Matrix Block Scaling for Machine Learning Precision

The patent divides the matrix into multiple blocks based on element attributes (e.g., magnitude ranges, physical meanings). Each block is processed independently with its own scaling transformation, allowing the system to handle elements of different orders separately while maintaining overall model generation efficiency. This segmentation enables precise control over each block's numerical properties without retraining the entire model.

The patent applies scaling transformations to change the parameters (magnitudes) of matrix elements within each block. By transforming elements to a common scale range while preserving their relative relationships and physical meanings, the model can process uniformly scaled inputs that improve solving precision without requiring model retraining, thus maintaining productivity while enhancing accuracy.

The patent applies different scaling transformations to different blocks of the matrix based on their specific attributes. Each block receives a tailored scaling approach appropriate to its characteristics (e.g., magnitude range, physical dimension), rather than applying a single global scaling method. This local quality approach improves precision for each block while keeping the preprocessing logic modular and manageable.

The patent performs scaling transformations on matrix blocks in advance, before feeding them to the machine learning model. By pre-processing the matrix to establish uniform scaling relationships among elements beforehand, the system eliminates the need for complex real-time preprocessing during model inference, thereby reducing overall preprocessing complexity while maintaining high solving precision.

The patent segments the matrix into blocks based on attribute similarities, allowing parallel processing of each block during scaling transformations. By organizing blocks with related elements together and processing them independently, the system minimizes the overhead of inter-block computations while achieving precise scaling, thus reducing overall processing time compared to processing all elements sequentially.

The patent develops a universal scaling transformation framework that can be applied to any block regardless of its specific attributes. This multi-functional approach uses consistent scaling principles across all blocks, enabling reuse of the same transformation logic and reducing the need for block-specific processing routines, thereby minimizing processing time while maintaining precision across diverse matrix elements.