For the complete documentation index, see llms.txt. Markdown versions of all pages are available by appending .md to any URL (e.g. /max/get-started.md).

Mojo function

apply_qk_rms_norm

def apply_qk_rms_norm[in_dtype: DType, out_dtype: DType, //, target: StringSlice[StaticConstantOrigin] = StringSlice("cpu")](q_out: TileTensor[out_dtype, Storage=q_out.Storage, address_space=q_out.address_space, linear_idx_type=q_out.linear_idx_type, element_size=q_out.element_size], k_out: TileTensor[out_dtype, Storage=k_out.Storage, address_space=k_out.address_space, linear_idx_type=k_out.linear_idx_type, element_size=k_out.element_size], gamma_q: TileTensor[DType.float32, Storage=gamma_q.Storage, address_space=gamma_q.address_space, linear_idx_type=gamma_q.linear_idx_type, element_size=gamma_q.element_size], gamma_k: TileTensor[DType.float32, Storage=gamma_k.Storage, address_space=gamma_k.address_space, linear_idx_type=gamma_k.linear_idx_type, element_size=gamma_k.element_size], qk_var: TileTensor[DType.float32, Storage=qk_var.Storage, address_space=qk_var.address_space, linear_idx_type=qk_var.linear_idx_type, element_size=qk_var.element_size], q: TileTensor[in_dtype, Storage=q.Storage, address_space=q.address_space, linear_idx_type=q.linear_idx_type, element_size=q.element_size], k: TileTensor[in_dtype, Storage=k.Storage, address_space=k.address_space, linear_idx_type=k.linear_idx_type, element_size=k.element_size], epsilon: Float32, rows: Int, q_cols: Int, k_cols: Int, ctx: DeviceContext)

Fused per-element QK-RMSNorm apply for two operands Q and K.

Given the already cross-rank-reduced per-row statistics qk_var [M, 2] (col 0 = mean(q^2), col 1 = mean(k^2), float32) and per-column float32 scales gamma_q [Nq] / gamma_k [Nk], applies in a single launch:

q_out[m,c] = cast((cast(q[m,c], f32) * rsqrt(qk_var[m,0] + eps)) * gamma_q[c], out_dtype) and likewise for K with column 1. The grouping ((x * rs) * gamma) then cast matches the unfused graph this replaces for bit-accuracy. This fuses the QK-RMSNorm apply chain (~7 tiny elementwise/View kernels) into one launch, used for cross-head QK-RMSNorm under tensor parallelism.

All operands (q / k activations, the outputs q_out / k_out, and the gamma_q / gamma_k / qk_var inputs) are passed directly as TileTensors and loaded/stored in-kernel, matching the in-file rms_norm gamma.load[...] idiom.

Parameters:

in_dtype (DType): Element type of both activation inputs (bfloat16 or float32).
out_dtype (DType): Element type of the outputs (typically equal to in_dtype).
target (StringSlice[StaticConstantOrigin]): "cpu" or a GPU target string.

Args:

q_out (TileTensor[out_dtype, Storage=q_out.Storage, address_space=q_out.address_space, linear_idx_type=q_out.linear_idx_type, element_size=q_out.element_size]): Scaled Q output, shape [M, Nq].
k_out (TileTensor[out_dtype, Storage=k_out.Storage, address_space=k_out.address_space, linear_idx_type=k_out.linear_idx_type, element_size=k_out.element_size]): Scaled K output, shape [M, Nk].
gamma_q (TileTensor[DType.float32, Storage=gamma_q.Storage, address_space=gamma_q.address_space, linear_idx_type=gamma_q.linear_idx_type, element_size=gamma_q.element_size]): Per-column float32 Q scales, shape [Nq].
gamma_k (TileTensor[DType.float32, Storage=gamma_k.Storage, address_space=gamma_k.address_space, linear_idx_type=gamma_k.linear_idx_type, element_size=gamma_k.element_size]): Per-column float32 K scales, shape [Nk].
qk_var (TileTensor[DType.float32, Storage=qk_var.Storage, address_space=qk_var.address_space, linear_idx_type=qk_var.linear_idx_type, element_size=qk_var.element_size]): Per-row float32 statistics, shape [M, 2] (col 0 = mean(q^2), col 1 = mean(k^2)).
q (TileTensor[in_dtype, Storage=q.Storage, address_space=q.address_space, linear_idx_type=q.linear_idx_type, element_size=q.element_size]): Q activations, shape [M, Nq].
k (TileTensor[in_dtype, Storage=k.Storage, address_space=k.address_space, linear_idx_type=k.linear_idx_type, element_size=k.element_size]): K activations, shape [M, Nk].
epsilon (Float32): RMSNorm epsilon, added to the variance before rsqrt.
rows (Int): Shared leading dimension of Q and K.
q_cols (Int): Number of columns of Q.
k_cols (Int): Number of columns of K.
ctx (DeviceContext): Device context (ignored on CPU).