# On the Learnability of Physical Concepts: Can a Neural Network Understand What's Real?

arXiv: https://arxiv.org/abs/2207.12186 · HTML: https://mlsanity.com/paper/2207.12186/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 39 references that are in the map.
- First posted on arXiv 25 Jul 2022.

## Builds on (most cited first, 3 of 3)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [The Information Complexity of Learning Tasks, their Structure and their Distance](https://mlsanity.com/paper/1904.03292/) (2019)

## Built on by (most cited first, 5 of 5)

- [B'MOJO: Hybrid State Space Realizations of Foundation Models with Eidetic and Fading Memory](https://mlsanity.com/paper/2407.06324/) (2024)
- [Taming AI Bots: Controllability of Neural States in Large Language Models](https://mlsanity.com/paper/2305.18449/) (2023)
- [AI Agents as Universal Task Solvers](https://mlsanity.com/paper/2510.12066/) (2025)
- [Meanings and Feelings of Large Language Models: Observability of Latent States in Generative AI](https://mlsanity.com/paper/2405.14061/) (2024)
- [Towards Visual Foundational Models of Physical Scenes](https://mlsanity.com/paper/2306.03727/) (2023)

## Abstract (arXiv)

We revisit the classic signal-to-symbol barrier in light of the remarkable ability of deep neural networks to generate realistic synthetic data. DeepFakes and spoofing highlight the feebleness of the link between physical reality and its abstract representation, whether learned by a digital computer or a biological agent. Starting from a widely applicable definition of abstract concept, we show that standard feed-forward architectures cannot capture but trivial concepts, regardless of the number of weights and the amount of training data, despite being extremely effective classifiers. On the other hand, architectures that incorporate recursion can represent a significantly larger class of concepts, but may still be unable to learn them from a finite dataset. We qualitatively describe the class of concepts that can be "understood" by modern architectures trained with variants of stochastic gradient descent, using a (free energy) Lagrangian to measure information complexity. Even if a concept has been understood, however, a network has no means of communicating its understanding to an external agent, except through continuous interaction and validation. We then characterize physical objects as abstract concepts and use the previous analysis to show that physical objects can be encoded by finite architectures. However, to understand physical concepts, sensors must provide persistently exciting observations, for which the ability to control the data acquisition process is essential (active perception). The importance of control depends on the modality, benefiting visual more than acoustic or chemical perception. Finally, we conclude that binding physical entities to digital identities is possible in finite time with finite resources, solving in principle the signal-to-symbol barrier problem, but we highlight the need for continuous validation.