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lines changed Original file line number Diff line number Diff line change @@ -13,8 +13,8 @@ Let's start with our cost function:
1313$$ \mathcal{L}(A_{ij}) = \sum_{i=1}^{N_\mathrm{out}} (z_i - y_i^k)^2 = \sum_{i=1}^{N_\mathrm{out}}
1414 \Biggl [ g\biggl (\underbrace{\sum_{j=1}^{N_\mathrm{in}} A_{ij} x^k_j}_{\equiv \alpha_i} \biggr ) - y^k_i \Biggr ]^2 $$
1515
16- where we'll refer to the product ${ \boldsymbol \alpha} \equiv {\bf
17- Ax}$ to help simplify notation. This means that ${\bf z} = g({ \boldsymbol \alpha})$.
16+ where we'll refer to the product $\boldsymbol{ \alpha} \equiv {\bf
17+ Ax}$ to help simplify notation. This means that ${\bf z} = g(\boldsymbol{ \alpha})$.
1818
1919We can compute the derivative with respect to a single matrix
2020element, $A_ {pq}$ by applying the chain rule:
Original file line number Diff line number Diff line change 44title : " PHY 546: Python for Scientific Computing"
55author : <a href="https://zingale.github.io">Michael Zingale</a>
66# logo: logo.png
7- copyright : " 2022"
7+ copyright : " 2022-2026 "
88
99# Force re-execution of notebooks on each build.
1010# See https://jupyterbook.org/content/execute.html
3030 use_repository_button : true
3131 extra_footer : |
3232 <p>
33- © 2023 -2026; CC-BY-NC-SA 4.0
33+ © 2022 -2026; CC-BY-NC-SA 4.0
3434 <p>
3535
3636sphinx :
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