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Mojo function

layer_norm_cpu

def layer_norm_cpu[dtype: DType, //, input_fn: def[width: Int, alignment: Int](Int, Int) capturing -> SIMD[dtype, width], gamma_fn: def[width: Int, rank: Int, alignment: Int](IndexList[rank]) capturing -> SIMD[dtype, width], output_fn: def[width: Int, alignment: Int](row: Int, col: Int, val: SIMD[dtype, width]) capturing -> None](num_rows: Int, num_cols: Int, beta: TileTensor[dtype, address_space=beta.address_space, linear_idx_type=beta.linear_idx_type, element_size=beta.element_size], epsilon: Scalar[dtype])

Computes layernorm(elementwise_fn(x)) across the last dimension of x, where layernorm is defined as $(x-mean(x))/(sqrt(var(x)+eps)*gamma_fn + beta$ .

Currently performs 3 passes over the input data. This can be reduced to 2 by fusing the add, mean, and variance loops using Welford's algorithm.

Parameters:

dtype (DType): The x and out buffers' elements dtype.
input_fn (def[width: Int, alignment: Int](Int, Int) capturing -> SIMD[dtype, width]): Function called to generate an input value.
gamma_fn (def[width: Int, rank: Int, alignment: Int](IndexList[rank]) capturing -> SIMD[dtype, width]): Function called to generate a gamma value.
output_fn (def[width: Int, alignment: Int](row: Int, col: Int, val: SIMD[dtype, width]) capturing -> None): Function called to store the output value.

Args:

num_rows (Int): The number of rows in the input tensor.
num_cols (Int): The number of columns in the input tensor.
beta (TileTensor[dtype, address_space=beta.address_space, linear_idx_type=beta.linear_idx_type, element_size=beta.element_size]): The beta value to use in the layernorm calculation.
epsilon (Scalar[dtype]): The eps value to use in the layernorm calculation.

def layer_norm_cpu[dtype: DType, rank: Int, //, input_fn: def[width: Int, rank: Int, alignment: Int](IndexList[rank]) capturing -> SIMD[dtype, width], gamma_fn: def[width: Int, rank: Int, alignment: Int](IndexList[rank]) capturing -> SIMD[dtype, width], output_fn: def[width: Int, rank: Int, alignment: Int](idx: IndexList[rank], val: SIMD[dtype, width]) capturing -> None](shape: IndexList[rank], beta: TileTensor[dtype, address_space=beta.address_space, linear_idx_type=beta.linear_idx_type, element_size=beta.element_size], epsilon: Scalar[dtype], ctx: Optional[DeviceContext] = None)