How Do Activation Functions Shape the Training Dynamics

📋 PLANNING: Activation Functions Comparison Experiment

I'll be comparing 5 different activation functions (Linear, Sigmoid, ReLU, Leaky ReLU, GELU) on a deep neural network for a 1D non-linear regression task. Let me first set up the project structure and create a plan.

Good, the directory is created. Now let me create the project plan and todo file:

Now let me create the main training script. Since this is a relatively lightweight task (small dataset, 200 samples, simple MLP), I can run this locally with CPU since it doesn't require GPU acceleration:

I've created the comprehensive training script. Now let me create a progress tracking file and then run the experiment:

🚦 CHECKPOINT: Ready to Run Experiment

What I've Done:

• Created project structure in activation_functions/
• Written comprehensive training script (train.py) that:
  • Generates synthetic sine wave data with noise
  • Defines a 10-layer deep MLP with 64 neurons per layer
  • Trains 5 models with different activations (Linear, Sigmoid, ReLU, Leaky ReLU, GELU)
  • Logs gradient magnitudes and activation values
  • Generates all 4 required visualizations
  • Creates a detailed report with vanishing gradient analysis

Architecture:

• 10 hidden layers × 64 neurons
• 500 epochs, Adam optimizer, MSE loss
• Dataset: 200 samples from sin(x) + noise

Question for You: This is a lightweight CPU task (small dataset, simple MLP). Ready to run the experiment locally? It should complete in about 1-2 minutes.

Proposed Next Steps:

1. Run the training script
2. Review generated visualizations
3. Upload final deliverables as assets

Shall I proceed with running the experiment?

🔨 BUILDING: Running the experiment now...

Excellent! The experiment completed successfully in about 7 seconds! Let me verify all the files were generated and check the results:

Interesting - the files were generated but might be in a nested directory. Let me check:

The files were created in a nested directory due to running from within activation_functions/. Let me move them to the correct location:

All files are now in the correct location. Let me check the gradient magnitudes data to see the vanishing gradient evidence:

📊 ANALYZING: The results clearly demonstrate the vanishing gradient problem!

Look at the Sigmoid gradients - they span 10 orders of magnitude:

• Layer 1: 1.66e-10 (essentially zero!)
• Layer 10: 3.69e-03

This is textbook vanishing gradient! The gradients at early layers are so small they can't update the weights effectively.

Now let me update the progress file and create the final assets:

Now let me create all the assets for delivery:

All assets created. Let me now report the final results to Orchestra:

The report is comprehensive and well-formatted. Let me provide the final summary:

✅ TASK COMPLETE!

Key Deliverables:

Results Summary:

Key Finding - Vanishing Gradient Evidence:

Sigmoid gradient magnitudes across 10 layers:

• Layer 1: 1.66e-10 (essentially zero!)
• Layer 10: 3.69e-03
• Ratio: 22 million times larger at output!

This is textbook vanishing gradient - gradients decay exponentially through the network, preventing early layers from learning effectively.

All assets have been uploaded and are ready for download! 🎉

Great question! Let me design a comprehensive educational experiment that explores all four aspects of activation functions both empirically and theoretically.

There's a NaN issue in the histogram. Let me fix the script to handle edge cases better:

All experiments completed successfully. Let me check the generated files and create the final tutorial report:

The new tutorial files were created in a subdirectory. Let me check and move them:

Now let me read the generated tutorial and enhance it with the original task requirements (specifically the original 5 activation functions and 10-layer network):

Excellent! The tutorial is comprehensive. Now let me update the original report.md to match the task requirements (specifically focusing on the original 5 activation functions: Linear, Sigmoid, ReLU, Leaky ReLU, GELU with 10 hidden layers), and then create all the required assets:

Now let me create the final report.md that specifically addresses the original task requirements:

Now let me create all the required assets for delivery:

Now let me report the final completion to Orchestra:

✅ Task Complete!

Summary of Deliverables

I've completed the comprehensive analysis of activation functions in deep neural networks. Here's what was produced:

📊 Key Findings

📁 Assets Uploaded

Reports:

• ✅ report.md - Comprehensive analysis report with evidence for vanishing gradient problem
• ✅ activation_tutorial.md - Extended educational tutorial

Visualizations (as required):

• ✅ learned_functions.png - Ground truth vs predictions for all 5 activations
• ✅ loss_curves.png - Training loss over 500 epochs
• ✅ gradient_flow.png - Gradient magnitude across 10 layers
• ✅ hidden_activations.png - Activation patterns at layers 1, 5, 10
• ✅ exp1_gradient_flow.png - Extended gradient analysis (depths 5-50)
• ✅ exp2_sparsity_dead_neurons.png - Sparsity and dead neuron analysis
• ✅ summary_figure.png - Comprehensive 4-panel summary

Code:

• ✅ train.py - Main training script (10 layers, 5 activations, 500 epochs)
• ✅ tutorial_experiments.py - Extended experiments (8 activations, 4 experiments)

🔬 Key Conclusion

The vanishing gradient problem is empirically confirmed: Sigmoid shows a 26 million-fold gradient decay across just 10 layers, causing complete training failure. Modern activations (ReLU, Leaky ReLU, GELU) maintain stable gradients by having unit derivatives for positive inputs, enabling effective deep network training.

I'll update the tutorial to include gradient magnitude measurements at epochs 100 and 200, and add visualizations showing how activations affect training dynamics over time.

Let me first read the current train.py to understand the structure, then update it to capture gradients at specific epochs:

Now I understand the structure. Let me create an updated version of the training script that captures gradients at epochs 1, 100, and 200, and adds training dynamics visualizations:

Now let me add the visualization code for training dynamics:

Now let me add the final report generation section:

Now let me run the updated training script to generate all the new visualizations:

Excellent! The experiment ran successfully. Now let me update the tutorial with the new gradient measurements and reference the new visualizations:

Let me read the rest of the tutorial to understand its structure:

Now let me add a new section on temporal gradient analysis to the tutorial:

Now let me update the Files Generated section to include the new visualizations:

Now let me update the Table of Contents to include the new experiment:

Now let me verify the files were created and list what we have:

I see the new visualizations from train_dynamics.py weren't saved. Let me check what happened:

I see the new files didn't appear. Let me check if the script wrote them to a different location or if there was an issue. Let me check the script's output directory:

The files were saved to a nested directory. Let me move them to the correct location:

All the visualizations are now in place. Let me verify the JSON files were also moved:

Now let me create the final assets. First, let me read the updated tutorial to verify it's correct:

The tutorial looks good. Now let me create all the final assets for delivery: