Our takeaway: Don’t just throw an optimizer at arbitrary grammars, design the grammar for descent!
Paper: Design for Descent: What Makes a Shape Grammar Easy to Optimize?
Authors: @milin_k_, @jackzzhang, @nmwsharp, @AdrianaSchulz7
Project: https://t.co/a8hEdmo23M
Can we apply gradient descent to discrete changes? In our new #SIGGRAPHAsia paper, we show that gradient descent can work on shape grammars, as in CAD and procedural modeling, but only if the grammars are designed correctly!
We show that these properties matter through ablations over grammar variants and compare against existing random-walk approaches like RJMCMC. Grammars that satisfy more of our guidelines consistently converge faster and reach better optima.
@_onionesque Linear algebra became category theory, it’s not really taught but at some point we should know everything. And it turns out linear algebra is actually important 🤣
@keenanisalive Great lecturers I had do all of these on the blackboard, sparingly. One caveat about pictures is that they can lead to bad intuition. For instance if we draw a closed set on the board it’s always a region bounded by a closed curve, but irl closed sets become extremely complex.
@EinsteinLeDuc @keenanisalive They can effortlessly create their own intuitions and link examples. In the extremes I’ve seen in class, they can “predict” what theorems come next despite having no prior knowledge of the lesson plan, because they extracted so much information from the definitions given.
Jack was one of the first students in our group 3DL! He did a couple of awesome works with us during his undergrad. Check out his papers and make sure to follow his journey as he starts as a PhD student in @uwcse with @AdrianaSchulz7 ! https://t.co/d83WyRX2tr
@sellan_s To me it feels like the other way around, the surface is an explicit system of equations. And implicit functions can be extracted locally at points on the surface, under conditions by IFT. So these functions (hence their graphs) are implicit in the surface.