Exploring Discrete Wavelets Transform for Natural Language Processing
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Wavelet transforms have been extensively studied in signal and image processing for their ability to represent data across multiple resolutions, isolate salient features, and provide compact yet informative representations. Motivated by these properties, this dissertation investigates the applicability of Discrete Wavelet Transforms (DWT) to Natural LanguageProcessing (NLP), with a focus on embedding representations, Large Language Models (LLM) and downstream task performance. We propose a wavelet-based framework for analyzing and transforming dense embedding vectors into multi-resolution representations that preserve salient semantic information while enabling substantial dimensionality reduction. Unlike conventional compression techniques that operate heuristically or rely solely on learned projections, DWT provides a mathematically grounded decomposition that separates low-frequency (global semantic structure) and high-frequency (fine-grained variation) components within embeddings. We conduct extensive empirical evaluations across semantic similarity benchmarks and multiple downstream tasks, using a range of embedding models, including large language models. Results demonstrate that DWT-based embeddings achieve dimensionality reductions of 50–75% with negligible performance degradation on semantic similarity tasks, and in many cases yield improved performance on downstream applications. Furthermore, we show that DWT can be integrated into existing model architectures to reduce computational overhead, accelerate processing time, and improve efficiency without compromising representational quality. Overall, this work establishes Discrete Wavelet Transforms as a principled and effective mechanism for multi-resolution embedding analysis, compression, and architectural enhancement in NLP systems, with particular promise for large-scale models and text summarization frameworks.
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