Venue: ICML 2026 (Poster) Category: Diffusion-Flow Policy Affiliations: Karlsruhe Institute of Technology (authors: Gyenes, Gospodinov, Frieling, Krohmer, Schreiber, Jia, Freymuth, Neumann)

Various 3D modalities have been proposed for high-precision imitation learning to compensate for the shortcomings of RGB-only policies. However, point-cloud policies that consume raw Cartesian (xyz) coordinates struggle to capture the fine geometric detail that high-precision manipulation demands. The authors trace this to the spectral bias of neural networks toward learning low-frequency functions: with Cartesian inputs, networks under-fit the high-frequency geometric structure that distinguishes nearly-identical poses, limiting precision.

The paper proposes mapping point clouds into a high-dimensional Fourier space via a parametric projection rather than feeding Cartesian coordinates directly to the policy. By lifting each point through learnable Fourier features, the policy can represent high-frequency functions of geometry, letting it leverage fine geometric detail more effectively than Cartesian features. This is presented as a broadly applicable input representation for point-cloud-based imitation learning, validated on both simulated and real platforms.

flowchart LR
    PC[Raw point cloud<br/>Cartesian xyz] --> PROJ[Parametric Fourier<br/>projection]
    PROJ --> HF[High-dimensional<br/>Fourier features]
    HF --> POL[Imitation-learning<br/>policy]
    POL --> ACT[High-precision<br/>actions]
    SB[Spectral bias →<br/>low-freq under-fitting] -. overcome by .-> HF

The approach is evaluated on challenging manipulation tasks from the RoboCasa and ManiSkill3 benchmarks, and on a real robot setup. The authors report that Fourier features let policies leverage geometric details more effectively than Cartesian features, improving high-precision point-cloud imitation learning. The publicly available abstract does not state specific success-rate numbers; quantitative results are in the full paper / project page (fourier-il.github.io/fourier-il).

This work isolates a clean, architecture-agnostic cause — spectral bias against high-frequency geometry — for the precision ceiling of point-cloud policies, and offers a simple parametric-Fourier input transform as a remedy. Because it is a drop-in representation change rather than a new policy class, it could broadly raise the precision floor of 3D imitation-learning methods in the 2026 VLA/manipulation landscape.

• ICML 2026: https://icml.cc/virtual/2026/poster/60655

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