# Learning Useful Representations of Recurrent Neural Network Weight Matrices

arXiv: https://arxiv.org/abs/2403.11998 · HTML: https://mlsanity.com/paper/2403.11998/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 43 references that are in the map.
- First posted on arXiv 18 Mar 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Socratic Models: Composing Zero-Shot Multimodal Reasoning with Language](https://mlsanity.com/paper/2204.00598/) (2022)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Behavioral Cloning from Observation](https://mlsanity.com/paper/1805.01954/) (2018)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [A Survey of Imitation Learning: Algorithms, Recent Developments, and Challenges](https://mlsanity.com/paper/2309.02473/) (2023)
- [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)
- [Mindstorms in Natural Language-Based Societies of Mind](https://mlsanity.com/paper/2305.17066/) (2023)
- [Going Beyond Linear Transformers with Recurrent Fast Weight Programmers](https://mlsanity.com/paper/2106.06295/) (2021)
- [Permutation Equivariant Neural Functionals](https://mlsanity.com/paper/2302.14040/) (2023)
- [Extracting Automata from Recurrent Neural Networks Using Queries and Counterexamples](https://mlsanity.com/paper/1711.09576/) (2017)
- [Classifying the classifier: dissecting the weight space of neural networks](https://mlsanity.com/paper/2002.05688/) (2020)
- [On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models](https://mlsanity.com/paper/1511.09249/) (2015)
- [Sequential Neural Networks as Automata](https://mlsanity.com/paper/1906.01615/) (2019)
- [Model Zoo: A Growing "Brain" That Learns Continually](https://mlsanity.com/paper/2106.03027/) (2021)
- [Signal Processing for Implicit Neural Representations](https://mlsanity.com/paper/2210.08772/) (2022)
- [Meta-Consolidation for Continual Learning](https://mlsanity.com/paper/2010.00352/) (2020)
- [Model Zoos: A Dataset of Diverse Populations of Neural Network Models](https://mlsanity.com/paper/2209.14764/) (2022)
- [Policy Evaluation Networks](https://mlsanity.com/paper/2002.11833/) (2020)
- [Parameter-Based Value Functions](https://mlsanity.com/paper/2006.09226/) (2020)
- [Fast Adaptation via Policy-Dynamics Value Functions](https://mlsanity.com/paper/2007.02879/) (2020)
- [General Policy Evaluation and Improvement by Learning to Identify Few But Crucial States](https://mlsanity.com/paper/2207.01566/) (2022)
- [Hyper-Representations: Self-Supervised Representation Learning on Neural Network Weights for Model Characteristic Prediction](https://mlsanity.com/paper/2110.15288/) (2021)
- [Goal-Conditioned Generators of Deep Policies](https://mlsanity.com/paper/2207.01570/) (2022)
- [Learning One Abstract Bit at a Time Through Self-Invented Experiments Encoded as Neural Networks](https://mlsanity.com/paper/2212.14374/) (2022)

## Built on by (most cited first, 15 of 15)

- [We Should Chart an Atlas of All the World's Models](https://mlsanity.com/paper/2503.10633/) (2025)
- [Deep Linear Probe Generators for Weight Space Learning](https://mlsanity.com/paper/2410.10811/) (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)
- [Learning Model Representations Using Publicly Available Model Hubs](https://mlsanity.com/paper/2510.02096/) (2025)
- [A Model Zoo on Phase Transitions in Neural Networks](https://mlsanity.com/paper/2504.18072/) (2025)
- [Few-shot Implicit Function Generation via Equivariance](https://mlsanity.com/paper/2501.01601/) (2025)
- [What Linear Probes Miss: Multi-View Probing for Weight-Space Learning](https://mlsanity.com/paper/2605.23410/) (2026)
- [The Impact of Model Zoo Size and Composition on Weight Space Learning](https://mlsanity.com/paper/2504.10141/) (2025)
- [Discovering Hidden Gems in Model Repositories](https://mlsanity.com/paper/2601.22157/) (2026)
- [Hyper-Representations: Learning from Populations of Neural Networks](https://mlsanity.com/paper/2410.05107/) (2024)
- [Finite Probes Suffice: Identifiability and Universality for Weight-Space Learning](https://mlsanity.com/paper/2609.33901/) (2026)
- [Transferable Graph Metanetworks](https://mlsanity.com/paper/2610.00420/) (2026)
- [SLEM: Spectrum-Aware Latent Expert Merging](https://mlsanity.com/paper/2610.16484/) (2026)

## Abstract (arXiv)

Recurrent Neural Networks (RNNs) are general-purpose parallel-sequential computers. The program of an RNN is its weight matrix. How to learn useful representations of RNN weights that facilitate RNN analysis as well as downstream tasks? While the mechanistic approach directly looks at some RNN's weights to predict its behavior, the functionalist approach analyzes its overall functionality-specifically, its input-output mapping. We consider several mechanistic approaches for RNN weights and adapt the permutation equivariant Deep Weight Space layer for RNNs. Our two novel functionalist approaches extract information from RNN weights by 'interrogating' the RNN through probing inputs. We develop a theoretical framework that demonstrates conditions under which the functionalist approach can generate rich representations that help determine RNN behavior. We release the first two 'model zoo' datasets for RNN weight representation learning. One consists of generative models of a class of formal languages, and the other one of classifiers of sequentially processed MNIST digits. With the help of an emulation-based self-supervised learning technique we compare and evaluate the different RNN weight encoding techniques on multiple downstream applications. On the most challenging one, namely predicting which exact task the RNN was trained on, functionalist approaches show clear superiority.