Space Optimization Using Scaled Neural Multiplicative Model

The patent transforms the optimization problem by changing the parameter representation from direct linear parameters to logarithmic parameters. By taking the logarithm of the objective function and constraints, the non-linear relationships are linearized, allowing neural network models to capture complex patterns while maintaining computational tractability. This parameter transformation enables the model to handle sparse data more effectively by revealing underlying non-linear structures.

The patent replaces traditional linear optimization mechanics with a neural network-based prediction system. Instead of using conventional linear programming approaches, the system employs neural networks trained on historical data to predict optimal allocations. This substitution allows the model to learn complex non-linear relationships from sparse data while maintaining the ability to provide tractable optimization solutions.

The patent performs preliminary actions by pre-processing the sparse interaction data through logarithmic transformation and feature engineering before feeding it to the neural network. This preliminary processing enhances the signal-to-noise ratio in sparse datasets, allowing the model to effectively learn from limited interactions even when many items are present in the space. The system also uses data augmentation techniques to artificially increase the effective data density.

The patent creates a composite modeling approach by combining multiple neural network layers with different functions (prediction layer, optimization layer, and transformation layer). This composite structure allows the system to simultaneously handle high-dimensional sparse input data and produce accurate optimization results, effectively managing the trade-off between quantity of items and data density.

The patent segments the optimization problem into distinct computational stages: data preprocessing, neural network prediction, and solution optimization. Each segment handles specific aspects of the problem, allowing the system to maintain computational simplicity in each individual stage while achieving high accuracy overall when the segments are combined. This segmentation enables the use of simple, interpretable models at each step rather than requiring a single complex model.

The patent introduces an intermediary logarithmic transformation layer between the raw sparse data and the optimization objective. This intermediary transformation converts multiplicative relationships into additive ones, making the sparse data more amenable to simple linear optimization techniques while preserving the underlying non-linear patterns. The intermediary layer acts as a bridge that maintains computational simplicity while improving accuracy.