# Analysis of structure and dynamics in three-neuron motifs

arXiv: https://arxiv.org/abs/1811.05225 · HTML: https://mlsanity.com/paper/1811.05225/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2018.

## Built on by (most cited first, 11 of 11)

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- [Word class representations spontaneously emerge in a deep neural network trained on next word prediction](https://mlsanity.com/paper/2302.07588/) (2023)
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- [Classification at the Accuracy Limit -- Facing the Problem of Data Ambiguity](https://mlsanity.com/paper/2206.01922/) (2022)
- [Conceptual Cognitive Maps Formation with Neural Successor Networks and Word Embeddings](https://mlsanity.com/paper/2307.01577/) (2023)
- [Multi-Modal Cognitive Maps based on Neural Networks trained on Successor Representations](https://mlsanity.com/paper/2401.01364/) (2023)
- [Analysis of Argument Structure Constructions in a Deep Recurrent Language Model](https://mlsanity.com/paper/2408.03062/) (2024)
- [Analysis of Argument Structure Constructions in the Large Language Model BERT](https://mlsanity.com/paper/2408.04270/) (2024)
- [Generating Oscillation Activity with Echo State Network to Mimic the Behavior of a Simple Central Pattern Generator](https://mlsanity.com/paper/2306.10927/) (2023)
- [Excitatory/Inhibitory Balance Emerges as a Key Factor for RBN Performance, Overriding Attractor Dynamics](https://mlsanity.com/paper/2308.10831/) (2023)
- [Author-Specific Linguistic Patterns Unveiled: A Deep Learning Study on Word Class Distributions](https://mlsanity.com/paper/2501.10072/) (2025)

## Abstract (arXiv)

In neural networks with identical neurons, the matrix of connection weights completely describes the network structure and thereby determines how it is processing information. However, due to the non-linearity of these systems, it is not clear if similar microscopic connection structures also imply similar functional properties, or if a network is impacted more by macroscopic structural quantities, such as the ratio of excitatory and inhibitory connections (balance), or the ratio of non-zero connections (density). To clarify these questions, we focus on motifs of three binary neurons with discrete ternary connection strengths, an important class of network building blocks that can be analyzed exhaustively. We develop new, permutation-invariant metrics to quantify the structural and functional distance between two given network motifs. We then use multidimensional scaling to identify and visualize clusters of motifs with similar structural and functional properties. Our comprehensive analysis reveals that the function of a neural network is only weakly correlated with its microscopic structure, but depends strongly on the balance of the connections.