A KAN-based Non-linear Factorization for Embedding Layer Compression

Among existing embedding compression approaches, low-rank factorization provides a simple and mathematically principled solution by approximating the embedding matrix with a reduced-rank decomposition. However, its practical effectiveness is often limited, as the resulting linear bottleneck constrains representational capacity. To overcome these limitations, we propose an enhanced factorization scheme that increases expressive power by introducing learnable non-linear projections within the compressed embedding layer. Our method is inspired by the Kolmogorov Arnold Networks (KAN) paradigm, which replaces fixed linear transformations with learnable univariate functions. Despite promising results in other domains, applications of KANs in NLP remain scarce and have so far been largely limited to final or task specific layers, rather than core representational components such as embedding layers. We evaluate the proposed approach by integrating the compressed embedding layer into the Skip-gram framework and comparing it against a standard low-rank baseline under matched parameter budgets on the Word Analogy and Semantic Similarity benchmarks. We further introduce an effective initialization strategy from a pre-trained, uncompressed embedding layer. The behavior of the model is analyzed both immediately after initialization and after a brief post-initialization refinement phase, considering training with the standard Skip-gram objective as well as variants augmented with distillation from the original embedding layer. Overall, our results show that augmenting low-rank factorization with learnable non-linear projections effectively mitigates the limitations of linear bottlenecks, yielding more faithful compressed embeddings under fixed dimensionality and suggesting a promising direction for embedding layer compression beyond purely linear methods.