# Tempo: Compiled Dynamic Deep Learning with Symbolic Dependence Graphs

arXiv: https://arxiv.org/abs/2501.05408 · HTML: https://mlsanity.com/paper/2501.05408/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 98 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [SentencePiece: A simple and language independent subword tokenizer and detokenizer for Neural Text Processing](https://mlsanity.com/paper/1808.06226/) (2018)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Taming Throughput-Latency Tradeoff in LLM Inference with Sarathi-Serve](https://mlsanity.com/paper/2403.02310/) (2024)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)

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

- [DVM: A Bytecode Virtual Machine Approach for Dynamic Tensor Computation](https://mlsanity.com/paper/2603.24239/) (2026)

## Abstract (arXiv)

Deep learning (DL) algorithms are often defined in terms of temporal relationships: a tensor at one timestep may depend on tensors from earlier or later timesteps. Such dynamic dependencies (and corresponding dynamic tensor shapes) are difficult to express and optimize: while eager DL systems support such dynamism, they cannot apply compiler-based optimizations; graph-based systems require static tensor shapes, which forces users to pad tensors or break-up programs into multiple static graphs. We describe Tempo, a new DL system that combines the dynamism of eager execution with the whole-program optimizations of graph-based compilation. Tempo achieves this through a declarative programming model with recurrent tensors, which include explicit temporal dimensions. Temporal dimensions can be indexed using symbolic expressions to express dynamic dependencies on past and future tensors. Based on this, Tempo constructs a symbolic dependence graph, which concisely encodes dynamic dependencies between operators, and applies whole-program optimizations, such as algebraic simplifications, vectorization, tiling, and fusion. By tiling dynamic dependencies into static-size blocks, Tempo can also reuse existing static code-generators. It then uses a polyhedral model to find a feasible execution schedule, which includes memory management operations. We show that Tempo achieves a 7× speedup over JAX for Llama-3.2-3B decoding; for reinforcement learning algorithms, Tempo achieves a 54× speedup, with 16× lower peak memory usage.