oh excellent pointer! That indeed matches our intuition

And variance in the behavior is not necessarily coupled with that in the features; for example see this paper for a dissociation between the two openreview.net/forum?id=Yuc...

What we found was that more consistent features during training does not guarantee more similar OOD behavior. In fact here stronger feature learning can lead to more variable OOD behavior, which we hypothesize was due to overfitting

Just looked at your paper, we’re basically motivated by the same question applied to different architectures! will try to visit your poster too

yay thanks Dan!!

Thanks to my amazing collaborators and my PI! @satpreetsingh.bsky.social @flavioh.bsky.social @kanakarajanphd.bsky.social

🔹Paper: arxiv.org/pdf/2410.03972
🔹Poster: Fri Dec 5, Poster #2001 at Exhibition Hall C, D, E

Happy to chat at NeurIPS or by email at [email protected]!

Our results:
- support the contravariance principle (Cao & @dyamins.bsky.social)
- reveal when weight- & dynamic-level variability move together (or opposite)
- give "knobs" for controlling degeneracy, whether you're studying shared mechanisms or individual variability in task-trained RNNs.

4️⃣ Regularization (L1, low-rank)
Both types of structural regularization reduce degeneracy across all levels. Regularization nudges networks toward more consistent, shared solutions.

3️⃣ Network size
When we fix feature learning (using µP), larger RNNs converge to more consistent solutions at all levels — weights, dynamics, and behavior.
A clean convergence-with-scale effect, demonstrated on RNNs across levels.

We then causally tested feature learning’s effect on degeneracy using µP scaling. Stronger feature learning reduces dynamical degeneracy & increases weight degeneracy (like harder tasks).
It also increases behavioral degeneracy under OOD inputs (likely due to overfitting).

2️⃣ Feature learning
Complex tasks push RNNs into feature learning, where the network has to adapt its internal weights and features to solve the task. Weights travel much farther from initialization, leading to more dispersed weights in the weight space (higher degeneracy).

1️⃣ Task complexity
As tasks get harder, we observe less degeneracy in dynamics/behavior, but more degeneracy in the weights.

When trained on harder tasks, RNNs converge to similar neural dynamics and OOD behavior, but their weight configurations diverge. Why?

Using 3,400 RNNs across 4 neuroscience-relevant tasks (flip-flop memory, working memory, pattern generation, path integration), we systematically varied:
- task complexity
- learning regime
- network size
- regularization

Our findings:

Our unified framework measures & controls degeneracy at 3 levels:
🎯 Behavior: variability in OOD performance
🧠 Dynamics: distance btwn neural trajectories, quantified by Dynamical Similarity Analysis
⚙️ Weights: permutation-invariant Frobenius distance btwn recurrent weights

RNNs trained from different seeds on the same task can show strikingly different internal solutions, even when they perform equally well. We call this solution degeneracy.

📍Excited to share that our paper was selected as a Spotlight at #NeurIPS2025!

arxiv.org/pdf/2410.03972

It started from a question I kept running into:

When do RNNs trained on the same task converge/diverge in their solutions?
🧵⬇️

Our next paper on comparing dynamical systems (with special interest to artificial and biological neural networks) is out!! Joint work with @annhuang42.bsky.social , as well as @satpreetsingh.bsky.social , @leokoz8.bsky.social , Ila Fiete, and @kanakarajanphd.bsky.social : arxiv.org/pdf/2510.25943