# Towards Arbitrary Motion Completing via Hierarchical Continuous Representation

arXiv: https://arxiv.org/abs/2512.21183 · HTML: https://mlsanity.com/paper/2512.21183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 24 Dec 2025.

## Builds on (most cited first, 30 of 32)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [T2M-GPT: Generating Human Motion from Textual Descriptions with Discrete Representations](https://mlsanity.com/paper/2301.06052/) (2023)
- [Executing your Commands via Motion Diffusion in Latent Space](https://mlsanity.com/paper/2212.04048/) (2022)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [MoMask: Generative Masked Modeling of 3D Human Motions](https://mlsanity.com/paper/2312.00063/) (2023)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Robust Motion In-betweening](https://mlsanity.com/paper/2102.04942/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [FLAME: Free-form Language-based Motion Synthesis & Editing](https://mlsanity.com/paper/2209.00349/) (2022)
- [TMR: Text-to-Motion Retrieval Using Contrastive 3D Human Motion Synthesis](https://mlsanity.com/paper/2305.00976/) (2023)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [MotionLCM: Real-time Controllable Motion Generation via Latent Consistency Model](https://mlsanity.com/paper/2404.19759/) (2024)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [HumanTOMATO: Text-aligned Whole-body Motion Generation](https://mlsanity.com/paper/2310.12978/) (2023)
- [VideoINR: Learning Video Implicit Neural Representation for Continuous Space-Time Super-Resolution](https://mlsanity.com/paper/2206.04647/) (2022)
- [HNeRV: A Hybrid Neural Representation for Videos](https://mlsanity.com/paper/2304.02633/) (2023)
- [NeMF: Neural Motion Fields for Kinematic Animation](https://mlsanity.com/paper/2206.03287/) (2022)
- [Motion Puzzle: Arbitrary Motion Style Transfer by Body Part](https://mlsanity.com/paper/2202.05274/) (2022)
- [MotionFix: Text-Driven 3D Human Motion Editing](https://mlsanity.com/paper/2408.00712/) (2024)
- [Single-Shot Motion Completion with Transformer](https://mlsanity.com/paper/2103.00776/) (2021)
- [MoDi: Unconditional Motion Synthesis from Diverse Data](https://mlsanity.com/paper/2206.08010/) (2022)
- [Iterative Motion Editing with Natural Language](https://mlsanity.com/paper/2312.11538/) (2023)
- [Latent Modulated Function for Computational Optimal Continuous Image Representation](https://mlsanity.com/paper/2404.16451/) (2024)

## Abstract (arXiv)

Physical motions are inherently continuous, and higher camera frame rates typically contribute to improved smoothness and temporal coherence. For the first time, we explore continuous representations of human motion sequences, featuring the ability to interpolate, inbetween, and even extrapolate any input motion sequences at arbitrary frame rates. To achieve this, we propose a novel parametric activation-induced hierarchical implicit representation framework, referred to as NAME, based on Implicit Neural Representations (INRs). Our method introduces a hierarchical temporal encoding mechanism that extracts features from motion sequences at multiple temporal scales, enabling effective capture of intricate temporal patterns. Additionally, we integrate a custom parametric activation function, powered by Fourier transformations, into the MLP-based decoder to enhance the expressiveness of the continuous representation. This parametric formulation significantly augments the model's ability to represent complex motion behaviors with high accuracy. Extensive evaluations across several benchmark datasets demonstrate the effectiveness and robustness of our proposed approach.