Publications

Relative Almost Sure Regret Bounds for Certainty Equivalence Control of Markov Jump Systems

Borna Sayedana

Mohammad Afshari

Peter E. Caines

Aditya Mahajan

In this paper, we consider learning and control problem in an unknown Markov jump linear system (MJLS) with perfect state observations. We f… (see more)irst establish a generic upper bound on regret for any learning based algorithm. We then propose a certainty equivalence-based learning alagrithm and show that this algorithm achieves a regret of

2023-12-13

2023 62nd IEEE Conference on Decision and Control (CDC) (published)

Weighted-Norm Bounds on Model Approximation in MDPs with Unbounded Per-Step Cost

Berk Bozkurt

Aditya Mahajan

Ashutosh Nayyar

Yi Ouyang

We consider the problem of designing a control policy for an infinite-horizon discounted cost Markov Decision Process (MDP) …

2023-12-13

IEEE Conference on Decision and Control (published)

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

Alexandre AGM Duval

Simon V. Mathis

Chaitanya K. Joshi

Victor Schmidt

Santiago Miret

Fragkiskos D. Malliaros

Taco Cohen

Pietro Lio’

Michael M. Bronstein

2023-12-12

ArXiv (preprint)

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

Alexandre AGM Duval

Simon V. Mathis

Chaitanya K. Joshi

Victor Schmidt

Santiago Miret

Fragkiskos D. Malliaros

Taco Cohen

Pietro Lio’

Michael M. Bronstein

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graph… (see more)s with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

2023-12-12

ArXiv (preprint)

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

Alexandre AGM Duval

Simon V. Mathis

Chaitanya K. Joshi

Victor Schmidt

Santiago Miret

Fragkiskos D. Malliaros

Taco Cohen

Pietro Lio’

Michael M. Bronstein

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graph… (see more)s with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

2023-12-12

ArXiv (preprint)

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

Alexandre AGM Duval

Simon V. Mathis

Chaitanya K. Joshi

Victor Schmidt

Santiago Miret

Fragkiskos D. Malliaros

Taco Cohen

Pietro Lio’

Michael M. Bronstein

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graph… (see more)s with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

2023-12-12

ArXiv (preprint)

Efficient Graphics Representation with Differentiable Indirection

Sayantan Datta

Carl Marshall

Zhao Dong

Zhengqin Li

Derek Nowrouzezahrai

We introduce differentiable indirection – a novel learned primitive that employs differentiable multi-scale lookup tables as an effective … (see more)substitute for traditional compute and data operations across the graphics pipeline. We demonstrate its flexibility on a number of graphics tasks, i.e., geometric and image representation, texture mapping, shading, and radiance field representation. In all cases, differentiable indirection seamlessly integrates into existing architectures, trains rapidly, and yields both versatile and efficient results.

2023-12-11

SIGGRAPH Asia 2023 Conference Papers (published)

Explorable Mesh Deformation Subspaces from Unstructured 3D Generative Models

Arman Maesumi

Paul Guerrero

Noam Aigerman

Vladimir Kim

Matthew Fisher

Siddhartha Chaudhuri

Daniel Ritchie

2023-12-11

SIGGRAPH Asia 2023 Conference Papers (published)

Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks

MohammadReza Davari

Eugene Belilovsky

The rapid development of AI systems has been greatly influenced by the emergence of foundation models. A common approach for targeted proble… (see more)ms involves fine-tuning these pre-trained foundation models for specific target tasks, resulting in a rapid spread of models fine-tuned across a diverse array of tasks. This work focuses on the problem of merging multiple fine-tunings of the same foundation model derived from a spectrum of auxiliary tasks. We introduce a new simple method, Model Breadcrumbs, which consists of a sparsely defined weight set that guides model adaptation within the weight space of a pre-trained model. These breadcrumbs are constructed by subtracting the weights from a pre-trained model before and after fine-tuning, followed by a sparsification process that eliminates weight outliers and negligible perturbations. Our experiments demonstrate the effectiveness of Model Breadcrumbs to simultaneously improve performance across multiple tasks. This contribution aligns with the evolving paradigm of updatable machine learning, reminiscent of the collaborative principles underlying open-source software development, fostering a community-driven effort to reliably update machine learning models. Our method is shown to be more efficient and unlike previous proposals does not require hyperparameter tuning for each new task added. Through extensive experimentation involving various models, tasks, and modalities we establish that integrating Model Breadcrumbs offers a simple, efficient, and highly effective approach for constructing multi-task models and facilitating updates to foundation models.

2023-12-11

ArXiv (preprint)

Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks

MohammadReza Davari

Eugene Belilovsky

The rapid development of AI systems has been greatly influenced by the emergence of foundation models. A common approach for targeted proble… (see more)ms involves fine-tuning these pre-trained foundation models for specific target tasks, resulting in a rapid spread of models fine-tuned across a diverse array of tasks. This work focuses on the problem of merging multiple fine-tunings of the same foundation model derived from a spectrum of auxiliary tasks. We introduce a new simple method, Model Breadcrumbs, which consists of a sparsely defined weight set that guides model adaptation within the weight space of a pre-trained model. These breadcrumbs are constructed by subtracting the weights from a pre-trained model before and after fine-tuning, followed by a sparsification process that eliminates weight outliers and negligible perturbations. Our experiments demonstrate the effectiveness of Model Breadcrumbs to simultaneously improve performance across multiple tasks. This contribution aligns with the evolving paradigm of updatable machine learning, reminiscent of the collaborative principles underlying open-source software development, fostering a community-driven effort to reliably update machine learning models. Our method is shown to be more efficient and unlike previous proposals does not require hyperparameter tuning for each new task added. Through extensive experimentation involving various models, tasks, and modalities we establish that integrating Model Breadcrumbs offers a simple, efficient, and highly effective approach for constructing multi-task models and facilitating updates to foundation models.

2023-12-11

ArXiv (preprint)

Model Breadcrumbs: Scaling Multi-Task Model Merging with Sparse Masks

MohammadReza Davari

Eugene Belilovsky

2023-12-11

ArXiv (preprint)