Embeddings, vectors, and arithmetic

I find it so fascinating that at the end of the article the author alludes to something I&#x27;ve started becoming aware of:<p>There is a zone of illegal thoughts, that becomes definable by model-training. A physical boundary in n-dimensional concept-space. An &quot;aligned&quot; or &quot;safe&quot; AI system knows where this boundary is and does not reach inside it. Vectors (embeddings) that would probe it should instead intersect the surface like a ray-trace in graphics, and return the embedded concept at minimum distance to the safe-idea-boundary.<p>Intuitively, we all know what this zone is. It&#x27;s the difference between being a wild barbarian and a gentleman. Or being chill vs antisocial. Seeing it in pure math is pretty awesome.

Perhaps I&#x27;m missing something but this looks like a heavy case of what&#x27;s old is new again - the original &quot;king - man + woman = queen&quot; paper is nearly a decade old:<p><a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1509.01692" rel="nofollow noreferrer">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1509.01692</a>

I found the missing link to the emoji page on Barney Hill&#x27;s Github in case anyone else was looking for it:<p><a href="https:&#x2F;&#x2F;www.barneyhill.com&#x2F;pages&#x2F;emoji&#x2F;index.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.barneyhill.com&#x2F;pages&#x2F;emoji&#x2F;index.html</a>

Really inspirational project. Does anyone know if there&#x27;s an analog of this to the LLM space? I.e. can you take the embedding of two sentences and get a &#x27;combined&#x27; sentence? Either by searching a corpus for the closest match or by feeding that combined embedding into an LLM that generates it.

So the question is: do embeddings form a linear space? I.e. does scaling and addition make any sense?

<i>&gt; At Prodia, we&#x27;ve started to investigate building safety systems by checking if the input prompts are within a distance threshold of known adult or illegal concepts.</i><p>This is why we can’t have nice AI things.<p>After my experience with RAG across a dozen models and god knows how many experiments against parts of Libgen’s archive in topics I’m familiar with, I’m not sure embeddings are actually useful for anything requiring any kind of accuracy. They’re great for low stakes purposes or as a step in a human driven workflow but like LLMs they’re a very fuzzy and often times inaccurate tool.

&quot;illegal concepts&quot;<p>Embeddings mean that when we have a thought police they can now be more targeted and effective than before. Any thought you express can be objectively measured &quot;using the euclidean distance or cosine similarity&quot; for illegal concepts, and censored, corrected or punished accordingly. I imagine that this will come early for comment sections on the web.