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<div class=""><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">This is an announcement of </span><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(7, 7, 6); background-color: rgb(255, 255, 255);">Yibo
Jiang</span><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">'s MS Presentation</span><span class="" style="font-family: Calibri, Helvetica, sans-serif; font-size: 11pt;"><br class="">
</span><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">===============================================</span></div>
<div class="x_elementToProof"><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Candidate: </span><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(7, 7, 6); background-color: rgb(255, 255, 255);">Yibo
Jiang</span></div>
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<div class="x_elementToProof"><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Date: Monday, March 25, 2024</span></div>
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<div class="x_elementToProof"><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Time: 11 am CT</span></div>
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</span><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Location: JCL 298</span><span class="" style="font-family: Calibri, Helvetica, sans-serif; font-size: 11pt;"><br class="">
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</span><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Title: Uncovering Meanings of Embeddings via Partial Orthogonality</span><span class="" style="font-family: Calibri, Helvetica, sans-serif; font-size: 11pt;"><br class="">
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</span><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Abstract: Machine learning tools often rely on embedding text as vectors of real numbers. In this paper, we study how the
semantic structure of language is encoded in the algebraic structure of such embeddings. Specifically, we look at a notion of" semantic independence" capturing the idea that, eg," eggplant" and" tomato" are independent given" vegetable". Although such examples
are intuitive, it is difficult to formalize such a notion of semantic independence. The key observation here is that any sensible formalization should obey a set of so-called independence axioms, and thus any algebraic encoding of this structure should also
obey these axioms. This leads us naturally to use partial orthogonality as the relevant algebraic structure. We develop theory and methods that allow us to demonstrate that partial orthogonality does indeed capture semantic independence. Complementary to this,
we also introduce the concept of independence preserving embeddings where embeddings preserve the conditional independence structures of a distribution, and we prove the existence of such embeddings and approximations to them.</span><span class="" style="font-family: Calibri, Helvetica, sans-serif; font-size: 11pt;"><br class="">
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<div class="x_elementToProof"><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Advisors: Victor Veitch</span></div>
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<div class="x_elementToProof"><span class="" style="font-family: Calibri; font-size: 14.6667px; color: rgb(33, 33, 33); background-color: rgb(255, 255, 255);">Committee Members: Victor Veitch, Haifeng Xu, Bryon Aragam, and Yuxin Chen</span></div>
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