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@@ -82,7 +82,7 @@ These inputs are short enough to fit within the model’s 512-token limit — no
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  The cited-paper encoder was trained jointly with the query-talk encoder under a **dual-encoder contrastive framework** inspired by Dense Passage Retrieval (Karpukhin et al., 2020).
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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)·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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  The cited-paper encoder was trained jointly with the query-talk encoder under a **dual-encoder contrastive framework** inspired by Dense Passage Retrieval (Karpukhin et al., 2020).
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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 $$sij = fT(Ti)·fR(Rj)$$ 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))]