How Does Gradient Clipping Help with Stabilizing Training?

📋 PLANNING: Gradient Clipping Experiment

This is an excellent experiment to demonstrate how gradient clipping stabilizes training! Let me break down the task:

Understanding the Experiment:

• We're creating a deliberately imbalanced dataset (990 'A' targets vs 10 'B' targets)
• When the model encounters a rare 'B' sample, it will produce a high loss (since it's trained mostly on 'A')
• This high loss leads to large gradients that can destabilize training
• Gradient clipping should prevent these sudden large updates

Key Points:

1. This is a lightweight local task - simple PyTorch model, small dataset (1000 samples), CPU-friendly
2. No need for Modal/GPU - this is a quick demonstration experiment
3. I'll use synthetic data as explicitly requested in the task

Let me set up the project structure and create the implementation:

Now let me implement the complete experiment script. This is a lightweight local task (simple model, 1000 samples, CPU-friendly), so I'll run it locally:

I've created the complete experiment script. Now let me run it to generate the plots and collect the metrics:

Excellent! The experiment ran successfully. I notice that the random seed is causing different rare sample indices for each run. Let me fix this to ensure both training runs use the exact same dataset for a fair comparison:

The experiment ran successfully. Let me verify the plots were created and then check them:

Now let me write the summary report:

Now let me update the progress file and create the assets for delivery:

Now let me create the assets for delivery:

✅ COMPLETE

Task Summary

I've successfully completed the gradient clipping experiment. Here's what was accomplished:

Key Deliverables

Key Findings

1. Gradient Spikes at Rare Samples: Both runs show gradient norms ~7x larger at the rare 'B' sample positions compared to typical samples

2. Clipping Effect: With clipping enabled, the actual weight updates are bounded at 1.0, preventing the rare samples from causing disproportionate changes

3. Training Stability: The clipped run showed smoother weight norm evolution with fewer sudden jumps

4. Convergence: Both runs converged successfully, with the clipped run achieving slightly better final loss (0.0011 vs 0.0039)

Conclusion

The experiment confirms the hypothesis: Gradient clipping stabilizes training by preventing sudden large weight updates caused by rare, high-loss data points. The red vertical lines in the plots clearly show that gradient spikes occur precisely at rare sample positions, and clipping effectively bounds these updates while preserving the model's ability to learn.

All assets have been uploaded for download.

Interesting! I can see Ziming Liu's blog has several Physics-of-AI posts. Let me explore the most relevant ones - particularly the "Optimization 1 -- Norm reparametrization" which seems directly related to our gradient clipping experiment, and a few others for context:

Let me try different URL patterns for these blog posts:

Excellent! I found the blog posts. Let me read the most relevant ones in detail - particularly the "Optimization 1 -- Norm reparametrization" and "Unigram toy model" posts which seem most related to our gradient clipping experiment:

This is fascinating! Let me also check the grokking post and the Pre-LN/Post-LN post for more context:

Let me first check our existing experiment code to understand the structure, then extend it with the new metrics:

Now I understand the structure. Let me create an extended experiment that tracks:

1. PCA-based effective dimensionality of embeddings (Prediction 2)
2. Per-class accuracy throughout training (Prediction 4)

✅ TASK COMPLETE!

Summary of Deliverables

Key Findings

The experiment confirms the hypothesis that gradient clipping stabilizes training by preventing sudden large weight updates from rare, high-loss samples. Here are the key results:

Physics-of-AI Interpretation

1. Velocity Limiter: Gradient clipping bounds step size without changing direction
2. Representation Preservation: Prevents gradient spikes from causing temporary embedding collapse
3. Weight Space Stability: Keeps training in a "Goldilocks zone" of weight norms

Important Nuance

Clipping alone doesn't solve class imbalance - both models achieved 0% rare class accuracy. The benefit is stability, not rare-class learning. For actual rare-class learning, combine with focal loss or class weighting.

Deliverables

✅ Report: final_report.md - Comprehensive Physics-of-AI analysis
✅ Code: final_experiment.py - Complete reproducible experiment
✅ Plots:

• final_comparison.png - 10-panel side-by-side comparison
• no_clipping.png - Baseline training metrics
• with_clipping.png - Clipped training metrics

All assets uploaded for download!