# Fast and Simplex: 2-Simplicial Attention in Triton

arXiv: https://arxiv.org/abs/2507.02754 · HTML: https://mlsanity.com/paper/2507.02754/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 45 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [DCN V2: Improved Deep & Cross Network and Practical Lessons for Web-scale Learning to Rank Systems](https://mlsanity.com/paper/2008.13535/) (2020)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Primer: Searching for Efficient Transformers for Language Modeling](https://mlsanity.com/paper/2109.08668/) (2021)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [Representational Strengths and Limitations of Transformers](https://mlsanity.com/paper/2306.02896/) (2023)
- [Systematic Generalization with Edge Transformers](https://mlsanity.com/paper/2112.00578/) (2021)

## Built on by (most cited first, 8 of 8)

- [FSVideo: Fast Speed Video Diffusion Model in a Highly-Compressed Latent Space](https://mlsanity.com/paper/2602.02092/) (2026)
- [Triangle Multiplication Is All You Need For Biomolecular Structure Representations](https://mlsanity.com/paper/2510.18870/) (2025)
- [Interleaved Head Attention](https://mlsanity.com/paper/2602.21371/) (2026)
- [Multi-Mixer Models: Flexible Sequence Modeling with Shared Representations](https://mlsanity.com/paper/2605.28769/) (2026)
- [How Smoothing is N-simplicial Attention?](https://mlsanity.com/paper/2512.15600/) (2025)
- [A Vision for Multisensory Intelligence: Sensing, Science, and Synergy](https://mlsanity.com/paper/2601.04563/) (2026)
- [Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs](https://mlsanity.com/paper/2606.28122/) (2026)
- [Linearized 2-Simplicial Attention](https://mlsanity.com/paper/2608.09307/) (2026)

## Abstract (arXiv)

Recent work has shown that training loss scales as a power law with both model size and the number of tokens, and that achieving compute-optimal models requires scaling model size and token count together. However, these scaling laws assume an infinite supply of data and apply primarily in compute-bound settings. As modern large language models increasingly rely on massive internet-scale datasets, the assumption that they are compute-bound is becoming less valid. This shift highlights the need for architectures that prioritize token efficiency. In this work, we investigate the use of the 2-simplicial Transformer, an architecture that generalizes standard dot-product attention to trilinear functions through an efficient Triton kernel implementation. We demonstrate that the 2-simplicial Transformer achieves better token efficiency than standard Transformers: for a fixed token budget, similarly sized models outperform their dot-product counterparts on tasks involving mathematics, coding, reasoning, and logic. We quantify these gains by demonstrating that 2-simplicial attention changes the exponent in the scaling laws for knowledge and reasoning tasks compared to dot product attention.