# Nautilus: An Auto-Scheduling Tensor Compiler for Efficient Tiled GPU Kernels

arXiv: https://arxiv.org/abs/2604.14825 · HTML: https://mlsanity.com/paper/2604.14825/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 16 Apr 2026.

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

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Efficient Large-Scale Language Model Training on GPU Clusters Using Megatron-LM](https://mlsanity.com/paper/2104.04473/) (2021)
- [AudioLM: a Language Modeling Approach to Audio Generation](https://mlsanity.com/paper/2209.03143/) (2022)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [DeepSpeed Inference: Enabling Efficient Inference of Transformer Models at Unprecedented Scale](https://mlsanity.com/paper/2207.00032/) (2022)
- [FlashInfer: Efficient and Customizable Attention Engine for LLM Inference Serving](https://mlsanity.com/paper/2501.01005/) (2025)
- [Ansor: Generating High-Performance Tensor Programs for Deep Learning](https://mlsanity.com/paper/2006.06762/) (2020)
- [Glow: Graph Lowering Compiler Techniques for Neural Networks](https://mlsanity.com/paper/1805.00907/) (2018)
- [FlashAttention-4: Algorithm and Kernel Pipelining Co-Design for Asymmetric Hardware Scaling](https://mlsanity.com/paper/2603.05451/) (2026)
- [MLIR: A Compiler Infrastructure for the End of Moore's Law](https://mlsanity.com/paper/2002.11054/) (2020)
- [Tiramisu: A Polyhedral Compiler for Expressing Fast and Portable Code](https://mlsanity.com/paper/1804.10694/) (2018)
- [Mirage: A Multi-Level Superoptimizer for Tensor Programs](https://mlsanity.com/paper/2405.05751/) (2024)
- [ThunderKittens: Simple, Fast, and Adorable AI Kernels](https://mlsanity.com/paper/2410.20399/) (2024)
- [Equality Saturation for Tensor Graph Superoptimization](https://mlsanity.com/paper/2101.01332/) (2021)
- [Tawa: Automatic Warp Specialization for Modern GPUs with Asynchronous References](https://mlsanity.com/paper/2510.14719/) (2025)
- [Neptune: Advanced ML Operator Fusion for Locality and Parallelism on GPUs](https://mlsanity.com/paper/2510.08726/) (2025)

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

- [Cleave: Scaling Tensor Program Optimization via Decoupled Algebraic Search and Operator Scheduling](https://mlsanity.com/paper/2610.07742/) (2026)

## Abstract (arXiv)

We present Nautilus, a novel tensor compiler that moves toward fully automated math-to-kernel optimization. Nautilus compiles a high-level algebraic specification of tensor operators into efficient tiled GPU kernels. Nautilus's successive lowering design allows high-level optimizations, expression rewrites, and tile optimizations to be jointly applied in a single end-to-end system. Nautilus presents a novel auto-scheduler that discovers sequences of high-level optimizations, while preserving the regular program structure needed by tile optimizers. Nautilus's auto-scheduler captures complex interactions and trade-offs in the high-level optimizations, including aggressive global transformations like advanced reduction fusion. Nautilus is the first end-to-end tensor compiler capable of starting from a math-like description of attention and automatically discovering FlashAttention-3-like kernels, offloading the entire burden of optimization from the programmer to the compiler. Across five transformer-based models and 150 evaluation configurations on NVIDIA GH200 and RTX 5090 GPUs, Nautilus achieves up to 23% higher throughput than state-of-the-art compilers on GH200 and up to 42% on RTX 5090, while matching or exceeding manually written cuDNN kernels on many long-sequence configurations.