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tyler-ingebrand committed Oct 16, 2024
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Expand Up @@ -270,13 +270,9 @@ <h2 class="title is-3">Smooth Loss Landscapes</h2>
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<img style="margin-bottom:1cm;" src="static/images/grad_cropped.png" alt="By decomposing the problem into separate parts, B2B exhibits a smooth loss landscape"/>
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Interestingly, decomposing the operator learning problem into separate parts leads to smoother loss
landscapes compared to DeepONet, which leverages an end-to-end approach.
This likely explains the faster convergence and better asymptotic performance of B2B.
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Expand All @@ -294,18 +290,14 @@ <h2 class="title is-3">Eigen Decomposition and Singular Value Decomposition</h2>
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<img width="75%" style="margin-bottom:1cm;" src="static/images/svd_cropped_transparent.png" alt="With small modifications to our algorithm, we recover the familiar ED and SVD algorithms."/>
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<img width="100%" style="margin-bottom:1cm;" src="static/images/svd_cropped_transparent.png" alt="With small modifications to our algorithm, we recover the familiar ED and SVD algorithms."/>
B2B is rooted in classical functional analysis. As a result, with minimal modifications, B2B can recover the algorithms for eigen decomposition and singular value decomposition.
While these approaches can only learn linear operators, they provide a means for analysing learned operators.
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