# Terra: Imperative-Symbolic Co-Execution of Imperative Deep Learning Programs

arXiv: https://arxiv.org/abs/2201.09210 · HTML: https://mlsanity.com/paper/2201.09210/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 23 Jan 2022.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [MXNet: A Flexible and Efficient Machine Learning Library for Heterogeneous Distributed Systems](https://mlsanity.com/paper/1512.01274/) (2015)
- [Checkmate: Breaking the Memory Wall with Optimal Tensor Rematerialization](https://mlsanity.com/paper/1910.02653/) (2019)
- [Device Placement Optimization with Reinforcement Learning](https://mlsanity.com/paper/1706.04972/) (2017)
- [Theano: A Python framework for fast computation of mathematical expressions](https://mlsanity.com/paper/1605.02688/) (2016)
- [TVM: An Automated End-to-End Optimizing Compiler for Deep Learning](https://mlsanity.com/paper/1802.04799/) (2018)
- [Optimizing CNN Model Inference on CPUs](https://mlsanity.com/paper/1809.02697/) (2018)
- [Transferable Graph Optimizers for ML Compilers](https://mlsanity.com/paper/2010.12438/) (2020)
- [Ordering Chaos: Memory-Aware Scheduling of Irregularly Wired Neural Networks for Edge Devices](https://mlsanity.com/paper/2003.02369/) (2020)
- [TensorFlow Eager: A Multi-Stage, Python-Embedded DSL for Machine Learning](https://mlsanity.com/paper/1903.01855/) (2019)
- [Chainer: A Deep Learning Framework for Accelerating the Research Cycle](https://mlsanity.com/paper/1908.00213/) (2019)
- [DyNet: The Dynamic Neural Network Toolkit](https://mlsanity.com/paper/1701.03980/) (2017)
- [Nimble: Lightweight and Parallel GPU Task Scheduling for Deep Learning](https://mlsanity.com/paper/2012.02732/) (2020)
- [LazyTensor: combining eager execution with domain-specific compilers](https://mlsanity.com/paper/2102.13267/) (2021)
- [AutoGraph: Imperative-style Coding with Graph-based Performance](https://mlsanity.com/paper/1810.08061/) (2018)
- [FusionStitching: Boosting Memory Intensive Computations for Deep Learning Workloads](https://mlsanity.com/paper/2009.10924/) (2020)
- [Stochastic Downsampling for Cost-Adjustable Inference and Improved Regularization in Convolutional Networks](https://mlsanity.com/paper/1801.09335/) (2018)
- [JANUS: Fast and Flexible Deep Learning via Symbolic Graph Execution of Imperative Programs](https://mlsanity.com/paper/1812.01329/) (2018)

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

- [Speculative Automated Refactoring of Imperative Deep Learning Programs to Graph Execution](https://mlsanity.com/paper/2504.05424/) (2025)

## Abstract (arXiv)

Imperative programming allows users to implement their deep neural networks (DNNs) easily and has become an essential part of recent deep learning (DL) frameworks. Recently, several systems have been proposed to combine the usability of imperative programming with the optimized performance of symbolic graph execution. Such systems convert imperative Python DL programs to optimized symbolic graphs and execute them. However, they cannot fully support the usability of imperative programming. For example, if an imperative DL program contains a Python feature with no corresponding symbolic representation (e.g., third-party library calls or unsupported dynamic control flows) they fail to execute the program. To overcome this limitation, we propose Terra, an imperative-symbolic co-execution system that can handle any imperative DL programs while achieving the optimized performance of symbolic graph execution. To achieve this, Terra builds a symbolic graph by decoupling DL operations from Python features. Then, Terra conducts the imperative execution to support all Python features, while delegating the decoupled operations to the symbolic execution. We evaluated the performance improvement and coverage of Terra with ten imperative DL programs for several DNN architectures. The results show that Terra can speed up the execution of all ten imperative DL programs, whereas AutoGraph, one of the state-of-the-art systems, fails to execute five of them.