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@@ -363,12 +361,12 @@ <h2 id="plans-for-the-week-april-21-25-2025" class="anchor">Plans for the week A
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<h2id="summary-of-variational-autoencoders-vaes" class="anchor">Summary of Variational Autoencoders (VAEs) </h2>
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<p>In our short summary of VAes, we will also remind you about the
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<p>In our summary of VAes from last time, we will also remind you about the
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mathematics of Boltzmann machines and the Kullback-Leibler divergence,
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leading to various ways to optimize the probability
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distributions, namely what is called
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<h2id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization" class="anchor">Boltzmann machines and energy-based models and contrastive optimization </h2>
<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
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@@ -214,13 +214,13 @@ <h2 id="plans-for-the-week-april-21-25-2025">Plans for the week April 21-25, 202
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</section>
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<section>
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<h2id="summary-of-variational-autoencoders-vaes">Summary of Variational Autoencoders (VAEs) </h2>
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<p>In our short summary of VAes, we will also remind you about the
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<p>In our summary of VAes from last time, we will also remind you about the
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mathematics of Boltzmann machines and the Kullback-Leibler divergence,
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leading to various ways to optimize the probability
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distributions, namely what is called
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<section>
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<h2id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization">Boltzmann machines and energy-based models and contrastive optimization </h2>
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</section>
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<section>
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<h2id="energy-models">Energy models </h2>
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<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
<h2id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization">Boltzmann machines and energy-based models and contrastive optimization </h2>
<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
<h2id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization">Boltzmann machines and energy-based models and contrastive optimization </h2>
<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
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