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Unrolled Autodiff of iterative Algorithms

When you have iterative parts in a computational graph (like optimization problems, linear solves, root-finding etc.) you can either unroll differentiate or implicitly differentiate them. The former has a counter-intuitive Jacobian converge (=Curse of Unrolling). Code: https://github.com/Ceyron/machine-lea... Here is the paper, this video is based on: https://arxiv.org/abs/2209.13271 ------ 👉 This educational series is supported by the world-leaders in integrating machine learning and artificial intelligence with simulation and scientific computing, Pasteur Labs and Institute for Simulation Intelligence. Check out https://simulation.science/ for more on their pursuit of 'Nobel-Turing' technologies (https://arxiv.org/abs/2112.03235 ), and for partnership or career opportunities. ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files (contributions are very welcome): https://github.com/Ceyron/machine-lea... 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff:   / felix-koehler   and   / felix_m_koehler   💸 : If you want to support my work on the channel, you can become a Patreon here:   / mlsim   🪙: Or you can make a one-time donation via PayPal: https://www.paypal.com/paypalme/Felix... ------- Timestamps: 00:00 Intro 00:50 Iterative processes and two modes of autodiff 02:00 Considered problem 04:32 Code Setup 04:51 Inner objective and analytical optimizer 07:19 Gradient Descent optimization 10:07 Primal/Forward convergence 14:58 Unrolled Differentiation 18:58 Assess Jacobian convergence 21:05 Explaining the result 23:48 Example plot for explanation 26:00 About the inflection point 27:00 Curse of Unrolling 28:00 Outro