# Wave-Based Semantic Memory with Resonance-Based Retrieval: A Phase-Aware Alternative to Vector Embedding Stores

arXiv: https://arxiv.org/abs/2509.09691 · HTML: https://mlsanity.com/paper/2509.09691/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 10 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)

## Built on by (most cited first, 1 of 1)

- [TRepLiNa: Layer-wise CKA+REPINA Alignment Improves Low-Resource Machine Translation in Aya-23 8B](https://mlsanity.com/paper/2510.06249/) (2025)

## Abstract (arXiv)

Conventional vector-based memory systems rely on cosine or inner product similarity within real-valued embedding spaces. While computationally efficient, such approaches are inherently phase-insensitive and limited in their ability to capture resonance phenomena crucial for meaning representation. We propose Wave-Based Semantic Memory, a novel framework that models knowledge as wave patterns psi(x) = A(x) eiφ(x) and retrieves it through resonance-based interference. This approach preserves both amplitude and phase information, enabling more expressive and robust semantic similarity. We demonstrate that resonance-based retrieval achieves higher discriminative power in cases where vector methods fail, including phase shifts, negations, and compositional queries. Our implementation, ResonanceDB, shows scalability to millions of patterns with millisecond latency, positioning wave-based memory as a viable alternative to vector stores for AGI-oriented reasoning and knowledge representation.