# TOD: GPU-accelerated Outlier Detection via Tensor Operations

arXiv: https://arxiv.org/abs/2110.14007 · HTML: https://mlsanity.com/paper/2110.14007/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 107 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Beyond Data and Model Parallelism for Deep Neural Networks](https://mlsanity.com/paper/1807.05358/) (2018)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Fast Approximate Nearest Neighbor Search With The Navigating Spreading-out Graph](https://mlsanity.com/paper/1707.00143/) (2017)
- [Alleviating the Inconsistency Problem of Applying Graph Neural Network to Fraud Detection](https://mlsanity.com/paper/2005.00625/) (2020)
- [A Comprehensive Survey and Experimental Comparison of Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2101.12631/) (2021)
- [VS-Quant: Per-vector Scaled Quantization for Accurate Low-Precision Neural Network Inference](https://mlsanity.com/paper/2102.04503/) (2021)
- [LSCP: Locally Selective Combination in Parallel Outlier Ensembles](https://mlsanity.com/paper/1812.01528/) (2018)
- [Large Graph Convolutional Network Training with GPU-Oriented Data Communication Architecture](https://mlsanity.com/paper/2103.03330/) (2021)
- [A Tensor Compiler for Unified Machine Learning Prediction Serving](https://mlsanity.com/paper/2010.04804/) (2020)
- [A Survey on Social Media Anomaly Detection](https://mlsanity.com/paper/1601.01102/) (2016)
- [Deep Learning with Dynamic Computation Graphs](https://mlsanity.com/paper/1702.02181/) (2017)
- [AutoAudit: Mining Accounting and Time-Evolving Graphs](https://mlsanity.com/paper/2011.00447/) (2020)
- [On Optimizing Operator Fusion Plans for Large-Scale Machine Learning in SystemML](https://mlsanity.com/paper/1801.00829/) (2018)
- [EMOGI: Efficient Memory-access for Out-of-memory Graph-traversal In GPUs](https://mlsanity.com/paper/2006.06890/) (2020)
- [On-the-fly Operation Batching in Dynamic Computation Graphs](https://mlsanity.com/paper/1705.07860/) (2017)
- [Bolt: Accelerated Data Mining with Fast Vector Compression](https://mlsanity.com/paper/1706.10283/) (2017)
- [Time Series Data Cleaning: From Anomaly Detection to Anomaly Repairing (Technical Report)](https://mlsanity.com/paper/2003.12396/) (2020)
- [Anomaly Detection at Scale: The Case for Deep Distributional Time Series Models](https://mlsanity.com/paper/2007.15541/) (2020)
- [Elle: Inferring Isolation Anomalies from Experimental Observations](https://mlsanity.com/paper/2003.10554/) (2020)
- [Benchmarking the Nvidia GPU Lineage: From Early K80 to Modern A100 with Asynchronous Memory Transfers](https://mlsanity.com/paper/2106.04979/) (2021)
- [Fairness-aware Outlier Ensemble](https://mlsanity.com/paper/2103.09419/) (2021)
- [PPQ-Trajectory: Spatio-temporal Quantization for Querying in Large Trajectory Repositories](https://mlsanity.com/paper/2010.13721/) (2020)

## Built on by (most cited first, 6 of 6)

- [PyGOD: A Python Library for Graph Outlier Detection](https://mlsanity.com/paper/2204.12095/) (2022)
- [Deep Learning Advancements in Anomaly Detection: A Comprehensive Survey](https://mlsanity.com/paper/2503.13195/) (2025)
- [MetaOOD: Automatic Selection of OOD Detection Models](https://mlsanity.com/paper/2410.03074/) (2024)
- [ADMoE: Anomaly Detection with Mixture-of-Experts from Noisy Labels](https://mlsanity.com/paper/2208.11290/) (2022)
- [ClimateLLM: Efficient Weather Forecasting via Frequency-Aware Large Language Models](https://mlsanity.com/paper/2502.11059/) (2025)
- [MEMO: Fine-grained Tensor Management For Ultra-long Context LLM Training](https://mlsanity.com/paper/2407.12117/) (2024)

## Abstract (arXiv)

Outlier detection (OD) is a key learning task for finding rare and deviant data samples, with many time-critical applications such as fraud detection and intrusion detection. In this work, we propose TOD, the first tensor-based system for efficient and scalable outlier detection on distributed multi-GPU machines. A key idea behind TOD is decomposing complex OD applications into a small collection of basic tensor algebra operators. This decomposition enables TOD to accelerate OD computations by leveraging recent advances in deep learning infrastructure in both hardware and software. Moreover, to deploy memory-intensive OD applications on modern GPUs with limited on-device memory, we introduce two key techniques. First, provable quantization speeds up OD computations and reduces its memory footprint by automatically performing specific floating-point operations in lower precision while provably guaranteeing no accuracy loss. Second, to exploit the aggregated compute resources and memory capacity of multiple GPUs, we introduce automatic batching, which decomposes OD computations into small batches for both sequential execution on a single GPU and parallel execution on multiple GPUs. TOD supports a diverse set of OD algorithms. Extensive evaluation on 11 real and 3 synthetic OD datasets shows that TOD is on average 10.9x faster than the leading CPU-based OD system PyOD (with a maximum speedup of 38.9x), and can handle much larger datasets than existing GPU-based OD systems. In addition, TOD allows easy integration of new OD operators, enabling fast prototyping of emerging and yet-to-discovered OD algorithms.