# Slow Feature Analysis as Variational Inference Objective

arXiv: https://arxiv.org/abs/2506.00580 · HTML: https://mlsanity.com/paper/2506.00580/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 5 of 5)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [Gradient-based Training of Slow Feature Analysis by Differentiable Approximate Whitening](https://mlsanity.com/paper/1808.08833/) (2018)

## Abstract (arXiv)

This work presents a novel probabilistic interpretation of Slow Feature Analysis (SFA) through the lens of variational inference. Unlike prior formulations that recover linear SFA from Gaussian state-space models with linear emissions, this approach relaxes the key constraint of linearity. While it does not lead to full equivalence to non-linear SFA, it recasts the classical slowness objective in a variational framework. Specifically, it allows the slowness objective to be interpreted as a regularizer to a reconstruction loss. Furthermore, we provide arguments, why -- from the perspective of slowness optimization -- the reconstruction loss takes on the role of the constraints that ensure informativeness in SFA. We conclude with a discussion of potential new research directions.