# Functional Distribution Networks (FDN)

arXiv: https://arxiv.org/abs/2510.17794 · HTML: https://mlsanity.com/paper/2510.17794/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Builds on (most cited first, 18 of 18)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [SMASH: One-Shot Model Architecture Search through HyperNetworks](https://mlsanity.com/paper/1708.05344/) (2017)
- [Bayesian Hypernetworks](https://mlsanity.com/paper/1710.04759/) (2017)

## Abstract (arXiv)

Modern probabilistic regressors often remain overconfident under distribution shift. Functional Distribution Networks (FDN) place input-conditioned distributions over network weights, producing predictive mixtures whose dispersion adapts to the input; we train them with a Monte Carlo beta-ELBO objective. We pair FDN with an evaluation protocol that separates interpolation from extrapolation and emphasizes simple OOD sanity checks. On controlled 1D tasks and small/medium UCI-style regression benchmarks, FDN remains competitive in accuracy with strong Bayesian, ensemble, dropout, and hypernetwork baselines, while providing strongly input-dependent, shift-aware uncertainty and competitive calibration under matched parameter and update budgets.