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@@ -84,9 +84,9 @@ The cited-paper encoder was trained jointly with the query-talk encoder under a
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  Each talk *Ti* and paper *Rj* is encoded into embeddings *fT(Ti)* and *fR(Rj)*.
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  Their dot-product similarity *sij = fT(Ti)路fR(Rj)* is optimized using a sigmoid-based binary loss supporting multiple positives per query:
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- \[
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  L = - \sum_i [y_i \log \sigma(s_i) + (1 - y_i)\log(1 - \sigma(s_i))]
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- \]
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  Negatives are sampled in-batch from other talk鈥損aper pairs.
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  Before training, a **domain adaptation stage** aligned each talk with its own paper鈥檚 abstract to adapt to scientific and spoken-language data.
 
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  Each talk *Ti* and paper *Rj* is encoded into embeddings *fT(Ti)* and *fR(Rj)*.
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  Their dot-product similarity *sij = fT(Ti)路fR(Rj)* is optimized using a sigmoid-based binary loss supporting multiple positives per query:
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+ $$
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  L = - \sum_i [y_i \log \sigma(s_i) + (1 - y_i)\log(1 - \sigma(s_i))]
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+ $$
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  Negatives are sampled in-batch from other talk鈥損aper pairs.
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  Before training, a **domain adaptation stage** aligned each talk with its own paper鈥檚 abstract to adapt to scientific and spoken-language data.