M. Boffi, Eric Vanden-Eijnden

We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles.

Stochastic Interpolants: A Unifying Framework for Flows and Diffusions

1 code implementation15 Mar 2023 Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden

The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient.


Probability flow solution of the Fokker-Planck equation

no code implementations9 Jun 2022 Nicholas M. Boffi, Eric Vanden-Eijnden

The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation.

Adversarially Robust Stability Certificates can be Sample-Efficient

no code implementations20 Dec 2021 Thomas T. C. K. Zhang, Stephen Tu, Nicholas M. Boffi, Jean-Jacques E. Slotine, Nikolai Matni

Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems.

Nonparametric adaptive control and prediction: theory and randomized algorithms

no code implementations7 Jun 2021 Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine

A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions.

Regret Bounds for Adaptive Nonlinear Control

no code implementations26 Nov 2020 Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine

We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances.

Learning Stability Certificates from Data

no code implementations13 Aug 2020 Nicholas M. Boffi, Stephen Tu, Nikolai Matni, Jean-Jacques E. Slotine, Vikas Sindhwani

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property.

The role of optimization geometry in single neuron learning

no code implementations15 Jun 2020 Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine

Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks.

A continuous-time analysis of distributed stochastic gradient

no code implementations28 Dec 2018 Nicholas M. Boffi, Jean-Jacques E. Slotine

We analyze the effect of synchronization on distributed stochastic gradient algorithms.

Distributed Optimization

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