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Optimizing the cross-entropy is equivalent to optimizing the log-likelihood of the parameters given the data, $\ell(\theta)$, which is what we want, i.e. find the parameters that most likely generated the data. So, the likelihood is defined as $$\mathcal{L}(\theta) = P(y \mid x; \theta),$$ i.e. a function of the parameters $\theta$. The log-likelihood is ...


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There are known architectures to implement this idea, namely, seamese networks, and also a training strategy, known as contrastive learning, that relies on the idea of comparing the output of neural networks. I will explain both of them briefly. The idea of seamese networks is exactly what you mentioned. You have a single model, $m$, that receives two inputs,...


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