> For the complete documentation index, see [llms.txt](https://sliu583.gitbook.io/blog/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://sliu583.gitbook.io/blog/conference/index/osdi-21/optimizations-and-scheduling-for-ml/pet-optimizing-tensor-programs-with-partially-equivalent-transformations-and-automated-corrections.md).

# PET: Optimizing Tensor Programs with Partially Equivalent Transformations and Automated Corrections

https\://www\.usenix.org/conference/osdi21/presentation/wang

* Current system considers only full equivalent transformations 
  * Pro: preserve functionality 
  * Con: miss optimization opportunities 
* Partial Equivalent Transformation 
  * Pro: better performance 
    * Faster ML operators 
    * More efficient tensor layouts 
    * HW-specific optimizations 
  * Con: potential accuracy loss 
* Key: benefits while preserving equivalence? 
  * Correction preserves equivalence 

![](https://2097630930-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MVORxAomcgtzVVUqmws%2F-Me_oGu5RA5axHm-VwUv%2F-Me_qz09wavPCMxBrYsP%2Fimage.png?alt=media\&token=e359a3d9-8c3d-40e4-9e97-f77833d78b51)

1. Super optimization
2. Multi-linearity of DNN computations 
   1. DNN computation = MLTP + non-linear activations 
   2. Reduce complexity from O(m\*n) to O(1) 

Corrector:

1. Re-compute the incorrect outputs using the original program 
2. opportunistically fuse correction kernels with other operators 
3. Eval: less than 1% overhead 

Program optimizer:

1. Search-based program optimizer 
   1. Beam search