# From Attention to Atoms: Spectral Dictionary Learning for Fast, Interpretable Language Models

arXiv: https://arxiv.org/abs/2505.00033 · HTML: https://mlsanity.com/paper/2505.00033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 29 Apr 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Learnable Multi-Scale Wavelet Transformer: A Novel Alternative to Self-Attention](https://mlsanity.com/paper/2504.08801/) (2025)
- [Spectral Dictionary Learning for Generative Image Modeling](https://mlsanity.com/paper/2504.17804/) (2025)

## Built on by (most cited first, 2 of 2)

- [Detecting Contextual Hallucinations in LLMs with Frequency-Aware Attention](https://mlsanity.com/paper/2602.18145/) (2026)
- [Wavelet Logic Machines: Learning and Reasoning in the Spectral Domain Without Neural Networks](https://mlsanity.com/paper/2507.19514/) (2025)

## Abstract (arXiv)

We propose a novel spectral generative modeling framework for natural language processing that jointly learns a global time varying Fourier dictionary and per token mixing coefficients, replacing the ubiquitous self attention mechanism in transformer architectures. By enforcing reconstruction losses in both the time domain (embedding reconstruction) and the frequency domain (via Short Time Fourier Transform magnitude matching) alongside a standard language modeling objective, and fitting a Gaussian Mixture Model (GMM) prior over the learned mixing vectors, our approach achieves competitive perplexity and generation quality on standard benchmarks such as WikiText2 and Penn Treebank. In contrast to the quadratic computation complexity of self attention, our method operates with linear complexity, delivering substantial efficiency gains. We demonstrate that spectral dictionary models can achieve competitive performance compared to transformer baselines while significantly reducing inference latency and memory footprint, offering a compelling alternative for scalable language modeling.