Fourier Features Let Agents Learn High Precision Policies with Imitation Learning
Balázs Gyenes, Emiliyan Gospodinov, Jan Frieling, Enrico Krohmer, Nicolas Schreiber, Xiaogang Jia, Niklas Freymuth, Gerhard Neumann
Abstract
High-precision robotic manipulation requires fine-grained spatial reasoning that is often difficult to achieve with RGB-only policies due to depth ambiguity and perspective scale issues. Policies that leverage 3D information directly, such as those based on point clouds, offer a stronger geometric prior over purely image-based ones, yet their performance remains highly task-dependent. We hypothesize that this discrepancy may be due to the spectral bias of neural networks towards learning low frequency functions, which especially affects architectures conditioned on slow-moving Cartesian features. We thus propose to map point clouds from Cartesian space into high-dimensional Fourier space, effectively equipping the point cloud encoder with direct access to high-frequency features. We experimentally validate the use of Fourier features on challenging manipulation tasks from the RoboCasa and ManiSkill3 benchmarks and on a real robot setup. Despite their simplicity, we find that Fourier features provide significant benefits across diverse encoder architectures and benchmarks and are robust across hyperparameters. Our results indicate that Fourier features let policies leverage geometric details more effectively than Cartesian features, showing their potential as a general-purpose tool for point cloud-based imitation learning. We provide source code and videos on our project page: https://fourier-il.github.io/fourier-il
AI Impact Assessments
(1 models)Scientific Impact Assessment
1. Core Contribution
The paper proposes a simple but effective modification to point cloud-based imitation learning: replacing raw Cartesian coordinates with Fourier feature mappings (sinusoidal encodings at multiple frequencies) before feeding them into point cloud encoders. The key insight is that neural networks' well-documented spectral bias—the tendency to learn low-frequency functions first—is particularly problematic for manipulation policies that must make fine-grained spatial distinctions (e.g., deciding whether to insert a peg or reposition it). By projecting 3D coordinates into a high-dimensional Fourier space, neighboring points that are nearly identical in Cartesian space become easily distinguishable, enabling sharper decision boundaries.
This is not a novel technique per se—Fourier feature mappings are well-established in NeRF and related fields (Tancik et al., 2020; Mildenhall et al., 2021). The contribution is the systematic application and validation of this idea across multiple point cloud encoder architectures in the context of diffusion-based imitation learning, along with analysis explaining why and when it helps.
2. Methodological Rigor
The experimental design is thorough and well-structured:
However, some limitations in rigor exist:
3. Potential Impact
Practical impact: The modification is trivially simple to implement (a non-parametric transformation requiring essentially no additional compute), making adoption frictionless. The paper explicitly argues Fourier features should be used with "practically any point cloud encoder," positioning this as a default preprocessing step rather than a specialized technique.
Architectural implications: The finding that Fourier features benefit even multimodal architectures (RGB + point cloud) is significant, as it suggests this could improve large-scale foundation models for robotic control that incorporate 3D information (e.g., PointVLA, Sugar, Lift3D).
Broader relevance: The spectral bias framing connects point cloud IL to a well-understood phenomenon in deep learning theory, potentially inspiring similar investigations in other domains where MLPs process spatial coordinates (e.g., GNN-based physics simulation, molecular dynamics).
The real-world improvement from 14.8% to 40.2% normalized score is substantial and practically meaningful, though the absolute numbers remain low, indicating this is not a complete solution to high-precision manipulation.
4. Timeliness & Relevance
The paper addresses a genuine bottleneck: despite theoretical advantages of 3D representations, point cloud-based policies often underperform expectations, and the field has increasingly moved toward complex hybrid 2D/3D architectures. The paper's argument that much of this complexity may be unnecessary if the fundamental spectral bias is addressed is timely and provocative. With the rapid scaling of robotic foundation models (π0, RT-2, etc.), simple improvements to 3D representation processing could have outsized impact.
5. Strengths & Limitations
Key Strengths:
Notable Limitations:
6. Additional Observations
The finding that Fourier features improve learning dynamics even in the absence of fine geometry (Section 6.1, Figure 7) is arguably the most scientifically interesting result, as it suggests the benefits extend beyond simply resolving spatial ambiguity. This could motivate theoretical investigation into how input representations affect optimization landscapes in policy learning.
The paper is clearly written, with effective figures (especially Figure 1) and a logical experimental progression from simulation to real world to analysis.
Generated Jun 11, 2026
Comparison History (19)
Paper 2 likely has higher scientific impact: it addresses a broadly used GNN component (positional encodings) and fills a clear theoretical gap about truncated variants that are standard in practice, yielding general expressivity results and guidance applicable across many graph domains (chemistry, biology, social networks, recommender systems). Its combination of theory plus empirical validation enhances rigor and uptake. Paper 1 is practically strong for robotics imitation learning, but its core idea (Fourier features) is an adaptation of a known technique and its impact is narrower to 3D manipulation pipelines.
Paper 1 introduces a broadly applicable algorithmic improvement (Fourier features) to address spectral bias in point cloud-based imitation learning. This fundamental insight enhances high-precision robotic manipulation across various architectures and real-world setups. In contrast, Paper 2 focuses on a highly specialized hardware issue (ADC distortion in memristors for ASR), which, while valuable, has a narrower scope and impact primarily limited to neuromorphic engineering and specialized hardware design.
Paper 2 likely has higher impact due to timeliness and breadth: it targets RLHF reward models central to modern AI deployment, safety, and governance. Its mechanistic/causal neuron-level analysis and ablation methodology can generalize across model types and inform future alignment techniques (disentanglement, controllability), affecting both research and practice. Paper 1 is a solid, practical contribution for robotics imitation learning, but Fourier features for high-frequency representation are less novel and its impact is narrower to point-cloud manipulation, whereas Paper 2 addresses a widely relevant, high-stakes bottleneck in aligned language model systems.
Paper 2 addresses the highly timely and impactful question of understanding how reinforcement learning post-training improves reasoning in LLMs—a central topic given the rapid rise of models like DeepSeek-R1 and OpenAI o1. Its mechanistic insights (strategy selection and strategy improvement) provide foundational understanding with broad implications for scaling reasoning capabilities across AI. Paper 1, while solid and practical, offers a more incremental contribution (applying known Fourier feature techniques to point cloud-based imitation learning) with narrower impact primarily in robotic manipulation.
While Paper 1 introduces a valuable technique for robotic manipulation, Paper 2 addresses a critical and widespread challenge in human-AI interaction: preference compliance in LLM agents. By compiling user corrections into executable runtime checks, TRACE offers a highly practical solution that significantly improves agent reliability over time. Its immediate applicability to the rapidly expanding field of interactive and coding agents gives it a broader, more timely scientific and real-world impact.
Paper 2 is likely to have higher scientific impact due to stronger cross-field relevance and timeliness: mechanistic interpretability and causal evaluation of internal routing in LLM architectures is a central, fast-moving topic with broad implications for AI safety, transparency, and model design. Its core contribution—showing that exposed routing tensors are not inherently interpretable and requiring causal interventions—offers a generally applicable methodological caution and evaluation framework. Paper 1 is useful and practical for robotics imitation learning, but Fourier features are a known technique and the impact is more domain-specific despite solid empirical validation.
Paper 2 proposes a fundamental theoretical and algorithmic advancement in Optimal Transport, a mathematical framework widely used across diverse fields like machine learning, biology, and graphics. By offering linear scaling and unified geometric solvers, it has a broader potential impact. Paper 1 provides a valuable but more narrowly focused empirical improvement for point-cloud-based imitation learning in robotics.
Paper 2 proposes a unifying mathematical framework for AI interpretability, a critical and rapidly growing field. By grounding interpretability in Lagrangian mechanics, it offers a fundamental paradigm shift with broad theoretical and practical implications across all of machine learning. Paper 1, while practically valuable, presents a more specialized architectural improvement for point cloud-based robotic manipulation, giving it a narrower scope of impact.
Paper 2 likely has higher scientific impact: it proposes a simple, broadly applicable technique (Fourier features for point-cloud imitation learning) validated across multiple major benchmarks and real-robot experiments, making it timely and readily adoptable by the robotics/ML community. The method targets a widely encountered limitation (spectral bias) and can transfer across tasks, architectures, and domains, increasing breadth and real-world applicability. Paper 1 is novel and clinically relevant, but evidence is currently limited to synthetic cardiac data and a narrower application area, which may reduce near-term impact.
Paper 1 addresses a fundamental limitation in graph machine learning (transductive learning) and proposes a roadmap for Graph Foundation Models in complex network dynamics. Its focus on zero-shot generalization across diverse networks has broad, cross-disciplinary implications for epidemiology, social sciences, and complex systems, offering a paradigm shift with higher potential for widespread theoretical and foundational impact compared to the domain-specific robotic manipulation improvements in Paper 2.