Bacon: Band-limited Coordinate Networks for Multiscale Scene Representation

Lindell, David B.; Veen, Dave Van; Park, Jeong Joon; Wetzstein, Gordon

doi:10.1109/cvpr52688.2022.01577

Cited by 58 publications

(27 citation statements)

References 51 publications

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“…4.3. Moreover, such rich space also contains many expressive neural networks, as shown by both the prior works [12,16,22,36] and by our experiment in Sec. 4.1.…”

Section: Polynomial Neural Fieldsmentioning

confidence: 64%

“…Kileel et al [33] and Choraria et al [11] studies the expressive power of PNNs. Our work establish the connection between PNNs and many neural fields such as MFN [22] and BACON [36]. We further extends polynomial neural networks by evaluating the polynomial with a set of basis functions such as the Fourier basis.…”

Section: Related Workmentioning

confidence: 98%

“…But these positional encodings are passed through a black-box neural networks, making it difficult to analyze properties of the final output. The most relevant works is BACON [36], which propose an initialization schema for multiplicative filter networks (MFNs) [21] that ensures the output to be upper-limited by certain bandwidth. This work generalizes BACON in two ways.…”

Section: Related Workmentioning

confidence: 99%

“…This definition allows a rich design space that subsumes several prior works. For example, MFN [22] and BACON [36] can be instantiated by setting g i to be either the linear layer or a masked multiplication layer. Similarly, if we set the basis to be B = {x n } n∈N , then we can show architectures proposed in Π-Net [16] are a subclass of PNF.…”

Section: Polynomial Neural Fieldsmentioning

confidence: 99%

“…We demonstrate that a PNF is capable of representing signals of different modalities including images, 3D signed distance fields, and radiance fields. We compare our Fourier PNF with state-of-the-art neural field representations such as BACON [36], SIREN [60], and Random Fourier Features [63].…”

Section: Expressivitymentioning

confidence: 99%

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Polynomial Neural Fields for Subband Decomposition and Manipulation

Yang¹,

Benaim²,

Jampani³

et al. 2023

Preprint

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Neural fields have emerged as a new paradigm for representing signals, thanks to their ability to do it compactly while being easy to optimize. In most applications, however, neural fields are treated like black boxes, which precludes many signal manipulation tasks. In this paper, we propose a new class of neural fields called polynomial neural fields (PNFs). The key advantage of a PNF is that it can represent a signal as a composition of a number of manipulable and interpretable components without losing the merits of neural fields representation. We develop a general theoretical framework to analyze and design PNFs. We use this framework to design Fourier PNFs, which match state-of-the-art performance in signal representation tasks that use neural fields. In addition, we empirically demonstrate that Fourier PNFs enable signal manipulation applications such as texture transfer and scale-space interpolation. Code is available at https://github.com/stevenygd/PNF. * Equal contribution. Part of this work was done while Guandao was a student researcher at Google. 36th Conference on Neural Information Processing Systems (NeurIPS 2022).

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“…4.3. Moreover, such rich space also contains many expressive neural networks, as shown by both the prior works [12,16,22,36] and by our experiment in Sec. 4.1.…”

Section: Polynomial Neural Fieldsmentioning

confidence: 64%

Section: Related Workmentioning

confidence: 98%

Section: Related Workmentioning

confidence: 99%

Section: Polynomial Neural Fieldsmentioning

confidence: 99%

Section: Expressivitymentioning

confidence: 99%

See 3 more Smart Citations