用数学轨迹生成可逆文本嵌入，无需训练和词汇表。
Harmonic Token Projection (HTP): A Vocabulary-Free, Training-Free, Deterministic, and Reversible Embedding Methodology
- 基于字符编码生成确定性谐波轨迹，实现符号到向量的映射。
- 在英语语义相似度任务中达到0.68的斯皮尔曼相关系数。
- 支持多语言、低延迟，适合需要透明性的应用场景。
本文提出谐波词元投影（HTP），一种无需训练、无词汇表、确定性的可逆文本嵌入方法。与依赖统计共现或优化的神经嵌入不同，HTP 将每个词元通过其 Unicode 整数表示解析为谐波轨迹，建立离散符号与连续向量空间之间的双射且可解释的映射。谐波形式确保相位一致的投影，保留结构与可逆性，从而仅通过几何对齐即可估计语义相似度。在语义文本相似度基准（STS-B）及其多语言扩展上的实验表明，HTP 在英文上取得0.68的斯皮尔曼相关系数，跨十种语言表现稳定，单句对计算开销极小，延迟低于毫秒级。结果表明，有意义的语义关系可源自确定性几何，为数据驱动嵌入提供了一种透明高效替代方案。
原文摘要 · Abstract (English)
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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