# Structure Is Not Enough: Leveraging Behavior for Neural Network Weight Reconstruction

arXiv: https://arxiv.org/abs/2503.17138 · HTML: https://mlsanity.com/paper/2503.17138/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 49 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 30 of 39)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Graph HyperNetworks for Neural Architecture Search](https://mlsanity.com/paper/1810.05749/) (2018)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [Predicting Neural Network Accuracy from Weights](https://mlsanity.com/paper/2002.11448/) (2020)
- [Equivariant Architectures for Learning in Deep Weight Spaces](https://mlsanity.com/paper/2301.12780/) (2023)
- [Asymmetric Valleys: Beyond Sharp and Flat Local Minima](https://mlsanity.com/paper/1902.00744/) (2019)
- [Parameter Prediction for Unseen Deep Architectures](https://mlsanity.com/paper/2110.13100/) (2021)
- [Learning to Learn with Generative Models of Neural Network Checkpoints](https://mlsanity.com/paper/2209.12892/) (2022)
- [Permutation Equivariant Neural Functionals](https://mlsanity.com/paper/2302.14040/) (2023)
- [Classifying the classifier: dissecting the weight space of neural networks](https://mlsanity.com/paper/2002.05688/) (2020)
- [Hyper-Representations as Generative Models: Sampling Unseen Neural Network Weights](https://mlsanity.com/paper/2209.14733/) (2022)
- [Deep Learning on Implicit Neural Representations of Shapes](https://mlsanity.com/paper/2302.05438/) (2023)
- [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)
- [HyperTransformer: Model Generation for Supervised and Semi-Supervised Few-Shot Learning](https://mlsanity.com/paper/2201.04182/) (2022)
- [Learning by Reconstruction Produces Uninformative Features For Perception](https://mlsanity.com/paper/2402.11337/) (2024)
- [Neural Functional Transformers](https://mlsanity.com/paper/2305.13546/) (2023)
- [HyperGAN: A Generative Model for Diverse, Performant Neural Networks](https://mlsanity.com/paper/1901.11058/) (2019)
- [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)

## Built on by (most cited first, 6 of 6)

- [Learning Model Representations Using Publicly Available Model Hubs](https://mlsanity.com/paper/2510.02096/) (2025)
- [A Model Zoo of Vision Transformers](https://mlsanity.com/paper/2504.10231/) (2025)
- [A Model Zoo on Phase Transitions in Neural Networks](https://mlsanity.com/paper/2504.18072/) (2025)
- [The Impact of Model Zoo Size and Composition on Weight Space Learning](https://mlsanity.com/paper/2504.10141/) (2025)
- [Unsupervised Behavioral Compression: Learning Low-Dimensional Policy Manifolds through State-Occupancy Matching](https://mlsanity.com/paper/2603.27044/) (2026)
- [Temporal Geometry of Deep Networks: Hyperbolic Representations of Training Dynamics for Intrinsic Explainability](https://mlsanity.com/paper/2610.03000/) (2026)

## Abstract (arXiv)

The weights of neural networks (NNs) have recently gained prominence as a new data modality in machine learning, with applications ranging from accuracy and hyperparameter prediction to representation learning or weight generation. One approach to leverage NN weights involves training autoencoders (AEs), using contrastive and reconstruction losses. This allows such models to be applied to a wide variety of downstream tasks, and they demonstrate strong predictive performance and low reconstruction error. However, despite the low reconstruction error, these AEs reconstruct NN models with deteriorated performance compared to the original ones, limiting their usability with regard to model weight generation. In this paper, we identify a limitation of weight-space AEs, specifically highlighting that a structural loss, that uses the Euclidean distance between original and reconstructed weights, fails to capture some features critical for reconstructing high-performing models. We analyze the addition of a behavioral loss for training AEs in weight space, where we compare the output of the reconstructed model with that of the original one, given some common input. We show a strong synergy between structural and behavioral signals, leading to increased performance in all downstream tasks evaluated, in particular NN weights reconstruction and generation.