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RMSNorm Variance Overflow in FP16

In RMSNorm, the sum of squared activations is computed. In large models (e.g., hidden dimension > 4096), summing the squares of fp16 activations can easily exceed 65,504 (the maximum fp16 value), causing an overflow to infinity. The subsequent step computes `1.0 / sqrt(inf)`, which results in 0. The activations are zeroed out, killing gradients and causing NaNs upon backpropagation.

Quick answer

In RMSNorm, the sum of squared activations is computed.

Root cause
In RMSNorm, the sum of squared activations is computed. In large models (e.g.
Recommended fix
Cast to FP32 for Variance Calculation variance = hidden_states.to(torch.float32).pow(2).mean(-1, keepdim=True) Casting the activations to fp32 before squaring and summing prevents the intermediate sum from overflowing, returning a safe fp16 value upon downcast.
How Denpex helps
Denpex investigates RMSNorm Variance Overflow in FP16 using the evidence you provide or your connected workload collects. Earlier rank, host or application evidence is needed to distinguish an initiating failure from a downstream report.
Model#Numerical Instability

What this failure is

RMSNorm Variance Overflow in FP16 is a Model failure seen during ML training runs. In RMSNorm, the sum of squared activations is computed. In large models (e.g., hidden dimension > 4096), summing the squares of fp16 activations can easily exceed 65,504 (the maximum fp16 value), causing an overflow to infinity. The subsequent step computes `1.0 / sqrt(inf)`, which results in 0. The activations are zeroed out, killing gradients and causing NaNs upon backpropagation. Common tags: Numerical Instability.

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Why it happens (the mechanism)

It appears as a standard exploding gradient issue, leading developers to aggressively tune learning rates or initialization, when in fact it is a deterministic precision limit.

What you'll observe

  • Loss is NaN at step 0
  • Gradients containing NaNs in LayerNorm/RMSNorm

Common symptoms and what they mean

SymptomWhy it happens
Model loss becomes NaN almost immediately at the start of training or unexpectedly during training.In RMSNorm, the sum of squared activations is computed. In large models (e.g., hidden dimension > 4096), summing the squares of fp16 activations can easily exceed 65,504 (the maximum fp16 value), causing an overflow to infinity. The subsequent step computes `1.0 / sqrt(inf)`, which results in 0. The activations are zeroed out, killing gradients and causing NaNs upon backpropagation.
Activations following the RMSNorm layer are mostly zeros or NaNs.In RMSNorm, the sum of squared activations is computed. In large models (e.g., hidden dimension > 4096), summing the squares of fp16 activations can easily exceed 65,504 (the maximum fp16 value), causing an overflow to infinity. The subsequent step computes `1.0 / sqrt(inf)`, which results in 0. The activations are zeroed out, killing gradients and causing NaNs upon backpropagation.

Which systems are affected

  • PyTorch
  • LLaMA
  • Custom Transformers

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.

  • ✓Check if hidden dimensions are extremely large.
  • ✓Log the intermediate `sum(x**2)` inside the RMSNorm layer to see if it hits `inf`.

Root cause

  • In RMSNorm, the sum of squared activations is computed. In large models (e.g., hidden dimension > 4096), summing the squares of fp16 activations can easily exceed 65,504 (the maximum fp16 value), causing an overflow to infinity. The subsequent step computes `1.0 / sqrt(inf)`, which results in 0. The activations are zeroed out, killing gradients and causing NaNs upon backpropagation.

The fix and how to prevent it

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