# A Theory of Machine Understanding via the Minimum Description Length Principle

arXiv: https://arxiv.org/abs/2504.00395 · HTML: https://mlsanity.com/paper/2504.00395/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 61 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Generalisation in humans and deep neural networks](https://mlsanity.com/paper/1808.08750/) (2018)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Discrete Variational Autoencoders](https://mlsanity.com/paper/1609.02200/) (2016)
- [Generative AI](https://mlsanity.com/paper/2309.07930/) (2023)
- [Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations](https://mlsanity.com/paper/1708.02691/) (2017)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [The Description Length of Deep Learning Models](https://mlsanity.com/paper/1802.07044/) (2018)
- [Permute, Quantize, and Fine-tune: Efficient Compression of Neural Networks](https://mlsanity.com/paper/2010.15703/) (2020)
- [Least Volume Analysis](https://mlsanity.com/paper/2404.17773/) (2024)

## Abstract (arXiv)

Deep neural networks trained through end-to-end learning have achieved remarkable success across various domains in the past decade. However, the end-to-end learning strategy, originally designed to minimize predictive loss in a black-box manner, faces two fundamental limitations: the struggle to form explainable representations in a self-supervised manner, and the inability to compress information rigorously following the Minimum Description Length (MDL) principle. These two limitations point to a deeper issue: an end-to-end learning model is not able to "understand" what it learns. In this paper, we establish a novel theory connecting these two limitations. We design the Spectrum VAE, a novel deep learning architecture whose minimum description length (MDL) can be rigorously evaluated. Then, we introduce the concept of latent dimension combinations, or what we term spiking patterns, and demonstrate that the observed spiking patterns should be as few as possible based on the training data in order for the Spectrum VAE to achieve the MDL. Finally, our theory demonstrates that when the MDL is achieved with respect to the given data distribution, the Spectrum VAE will naturally produce explainable latent representations of the data. In other words, explainable representations--or "understanding"--can emerge in a self-supervised manner simply by making the deep network obey the MDL principle. In our opinion, this also implies a deeper insight: To understand is to compress. At its core, our theory advocates for a shift in the training objective of deep networks: not only to minimize predictive loss, but also to minimize the description length regarding the given data. That is, a deep network should not only learn, but also understand what it learns. This work is entirely theoretical and aims to inspire future research toward self-supervised, explainable AI grounded in the MDL principle.