Is this a hardware or a software issue?

Software failures can look like either layer depending on the symptom. The discriminator is the resolution of the symptom to the recommended fix: if applying the steps under "How to fix it" eliminates the symptom, this is a software/configuration class issue regardless of the hardware it surfaced on. Repeat the fix on a fresh node to confirm.

How long does the fix typically take?

Most resolutions from this entry take 10 to 30 minutes of engineer time once the diagnosis is confirmed. Long fixes come from skipping the diagnosis step and chasing apparent symptoms (validation drift, memory growth, slow throughput) instead of the actual root cause listed above. Apply the fix in a small experiment first, then roll it forward.

Does this affect inference or only training?

Primarily this is a software failure observed during training, but the same misconfiguration can leak into downstream evaluation and serving. Treat the prevention checklist as a guardrail: any pipeline that touches a trained checkpoint should re-validate the failure mode before promoting the model.

What's the cheapest way to confirm this is the problem?

Cheapest signal: reproduce the symptom on a 1-GPU toy run with the same configuration. If the toy run exhibits the same behavior, the cause is the configuration rather than the cluster. If only the multi-GPU run is affected, the failure is a distributed interaction, so PyTorch is the most likely layer to inspect.

Can the Denpex platform detect this automatically?

Yes. Denpex correlates the symptoms in this entry against your training logs in real time and surfaces the failure taxonomy, root cause, and exact remediation command on the console. Three full diagnoses are included free during signup, and the encyclopedia entry you are reading is generated from the same signal library that powers the platform.

What related failures should I check next?

Closely related failures cluster around #Numerical Instability. After applying this fix, validate against the related entries below to confirm no overlapping cause is masking as this one. Engineers routinely discover that the dominant failure mode is actually a second, sibling failure compounded on top.

Will this recur after the fix?

Applied once with the prevention checklist, this failure does not recur under normal operation. The recurring variant most engineers encounter is the re-emergence of the same symptom on a different model or stack after Numerical Instability is upgraded. Pin compatible versions and rerun the prevention smoke test on every dependency change.

Is there a fingerprint I can monitor?

Yes. Training proceeds normally for thousands of steps and then abruptly diverges. is the highest-signal fingerprint. Wire a metric or alert on that signal (or its absence after the fix) so you can detect the recurrence automatically. The Denpex platform encodes this exact fingerprint and surfaces it directly in the dashboard.

What is the official documentation that covers this?

Reference documentation is listed in the References section at the bottom of this entry. The most authoritative URLs are the upstream framework docs and the issue trackers cited; the Denpex entry synthesizes both into the executive, engineer, and on-call perspectives so each audience can act without reading every linked source.

Does this entry include working code?

Yes. The "Code Examples" section contains copy-paste-ready snippets that target the most common stacks (PyTorch, Hugging Face Trainer, DeepSpeed, Megatron-LM, vLLM/Transformers). Each snippet is annotated with why it works so you can adapt the pattern to your own framework without losing fidelity.

Adam Epsilon Underflow in FP16 Mixed Precision

Q: What does this failure look like in production?

In production this failure typically appears during the first tens-to-hundreds of training steps: loss curves become non-monotonic, validation metrics plateau above the baseline, and downstream checkpoints either diverge or fail to improve. Engineers frequently misread it as data drift when the underlying mechanism is when using fp16 for the optimizer state (or when the epsilon value itself is cast to fp16), the default adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in fp16 is ~6e-5). when the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields nan weights.. Validating against the symptom list in this entry is the fastest way to confirm the diagnosis.

Q: How does this scale from 1 GPU to 1000 GPUs?

At single-GPU scale the symptom usually looks like slow convergence or a single anomalous loss value. At 64+ GPU scale, distributed interactions amplify when using fp16 for the optimizer state (or when the epsilon value itself is cast to fp16), the default adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in fp16 is ~6e-5). when the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields nan weights. through collectives, and the failure can manifest as a full job abort. Always reproduce the fix at the smallest cluster configuration that still exhibits the symptom before promoting to production scale.

When using FP16 for the optimizer state (or when the epsilon value itself is cast to FP16), the default Adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in FP16 is ~6e-5). When the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields NaN weights.

Quick answer

Symptom: RuntimeError: Function 'LogBackward' returned nan values in its ith output
Root cause: When using FP16 for the optimizer state (or when the epsilon value itself is cast to FP16), the default Adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in FP16 is ~6e-5). When the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields NaN weights.
Recommended fix: Increase Adam Epsilon optimizer = torch.optim.AdamW(model.parameters(), lr=1e-4, eps=1e-5) Increasing epsilon to 1e-5 ensures it is safely representable in FP16 and avoids division by zero.
How Denpex helps: Denpex matches Adam Epsilon Underflow in FP16 Mixed Precision across every rank in a distributed run and reports which rank failed first, so you act on the initiating node instead of the loudest one.

Software#Numerical Instability

What this failure is

Adam Epsilon Underflow in FP16 Mixed Precision is a Software failure seen during ML training runs. When using FP16 for the optimizer state (or when the epsilon value itself is cast to FP16), the default Adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in FP16 is ~6e-5). When the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields NaN weights. Common tags: Numerical Instability.

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Why it happens (the mechanism)

Engineers often assume the learning rate is too high or gradient clipping is missing. However, gradient clipping only restricts the numerator; it does nothing to prevent division by zero in the denominator.

What you'll observe

Loss is NaN
RuntimeError: Function 'LogBackward' returned nan values in its ith output
Attempted loss scale: 1, reducing to 1

Common symptoms and what they mean

Symptom	Why it happens
Training proceeds normally for thousands of steps and then abruptly diverges.	When using FP16 for the optimizer state (or when the epsilon value itself is cast to FP16), the default Adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in FP16 is ~6e-5). When the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields NaN weights.
The loss suddenly becomes NaN during an optimizer step.	When using FP16 for the optimizer state (or when the epsilon value itself is cast to FP16), the default Adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in FP16 is ~6e-5). When the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields NaN weights.
Model weights become entirely NaN.	When using FP16 for the optimizer state (or when the epsilon value itself is cast to FP16), the default Adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in FP16 is ~6e-5). When the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields NaN weights.

Which systems are affected

PyTorch
Transformers
Mixed Precision Training

How to confirm this is the problem

Use this checklist to test the hypothesis against a small reproduction. No single line proves the root cause, so preserve the preceding events and compare one variable at a time.

✓Inspect the optimizer states to see if variance buffers are 0.
✓Enable PyTorch anomaly detection using torch.autograd.set_detect_anomaly(True).
✓Print the minimum and maximum values of the gradients right before the optimizer step.

Searchable error signature

search key

RuntimeError: Function 'LogBackward' returned nan values in its ith output

Use this text as a lookup key in logs and upstream issue trackers. It is not presented as a captured customer log. Confirm the cause from your own preceding events, versions, configuration and the cited references.

The fix and the prevention pattern

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Root cause

When using FP16 for the optimizer state (or when the epsilon value itself is cast to FP16), the default Adam epsilon of 1e-8 underflows to 0 (since the smallest representable subnormal in FP16 is ~6e-5). When the moving average of squared gradients approaches zero, the denominator becomes exactly zero, causing a division by zero that yields NaN weights.

The fix and how to prevent it

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References

↗Adam epsilon fp16 issues

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