Differentiable Logic Cellular Automata — https://google-research.github.io/self-organising-systems/difflogic-ca/?hn
#HackerNews #Differentiable #Logic #Cellular #Automata #research #AI #machinelearning #selforganizing-systems

@schmitz (left) explaining his recent work on making #dftk algorithmically #differentiable at the #cecam workshop on #dft and #ai (https://www.cecam.org/workshop-details/1281). With his work derivatives of key density-functional theory quantities like forces or band structures wrt. model parameters can now be easily computed.

Deep Learning with Jax
https://www.manning.com/books/deep-learning-with-jax
#ycombinator #neural_networks #Python #Google #Flax #Haiku #gradient_processing #optimization #numerical #computations #federated_learning #parallelized #distributed #primitives #differentiable

The #Zhukovsky #Aerofoil (sometimes transliterated as #Joukowsky from #Russian), is a 2D model of #streamlined #Airflow past a #wing. It uses #ComplexVariable and is an #AnalyticFunction (i.e. #Differentiable everywhere, save at isolated #Singularities). Take a circle in the #ComplexPlane which is not quite centred at the #origin but passes through the #coordinate (1,0) or (z=1+0i).

#MyWork #CCBYSA #AppliedMathematics #WxMaxima #FreeSoftware #Aeronautics #Aerodynamics #LaminarFlow

Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

- Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

- Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

#Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods

I am again ready to fight this world, like nothing happened in the last few days....
#differentiable #ache #unformidable

#Juliacon #workshops are out :julia: !

So many cool stuff! I am particularly looking forward to

- #webdev with #genieframework

- #differentiable #programming on #gpu

- #imageprocessing with #julialang

what are your favorites?

https://pretalx.com/juliacon2023/featured/

see you in #boston in a few months!

The usual recipe to inject constraints is to #relax them to make them #differentiable or to enforce them during training, by encoding them into auxiliary #losses...

This however does not guarantee that at test and #deployment time predictions will satisfy the constraints...

3/

@emtiyaz @mathieualain

Totally agree!

Looking forward to hear from you @emtiyaz on this recent paper where you can have a #differentiable #layer that encodes #logical #constraints and provably #guarantees that the predictions of a #neural net satisfy the constraint!

By making everything modular and compartimentalized (plug&play) you can easily integrate #symbolic and #neural #reasoning

https://openreview.net/forum?id=o-mxIWAY1T8

@tiago_j_m Hey do you know about #combinatorial #species? I've been researching these marvelous gizmos for a few years, and tying their development into larger theoretical mosaics. They are closely related to advances in #evolutionary/#genetic and #differentiable #programming.

immersion is a #differentiable function between differentiable manifolds whose derivative is everywhere injective.

immersion is a #differentiable function between differentiable manifolds whose derivative is everywhere injective.