# TRADI: Tracking deep neural network weight distributions for uncertainty estimation

arXiv: https://arxiv.org/abs/1912.11316 · HTML: https://mlsanity.com/paper/1912.11316/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2019.

## Built on by (most cited first, 30 of 39)

- [Packed-Ensembles for Efficient Uncertainty Estimation](https://mlsanity.com/paper/2210.09184/) (2022)
- [DenseHybrid: Hybrid Anomaly Detection for Dense Open-set Recognition](https://mlsanity.com/paper/2207.02606/) (2022)
- [PaSCo: Urban 3D Panoptic Scene Completion with Uncertainty Awareness](https://mlsanity.com/paper/2312.02158/) (2023)
- [Triggering Failures: Out-Of-Distribution detection by learning from local adversarial attacks in Semantic Segmentation](https://mlsanity.com/paper/2108.01634/) (2021)
- [Maskomaly:Zero-Shot Mask Anomaly Segmentation](https://mlsanity.com/paper/2305.16972/) (2023)
- [MUAD: Multiple Uncertainties for Autonomous Driving, a benchmark for multiple uncertainty types and tasks](https://mlsanity.com/paper/2203.01437/) (2022)
- [Robust Semantic Segmentation with Superpixel-Mix](https://mlsanity.com/paper/2108.00968/) (2021)
- [Mask2Anomaly: Mask Transformer for Universal Open-set Segmentation](https://mlsanity.com/paper/2309.04573/) (2023)
- [Dense outlier detection and open-set recognition based on training with noisy negative images](https://mlsanity.com/paper/2101.09193/) (2021)
- [Latent Discriminant deterministic Uncertainty](https://mlsanity.com/paper/2207.10130/) (2022)
- [Make Me a BNN: A Simple Strategy for Estimating Bayesian Uncertainty from Pre-trained Models](https://mlsanity.com/paper/2312.15297/) (2023)
- [A Symmetry-Aware Exploration of Bayesian Neural Network Posteriors](https://mlsanity.com/paper/2310.08287/) (2023)
- [Towards Understanding and Quantifying Uncertainty for Text-to-Image Generation](https://mlsanity.com/paper/2412.03178/) (2024)
- [Dense Out-of-Distribution Detection by Robust Learning on Synthetic Negative Data](https://mlsanity.com/paper/2112.12833/) (2021)
- [C^*-algebra Net: A New Approach Generalizing Neural Network Parameters to C^*-algebra](https://mlsanity.com/paper/2206.09513/) (2022)
- [Hybrid Open-set Segmentation with Synthetic Negative Data](https://mlsanity.com/paper/2301.08555/) (2023)
- [ProbVLM: Probabilistic Adapter for Frozen Vision-Language Models](https://mlsanity.com/paper/2307.00398/) (2023)
- [A Generalized Zero-Shot Quantization of Deep Convolutional Neural Networks via Learned Weights Statistics](https://mlsanity.com/paper/2112.02834/) (2021)
- [The Robust Semantic Segmentation UNCV2023 Challenge Results](https://mlsanity.com/paper/2309.15478/) (2023)
- [Quantum-Cognitive Neural Networks: Assessing Confidence and Uncertainty with Human Decision-Making Simulations](https://mlsanity.com/paper/2412.08010/) (2024)
- [Torch-Uncertainty: A Deep Learning Framework for Uncertainty Quantification](https://mlsanity.com/paper/2511.10282/) (2025)
- [Probing Contextual Diversity for Dense Out-of-Distribution Detection](https://mlsanity.com/paper/2208.14195/) (2022)
- [Likelihood Annealing: Fast Calibrated Uncertainty for Regression](https://mlsanity.com/paper/2302.11012/) (2023)
- [Compiled Models, Built-In Exploits: Uncovering Pervasive Bit-Flip Attack Surfaces in DNN Executables](https://mlsanity.com/paper/2309.06223/) (2023)
- [Improving Semantic Uncertainty Quantification in LVLMs with Semantic Gaussian Processes](https://mlsanity.com/paper/2512.14177/) (2025)
- [Block Format Error Bounds and Optimal Block Size Selection](https://mlsanity.com/paper/2210.05470/) (2022)
- [Statistical Modeling of Soft Error Influence on Neural Networks](https://mlsanity.com/paper/2210.05876/) (2022)
- [Pixel is All You Need: Adversarial Trajectory-Ensemble Active Learning for Salient Object Detection](https://mlsanity.com/paper/2212.06493/) (2022)
- [Learning to Generate Training Datasets for Robust Semantic Segmentation](https://mlsanity.com/paper/2308.02535/) (2023)
- [Exploiting Unstructured Sparsity in Fully Homomorphic Encrypted DNNs](https://mlsanity.com/paper/2503.09184/) (2025)

## Abstract (arXiv)

During training, the weights of a Deep Neural Network (DNN) are optimized from a random initialization towards a nearly optimum value minimizing a loss function. Only this final state of the weights is typically kept for testing, while the wealth of information on the geometry of the weight space, accumulated over the descent towards the minimum is discarded. In this work we propose to make use of this knowledge and leverage it for computing the distributions of the weights of the DNN. This can be further used for estimating the epistemic uncertainty of the DNN by sampling an ensemble of networks from these distributions. To this end we introduce a method for tracking the trajectory of the weights during optimization, that does not require any changes in the architecture nor on the training procedure. We evaluate our method on standard classification and regression benchmarks, and on out-of-distribution detection for classification and semantic segmentation. We achieve competitive results, while preserving computational efficiency in comparison to other popular approaches.