# A simple probabilistic neural network for machine understanding

arXiv: https://arxiv.org/abs/2210.13179 · HTML: https://mlsanity.com/paper/2210.13179/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [Restricted Boltzmann Machine, recent advances and mean-field theory](https://mlsanity.com/paper/2011.11307/) (2020)
- [Data-driven emergence of convolutional structure in neural networks](https://mlsanity.com/paper/2202.00565/) (2022)
- [Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines](https://mlsanity.com/paper/2105.13889/) (2021)
- [Thermodynamics of Restricted Boltzmann Machines and related learning dynamics](https://mlsanity.com/paper/1803.01960/) (2018)
- [Disentangling representations in Restricted Boltzmann Machines without adversaries](https://mlsanity.com/paper/2206.11600/) (2022)
- [Quantifying Relevance in Learning and Inference](https://mlsanity.com/paper/2202.00339/) (2022)
- [An Infinite Restricted Boltzmann Machine](https://mlsanity.com/paper/1502.02476/) (2015)
- [Minimum Description Length codes are critical](https://mlsanity.com/paper/1809.00652/) (2018)
- [The Stochastic complexity of spin models: Are pairwise models really simple?](https://mlsanity.com/paper/1702.07549/) (2017)

## Built on by (most cited first, 1 of 1)

- [Absolute abstraction: a renormalisation group approach](https://mlsanity.com/paper/2407.01656/) (2024)

## Abstract (arXiv)

We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an em a priori organisation of the feature space. We derive the internal representation by requiring that it satisfies the principles of maximal relevance and of maximal ignorance about how different features are combined. We show that, when hidden units are binary variables, these two principles identify a unique model -- the Hierarchical Feature Model (HFM) -- which is fully solvable and provides a natural interpretation in terms of features. We argue that learning machines with this architecture enjoy a number of interesting properties, like the continuity of the representation with respect to changes in parameters and data, the possibility to control the level of compression and the ability to support functions that go beyond generalisation. We explore the behaviour of the model with extensive numerical experiments and argue that models where the internal representation is fixed reproduce a learning modality which is qualitatively different from that of traditional models such as Restricted Boltzmann Machines.