Write Triton LayerNorm Kernel

To implement numerically stable LayerNorm in Triton, use per-row program instances for single-pass mean and variance computation, enforcing PyTorch-compatible epsilon placement and dividing the denominator by H.

Yes, a single Triton kernel can support both LayerNorm and RMSNorm by toggling mean subtraction, allowing optional learnable gamma and beta affine parameters for flexible normalization across rows.

Yes, the Triton LayerNorm kernel is backward pass ready by outputting mean and rstd intermediate values during the forward training pathway, providing necessary data for gradient computation.

The Triton normalization kernel handles non-divisible hidden dimensions by masking out-of-bounds elements during vectorized tile processing, ensuring correct computation while keeping memory traffic efficient.

The best way to apply affine parameters in a fused GPU normalization kernel is integrating learnable gamma and beta directly into the single-pass normalization execution path.

Custom Triton LayerNorm outputs mismatch PyTorch references when epsilon placement is incorrect or the variance denominator fails to divide by H, requiring strict numerical alignment for stability.