# Manifold Projection and Iterative Autoencoder Refinement for Masked Language Modeling

arXiv: https://arxiv.org/abs/2609.30288 · HTML: https://mlsanity.com/paper/2609.30288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 27 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kernel](https://mlsanity.com/paper/1908.11775/) (2019)
- [Synthesizer: Rethinking Self-Attention in Transformer Models](https://mlsanity.com/paper/2005.00743/) (2020)
- [Funnel-Transformer: Filtering out Sequential Redundancy for Efficient Language Processing](https://mlsanity.com/paper/2006.03236/) (2020)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [Hierarchical Transformers Are More Efficient Language Models](https://mlsanity.com/paper/2110.13711/) (2021)
- [Implicit Regularization Towards Rank Minimization in ReLU Networks](https://mlsanity.com/paper/2201.12760/) (2022)
- [Implicit Rank-Minimizing Autoencoder](https://mlsanity.com/paper/2010.00679/) (2020)
- [HyperMixer: An MLP-based Low Cost Alternative to Transformers](https://mlsanity.com/paper/2203.03691/) (2022)
- [Low-rank bias, weight decay, and model merging in neural networks](https://mlsanity.com/paper/2502.17340/) (2025)
- [A Variational AutoEncoder for Transformers with Nonparametric Variational Information Bottleneck](https://mlsanity.com/paper/2207.13529/) (2022)
- [Denoising Diffusion Generative Models Secretly Calculate Attentions](https://mlsanity.com/paper/2609.00885/) (2026)

## Abstract (arXiv)

In Transformer-based masked language models, attention is the primary mechanism for context mixing, but there are other ways to mix data across tokens. Recent attention-free mixers replace attention with fixed or hypernetwork-generated MLPs, alternating their dynamic, content-dependent weighting for computational simplicity. We build an alternative that gets the same property from a low-rank bottleneck autoencoder. We replace attention with a stack of autoencoder-based mixing modules, one operating over local neighborhoods, one over the full sequence, and one across attention heads, each compressing and reconstructing its input through a bottleneck, and its width is a hyperparameter rather than a training effect. In masked positions, we introduce an iterative refinement procedure that has two distinct steps. A pulling step that pulls an embedding representation toward a weighted average of its neighbors, and a correcting step that projects the result back to the learned manifold via an autoencoder. Our architecture achieves a significant portion of attention's performance at about 1.9 × fewer FLOPs when pretrained on C4 and evaluated with parameter-matched BERT baselines. Our model equals parameter-matched BERT and TinyBERT baselines on the rarest-token frequency bucket using a frequency-aware training schedule that samples rare tokens more than uniformly for the masking tasks.