# Bayesian reconstruction of memories stored in neural networks from their connectivity

arXiv: https://arxiv.org/abs/2105.07416 · HTML: https://mlsanity.com/paper/2105.07416/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 115 references that are in the map.
- First posted on arXiv 16 May 2021.

## Builds on (most cited first, 12 of 12)

- [Statistical physics of inference: Thresholds and algorithms](https://mlsanity.com/paper/1511.02476/) (2015)
- [Spectral redemption: clustering sparse networks](https://mlsanity.com/paper/1306.5550/) (2013)
- [Linking connectivity, dynamics and computations in low-rank recurrent neural networks](https://mlsanity.com/paper/1711.09672/) (2017)
- [MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel](https://mlsanity.com/paper/1507.03857/) (2015)
- [Notes on computational-to-statistical gaps: predictions using statistical physics](https://mlsanity.com/paper/1803.11132/) (2018)
- [The interplay between randomness and structure during learning in RNNs](https://mlsanity.com/paper/2006.11036/) (2020)
- [Phase Transitions in Sparse PCA](https://mlsanity.com/paper/1503.00338/) (2015)
- [Glassy nature of the hard phase in inference problems](https://mlsanity.com/paper/1805.05857/) (2018)
- [Approximate Survey Propagation for Statistical Inference](https://mlsanity.com/paper/1807.01296/) (2018)
- [Adapting to Unknown Noise Distribution in Matrix Denoising](https://mlsanity.com/paper/1810.02954/) (2018)
- [Generalized Approximate Survey Propagation for High-Dimensional Estimation](https://mlsanity.com/paper/1905.05313/) (2019)
- [Streaming Bayesian inference: theoretical limits and mini-batch approximate message-passing](https://mlsanity.com/paper/1706.00705/) (2017)

## Built on by (most cited first, 2 of 2)

- [Matrix factorization with neural networks](https://mlsanity.com/paper/2212.02105/) (2022)
- [Evidence of Replica Symmetry Breaking under the Nishimori conditions in epidemic inference on graphs](https://mlsanity.com/paper/2502.13249/) (2025)

## Abstract (arXiv)

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in a recurrent network of neurons, given its synaptic connectivity matrix. Here, we address this question by determining when solving such an inference problem is theoretically possible in specific attractor network models and by providing a practical algorithm to do so. The algorithm builds on ideas from statistical physics to perform approximate Bayesian inference and is amenable to exact analysis. We study its performance on three different models, compare the algorithm to standard algorithms such as PCA, and explore the limitations of reconstructing stored patterns from synaptic connectivity.