A Survey of Weight Space Learning: Understanding, Representation, and Generation

TL;DR

This survey explores the emerging field of Weight Space Learning, which treats neural network weights as a meaningful domain for analysis, representation, and generation, impacting various applications like model retrieval and neural architecture search.

Contribution

It provides the first unified taxonomy of WSL, categorizing methods into understanding, representation, and generation, and discusses their practical applications.

Findings

Weight space exhibits rich structure, symmetries, and organized distributions.

Methods enable model retrieval, continual learning, and neural architecture search.

Weight space can be effectively embedded, compared, and synthesized.

Abstract

Neural network weights are typically viewed as the end product of training, while most deep learning research focuses on data, features, and architectures. However, recent advances show that the set of all possible weight values (weight space) itself contains rich structure: pretrained models form organized distributions, exhibit symmetries, and can be embedded, compared, or even generated. Understanding such structures has tremendous impact on how neural networks are analyzed and compared, and on how knowledge is transferred across models, beyond individual training instances. This emerging research direction, which we refer to as Weight Space Learning (WSL), treats neural weights as a meaningful domain for analysis and modeling. This survey provides the first unified taxonomy of WSL. We categorize existing methods into three core dimensions: Weight Space Understanding (WSU), which studies the geometry and symmetries of weights; Weight Space Representation (WSR), which learns embeddings over model weights; and Weight Space Generation (WSG), which synthesizes new weights through hypernetworks or generative models. We further show how these developments enable practical applications, including model retrieval, continual and federated learning, neural architecture search, and data-free reconstruction. By consolidating fragmented progress under a coherent framework, this survey highlights weight space as a learnable, structured domain with growing impact across model analysis, transferring, and weight generation. We release an accompanying resource at https://github.com/Zehong-Wang/Awesome-Weight-Space-Learning.