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cathillIs machine learning merely a form of curve-fitting? <a href="https://mastodon.social/tags/machinelearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#machinelearning</a> <a href="https://mastodon.social/tags/ai" class="mention hashtag" rel="nofollow noopener" target="_blank">#ai</a> <a href="https://mastodon.social/tags/curvefitting" class="mention hashtag" rel="nofollow noopener" target="_blank">#curvefitting</a> <a href="https://mastodon.social/tags/linearregression" class="mention hashtag" rel="nofollow noopener" target="_blank">#linearregression</a> <a href="https://mastodon.social/tags/buzzwords" class="mention hashtag" rel="nofollow noopener" target="_blank">#buzzwords</a>

SplinesThe classic <a href="https://pixelfed.social/discover/tags/IonicScroll?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#IonicScroll</a> is the most complex of all components in the <a href="https://pixelfed.social/discover/tags/IonicOrder?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#IonicOrder</a> mainly because it is poorly documented, if at all, and even poorly understood. It is as if the classical architects deliberately concealed its enigmatic design secrets within the confines of a smooth elegant shell that could only be revealed after intense study and analysis. I got this impression because I spent years searching for credible and actionable documentation on how to recreate this beautiful design in a <a href="https://pixelfed.social/discover/tags/CAD?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#CAD</a> tool. In the Age of Internet and Social Media, my web searches always disappointed me because the results lacked something vital in one respect or another. Over the years, I created hundreds of versions of the scroll that looked so perfect and pleasing that I thought I had cracked it, only to find some flaw or another in my work. So, it is with caution that I present my work on the scroll in the hopes that someone will build upon this knowledge and either validate the design, or correct it and share it with me and the rest of the world. Looking back at my progress, I'm now surprised at how remarkably simple and elegant the design is that defied familiar geometrical construction techniques I had been using until now. As I mentioned in my introductory post, this design can be recreated by drawing simple 2-dimensional lines and circular arcs, but instead of just <a href="https://pixelfed.social/discover/tags/primaryProfileCurves?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#primaryProfileCurves</a>, we will use up to three additional sets of curves — <a href="https://pixelfed.social/discover/tags/secondaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#secondaryCurves</a>, <a href="https://pixelfed.social/discover/tags/tertiaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#tertiaryCurves</a>, and <a href="https://pixelfed.social/discover/tags/quaternaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#quaternaryCurves</a> — each derived from the previous set. I extracted the <a href="https://pixelfed.social/discover/tags/primaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#primaryCurves</a> after a lengthy trial-and-error process that involved <a href="https://pixelfed.social/discover/tags/curveFitting?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#curveFitting</a> image scans from <a href="https://pixelfed.social/discover/tags/Vignola?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#Vignola</a>’s book, <a href="https://pixelfed.social/discover/tags/RegolaArchitettura?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#RegolaArchitettura</a>. I had to <a href="https://pixelfed.social/discover/tags/reverseEngineer?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#reverseEngineer</a> the details because the measurements have either been lost, or are locked away in some library. Even though we start with lines and arcs, the end results are always <a href="https://pixelfed.social/discover/tags/NURBS?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#NURBS</a> curves and surfaces, but everything is done by the CAD tool, and no additional math is needed.

Victoria Stuart 🇨🇦 🏳️‍⚧️Predicting Ordinary Differential Equations with Transformers <a href="https://arxiv.org/abs/2307.12617" rel="nofollow noopener" translate="no" target="_blank">https://arxiv.org/abs/2307.12617</a>The application of ML / transformers to ODE is fascinating. There's a terrific 2019-01 blog post that covers this (and more!): 👍️Understanding Neural ODE's <a href="https://jontysinai.github.io/jekyll/update/2019/01/18/understanding-neural-odes.html" rel="nofollow noopener" translate="no" target="_blank">https://jontysinai.github.io/jekyll/update/2019/01/18/understanding-neural-odes.html</a> Discussion: <a href="https://news.ycombinator.com/item?id=18978764" rel="nofollow noopener" translate="no" target="_blank">https://news.ycombinator.com/item?id=18978764</a>Transformer (machine learning model): <a href="https://en.wikipedia.org/wiki/Transformer_(machine_learning_model)" rel="nofollow noopener" translate="no" target="_blank">https://en.wikipedia.org/wiki/Transformer_(machine_learning_model)</a><a href="https://mastodon.social/tags/ML" class="mention hashtag" rel="nofollow noopener" target="_blank">#ML</a> <a href="https://mastodon.social/tags/OCE" class="mention hashtag" rel="nofollow noopener" target="_blank">#OCE</a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mastodon.social/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#MachineLearning</a> <a href="https://mastodon.social/tags/transformers" class="mention hashtag" rel="nofollow noopener" target="_blank">#transformers</a> <a href="https://mastodon.social/tags/MathematicalModeling" class="mention hashtag" rel="nofollow noopener" target="_blank">#MathematicalModeling</a> <a href="https://mastodon.social/tags/regression" class="mention hashtag" rel="nofollow noopener" target="_blank">#regression</a> <a href="https://mastodon.social/tags/CurveFitting" class="mention hashtag" rel="nofollow noopener" target="_blank">#CurveFitting</a> <a href="https://mastodon.social/tags/differentiation" class="mention hashtag" rel="nofollow noopener" target="_blank">#differentiation</a>

Richard CreamerHere is a 2019 tutorial project I did for people new to <a href="https://c.im/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#MachineLearning</a> and who may have rusty Calculus skills (which I tried to gently re-introduce).This simplified intro covers some <a href="https://c.im/tags/ML" class="mention hashtag" rel="nofollow noopener" target="_blank">#ML</a> concepts from the perspective of least-squares curve fitting, perhaps a more intuitive topic.R source code is included for the 50+ plots and their calculations.<a href="https://c.im/tags/rstats" class="mention hashtag" rel="nofollow noopener" target="_blank">#rstats</a> <a href="https://c.im/tags/CurveFitting" class="mention hashtag" rel="nofollow noopener" target="_blank">#CurveFitting</a><a href="https://sites.google.com/view/rcreamer/home/techstem/mlintro" rel="nofollow noopener" translate="no" target="_blank">https://sites.google.com/view/rcreamer/home/techstem/mlintro</a>

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