Beyond Sinusoids: A Morlet Wavelet Framework for Transformer Positional Encoding
Standard positional encodings for transformers - sinusoidal and rotary (RoPE) - treat every position as equally local: they encode where a token is, but not how far its positional influence should extend. We propose that the Morlet wavelet, which simultaneously minimises uncertainty in position and frequency, is the natural basis for positional encoding, and introduce Morlet Positional Encoding (MoPE): each embedding dimension learns its own frequency and locality bandwidth from data. The main theoretical result is a unification: sinusoidal PE and the RoPE correlation kernel both emerge as limiting cases of MoPE when locality is switched off (sigma_i -> infinity). The phase of MoPE recove...
| Authors | Athanasios Zeris |
|---|---|
| Primary category | cs.LG |
| Published | 31 May 2026 |
| Last updated at source | 31 May 2026 |
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