# JoFormer (Journey-based Transformer): Theory and Empirical Analysis on the Tiny Shakespeare Dataset

arXiv: https://arxiv.org/abs/2506.08652 · HTML: https://mlsanity.com/paper/2506.08652/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 6 references that are in the map.
- First posted on arXiv 10 Jun 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning](https://mlsanity.com/paper/2505.15507/) (2025)

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

- [Knowledge Graph and Hypergraph Transformers with Repository-Attention and Journey-Based Role Transport](https://mlsanity.com/paper/2603.03304/) (2026)

## Abstract (arXiv)

Transformers have demonstrated remarkable success in sequence modeling, yet effectively incorporating positional information remains a challenging and active area of research. In this paper, we introduce JoFormer, a journey-based Transformer architecture grounded in a recently proposed non-commutative algebra for composing transformations across positions. JoFormer represents relative positions through learnable directional transforms that are sequentially composed along the input, thereby extending and generalizing existing approaches based on relative position representations. We derive the JoFormer attention mechanism from first principles and show that it subsumes standard methods such as rotary transformations as special cases. To evaluate its effectiveness, we compare JoFormer to the RoFormer baseline on the Tiny Shakespeare character-level language modeling task. Our results demonstrate that JoFormer consistently achieves lower perplexity and faster convergence, highlighting the advantages of its more expressive, journey-based treatment of position. Notably, the per-token JoFormer is still a primitive, conceptual variant with layer-independent angles, yet it already demonstrates strong performance-underscoring its promise as a proof of concept for more expressive architectures. We conclude by discussing how JoFormer offers a principled approach to integrating positional structure into Transformer architectures. The code used in this work is available at https://github.com/mahesh-godavarti/joformer.