# Classifying the classifier: dissecting the weight space of neural networks

arXiv: https://arxiv.org/abs/2002.05688 · HTML: https://mlsanity.com/paper/2002.05688/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2020.

## Built on by (most cited first, 30 of 65)

- [Equivariant Architectures for Learning in Deep Weight Spaces](https://mlsanity.com/paper/2301.12780/) (2023)
- [Permutation Equivariant Neural Functionals](https://mlsanity.com/paper/2302.14040/) (2023)
- [What Does Rotation Prediction Tell Us about Classifier Accuracy under Varying Testing Environments?](https://mlsanity.com/paper/2106.05961/) (2021)
- [Graph Neural Networks for Learning Equivariant Representations of Neural Networks](https://mlsanity.com/paper/2403.12143/) (2024)
- [Graph Metanetworks for Processing Diverse Neural Architectures](https://mlsanity.com/paper/2312.04501/) (2023)
- [Neural Functional Transformers](https://mlsanity.com/paper/2305.13546/) (2023)
- [Towards Scalable and Versatile Weight Space Learning](https://mlsanity.com/paper/2406.09997/) (2024)
- [Model Zoos: A Dataset of Diverse Populations of Neural Network Models](https://mlsanity.com/paper/2209.14764/) (2022)
- [Equivariant Deep Weight Space Alignment](https://mlsanity.com/paper/2310.13397/) (2023)
- [Model Swarms: Collaborative Search to Adapt LLM Experts via Swarm Intelligence](https://mlsanity.com/paper/2410.11163/) (2024)
- [Universal Neural Functionals](https://mlsanity.com/paper/2402.05232/) (2024)
- [We Should Chart an Atlas of All the World's Models](https://mlsanity.com/paper/2503.10633/) (2025)
- [Improved Generalization of Weight Space Networks via Augmentations](https://mlsanity.com/paper/2402.04081/) (2024)
- [Scale Equivariant Graph Metanetworks](https://mlsanity.com/paper/2406.10685/) (2024)
- [On the Strong Correlation Between Model Invariance and Generalization](https://mlsanity.com/paper/2207.07065/) (2022)
- [Confidence and Dispersity Speak: Characterising Prediction Matrix for Unsupervised Accuracy Estimation](https://mlsanity.com/paper/2302.01094/) (2023)
- [Learning on LoRAs: GL-Equivariant Processing of Low-Rank Weight Spaces for Large Finetuned Models](https://mlsanity.com/paper/2410.04207/) (2024)
- [The Empirical Impact of Neural Parameter Symmetries, or Lack Thereof](https://mlsanity.com/paper/2405.20231/) (2024)
- [Monomial Matrix Group Equivariant Neural Functional Networks](https://mlsanity.com/paper/2409.11697/) (2024)
- [Deep Linear Probe Generators for Weight Space Learning](https://mlsanity.com/paper/2410.10811/) (2024)
- [Learning Useful Representations of Recurrent Neural Network Weight Matrices](https://mlsanity.com/paper/2403.11998/) (2024)
- [On the Relationship Between Explanation and Prediction: A Causal View](https://mlsanity.com/paper/2212.06925/) (2022)
- [How to Train Neural Field Representations: A Comprehensive Study and Benchmark](https://mlsanity.com/paper/2312.10531/) (2023)
- [Unsupervised Model Tree Heritage Recovery](https://mlsanity.com/paper/2405.18432/) (2024)
- [Hyper-Representations: Self-Supervised Representation Learning on Neural Network Weights for Model Characteristic Prediction](https://mlsanity.com/paper/2110.15288/) (2021)
- [Symmetry Discovery for Different Data Types](https://mlsanity.com/paper/2410.09841/) (2024)
- [Learning on Model Weights using Tree Experts](https://mlsanity.com/paper/2410.13569/) (2024)
- [GradMetaNet: An Equivariant Architecture for Learning on Gradients](https://mlsanity.com/paper/2507.01649/) (2025)
- [Structure Is Not Enough: Leveraging Behavior for Neural Network Weight Reconstruction](https://mlsanity.com/paper/2503.17138/) (2025)
- [ORAL: Prompting Your Large-Scale LoRAs via Conditional Recurrent Diffusion](https://mlsanity.com/paper/2503.24354/) (2025)

## Abstract (arXiv)

This paper presents an empirical study on the weights of neural networks, where we interpret each model as a point in a high-dimensional space -- the neural weight space. To explore the complex structure of this space, we sample from a diverse selection of training variations (dataset, optimization procedure, architecture, etc.) of neural network classifiers, and train a large number of models to represent the weight space. Then, we use a machine learning approach for analyzing and extracting information from this space. Most centrally, we train a number of novel deep meta-classifiers with the objective of classifying different properties of the training setup by identifying their footprints in the weight space. Thus, the meta-classifiers probe for patterns induced by hyper-parameters, so that we can quantify how much, where, and when these are encoded through the optimization process. This provides a novel and complementary view for explainable AI, and we show how meta-classifiers can reveal a great deal of information about the training setup and optimization, by only considering a small subset of randomly selected consecutive weights. To promote further research on the weight space, we release the neural weight space (NWS) dataset -- a collection of 320K weight snapshots from 16K individually trained deep neural networks.