---
title: "Tensor Comprehensions — paper by Vasilache et al. (2018)"
description: "The authors introduce Tensor Comprehensions (TC), a compact domain-specific language based on… 95 references, cited by 85 papers here."
authors: ["Nicolas Vasilache", "Oleksandr Zinenko", "Theodoros Theodoridis", "Priya Goyal", "Zachary DeVito", "William S. Moses", "Sven Verdoolaege", "Andrew Adams", "Albert Cohen"]
year: 2018
venue: "arXiv:1802.04730"
source: "https://arxiv.org/abs/1802.04730"
doi: "10.48550/arxiv.1802.04730"
arxiv: "1802.04730"
licence: "arXiv — non-exclusive licence to distribute"
licence_url: "https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/vasilache-2018-tensor-comprehensions-framework-agnostic-high/"
---
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# Tensor Comprehensions: Framework-Agnostic High-Performance Machine Learning Abstractions

**Authors:** Nicolas Vasilache, Oleksandr Zinenko, Theodoros Theodoridis, [Priya Goyal](https://md.research.elamur.ai/free/en/authors/priya-goyal/), Zachary DeVito, William S. Moses, Sven Verdoolaege, Andrew Adams and Albert Cohen · **Year:** 2018 · **Venue:** arXiv:1802.04730 · **Licence:** [arXiv — non-exclusive licence to distribute](https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html)

**Links:** [Publisher's page](https://arxiv.org/abs/1802.04730) · [PDF](https://arxiv.org/pdf/1802.04730) · [DOI 10.48550/arxiv.1802.04730](https://doi.org/10.48550/arxiv.1802.04730) · [arXiv 1802.04730](https://arxiv.org/abs/1802.04730) · [OpenAlex](https://openalex.org/W2786320458)

**Citations:** 238 citations (OpenAlex, 2026-10-14) · [85](https://md.research.elamur.ai/free/en/papers/vasilache-2018-tensor-comprehensions-framework-agnostic-high/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Deep learning frameworks such as TensorFlow, PyTorch and Caffe2 mostly hand computation off to vendor libraries like CUDNN and CUBLAS. When researchers invent an operator those libraries do not cover, they must write a custom kernel by hand, which is costly and often slow. Even supported operators lose speed, because the libraries cannot fuse work across operators or adapt to specific tensor shapes.

The authors introduce Tensor Comprehensions (TC), a compact domain-specific language based on Einstein notation that infers tensor ranges and shapes automatically. A polyhedral just-in-time compiler turns TC programs into CUDA kernels, applying fusion, tiling, promotion into faster memory levels and specialization to concrete sizes. An autotuner searches mapping options and stores the best versions in a compilation cache. The system connects to PyTorch and Caffe2 through the ATen tensor library.

On ML-relevant kernels and on a Facebook production model, the generated code runs up to 4× faster than NVIDIA libraries. This lets domain experts get fast GPU code for new layers directly from a mathematical description.

## Key points
- Main components: the TC language, a polyhedral JIT compiler targeting CUDA, and an autotuner with a compilation cache. Integration with PyTorch and Caffe2 goes through ATen.
- Fused lookup-table embeddings (2LUT) were tested at sizes E1 = E2 = 10^7, D = 64 and L1 = L2 = 50. The synthesized kernel ran about 4× faster than the CUB-based Caffe2 reference (4.1× on Pascal). A new two-stage shared-memory loading scheme was essential: without it, performance dropped by more than 5×.
- MLP3 (three fused MLP layers) compiles into a single CUDA kernel, whereas frameworks typically issue 3–9 kernel calls. It runs up to 3.6× faster than the CUDNN/CUBLAS-based Caffe2 reference: 32 µs of runtime plus about 25 µs of overhead, partly caused by NVRTC.
- On Pascal, a single fcrelu layer ran as much as 1.5× faster than CUBLAS, even without register-level optimization.
- Planned future work includes:
  - more hardware targets;
  - systematic data-layout transformations;
  - automatic DAG partitioning;
  - symbolic autodiff on TC;
  - sparse and mixed-precision types.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Nicolas Vasilache, Oleksandr Zinenko, Theodoros Theodoridis, Priya Goyal, Zachary DeVito, William S. Moses, Sven Verdoolaege, Andrew Adams and Albert Cohen. 2018. Tensor Comprehensions: Framework-Agnostic High-Performance Machine Learning Abstractions. arXiv:1802.04730.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{vasilache2018tensor,
  title = {{Tensor Comprehensions: Framework-Agnostic High-Performance Machine Learning Abstractions}},
  author = {Nicolas Vasilache, Oleksandr Zinenko, Theodoros Theodoridis, Priya Goyal, Zachary DeVito, William S. Moses, Sven Verdoolaege, Andrew Adams and Albert Cohen},
  year = {2018},
  doi = {10.48550/arxiv.1802.04730},
  eprint = {1802.04730},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1802.04730}
}
```

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*Updated 2 November 2026*