fused layernorm

**Fused layernorm** is the **single-kernel implementation of layer normalization that combines statistics, normalization, and affine transform steps** - it replaces multi-pass implementations with a tighter and more bandwidth-efficient execution path. **What Is Fused layernorm?** - **Definition**: LayerNorm kernel that computes mean and variance, applies normalization, and writes scaled output in one pass. - **Numerical Core**: Uses stable online variance methods and epsilon handling for robust mixed-precision execution. - **Memory Behavior**: Avoids repeated reads and writes of the same activation block. - **Model Context**: Widely used in transformer blocks where LayerNorm appears frequently. **Why Fused layernorm Matters** - **Step-Time Impact**: Even modest per-call savings compound across many layers and tokens. - **Bandwidth Relief**: Reduced memory traffic improves utilization on memory-bound training jobs. - **Kernel Efficiency**: Better vectorization and warp-level reduction lower overhead versus naive implementations. - **Inference Gain**: Token-level latency improves when normalization becomes a cheaper stage. - **Operational Consistency**: Standard fused kernels provide predictable behavior across workloads. **How It Is Used in Practice** - **Backend Enablement**: Select fused LayerNorm implementations from framework or custom kernel libraries. - **Shape Tuning**: Benchmark hidden-size dependent kernels to choose best launch configuration. - **Parity Validation**: Confirm statistical equivalence and gradient correctness against reference LayerNorm. Fused layernorm is **a practical micro-optimization with macro impact in transformer pipelines** - reducing normalization overhead helps unlock better end-to-end throughput.