http://programmer.ie/tags/least-squares/ Recent content in Least Squares on Programmer.ie: Modern AI programming Hugo en-us Mon, 07 Sep 2026 14:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/18-chapter/ Mon, 07 Sep 2026 14:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/18-chapter/ <p><em>Part VI — Crossing Embedding Spaces</em></p> <h2 id="the-question-stated-carefully">The question, stated carefully</h2> <p>We have two encoders, <code>E_A</code> and <code>E_B</code>, and a set of objects <code>x</code>. Each object has two representations: <code>E_A(x)</code> in space A, <code>E_B(x)</code> in space B. Chapter 16 established these live in unrelated coordinate systems.</p> <p>The question:</p> <blockquote> <p><strong>Does there exist a map <code>T</code> such that <code>T(E_A(x)) ≈ E_B(x)</code> for objects <code>x</code> the map was never trained on — and by what standard do we judge &ldquo;≈&rdquo;?</strong></p>