http://programmer.ie/tags/geometry-preservation/ Recent content in Geometry Preservation on Programmer.ie: Modern AI programming Hugo en-us Wed, 09 Sep 2026 02:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/26-chapter/ Wed, 09 Sep 2026 02:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/26-chapter/ <p><em>Research Coda — What Alignment Really Preserves</em></p> <h2 id="preserve-the-geometry-is-not-a-complete-instruction">&ldquo;Preserve the geometry&rdquo; is not a complete instruction</h2> <p>A bridge translates vectors from space A into space B.</p> <p>The natural instinct is to say:</p> <blockquote> <p>Preserve the source geometry while you translate.</p></blockquote> <p>That sounds obviously correct. If two source points are close, keep them close. If two source points are far apart, keep them far apart. Preserve pairwise cosine, distances, neighborhoods.</p> <p>But Chapter 16 established something uncomfortable: different encoders do not merely rotate the same universe. They can disagree on neighborhoods, density, rank order, hard distinctions, and calibration.</p>