neuralop.layers.embeddings.SinusoidalEmbedding

class neuralop.layers.embeddings.SinusoidalEmbedding(in_channels: int, num_frequencies: int = None, embedding_type: str = 'transformer', max_positions: int = 10000)[source]

Sinusoidal positional embedding for enriching coordinate inputs with spectral information.

This class provides sinusoidal positional embeddings in two styles: Transformer-style and NeRF-style. It lifts low-dimensional coordinates into a richer spectral representation by encoding them as periodic functions (sines and cosines) at multiple frequencies.

The embedding enhances a model’s ability to capture fine-scale variations and high-frequency dynamics by providing a hierarchy of frequency components alongside the original coordinates.

Parameters:

in_channelsint

Number of input channels to embed (dimensionality of input coordinates)

num_freqsint, optional

Number of frequency levels L in the embedding. Each level contributes a sine and cosine pair, resulting in 2L output channels per input channel. By default, set to the number of input channels.

embedding_type{‘transformer’, ‘nerf’}, optional

Type of embedding to apply, by default ‘transformer’

Transformer-style [1]: For each input coordinate p and frequency level k (0 ≤ k < L): - g(p)_{2k} = sin(p / max_positions^{k/L}) - g(p)_{2k+1} = cos(p / max_positions^{k/L})

NeRF-style [2]: For each input coordinate p and frequency level k (0 ≤ k < L): - g(p)_{2k} = sin(2^k * π * p) - g(p)_{2k+1} = cos(2^k * π * p)

max_positionsint, optional

Maximum number of positions for transformer-style encoding, by default 10000. Only used when embedding_type=’transformer’.

Attributes:

out_channels

required property for linking/composing model layers

Methods

forward(x)

Notes

• Input shape: (batch, n_in, in_channels) or (n_in, in_channels)

• Output shape: (batch, n_in, 2*num_freqs*in_channels) or (n_in, 2*num_freqs*in_channels)

• Ensure the highest frequency satisfies the Nyquist criterion: - Transformer: f_max < N/2 where N is the number of sampling points - NeRF: 2^{L-1} < N/2, i.e., L < 1 + log₂(N/2)

References

[1]

Vaswani, A. et al. “Attention Is All You Need”. NeurIPS 2017, https://proceedings.neurips.cc/paper_files/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf

[2]

Mildenhall, B. et al. “NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis”. ArXiv 2020, https://arxiv.org/pdf/2003.08934

Examples

See examples/layers/plot_sinusoidal_embeddings.py for comprehensive visualizations

property out_channels

required property for linking/composing model layers

forward(x)[source]

Parameters:

x: torch.Tensor

shape (n_in, self.in_channels) or (batch, n_in, self.in_channels)