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    <title>Editorial Memory on Programmer.ie: Modern AI programming</title>
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      <title>From Deltas to Operators</title>
      <link>http://programmer.ie/books/embeddings-from-first-principles/23-chapter/</link>
      <pubDate>Mon, 07 Sep 2026 15:10:00 +0000</pubDate>
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      <description>&lt;p&gt;&lt;em&gt;Part VII — What Survives Transformation&lt;/em&gt;&lt;/p&gt;&#xA;&lt;h2 id=&#34;the-other-thing-a-subtraction-might-mean&#34;&gt;The other thing a subtraction might mean&lt;/h2&gt;&#xA;&lt;p&gt;&lt;code&gt;king − man + woman ≈ queen&lt;/code&gt; is the famous demonstration that a &lt;em&gt;direction&lt;/em&gt; in embedding space can correspond to a semantic relation. It is also, as Chapter 2 noted, partly curated and works best locally — and it has a long list of documented problems: the offset method&amp;rsquo;s success is entangled with plain cosine-neighbourhood structure, so a &amp;ldquo;the direction transfers&amp;rdquo; result has to beat the baseline of &lt;em&gt;ignoring the offset and returning the nearest neighbour of the source word&lt;/em&gt; (&lt;a href=&#34;https://aclanthology.org/W16-2503/&#34;&gt;Linzen, 2016&lt;/a&gt;); and performance varies wildly by relation type (&lt;a href=&#34;https://aclanthology.org/S17-1017/&#34;&gt;Rogers, Drozd &amp;amp; Li, 2017&lt;/a&gt;).&lt;/p&gt;</description>
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