# Analyzing Populations of Neural Networks via Dynamical Model Embedding

## TL;DR

This paper introduces DYNAMO, a novel algorithm that embeds neural networks into a low-dimensional manifold, enabling analysis, clustering, averaging, and semi-supervised learning of models based on their high-level computational similarities.

## Contribution

DYNAMO constructs a model embedding space for neural networks, facilitating interpretation and manipulation of models beyond traditional parameter-based methods.

## Key findings

- Model embedding spaces cluster networks by computational process
- Model averaging produces networks with similar performance
- Semi-supervised learning benefits from the embedding space

## Abstract

A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an algorithm that constructs low-dimensional manifolds where each point corresponds to a neural network model, and two points are nearby if the corresponding neural networks enact similar high-level computational processes. DYNAMO takes as input a collection of pre-trained neural networks and outputs a meta-model that emulates the dynamics of the hidden states as well as the outputs of any model in the collection. The specific model to be emulated is determined by a model embedding vector that the meta-model takes as input; these model embedding vectors constitute a manifold corresponding to the given population of models. We apply DYNAMO to both RNNs and CNNs, and find that the resulting model embedding spaces enable novel applications: clustering of neural networks on the basis of their high-level computational processes in a manner that is less sensitive to reparameterization; model averaging of several neural networks trained on the same task to arrive at a new, operable neural network with similar task performance; and semi-supervised learning via optimization on the model embedding space. Using a fixed-point analysis of meta-models trained on populations of RNNs, we gain new insights into how similarities of the topology of RNN dynamics correspond to similarities of their high-level computational processes.