  The challenge of limited availability of data for training in machine
learning arises in many applications and the impact on performance and
generalization is serious. Traditional data augmentation methods aim to enhance
training with a moderately sufficient data set. Generative models like
Generative Adversarial Networks (GANs) often face problematic convergence when
generating significant and diverse data samples. Diffusion models, though
effective, still struggle with high computational cost and long training times.
This paper introduces an innovative Expansive Synthesis model that generates
large-scale, high-fidelity datasets from minimal samples. The proposed approach
exploits expander graph mappings and feature interpolation to synthesize
expanded datasets while preserving the intrinsic data distribution and feature
structural relationships. The rationale of the model is rooted in the
non-linear property of neural networks' latent space and in its capture by a
Koopman operator to yield a linear space of features to facilitate the
construction of larger and enriched consistent datasets starting with a much
smaller dataset. This process is optimized by an autoencoder architecture
enhanced with self-attention layers and further refined for distributional
consistency by optimal transport. We validate our Expansive Synthesis by
training classifiers on the generated datasets and comparing their performance
to classifiers trained on larger, original datasets. Experimental results
demonstrate that classifiers trained on synthesized data achieve performance
metrics on par with those trained on full-scale datasets, showcasing the
model's potential to effectively augment training data. This work represents a
significant advancement in data generation, offering a robust solution to data
scarcity and paving the way for enhanced data availability in machine learning
applications.
