𝐶𝑎𝑟𝑎𝑚𝑖𝑧𝑎𝑟𝑢'𝑠 𝐵𝑙𝑜𝑔 feed:2023:11:24

Advanced Linear Algebra: Vector Spaces & Matrix Decompositions

anonymous@undisclosed.example.com (Anonymous) — Mon, 04 Dec 2023 21:20:22 +0000

Advanced Linear Algebra: Vector Spaces & Matrix Decompositions

Playlist Link

abstract, Linear-algebra, Anthony-Bosman

Controlled Sparsity via Constrained Optimization

anonymous@undisclosed.example.com (Anonymous) — Fri, 24 Nov 2023 22:14:20 +0000

Controlled Sparsity via Constrained Optimization

Abstract:

Penalty-based regularization is extremely popular in ML. However, this powerful technique can require an expensive trial-and-error process for tuning the penalty coefficient. In this paper, we take sparse training of deep neural networks as a case study to illustrate the advantages of a constrained optimization approach: improved tunability, and a more interpretable hyperparameter. Our proposed technique (i) has a negligible computational overhead, (ii) reliably achieves arbitrary sparsity targets “in one shot” while retaining high accuracy, and (iii) scales successfully to large residual models and datasets.

In this talk, I will also give a brief introduction to Cooper External Link, a general-purpose, deep learning-first library for constrained optimization in Pytorch. Cooper was developed as part of the research direction above, and was born out of the need to handle constrained optimization problems for which the loss or constraints may not be “nicely behaved” or “theoretically tractable”, as is often the case in DL.

Sparsity, optimization, Regularization, Jose-Gallego-Posada

DAEs

anonymous@undisclosed.example.com (Anonymous) — Sun, 03 Nov 2024 02:35:43 +0000

DAEs

Differentiable Simulation Methods for Robotic Agent Design

anonymous@undisclosed.example.com (Anonymous) — Mon, 04 Dec 2023 21:22:55 +0000

Differentiable Simulation Methods for Robotic Agent Design

Thesis, external link

Abstract

Designing robots with extreme performance in a given task has long been an exciting research problem drawing attention from researchers in robotics, graphics, and artificial intelligence. As a robot is a combination of its hardware and software, an optimal robot requires both an excellent implementation of its hardware (e.g., morphological, topological, and geometrical designs) and an outstanding design of its software (e.g., perception, planning, and control algorithms). While we have seen promising breakthroughs for automating a robot's software design with the surge of deep learning in the past decade, exploration of optimal hardware design is much less automated and is still mainly driven by human experts, a process that is both labor-intensive and error-prone. Furthermore, experts typically optimize a robot's hardware and software separately, which may miss optimal designs that can only be revealed by optimizing its hardware and software simultaneously. This thesis argues that it is time to rethink robot design as a holistic process where a robot's body and brain should be co-optimized jointly and automatically. In this thesis, we present a computational robot design pipeline with differentiable simulation as a key player. We first introduce the concept of computational robot design on a real-world copter whose geometry and controller are co-optimized with a differentiable simulator, resulting in a custom copter that outperforms designs suggested by human experts by a substantial margin. Next, we push the boundary of differentiable simulation by developing advanced differentiable simulators for soft-body and fluid dynamics. Contrary to traditional belief, we show that deriving gradients for such intricate, high-dimensional physics systems can be both science and art. Finally, we discuss challenges in transferring computational designs discovered in simulation to real-world hardware platforms. We present a solution to this simulation-to-reality transfer problem using our differentiable simulator on an example of modeling and controlling a real-world soft underwater robot. We conclude this thesis by discussing open research directions in differentiable simulation and envisioning a fully automated computational design pipeline for real-world robots in the future.

MIT, robotics, Differentiable-Simulation, optimization

Differential and Integral Calculus 1

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:51:11 +0000

Differential and Integral Calculus 1

Differential and integral calculus I -international. Dr. Aviv Censor Course no. 104003

Freshman students at the Technion are required to take the Calculus mathematics course, a challenging course covering quite a few topics that are necessary for future academic reference: Functions – Limits and Continuity, Sequences, Derivatives, The Basic Theorems of the Differential Calculus, Indefinite Integrals, Definite Integrals and the Fundamental Theorem of Calculus, Improper Integrals, Series and Power Series.

Due to course intensity lecturers encourage students to take part in all classes, participate, complete all home-work assignments, ask questions during office hours and inevitably - work hard.

According to course lecturer Aviv Censor: “Calculus is like swimming or bicycle riding. You can't learn by watching someone else, even if that someone is Michael Phelps and even if you (think you) understand everything they are doing.

Our students at the international school come from over 30 countries, they work hard and work together to succeed. We believe that just like swimming or biking, math can be fun!”

For additional information about our Engineering Undergraduate and Freshman Programs please visit:

External Link

course, math, Technion, Calculus, Aviv-Censor

Differential and Integral Calculus 2

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:51:30 +0000

Differential and Integral Calculus 2

Direct Methods for Sparse Linear Systems

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:50:20 +0000

Direct Methods for Sparse Linear Systems

Playlist Link

Abstract

A series of 42 lectures on sparse matrix algorithms. Covers material from my book, “Direct Methods for Sparse Linear Systems”, published by SIAM External Link. Lecture notes are at External Link (start with siam06.pdf, and then notes2.pdf to notes7.pdf). The sequence of lectures follows the sequence of the lecture notes, and also the sequence in the book. I will be posting a list of topics covered in each lecture, as well.

course, math, numerics, Direct-Methods, Sparse-Linear-Systems, Tim-Davis

Geometric mechanics of continuum and articulated soft robots

anonymous@undisclosed.example.com (Anonymous) — Fri, 24 Nov 2023 20:30:32 +0000

Geometric mechanics of continuum and articulated soft robots

Talk at the IROS 2020 Tutorial “Review on Screw Theory and Geometric Robot Dynamics”

A Geometrically Exact Model for Soft Continuum Robots: The Finite Element Deformation Space Formulation

mechanics-of-continuum, lie-group, lie-algebra, soft-robots, robotics, Stanislao-Grazioso

So You Think You Know How to Take Derivatives? | Steven Johnson

anonymous@undisclosed.example.com (Anonymous) — Fri, 24 Nov 2023 20:16:26 +0000

So You Think You Know How to Take Derivatives? | Steven Johnson

Abstract

Derivatives are seen as the “easy” part of learning calculus: a few simple rules, and every function's derivatives are at your fingertips! But these basic techniques can turn bewildering if you are faced with much more complicated functions like a matrix determinant (what is a derivative “with respect to a matrix” anyway?), the solution of a differential equation, or a huge engineering calculation like a fluid simulation or a neural-network model. And needing such derivatives is increasingly common thanks to the growing prevalence of machine learning, large-scale optimization, and many other problems demanding sensitivity analysis of complex calculations. Although many techniques for generalizing and applying derivatives are known, that knowledge is currently scattered across a diverse literature, and requires students to put aside their memorized rules and re-learn what a derivative really is: linearization. In 2022 and 2023, Alan and I put together a one-month, 16-hour “Matrix Calculus” course at MIT that refocuses differential calculus on the linear algebra at its heart, and we hope to remind you that derivatives are not a subject that is “done” after your second semester of calculus

optimization, Derivatives, automatic-differentiation, algorithmic-differentiation

The Corrs - Angel

anonymous@undisclosed.example.com (Anonymous) — Fri, 24 Nov 2023 22:07:15 +0000

The Corrs - Angel

The-Corrs, song

The Corrs - Would You Be Happier

anonymous@undisclosed.example.com (Anonymous) — Fri, 24 Nov 2023 22:09:05 +0000

The Corrs - Would You Be Happier

The-Corrs, song