Liquid Networks with Mixture Density Heads for Efficient Imitation Learning

arXiv cs.LG / 3/31/2026

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Key Points

The paper compares liquid neural networks with mixture density heads to diffusion policies for imitation learning on Push-T, RoboMimic Can, and PointMaze using a shared-backbone protocol that controls for backbone and training differences.
Liquid policies match the task performance using about half the parameters (4.3M vs. 8.6M), lower offline prediction error by 2.4×, and improve inference speed by 1.8×.
Across sample-efficiency tests from 1% to 46.42% of training data, liquid models show more consistent robustness, with the biggest improvements in low- and medium-data regimes.
Closed-loop experiments on Push-T and PointMaze align directionally with offline metrics but are noisier, suggesting that better offline density modeling helps but doesn’t fully predict closed-loop deployment success.
Overall, the authors position liquid recurrent multimodal policies with mixture density heads as a compact and practical alternative to iterative denoising methods for imitation learning.

Abstract

We compare liquid neural networks with mixture density heads against diffusion policies on Push-T, RoboMimic Can, and PointMaze under a shared-backbone comparison protocol that isolates policy-head effects under matched inputs, training budgets, and evaluation settings. Across tasks, liquid policies use roughly half the parameters (4.3M vs. 8.6M), achieve 2.4x lower offline prediction error, and run 1.8 faster at inference. In sample-efficiency experiments spanning 1% to 46.42% of training data, liquid models remain consistently more robust, with especially large gains in low-data and medium-data regimes. Closed-loop results on Push-T and PointMaze are directionally consistent with offline rankings but noisier, indicating that strong offline density modeling helps deployment while not fully determining closed-loop success. Overall, liquid recurrent multimodal policies provide a compact and practical alternative to iterative denoising for imitation learning.