Harmonic Token Projection (HTP): A Vocabulary-Free, Training-Free, Deterministic, and Reversible Embedding Methodology

• URL: http://arxiv.org/abs/2511.20665v1
• Date: Mon, 10 Nov 2025 20:51:18 GMT
• Title: Harmonic Token Projection (HTP): A Vocabulary-Free, Training-Free, Deterministic, and Reversible Embedding Methodology
• Abstract summary: The Harmonic Token Projection (HTP) is a reversible and deterministic framework for generating text embeddings without training, vocabularies, or parameters.<n>HTP achieves a Spearman correlation of rho = 0.68 in English, maintaining stable performance across ten languages.<n>This demonstrates that meaningful semantic relations can emerge from deterministic geometry, offering a transparent and efficient alternative to data-driven embeddings.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces the Harmonic Token Projection (HTP), a reversible and deterministic framework for generating text embeddings without training, vocabularies, or stochastic parameters. Unlike neural embeddings that rely on statistical co-occurrence or optimization, HTP encodes each token analytically as a harmonic trajectory derived from its Unicode integer representation, establishing a bijective and interpretable mapping between discrete symbols and continuous vector space. The harmonic formulation provides phase-coherent projections that preserve both structure and reversibility, enabling semantic similarity estimation from purely geometric alignment. Experimental evaluation on the Semantic Textual Similarity Benchmark (STS-B) and its multilingual extension shows that HTP achieves a Spearman correlation of \r{ho} = 0.68 in English, maintaining stable performance across ten languages with negligible computational cost and sub-millisecond latency per sentence pair. This demonstrates that meaningful semantic relations can emerge from deterministic geometry, offering a transparent and efficient alternative to data-driven embeddings. Keywords: Harmonic Token Projection, reversible embedding, deterministic encoding, semantic similarity, multilingual representation.

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