Merge branch 'main' into copilot/adjust-ci-to-use-netlify-cli

Author: mmcky

.github/workflows/collab.yml

@@ -1,15 +1,19 @@
 name: Build Project on Google Collab (Execution)
-on: [pull_request]
+on:
+  schedule:
+    # Execute weekly on Monday at 4am UTC (offset from cache.yml)
+    - cron: '0 4 * * 1'
+  workflow_dispatch:
 jobs:
   execution-checks:
     runs-on: "runs-on=${{ github.run_id }}/family=g4dn.2xlarge/image=ubuntu24-gpu-x64/disk=large"
+    permissions:
+      issues: write # required for creating issues on execution failure
     container:
       image: docker://us-docker.pkg.dev/colab-images/public/runtime:latest
       options: --gpus all
     steps:
       - uses: actions/checkout@v5
-        with:
-          ref: ${{ github.event.pull_request.head.sha }}
       # Install build software
       - name: Install Build Software & LaTeX
         shell: bash -l {0}
@@ -46,3 +50,43 @@ jobs:
         with:
           name: execution-reports
           path: _build/html/reports
+      - name: Create execution failure report
+        if: failure()
+        run: |
+          cat > execution-failure-report.md << 'EOF'
+          # Colab Execution Failure Report
+
+          The weekly Google Colab execution check has failed. This indicates that one or more notebooks failed to execute properly in the Colab environment.
+
+          ## Details
+
+          **Workflow Run:** [${{ github.run_id }}](https://github.com/${{ github.repository }}/actions/runs/${{ github.run_id }})
+          **Date:** ${{ github.event.head_commit.timestamp || github.event.schedule }}
+          **Branch:** ${{ github.ref_name }}
+          **Commit:** ${{ github.sha }}
+
+          ## Execution Reports
+
+          Detailed execution reports have been uploaded as artifacts to this workflow run. Please check the following:
+
+          1. Download the `execution-reports` artifact from the workflow run
+          2. Review the failed notebook execution logs
+          3. Fix any execution issues in the notebooks
+          4. Test locally or in Colab before merging
+
+          ## Next Steps
+
+          1. Investigate the failure by reviewing the execution reports
+          2. Fix the identified issues
+          3. Test the fixes
+          4. Close this issue once resolved
+
+          This is an automated issue created by the weekly Colab execution check.
+          EOF
+      - name: Create Issue on Execution Failure
+        if: failure()
+        uses: peter-evans/create-issue-from-file@v5
+        with:
+          title: "Weekly Colab Execution Check Failed - ${{ github.run_id }}"
+          content-filepath: execution-failure-report.md
+          labels: execution-failure, automated-issue, colab

lectures/back_prop.md

@@ -201,7 +201,7 @@ $$ (eq:sgd)
 
 where $\frac{d {\mathcal L}}{dx_{N+1}}=-\left(x_{N+1}-y\right)$ and $\alpha > 0 $ is a step size.
 
-(See [this](https://en.wikipedia.org/wiki/Gradient_descent#Description) and [this](https://en.wikipedia.org/wiki/Newton%27s_method) to gather insights about how stochastic gradient descent
+(See [this](https://en.wikipedia.org/wiki/Gradient_descent#Description) and [this](https://en.wikipedia.org/wiki/Newton's_method) to gather insights about how stochastic gradient descent
 relates to Newton's method.)
 
 To implement one step of this parameter update rule, we want  the vector of derivatives $\frac{dx_{N+1}}{dp_k}$.
@@ -540,7 +540,7 @@ Image(fig.to_image(format="png"))
 It  is  fun to think about how deepening the neural net for the above example affects the quality of  approximation 
 
 
-* If the network is too deep, you'll run into the [vanishing gradient problem](https://neuralnetworksanddeeplearning.com/chap5.html)
+* If the network is too deep, you'll run into the [vanishing gradient problem](https://en.wikipedia.org/wiki/Vanishing_gradient_problem)
 * Other parameters such as the step size and the number of epochs can be as  important or more important than the number of layers in the situation considered in this lecture.
 * Indeed, since $f$ is a linear function of $x$, a one-layer network with the identity map as an activation would probably work best.