Nicholas Boffi @nmboffi Twitter profile | Pikagi

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Nicholas Boffi

@nmboffi

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Incoming Assistant Professor at CMU. Courant Instructor @NYU_Courant . Prev. @Harvard , @MIT , @GoogleAI , @BerkeleyLab , @FulbrightPrgrm , @doecsgf , @NorthwesternU .

New York City

https://t.co/EHCaYmzhcT

Joined July 2023

Don't wanna be here? Send us removal request.

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@nmboffi

Nicholas Boffi

15 days

🔥❤️‍🔥🥳🍾 New paper alert! ❤️‍🔥🔥🍾🥳 Quite stoked about this recent collaboration with @msalbergo and @evdende2 ! We introduce a new class of generative models that we call **flow map matching models**, which learn the flow map of a probability flow ODE.

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Flow Map Matching

Generative models based on dynamical transport of measure, such as diffusion models, flow matching models, and stochastic interpolants, learn an ordinary or stochastic differential equation whose...

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@nmboffi

Nicholas Boffi

3 months

Very excited to announce that in September 2024 I will be joining the faculty at @CarnegieMellon as a tenure-track assistant professor of computational mathematics and as an affiliated faculty in machine learning at @mldcmu !

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@nmboffi

Nicholas Boffi

9 months

Very excited to announce new work () with Eric Vanden-Eijnden from @NYUCourant . We leverage a correspondence between the Fokker-Planck equation and the score-based diffusion method of @DrYangSong , @StefanoErmon to compute the entropy of active systems. 1/n

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@nmboffi

Nicholas Boffi

3 months

Really nice review of large deviations and statistical mechanics:

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The large deviation approach to statistical mechanics

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study,...

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@nmboffi

Nicholas Boffi

9 months

Our results confirm previous theoretical and computational predictions that the entropy production for systems undergoing motility-induced phase separation is concentrated on interfaces, e.g. and . More results on arxiv! 7/n

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Entropy Production in Field Theories without Time-Reversal Symmetry: Quantifying the Non-Equilibr...

Active matter systems, composed of individual agents that use energy to self-propel, operate far from thermal equilibrium. But markers of nonequilibrium at macroscopic scales are often elusive. A new...

journals.aps.org

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@nmboffi

Nicholas Boffi

11 months

*Very* excited to broadcast some recently-published work with Eric Vanden-Eijnden at @NYU_Courant , which just appeared in @MLSTjournal a few weeks ago (). Some eye candy from the publication below.

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@nmboffi

Nicholas Boffi

3 months

Really interesting new paper on self-supervised learning and PDEs.

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@nmboffi

Nicholas Boffi

9 months

Remarkably, a single network trained with 4096 particles also generalizes to new regions of the phase diagram, as evidenced by varying the packing fraction (phi). We trained with phi=0.5. 4/n

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@nmboffi

Nicholas Boffi

10 months

@sp_monte_carlo Following up on @msalbergo and refining the suggestion by @mufan_li , you can derive an *equality* for the KL between any two time marginals by appealing to the corresponding Fokker-Planck equations. This also works for transport equations, but the result is weaker. See the paper!

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@nmboffi

Nicholas Boffi

9 months

The correspondence between the Fokker-Planck equation and score-based diffusion is laid out in the infographic below. 5/n

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@nmboffi

Nicholas Boffi

4 months

Was a lot of fun working on this one, and I’m glad to see it finally published!

@Ariel_4321

Ariel Amir

4 months

Our first paper with the new eLife model is out: The work studies, primarily computationally, a model for microbial evolution, where the strength of epistasis can be tuned, and shows that this leads to a slow-down of the fitness trajectory dynamics.

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@nmboffi

Nicholas Boffi

6 months

@gabrielpeyre See also !

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Probability flow solution of the Fokker-Planck equation

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...

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@nmboffi

Nicholas Boffi

8 months

@FlorentinGuth We had a review that was almost certainly written by ChatGPT

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@nmboffi

Nicholas Boffi

11 months

We develop a new, flow-based method for solving the time-dependent Fokker-Planck equation. Motivated by recent advances in generative modeling -- in particular, score-based diffusion -- we recast the Fokker-Planck equation as an equivalent, score-based transport equation.

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@nmboffi

Nicholas Boffi

9 months

Fundamentally, the key is view the system from a *deterministic* perspective along the probability flow, rather than a stochastic perspective. This leads to simpler, more interpretable dynamics, along with hard-to-estimate quantities like the entropy production rate. 6/n

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@nmboffi

Nicholas Boffi

7 months

@MountainOfMoon I submitted an application — I hope you find it interesting!

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@nmboffi

Nicholas Boffi

11 months

In addition, the method can be used to generate other interesting outputs, such as effective deterministic phase portraits for stochastic systems, as shown in the first tweet. Code is written in jax and available at .

GitHub - nmboffi/sbtm: Repository for score-based transport modeling.

Repository for score-based transport modeling. Contribute to nmboffi/sbtm development by creating an account on GitHub.

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@nmboffi

Nicholas Boffi

4 months

@PreetumNakkiran I’m a big fan of the continuous time view.

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@nmboffi

Nicholas Boffi

9 months

The key to scale to such high-dimensionality is to introduce a spatially-local transformer neural network that operates directly on the particles. We found that when trained with 4096 particles it makes excellent predictions for much higher-dimensional systems. 3/n

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@nmboffi

Nicholas Boffi

9 months

The movie above contains 32,768 active swimmers undergoing motility-induced phase separation, corresponding to a 131,072-dimensional Fokker-Planck equation. The particles are colored by two different definitions of their contribution to the entropy production rate. 2/n

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@nmboffi

Nicholas Boffi

11 months

We show that by performing a kind of sequential, self-consistent score matching procedure, one can control the KL divergence from the model to the ideal solution of the equation. This leads to a loss that can be efficiently minimized over neural nets.

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@nmboffi

Nicholas Boffi

11 months

@joanbruna @msalbergo @gabrielpeyre Thanks Joan! Commenting because I’m on twitter now :)

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@nmboffi

Nicholas Boffi

11 months

Anyone know if there is support for any of the recent memory efficient attention implementations such as FlashAttention or FlashAttention 2 in jax? Tagging some jax maestros -- @SingularMattrix @PatrickKidger -- any network library okay with me.

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@nmboffi

Nicholas Boffi

11 months

And here's the method applied to a low-dimensional system describing the motion of an active swimmer, where we can visualize 10^5 samples simultaneously.

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@nmboffi

Nicholas Boffi

4 months

@sp_monte_carlo It’s Jarzynski-Crooks, essentially!

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@nmboffi

Nicholas Boffi

11 months

Practically, this gives access to several interesting quantities that are not available from trajectories of the underlying SDE, such as evaluation of the density and estimation of the entropy production rate, a quantity of interest in the active matter community.

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@nmboffi

Nicholas Boffi

4 months

@QuanquanGu Flow matching models (equivalently stochastic interpolants) are more general and include diffusions as a special case. They can bridge two arbitrary densities exactly in finite time -- diffusions use Gaussians and need infinite time. See for more details!

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Stochastic Interpolants: A Unifying Framework for Flows and Diffusions

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a...

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@nmboffi

Nicholas Boffi

3 months

@atalwalkar @JunhongShen1 @__tm__157 This is really cool stuff. Coming from a background in computational math and numerical PDEs, it’s surprising to me that LLMs would work here, because the data is so fundamentally different. I’ll have a closer look at the paper, but any idea why the LLM has a useful inductive

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@nmboffi

Nicholas Boffi

9 months

@y0b1byte Beamer presentations can be great I think, but this approach is not the way

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@nmboffi

Nicholas Boffi

11 months

Practically, this gives access to several interesting quantities that are not available from trajectories of the underlying SDE, such as evaluation of the density and the entropy production rate, a quantity of interest in the active matter community.

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@nmboffi

Nicholas Boffi

8 months

@HazanPrinceton @TravisEGibson See also our work with Stephen Tu on a related topic:

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Regret Bounds for Adaptive Nonlinear Control

We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances. We prove the first finite-time regret bounds for adaptive nonlinear control...

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@nmboffi

Nicholas Boffi

11 months

Solving the resulting equation via the method of characteristics leads to the probability flow ODE, which dynamically builds a transport map from the initial condition to the solution at any later time.

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@nmboffi

Nicholas Boffi

23 days

@Majumdar_Ani @GoogleDeepMind Congrats!!

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@nmboffi

Nicholas Boffi

11 months

We show that by performing a kind of sequential, self-consistent score matching procedure, one can control the KL divergence from the model to the ideal solution of the equation. This leads to a loss that can be efficiently minimized over neural nets.

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@nmboffi

Nicholas Boffi

4 months

@QuanquanGu I wasn't aware of SPIN, but it sounds great! I'll share with my colleagues.

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@nmboffi

Nicholas Boffi

11 months

@2prime_PKU @NU_IEMS @nyu Congrats, Yiping, excited for you to join us next year!

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@nmboffi

Nicholas Boffi

11 months

@SingularMattrix @PatrickKidger thanks!!

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@nmboffi

Nicholas Boffi

2 months

@afedercooper @YaleCompsci @yaleisp congrats!

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@nmboffi

Nicholas Boffi

11 months

We apply the method to several high-dimensional systems of interacting particles, for which standard PDE solvers do not apply. Here's the method applied to a 100-dimensional system of interacting particles chasing a moving trap, where we visualize the evolution of a single sample

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@nmboffi

Nicholas Boffi

11 months

We develop a new, flow-based method for solving the time-dependent Fokker-Planck equation. Motivated by recent advances in generative modeling -- in particular, score-based diffusion -- we recast the Fokker-Planck equation as an equivalent, score-based transport equation.

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