Vectron: I stopped asking them to imagine it Why I built a navigable 3D map of an LLM's meaning, and why measuring where it lies is the other half of the project Transcript of the narrated version (6 min). Narrated with a synthetic voice (Larry). The writing is Esteban Rey's — kilowatto.com. --- Vectron: I stopped asking them to imagine it. Why I built a navigable 3D map of an LLM's meaning, and why measuring where it lies is the other half of the project. I teach an artificial intelligence course almost every month, which consists of four sessions, each lasting an hour and a half. At some point in the first session, I always end up in the same place, where I ask the audience to imagine a language model, not as a traditional database of tables and rows, but as something closer to a space. The problem is, I don't control that imagination, as everyone in the room builds a different metaphor, and several of those metaphors are wrong. I noticed this issue quickly, and when I showed them the language model instead of asking them to imagine it, even if it was just a rough sketch on the whiteboard, the whole session changed. Over time, this approach led to the development of a fully didactic system, which is Vectron. What it is, without metaphors. Vectron is a public 3D map of meaning, live at vectron.kilowatto.com. Every particle in the cube represents a real word from a corpus of 20,473 concepts, and its position is determined by a real 1,024-dimensional embedding generated by bge-m3, which is then compressed down to 3 coordinates via PCA. This is not a mockup or a prerecorded animation. When you type a sentence, it gets tokenized using the same BPE, cl100k_base, that a real model uses. If you pin a particle, its neighbors are retrieved from an actual vector search in Cloudflare Vectorize, which searches across the full 1,024 dimensions, not just the 3 visible on screen. When comparing two concepts, the cosine similarity displayed is the actual cosine similarity. The entire system consists of Workers, Vectorize, D1, R2, and Workers AI, with the frontend built in Three.js on top of WebGPU, which can handle 20,473 particles in a single draw call. The corpus continues to grow every 30 minutes via cron. Why I didn't leave it as a weekend curiosity. I've spent more than 25 years in technology, most of it building companies, including Ignia Cloud, my investments, and Yucatech Festival. Vectron wasn't born from that same ambition. It came from exactly the same place as my classroom frustration, which is the idea that if something can be shown instead of described, it should be shown properly, even if that means going deep into shaders, PCA, and GPU rendering instead of leaving it as a weekend experiment. Teaching where it lies, too. The part of the project I'm proudest of isn't the part that looks pretty, it's the part that measures, with real numbers over the corpus, how much you should trust what you're looking at. Vectron measures several key aspects of itself, including the fact that the 3 visible axes retain just 11.69% of the real variance, and the full 16 components don't even reach 26%. Additionally, around 31% of the neighbors the screen suggests are invented by the projection, with a trustworthiness of 0.694 at k=10. The cosine similarity between two completely unrelated words is 0.412, indicating that zero similarity does not exist. Furthermore, there is real clustering, with one concept showing up in 77 neighbor lists, compared to an average of 10. This data informs the product's most important design decision, which is that the promise is tied to the query you make, not to where the points happen to land. The lines connecting concepts are the honest channel, representing real cosine similarity in 1,024 dimensions, whereas position is the dishonest channel, representing only 11.69% of the variance. As a result, the lines were kept, but with several corrections, including a cap on how many lines get drawn, thickness proportional to the real cosine similarity, a label declaring what you asked, and lines cut short when the relationship isn't reciprocal. The moment I knew it was going to work. It wasn't when I finished the rendering, or when the corpus hit its target of 20,473 concepts. It was in a course, showing it to my students, when they pinned a word and watched its real neighbors light up in space. That "ahh, now I get it" look I'd been chasing for years with whiteboard drawings — I finally saw it happen in real time, without having to explain anything further. What's next. Vectron doesn't stop at a single level. There's a version for someone who has never touched a language model, with no jargon, and 300 curated concepts instead of the full 20,473, because fewer elements produce more real learning. There's an intermediate version, which includes tokens, embeddings, and a failure lab. Additionally, there's an advanced version, for those who want the full instrument, which provides the unedited math and control over the corpus. Splitting by level of expertise, rather than by difficulty, is what separates a novice looking at surface features from an expert looking at deep principles. The project keeps correcting itself. When one of the audits I ran on it, six in total, with more than 190 verified references, found that the corpus proved nothing about real bilingualism, I ran the proper protocol and it turned out Spanish scored correctly 50.7% of the time against 100% for English, a gap entirely between languages. This issue got fixed by embedding both forms, and today it's 99.3%. The real idea behind Vectron is an educational tool about artificial intelligence that applies to itself the same scrutiny it teaches people to demand from any AI. Vectron is designed to be interactive, allowing users to play with it and evaluate how well or how badly it explains something they used to be asked only to imagine.