# Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning

arXiv: https://arxiv.org/abs/2610.06023 · HTML: https://mlsanity.com/paper/2610.06023/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 54 references that are in the map.
- First posted on arXiv 5 Oct 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Sparse PCA via Covariance Thresholding](https://mlsanity.com/paper/1311.5179/) (2013)
- [coVariance Neural Networks](https://mlsanity.com/paper/2205.15856/) (2022)
- [Explainable Brain Age Prediction using coVariance Neural Networks](https://mlsanity.com/paper/2305.18370/) (2023)
- [Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification](https://mlsanity.com/paper/1803.02553/) (2018)
- [Deep Iterative and Adaptive Learning for Graph Neural Networks](https://mlsanity.com/paper/1912.07832/) (2019)
- [Algorithms for Learning Graphs in Financial Markets](https://mlsanity.com/paper/2012.15410/) (2020)
- [Robust Graph Filter Identification and Graph Denoising from Signal Observations](https://mlsanity.com/paper/2210.08488/) (2022)
- [Online Discriminative Graph Learning from Multi-Class Smooth Signals](https://mlsanity.com/paper/2101.00184/) (2021)
- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [Deep Transfer Learning with Graph Neural Network for Sensor-Based Human Activity Recognition](https://mlsanity.com/paper/2203.07910/) (2022)
- [Spatiotemporal Covariance Neural Networks](https://mlsanity.com/paper/2409.10068/) (2024)
- [Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes](https://mlsanity.com/paper/2007.03266/) (2020)
- [Sparse Covariance Neural Networks](https://mlsanity.com/paper/2410.01669/) (2024)
- [Transferability of coVariance Neural Networks and Application to Interpretable Brain Age Prediction using Anatomical Features](https://mlsanity.com/paper/2305.01807/) (2023)
- [Robust Graph Neural Network based on Graph Denoising](https://mlsanity.com/paper/2312.06557/) (2023)
- [Covariance Density Neural Networks](https://mlsanity.com/paper/2505.11139/) (2025)
- [Disentangling Neurodegeneration with Brain Age Gap Prediction Models: A Graph Signal Processing Perspective](https://mlsanity.com/paper/2510.12763/) (2025)
- [ASGNN: Graph Neural Networks with Adaptive Structure](https://mlsanity.com/paper/2210.01002/) (2022)
- [Covariance Scattering Transforms](https://mlsanity.com/paper/2511.08878/) (2025)
- [Task-driven Heterophilic Graph Structure Learning](https://mlsanity.com/paper/2512.23406/) (2025)
- [Learning Graph Topology with Functional Priors via Bilevel Optimization](https://mlsanity.com/paper/2606.13885/) (2026)
- [Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs](https://mlsanity.com/paper/2609.10490/) (2026)
- [Precision Neural Networks: Joint Graph And Relational Learning](https://mlsanity.com/paper/2509.14821/) (2025)

## Abstract (arXiv)

Exploiting meaningful latent structures from data to solve downstream tasks is a fundamental challenge in signal processing and machine learning. While Principal Component Analysis (PCA) and coVariance Neural Networks (VNNs) successfully leverage the covariance matrix to process data, they inherently capture both direct and indirect correlations. The precision matrix (inverse covariance) overcomes this by explicitly encoding conditional independencies, making it largely studied in graphical lasso and graph topology identification. However, finite-sample precision estimates are notoriously unstable, and regularized estimators remain task-agnostic. In this work, our principal contribution is tackling the challenging problem of task-aware graph inference. We propose Precision Neural Networks-Joint (PNN-Joint), a framework that jointly estimates a sparse, statistically grounded precision matrix alongside graph neural network weights via an alternating optimization scheme. As a foundational framework to support this, we introduce Precision Neural Networks (PNNs), a broader class of graph convolutional networks operating on precision estimators, and establish their spectral connections to PCA and VNNs alongside their stability to finite-sample errors. Extensive empirical evaluations on synthetic data, as well as real-world neuroimaging and motion sensor datasets, demonstrate that PNN-Joint yields highly interpretable task-aware graphs, exhibits remarkable robustness in low-data regimes, and consistently achieves the best or second-best performance among competitors on real-world tasks.