http://programmer.ie/tags/similarity/ Recent content in Similarity on Programmer.ie: Modern AI programming Hugo en-us Mon, 07 Sep 2026 12:20:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/15-chapter/ Mon, 07 Sep 2026 12:20:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/15-chapter/ <p><em>Part IV — Measuring the Representation</em></p> <h2 id="two-pairs-same-cosine-different-situations">Two pairs, same cosine, different situations</h2> <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>Pair 1: cos = 0.78 </span></span><span style="display:flex;"><span> the query&#39;s nearest neighbor scores 0.78; the 2nd scores 0.44 </span></span><span style="display:flex;"><span> the region is sparse; the ranking is stable under paraphrase </span></span><span style="display:flex;"><span> → a confident, isolated match </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span>Pair 2: cos = 0.78 </span></span><span style="display:flex;"><span> the nearest neighbor scores 0.78; the 2nd, 3rd, 4th score 0.77, 0.76, 0.76 </span></span><span style="display:flex;"><span> the region is a dense hub; re-embedding the query with a typo flips the top result </span></span><span style="display:flex;"><span> → a coin toss dressed as a match </span></span></code></pre></div><p>The scalar is identical. The situations are not. Everything that distinguishes them is geometric information the cosine threw away.</p>