# A Similarity-preserving Neural Network Trained on Transformed Images Recapitulates Salient Features of the Fly Motion Detection Circuit

arXiv: https://arxiv.org/abs/2102.05503 · HTML: https://mlsanity.com/paper/2102.05503/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 10 Feb 2021.

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

- [A Hebbian/Anti-Hebbian Neural Network for Linear Subspace Learning: A Derivation from Multidimensional Scaling of Streaming Data](https://mlsanity.com/paper/1503.00669/) (2015)
- [Why do similarity matching objectives lead to Hebbian/anti-Hebbian networks?](https://mlsanity.com/paper/1703.07914/) (2017)
- [A Normative Theory of Adaptive Dimensionality Reduction in Neural Networks](https://mlsanity.com/paper/1511.09426/) (2015)
- [A Hebbian/Anti-Hebbian Network Derived from Online Non-Negative Matrix Factorization Can Cluster and Discover Sparse Features](https://mlsanity.com/paper/1503.00680/) (2015)
- [Optimal local estimates of visual motion in a natural environment](https://mlsanity.com/paper/1812.11878/) (2018)

## Built on by (most cited first, 3 of 3)

- [A Normative and Biologically Plausible Algorithm for Independent Component Analysis](https://mlsanity.com/paper/2111.08858/) (2021)
- [Normative framework for deriving neural networks with multi-compartmental neurons and non-Hebbian plasticity](https://mlsanity.com/paper/2302.10051/) (2023)
- [Duality Principle and Biologically Plausible Learning: Connecting the Representer Theorem and Hebbian Learning](https://mlsanity.com/paper/2309.16687/) (2023)

## Abstract (arXiv)

Learning to detect content-independent transformations from data is one of the central problems in biological and artificial intelligence. An example of such problem is unsupervised learning of a visual motion detector from pairs of consecutive video frames. Rao and Ruderman formulated this problem in terms of learning infinitesimal transformation operators (Lie group generators) via minimizing image reconstruction error. Unfortunately, it is difficult to map their model onto a biologically plausible neural network (NN) with local learning rules. Here we propose a biologically plausible model of motion detection. We also adopt the transformation-operator approach but, instead of reconstruction-error minimization, start with a similarity-preserving objective function. An online algorithm that optimizes such an objective function naturally maps onto an NN with biologically plausible learning rules. The trained NN recapitulates major features of the well-studied motion detector in the fly. In particular, it is consistent with the experimental observation that local motion detectors combine information from at least three adjacent pixels, something that contradicts the celebrated Hassenstein-Reichardt model.