# Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks

arXiv: https://arxiv.org/abs/2102.12567 · HTML: https://mlsanity.com/paper/2102.12567/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 20 of 20)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Practical Gauss-Newton Optimisation for Deep Learning](https://mlsanity.com/paper/1706.03662/) (2017)
- [Convolutional Networks with Dense Connectivity](https://mlsanity.com/paper/2001.02394/) (2020)
- [Stochastic Mirror Descent on Overparameterized Nonlinear Models: Convergence, Implicit Regularization, and Generalization](https://mlsanity.com/paper/1906.03830/) (2019)
- [Practical sketching algorithms for low-rank matrix approximation](https://mlsanity.com/paper/1609.00048/) (2016)
- [Understanding Impacts of High-Order Loss Approximations and Features in Deep Learning Interpretation](https://mlsanity.com/paper/1902.00407/) (2019)
- [Single-Pass PCA of Large High-Dimensional Data](https://mlsanity.com/paper/1704.07669/) (2017)

## Built on by (most cited first, 30 of 32)

- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Unpacking Failure Modes of Generative Policies: Runtime Monitoring of Consistency and Progress](https://mlsanity.com/paper/2410.04640/) (2024)
- [Real-Time Anomaly Detection and Reactive Planning with Large Language Models](https://mlsanity.com/paper/2407.08735/) (2024)
- [On the Practicality of Deterministic Epistemic Uncertainty](https://mlsanity.com/paper/2107.00649/) (2021)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [A System-Level View on Out-of-Distribution Data in Robotics](https://mlsanity.com/paper/2212.14020/) (2022)
- [Activation-Informed Merging of Large Language Models](https://mlsanity.com/paper/2502.02421/) (2025)
- [STAP: Sequencing Task-Agnostic Policies](https://mlsanity.com/paper/2210.12250/) (2022)
- [Trust Your Robots! Predictive Uncertainty Estimation of Neural Networks with Sparse Gaussian Processes](https://mlsanity.com/paper/2109.09690/) (2021)
- [ORFit: One-Pass Learning via Bridging Orthogonal Gradient Descent and Recursive Least-Squares](https://mlsanity.com/paper/2207.13853/) (2022)
- [Task-Relevant Failure Detection for Trajectory Predictors in Autonomous Vehicles](https://mlsanity.com/paper/2207.12380/) (2022)
- [Epistemic Uncertainty Quantification For Pre-trained Neural Network](https://mlsanity.com/paper/2404.10124/) (2024)
- [A Holistic Assessment of the Reliability of Machine Learning Systems](https://mlsanity.com/paper/2307.10586/) (2023)
- [Uncertainty in Contrastive Learning: On the Predictability of Downstream Performance](https://mlsanity.com/paper/2207.09336/) (2022)
- [Monitoring of Perception Systems: Deterministic, Probabilistic, and Learning-based Fault Detection and Identification](https://mlsanity.com/paper/2205.10906/) (2022)
- [PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction](https://mlsanity.com/paper/2312.04658/) (2023)
- [Task-Driven Detection of Distribution Shifts with Statistical Guarantees for Robot Learning](https://mlsanity.com/paper/2106.13703/) (2021)
- [Tractable Uncertainty-Aware Meta-Learning](https://mlsanity.com/paper/2210.01881/) (2022)
- [Detecting and Mitigating System-Level Anomalies of Vision-Based Controllers](https://mlsanity.com/paper/2309.13475/) (2023)
- [Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models](https://mlsanity.com/paper/2309.06655/) (2023)
- [Bayes without Underfitting: Fully Correlated Deep Learning Posteriors via Alternating Projections](https://mlsanity.com/paper/2410.16901/) (2024)
- [Data Lifecycle Management in Evolving Input Distributions for Learning-based Aerospace Applications](https://mlsanity.com/paper/2209.06855/) (2022)
- [RuleFuser: An Evidential Bayes Approach for Rule Injection in Imitation Learned Planners and Predictors for Robustness under Distribution Shifts](https://mlsanity.com/paper/2405.11139/) (2024)
- [Beyond the Norms: Detecting Prediction Errors in Regression Models](https://mlsanity.com/paper/2406.06968/) (2024)
- [SketchOGD: Memory-Efficient Continual Learning](https://mlsanity.com/paper/2305.16424/) (2023)
- [Gradients of Functions of Large Matrices](https://mlsanity.com/paper/2405.17277/) (2024)
- [Open-Set Semantic Uncertainty Aware Metric-Semantic Graph Matching](https://mlsanity.com/paper/2409.11555/) (2024)
- [Contrast transfer functions help quantify neural network out-of-distribution generalization in HRTEM](https://mlsanity.com/paper/2512.09067/) (2025)
- [Foundation models on the bridge: Semantic hazard detection and safety maneuvers for maritime autonomy with vision-language models](https://mlsanity.com/paper/2512.24470/) (2025)
- [Perturb and Correct: Post-Hoc Ensembles using Affine Redundancy](https://mlsanity.com/paper/2605.01632/) (2026)

## Abstract (arXiv)

In order to safely deploy Deep Neural Networks (DNNs) within the perception pipelines of real-time decision making systems, there is a need for safeguards that can detect out-of-training-distribution (OoD) inputs both efficiently and accurately. Building on recent work leveraging the local curvature of DNNs to reason about epistemic uncertainty, we propose Sketching Curvature of OoD Detection (SCOD), an architecture-agnostic framework for equipping any trained DNN with a task-relevant epistemic uncertainty estimate. Offline, given a trained model and its training data, SCOD employs tools from matrix sketching to tractably compute a low-rank approximation of the Fisher information matrix, which characterizes which directions in the weight space are most influential on the predictions over the training data. Online, we estimate uncertainty by measuring how much perturbations orthogonal to these directions can alter predictions at a new test input. We apply SCOD to pre-trained networks of varying architectures on several tasks, ranging from regression to classification. We demonstrate that SCOD achieves comparable or better OoD detection performance with lower computational burden relative to existing baselines.