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    <title>Semantic Checksum on Programmer.ie: Modern AI programming</title>
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    <description>Recent content in Semantic Checksum on Programmer.ie: Modern AI programming</description>
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    <lastBuildDate>Mon, 07 Sep 2026 15:00:00 +0000</lastBuildDate>
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      <title>Can a Smaller Representation Preserve a Larger One?</title>
      <link>http://programmer.ie/books/embeddings-from-first-principles/22-chapter/</link>
      <pubDate>Mon, 07 Sep 2026 15:00:00 +0000</pubDate>
      <guid>http://programmer.ie/books/embeddings-from-first-principles/22-chapter/</guid>
      <description>&lt;p&gt;&lt;em&gt;Part VII — What Survives Transformation&lt;/em&gt;&lt;/p&gt;&#xA;&lt;h2 id=&#34;two-vectors-for-one-document&#34;&gt;Two vectors for one document&lt;/h2&gt;&#xA;&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; style=&#34;color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;&#34;&gt;&lt;code class=&#34;language-text&#34; data-lang=&#34;text&#34;&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;full_doc      →  E(full_doc)        one vector&#xA;&lt;/span&gt;&lt;/span&gt;&lt;span style=&#34;display:flex;&#34;&gt;&lt;span&gt;summary(doc)  →  E(summary(doc))    one vector&#xA;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;Both are single vectors of the same dimension. One was produced from 4,000 words; the other from 120. The question:&lt;/p&gt;&#xA;&lt;blockquote&gt;&#xA;&lt;p&gt;&lt;strong&gt;How much of the document&amp;rsquo;s representational geometry survives when the document is compressed — and is the surviving-or-not a signal we can use?&lt;/strong&gt;&lt;/p&gt;&lt;/blockquote&gt;&#xA;&lt;p&gt;If &lt;code&gt;E(summary)&lt;/code&gt; lands where &lt;code&gt;E(full_doc)&lt;/code&gt; lands &lt;em&gt;and&lt;/em&gt; behaves like it under retrieval and clustering, the summary is a faithful compression in the sense the embedding cares about. If it drifts, something was dropped — and &lt;em&gt;which&lt;/em&gt; direction it drifted may tell us what.&lt;/p&gt;</description>
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