# Spectral Retrieval: Multi-Scale Sinc Convolution over Token Embeddings for Localized Retrieval in LLM Multi-Agent Systems

arXiv: https://arxiv.org/abs/2605.24764 · HTML: https://mlsanity.com/paper/2605.24764/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 23 May 2026.

## Builds on (most cited first, 12 of 12)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [SPLADE: Sparse Lexical and Expansion Model for First Stage Ranking](https://mlsanity.com/paper/2107.05720/) (2021)
- [On the Theoretical Limitations of Embedding-Based Retrieval](https://mlsanity.com/paper/2508.21038/) (2025)

## Abstract (arXiv)

[Abridged] - Spectral Retrieval is a plug-in re-ranking stage that interpolates between per-token MaxSim and mean-pool retrieval through a multi-scale sinc convolution over token embeddings. In standard dense retrieval each document is one mean-pooled vector; when relevance localises into a short subspan, the signal averages into noise. Spectral Retrieval reuses per-token embeddings from a late-interaction index and convolves them with a normalised sinc kernel at multiple scales. At L=1 the kernel acts as the identity, recovering per-token MaxSim; as L grows it approaches a uniform filter, recovering mean pooling. The maximum cosine over positions and scales yields a score provably no less informative than either endpoint. On a controlled synthetic benchmark with 1,000 documents and planted single-position spikes, mean-pool retrieval sits at chance (Recall@10 ~ 0.02) regardless of spike strength, while Spectral Retrieval reaches Recall@10 = 1.0 once the planted cosine exceeds the corpus-level token noise floor. On LIMIT-small with a frozen all-mpnet-base-v2 encoder, Spectral Retrieval lifts Recall@10 from 0.33 to 0.90, MRR from 0.22 to 0.79, and strict Success@10 from 0.12 to 0.84, without retraining. The method fits naturally into multi-agent LLM systems, where each agent benefits from a tighter, role-specific retrieval window over a shared corpus.