http://programmer.ie/tags/coordinate-systems/ Recent content in Coordinate Systems on Programmer.ie: Modern AI programming Hugo en-us Mon, 07 Sep 2026 13:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/16-chapter/ Mon, 07 Sep 2026 13:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/16-chapter/ <p><em>Part V — Embedding Spaces Are Not Universal</em></p> <h2 id="the-same-sentence-three-universes">The same sentence, three universes</h2> <p>Embed one sentence with three models:</p> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>model A (384-d): [ ... ] </span></span><span style="display:flex;"><span>model B (768-d): [ ... ] </span></span><span style="display:flex;"><span>model C (768-d): [ ... ] </span></span></code></pre></div><p>A and B differ in length, so nobody expects to compare them coordinate-wise. But B and C are both 768-dimensional. Line up their vectors and compute the cosine between B&rsquo;s vector and C&rsquo;s vector for the same sentence:</p>