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This research proposes a novel training paradigm for implicit neural representations by shifting from dense spatiotemporal sampling to sequence-level supervision over spatial locations. The approach significantly reduces computational costs while improving reconstruction quality for time-varying volumetric data and demonstrates enhanced capacity allocation when combined with mixture-of-experts architectures.
From Scalars to Time Series: Rethinking Implicit Neural Representations for Time-Varying Volumetric Data
arXiv:2607.20970v1 Announce Type: new Abstract: Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time. This coordinate-wise formulation requires extensive sampling during optimization, leading to high computational cost and inefficient use of temporal structure. In this work, we revisit this design choice and show that dense spatiotemporal sampling is not necessary for learning time-varying fields. Instead, we represent the data as a collection of spatially indexed time series and train INRs using sequence-level supervision over each spatial location, rather than coordinate-wise scalar samples. This reformulation eliminates the need for dense spatiotemporal sampling and instead learns each spatial location from its full temporal evolution in a structured manner. We demonstrate that this representation is compatible with a range of existing INR architectures and consistently improves reconstruction quality, while significantly reducing training cost. Furthermore, we show that this formulation can be combined with mixture-of-experts architectures, and that our MoE instantiation further improves reconstruction quality compared to both the base reformulation and existing MoE-based INR methods, providing a stronger capacity allocation under heterogeneous temporal dynamics.
Abstract:Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time. This coordinate-wise formulation requires extensive sampling during optimization, leading to high computational cost and inefficient use of temporal structure. In this work, we revisit this design choice and show that dense spatiotemporal sampling is not necessary for learning time-varying fields. Instead, we represent the data as a collection of spatially indexed time series and train INRs using sequence-level supervision over each spatial location, rather than coordinate-wise scalar samples. This reformulation eliminates the need for dense spatiotemporal sampling and instead learns each spatial location from its full temporal evolution in a structured manner. We demonstrate that this representation is compatible with a range of existing INR architectures and consistently improves reconstruction quality, while significantly reducing training cost. Furthermore, we show that this formulation can be combined with mixture-of-experts architectures, and that our MoE instantiation further improves reconstruction quality compared to both the base reformulation and existing MoE-based INR methods, providing a stronger capacity allocation under heterogeneous temporal dynamics.
Artificial Intelligence (cs.AI)
arXiv:2607.20970 [cs.AI]
(or arXiv:2607.20970v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.20970 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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