diff --git a/content/chapters/15_regularization/15-09-wd.md b/content/chapters/15_regularization/15-09-wd.md
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+---
+title: "Chapter 15.09: Weight decay and L2"
+weight: 15009
+---
+In this section, we show that L2 regularization with gradient descent is equivalent to weight decay and see how weight decay changes the optimization trajectory.
+
+<!--more-->
+
+### Lecture video
+
+{{< video id="xASHDEAWP0U" >}}
+
+### Lecture slides
+
+{{< pdfjs file="https://github.com/slds-lmu/lecture_sl/blob/main/slides-pdf/slides-regu-wd-vs-l2.pdf" >}}
diff --git a/content/chapters/15_regularization/15-09-geom-l2.md b/content/chapters/15_regularization/15-10-geom-l2.md
similarity index 86%
rename from content/chapters/15_regularization/15-09-geom-l2.md
rename to content/chapters/15_regularization/15-10-geom-l2.md
index 61f213b..52f49ef 100644
--- a/content/chapters/15_regularization/15-09-geom-l2.md
+++ b/content/chapters/15_regularization/15-10-geom-l2.md
@@ -1,6 +1,6 @@
 ---
-title: "Chapter 15.09: Geometry of L2 Regularization"
-weight: 15009
+title: "Chapter 15.10: Geometry of L2 Regularization"
+weight: 15010
 ---
 In this section, we provide a geometric understanding of \\(L2\\) regularization, showing how parameters are shrunk according to the eigenvalues of the Hessian of empirical risk, and discuss its correspondence to weight decay. 
 
diff --git a/content/chapters/15_regularization/15-10-geom-l1.md b/content/chapters/15_regularization/15-11-geom-l1.md
similarity index 83%
rename from content/chapters/15_regularization/15-10-geom-l1.md
rename to content/chapters/15_regularization/15-11-geom-l1.md
index a76c553..489d945 100644
--- a/content/chapters/15_regularization/15-10-geom-l1.md
+++ b/content/chapters/15_regularization/15-11-geom-l1.md
@@ -1,6 +1,6 @@
 ---
-title: "Chapter 15.10: Geometry of L1 Regularization"
-weight: 15010
+title: "Chapter 15.11: Geometry of L1 Regularization"
+weight: 15011
 ---
 In this section, we provide a geometric understanding of \\(L1\\) regularization and show that it encourages sparsity in the parameter vector.
 
diff --git a/content/chapters/15_regularization/15-11-early-stopping.md b/content/chapters/15_regularization/15-12-early-stopping.md
similarity index 84%
rename from content/chapters/15_regularization/15-11-early-stopping.md
rename to content/chapters/15_regularization/15-12-early-stopping.md
index ce0783a..0286c92 100644
--- a/content/chapters/15_regularization/15-11-early-stopping.md
+++ b/content/chapters/15_regularization/15-12-early-stopping.md
@@ -1,6 +1,6 @@
 ---
-title: "Chapter 15.11: Early Stopping"
-weight: 15011
+title: "Chapter 15.12: Early Stopping"
+weight: 15012
 ---
 In this section, we introduce early stopping and show how it can act as a regularizer. 
 
diff --git a/content/chapters/15_regularization/15-12-ridge-deep.md b/content/chapters/15_regularization/15-13-ridge-deep.md
similarity index 79%
rename from content/chapters/15_regularization/15-12-ridge-deep.md
rename to content/chapters/15_regularization/15-13-ridge-deep.md
index 7df9bf5..aa0bbad 100644
--- a/content/chapters/15_regularization/15-12-ridge-deep.md
+++ b/content/chapters/15_regularization/15-13-ridge-deep.md
@@ -1,6 +1,6 @@
 ---
-title: "Chapter 15.12: Details on Ridge Regression: Deep Dive"
-weight: 15012
+title: "Chapter 15.13: Details on Ridge Regression: Deep Dive"
+weight: 15013
 ---
 In this section, we consider Ridge regression as row-augmentation and as minimizing risk under feature noise. We also discuss the bias-variance tradeoff.
 
diff --git a/content/chapters/15_regularization/15-13-lasso-deep.md b/content/chapters/15_regularization/15-14-lasso-deep.md
similarity index 77%
rename from content/chapters/15_regularization/15-13-lasso-deep.md
rename to content/chapters/15_regularization/15-14-lasso-deep.md
index 33cf405..b2bbb40 100644
--- a/content/chapters/15_regularization/15-13-lasso-deep.md
+++ b/content/chapters/15_regularization/15-14-lasso-deep.md
@@ -1,6 +1,6 @@
 ---
-title: "Chapter 15.13: Soft-thresholding and L1 regularization: Deep Dive"
-weight: 15013
+title: "Chapter 15.14: Soft-thresholding and L1 regularization: Deep Dive"
+weight: 15014
 ---
 In this section, we prove the previously stated proposition regarding soft-thresholding and L1 regularization.