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We also built 2 simple nonlinear systems (A, B) with identical eigenvalues but different eigenvectors. As expected, Wasserstein-based kwDSA struggles to separate them. All 3 fastDSA variants reliably distinguish A vs B (represented w/ MDS).

Under strong noise, we repeat the transformation tests (Plus kernelDMD+Wasserstein distance (kwDSA)). kwDSA highlights a key pitfall: relying mainly on eigenvalues (ignoring eigenvectors) can miss fine dynamical differences. fastDSA alternatives remain sensitive and perform well even at high noise.

Next we tested sensitivity to dynamical change by morphing a ring attractor into a line attractor (same model). fastDSA distances jump at the ring↔line transition, capturing topology change—unlike Procrustes—while being way faster than DSA.

We first tested whether fastDSA is invariant to purely geometric deformations—changes that preserve the same underlying dynamics and attractor topology. All 3 fastDSA variants are faithful to dynamics and remain stable across geometric deformations, while being computationally more efficient.

With different forms of noise, we showed how well the rank estimate supports DMD reconstruction. Across noise levels, the method detects the rank at the knee point automatically (with no tuning)

Our method efficiently estimates the rank of delay embeddings of a dynamical system. For example, on Lorenz trajectories projected to higher dimensions, the estimated order matches the true latent rank and aligns with AIC/BIC baselines.

We made DSA up to 150 times faster 🤯 by introducing 3 new optimization objectives and solvers to speed up the DSA alignment step. Instead of enforcing exact orthogonality at every iteration, we use faster formulations that approximate or penalize the constraint.

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Arman Behrad @armanbehrad.bsky.social · 30/09/2025

Wanna compare dynamics across neural data, RNNs, or dynamical systems? We got a fast and furious method🏎️ The 1st preprint of my PhD 🥳 fast dynamical similarity analysis (fastDSA): 📜: arxiv.org/abs/2511.22828 💻: github.com/CMC-lab/fast... I’ll be @cosynemeeting.bsky.social - happy to chat 😉

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(4/4) How about a simulation of more naturalistic setting?

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Arman Behrad @armanbehrad.bsky.social · 30/09/2025

(3/4) Next: biological networks. We applied UNITE to V4 activity (PSTH) from a monkey doing a visual cognitive task. 🐒👁️

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Arman Behrad @armanbehrad.bsky.social · 30/09/2025

(2/4) First test: an RNN solving a cognitive task. UNITE identify state transitions without supervision. 🔍

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(4/4) Finally, we highlight cases where FastDSA outperforms other dynamical similarity metrics—while remaining robust to noise.

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(3/4) Next, we present experiments showing why geometrical methods fail. Both DSA and FastDSA achieve similar results—but FastDSA is 10–15× faster.

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(2/4) We first outline the general structure of the algorithm.

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