Last year I had formed a project of making web animations to explain the unintuitive aspects of high-dimensional spaces. I was inspired by the impressive demo of anime.js<\/a>, a presentation given by prof. Lutz D\u00fcmbgen<\/a> at the University of Bern, and the fact that I often struggled to get the right intuitions when reasoning about what goes on in the high-dimensions spaces of neural networks. So I met with a math professor (I work at a university), and together we worked out a few theorems and properties that fit with this topic. And then…<\/p>\n\n\n\n Nothing happened. The reality of my PhD caught back to me, I realized I didn’t have enough time to allocate to that project at the moment, and so I shelved it. I do not work much on front-end, so, even though early-2025 AI tools could help bridge the gap of my unfamiliarity, there remained the work of designing the visualisations. That was too much for me at the time.<\/p>\n\n\n\n Fast-forward to last Wednesday. I see impressive demos of Claude one-shotting complex applications, and praise for GLM 5.3<\/a> as being almost SOTA. Coincidentally, GLM 5.3 was immediately made available through Mistral API which I had chosen (I like open-source models) to use in a Pi instance (I like open-source software too). So, I decided to test its capability on the shelved project from last year.<\/p>\n\n\n\n I dictated one prompt in Pi and left it to work for a dozen of minutes, and I was really impressed with the result… Not only the ideas of what to represent were good, but the execution was excellent too.<\/p>\n\n\n\n I want you to make a single page application with a few visualizations to help people have a better understanding of high dimensions geometry, especially the points where high dimensions operate in a different manner than low dimensions. For example the fact that a sphere in high dimensions has most of its weight on the surface and almost nothing in the center, things like that. So, first think of a few properties of this kind that high dimensions have and then for each of those try to think of a way to make it understandable and to help people visualize it and then execute on these visualizations. The whole thing should be in a single HTML file, so you can have separate CSS and JavaScript on the side. But in the end it should be just one page. And the main point is for it to help the understanding.<\/mark><\/em><\/p>\n<\/details>\n\n\n\n The agent produced 5 ideas of unintuitive principles to represent; all of which were on the list I had made over a year before. Not only that, but it also had ideas of how to represent these principles, which I hadn’t worked on.<\/p>\n\n\n\n The caveat is that the visualisations were not easy to understand, even for me who had the topic. So I needed a few follow-up prompts to make it add 3D animations to make the whole thing more intuitive. I also gave it the other ideas I had listed, for the agent to make visualisations of them too.<\/p>\n\n\n\n The agent built it all with HTML, CSS and JavaScript, and it worked on the first try. It had no bugs and was aesthetically good-looking. Even the visualization settings and little scrolling animations worked flawlessly, while I know I would have needed painstaking sessions of debugging.<\/p>\n\n\n\n It was also not the purple gradient style that we got used to associating with AI outputs. Instead, it made clear and readable text and figures, with the right amount of color to make things pretty but not distracting.<\/p>\n\n\n\n I was really impressed at the speed and quality I obtained with this Pi + GLM5.3 combination, and how little supervision it needed. The cost of tokens was very low too (around ~$2). I ended up working a few hours more on this project, and I didn’t look at the code even once.<\/p>\n\n\n\n After a few more iterations to improve the app, I made it available online with GitLab Pages (it fits in a single HTML page): https:\/\/jchataigne.gitlab.io\/h-dim\/<\/a><\/p>\n\n\n\nProject<\/h4>\n\n\n\n
the prompt <\/summary>\n
Ideas<\/h5>\n\n\n\n
Execution<\/h5>\n\n\n\n
Conclusion<\/h4>\n\n\n\n