# Structured Multidimensional Representation Learning for Large Language Models

arXiv: https://arxiv.org/abs/2603.05727 · HTML: https://mlsanity.com/paper/2603.05727/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 5 Mar 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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [TRAWL: Tensor Reduced and Approximated Weights for Large Language Models](https://mlsanity.com/paper/2406.17261/) (2024)

## Abstract (arXiv)

Transformer architectures achieve state-of-the-art performance across a wide range of pattern recognition and natural language processing tasks, but their scaling is accompanied by substantial parameter growth and redundancy in the embedding dimension. In this work, we introduce a structured spectral factorization of the embedding space based on the L-product for third-order tensors. By reshaping token representations into spectral tensor slices and performing attention and feed-forward operations in the transform domain, we obtain a Tensor Transformer architecture that decomposes the encoder into p independent spectral sub-transformers while preserving standard Transformer semantics. We prove that the proposed L-Transformer is spectrally equivalent to p parallel Transformers operating on reduceddimensional embeddings, which yields approximately 1/p reduction (up to lower-order terms such as biases and normalization parameters) in encoder parameters under fixed total embedding size. When instantiated with a real-valued Discrete Cosine Transform (DCT), the method remains fully differentiable and compatible with existing training pipelines. Beyond compression, the spectral decomposition introduces an inductive bias over embedding frequencies, enabling slice-dependent frequency scaling that improves generalization. Experiments on IMDB and AG~News show that the proposed model can substantially reduce encoder parameters (up to 75% for p=4) while maintaining competitive accuracy. On IMDB, the tensorized encoder matches or improves upon the standard baseline under compression, whereas on AG~News at moderate width we observe a small accuracy decrease in exchange for a 4 times encoder reduction; at BERT-base width (d=768), performance returns to parity.