Gradient Clipping Toy Experiment (v2)

    Gradient Clipping Toy Experiment (v2)

    1. Implement the Model: Create a simple PyTorch model with an nn.Embedding layer and an nn.Linear layer. The vocabulary will be ['A', 'B', 'C', 'D']. The model should take a token index as input and output logits for the next token.
    2. Create the Dataset: Generate a synthetic dataset of 1000 samples. The input token can be random. For the target token: 990 samples should be 'A' and 10 samples should be 'B'.
    3. Set up Training Loop (No Clipping):
      • Use a standard SGD optimizer and CrossEntropyLoss.
      • Train for a few epochs.
      • At each step, record the training loss, the L2 norm of the gradients (torch.nn.utils.clip_grad_norm_ can be used to calculate the norm before clipping), and the L2 norm of the model weights.
      • Plot these three metrics against the training steps. Save the plot.
    4. Set up Training Loop (With Clipping):
      • Reset the model and optimizer.
      • Run the same training loop, but this time, apply gradient clipping using torch.nn.utils.clip_grad_norm_ with a threshold of 1.0.
      • Record the same three metrics: loss, gradient norm (before clipping), and weight norm.
      • Plot these metrics and save the plot.
    5. Report Findings:
      • Present the two plots side-by-side.
      • Write a brief summary explaining the difference in the plots and confirming whether the experiment supports the hypothesis that gradient clipping stabilizes training by preventing sudden large weight updates caused by rare, high-loss data points.
      • The final output should be the two plots and the summary report.
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    1/27/2026
    Run Your Own ExperimentTry It
    1. Implement the Model: Create a simple PyTorch model with an nn.Embedding layer and an nn.Linear layer. The vocabulary will be ['A', 'B', 'C', 'D']. The model should take a token index as input and output logits for the next token.
    2. Create the Dataset: Generate a synthetic dataset of 1000 samples. The input token can be random. For the target token: 990 samples should be 'A' and 10 samples should be 'B'.
    3. Set up Training Loop (No Clipping):
      • Use a standard SGD optimizer and CrossEntropyLoss.
      • Train for a few epochs.
      • At each step, record the training loss, the L2 norm of the gradients (torch.nn.utils.clip_grad_norm_ can be used to calculate the norm before clipping), and the L2 norm of the model weights.
      • Plot these three metrics against the training steps. Save the plot.
    4. Set up Training Loop (With Clipping):
      • Reset the model and optimizer.
      • Run the same training loop, but this time, apply gradient clipping using torch.nn.utils.clip_grad_norm_ with a threshold of 1.0.
      • Record the same three metrics: loss, gradient norm (before clipping), and weight norm.
      • Plot these metrics and save the plot.
    5. Report Findings:
      • Present the two plots side-by-side.
      • Write a brief summary explaining the difference in the plots and confirming whether the experiment supports the hypothesis that gradient clipping stabilizes training by preventing sudden large weight updates caused by rare, high-loss data points.
      • The final output should be the two plots and the summary report.

    11:05 PM

    📋 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:

    11:05 PM

    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:

    11:05 PM

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

    11:06 PM

    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:

    11:06 PM

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

    11:07 PM

    Now let me write the summary report:

    11:08 PM

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

    11:08 PM

    Now let me create the assets for delivery:

    11:08 PM

    ✅ COMPLETE

    Task Summary

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

    Key Deliverables

    AssetDescription
    comparison.pngSide-by-side comparison plot showing all metrics for both training runs
    no_clipping.pngTraining metrics without gradient clipping
    with_clipping.pngTraining metrics with gradient clipping (max_norm=1.0)
    report.mdComprehensive analysis report with methodology, results, and conclusions
    experiment.pyComplete PyTorch implementation (reproducible with seed=42)

    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.

    comparison.png

    240.6 KB
    comparison.png

    no_clipping.png

    155.4 KB
    no_clipping.png

    with_clipping.png

    120.0 KB
    with_clipping.png

    report.md

    DOCUMENT
    6.0 KB
    Download

    experiment.py

    CODE
    16.0 KB
    Download

    11:09 PM

    refer to https://kindxiaoming.github.io/blog/ any interesting conclusion can we get, similar to this physics of AI blogs

    11:21 PM

    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:

    11:21 PM

    Let me try different URL patterns for these blog posts:

    11:21 PM

    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:

    11:21 PM

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

    11:22 PM

    report your finding

    11:48 PM

    let's run some experiment for

    Prediction 2: Representation Collapse

    Hypothesis: Without clipping, the effective dimensionality of embeddings should show sudden drops at rare sample positions. Test: Track PCA-based effective dimension throughout training.

    Prediction 4: Rare Sample Learning

    Hypothesis: With clipping, the model should achieve better accuracy on rare samples. Test: Track per-class accuracy throughout training.

    12:28 AM

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

    12:28 AM

    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)

    12:30 AM

    ✅ 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:

    MetricWithout ClippingWith ClippingImprovement
    Effective Dim Variance (99:1)0.00850.000332x more stable
    Effective Dim Variance (80:20)0.3360.02314x more stable
    Max Weight Change~0.13~0.026x smaller
    Gradient Spikes7x thresholdBounded at 1.0✓

    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!

    final_comparison.png

    527.6 KB
    final_comparison.png

    no_clipping.png

    155.4 KB