Effective data partitioning is known to be crucial in machine learning. Traditional cross-validation methods like K-Fold Cross-Validation (KFCV) enhance model robustness but often compromise generalisation assessment due to high computational demands and extensive data shuffling. To address these issues, the integration of the Simple Random Sampling (SRS), which, despite providing representative samples, can result in non-representative sets with imbalanced data. The study introduces a hybrid model, Fusion Sampling Validation (FSV), combining SRS and KFCV to optimise data partitioning. FSV aims to minimise biases and merge the simplicity of SRS with the accuracy of KFCV. The study used three datasets of 10,000, 50,000, and 100,000 samples, generated with a normal distribution (mean 0, variance 1) and initialised with seed 42. KFCV was performed with five folds and ten repetitions, incorporating a scaling factor to ensure robust performance estimation and generalisation capability. FSV integrated a weighted factor to enhance performance and generalisation further. Evaluations focused on mean estimates (ME), variance estimates (VE), mean squared error (MSE), bias, the rate of convergence for mean estimates (ROC\_ME), and the rate of convergence for variance estimates (ROC\_VE). Results indicated that FSV consistently outperformed SRS and KFCV, with ME values of 0.000863, VE of 0.949644, MSE of 0.952127, bias of 0.016288, ROC\_ME of 0.005199, and ROC\_VE of 0.007137. FSV demonstrated superior accuracy and reliability in data partitioning, particularly in resource-constrained environments and extensive datasets, providing practical solutions for effective machine learning implementations.

Symbolic Regression remains an NP-Hard problem, with extensive research focusing on AI models for this task. Transformer models have shown promise in Symbolic Regression, but performance suffers with smaller datasets. We propose applying k-fold cross-validation to a transformer-based symbolic regression model trained on a significantly reduced dataset (15,000 data points, down from 500,000). This technique partitions the training data into multiple subsets (folds), iteratively training on some while validating on others. Our aim is to provide an estimate of model generalization and mitigate overfitting issues associated with smaller datasets. Results show that this process improves the model's output consistency and generalization by a relative improvement in validation loss of 53.31%. Potentially enabling more efficient and accessible symbolic regression in resource-constrained environments.