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Latent Mixture of Symmetries for Sample-Efficient Dynamic Learning

NeurIPS 2025 · Probabilistic and scientific modeling › Dynamical systems · approach: Latent dynamics models · 0 citations (OpenAlex)

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Proposes Latent MoS, a mixture-of-symmetries latent dynamics model (gated mixture of Lie-group-based latent flows inside a Latent ODE framework, stacked hierarchically) for sample-efficient learning of dynamics from low-resolution, irregularly sampled data.

Problem

Learning system dynamics from sparse, low-resolution, irregularly sampled measurements, where existing symmetry-discovery methods assume a single global symmetry group and decouple discovery from dynamic learning.

Approach

Replace the unstructured ODE update in Latent ODE with a sparse, softmax-gated mixture of latent flows, each a structured Lie-group action (planar rotation, translation, scaling, and their second-order compositions) whose parameters depend on time and latent state, plus a multi-level stacking to capture long-term equivariance.

Key results

• On extrapolation at 90% drop rate, Latent MoS reports MSE 0.62e-2 on Spiral versus 1.04e-2 for the best baseline Latent ODE, and 0.32e-2 on Glycolytic versus 0.52e-2 for RNN-Delta_t.
• Interpolation at 90% drop rate on Glycolytic: Latent MoS MSE 0.33e-2 versus 4.66e-2 for Contiformer and 11.24e-2 for Latent ODE.
• In the MBPO control experiment, MBPO-MoS achieves final frequency deviation -0.024 and integral cost 0.081, versus 0.51 for PPO.

Measured effects reported in the paper

Surprising findings

• Latent MoS on Lotka at 90% interpolation/extrapolation is not always best; Latent ODE wins at some drop rates (e.g., extrapolation at 90% on Lotka 0.43 vs 0.61 for Latent MoS).
• Removing the translational expert improved Glycolytic MSE to 0.001, suggesting that simpler expert sets can outperform the full mixture.

Limitations

• Candidate symmetry set (rotation, translation, scaling and their compositions) does not cover all Lie group representations.
• Performance depends on hyperparameters such as number of active experts K0; large K0 leads to overfitting.
• Not suited to systems lacking local symmetries, such as chaotic or purely stochastic processes.

Experimental setup

Datasets: Spiral ODE Glycolytic oscillator Lotka-Volterra Electricity load (Flores, Azores) NIST PV solar dataset Power system event simulations (Illinois 200-node) UCI air quality ECG200 (UCR archive)

Benchmarks: Spiral Glycolytic Lotka Load Solar Power event Air quality ECG

Metrics: test MSE

Baselines: EqSINDy EqGP RNN-Delta_t ODE-RNN Neural CDE ContiFormer Latent ODE Informer Autoformer PPO MBPO-GP

Builds on: Latent ODE ODE-RNN Neural ODE Mixture of Experts EqSINDy

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