Normalization

Normalization on AIE-ML Devices

Introduction

This example demonstrates normalization of a 2D data frame on AIE-ML devices.

It demonstrates, in Vitis Model Composer, the following features of AIE-ML devices:

• Shared buffers for AIE-ML memory tiles
• bfloat16 data type

Algorithm

This example targets z-score normalization that scales elements of a frame, making the frame output have the following distribution:

Assume the input frame is a COL * ROW matrix (data is stored column first). For each element in a frame, it computes the corresponding element as:

Where:

For this example, the following specifications are chosen:

• COL: 128
• ROW: 384
• Data Type: bfloat16

Design

The Vitis Model Composer model imports the normalization design as AI Engine Kernel blocks. For a detailed description of the example design and its kernel functions, refer to the AIE-ML Performance Analysis Tutorial. The Vitis Model Composer example uses Version 4 of the normalization design.

Here are the relevant features of the Vitis Model Composer model:

• Design inputs are provided via the model callbacks. To view the callbacks, right-click on the design canvas, select Model Properties, then Callbacks.
• In the InitFcn callback, tiling parameters for the shared buffers are defined in MATLAB structure arrays. For example, the tiling parameters for the input shared buffer are displayed below.

% Input Memtile, Write Access
mtxA_w = [];
for i=0:2
    pattern = struct('buffer_dimension', [COL,ROW], 'tiling_dimension', [COL,ROW/PLIO_NUM], 'offset', [0,ROW/PLIO_NUM*i]);
    mtxA_w = [mtxA_w, pattern];
end

% Input Memtile, Read Access
mtxA_r = [];
for i=0:5
    pattern = struct('buffer_dimension', [COL,ROW], 'tiling_dimension', [K_COL,K_ROW], 'offset', [0,K_ROW*i])
    mtxA_r = [mtxA_r, pattern];
end

This shared buffer has 3 write (input) ports and 5 read (output) ports. The tiling parameters are stored in 3x1 and 5x1, respectively, MATLAB structure arrays. For more information on the format of the MATLAB structure, refer to the Shared Buffer block help.

• The AI Engine design inputs and outputs bfloat16 floating-point data. The Convert To Bfloat16 and Convert From Bfloat16 blocks convert between the Simulink single data type and the bfloat16 data type.
• Because this design has a feedback loop within the AI Engine subsystem, an Algebraic Loop Breaker block is needed to compile and run the model. For more information, see the Algebraic Loop Breaker block help.

The mean and variance of both the input and output signal are displayed. Note that the mean of the output signal is less than 1, and the variance of the output signal is 1. This is the result of the normalization algorithm.

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