Scalable Neural Video Representations with Learnable Positional Features
Abstract
Succinct representation of complex signals using coordinate-based neural representations (CNRs) has seen great progress, and several recent efforts focus on extending them for handling videos.
Here, the main challenge is how to (a) alleviate a compute-inefﬁciency in training CNRs to (b) achieve high-quality video encoding while (c) maintaining the parameter-efﬁciency.
To meet all requirements (a), (b), and (c) simultaneously, we propose neural video representations with learnable positional features (NVP), a novel CNR by introducing “learnable positional features” that effectively amortize a video as latent codes.
Speciﬁcally, we ﬁrst present a
CNR architecture based on designing 2D latent keyframes to learn the common video contents across each spatio-temporal axis, which dramatically improves all of those three requirements.
Then, we propose to utilize existing powerful image and video codecs as a compute-/memory-efﬁcient compression procedure of latent codes.
We demonstrate the superiority of NVP on the popular UVG benchmark; compared with prior arts, NVP not only trains 2 times faster (less than 5 minutes) but also exceeds their encoding quality as 34.07 → 34.57 (measured with the PSNR metric), even using > 8 times fewer parameters.
We also show intriguing properties of NVP, e.g .,
video inpainting, video frame interpolation, etc.
Introduction
Recent advances in coordinate-based neural representations (CNRs) [9, 13, 17, 40, 46] have shown great promise in the ﬁeld as a new paradigm for representing complex signals, including gigapixel images [29, 34], audios [40], 3D scenes [30, 33, 35], and even large city-scale street views [47].
Instead of storing signal outputs as a coordinate grid ( e.g ., image pixels), whose memory requirement scales unfavorably in terms of resolution and dimension, CNRs represent each signal as a compactly parameterized, continuous neural network; they interpret a signal as a coordinate-to-value function and train a neural network to approximate this mapping.
CNRs enjoy numerous appealing properties, including data compression [11, 12, 59], super-resolution [6], novel view synthesis [18, 22, 33, 54], and generative modeling of complex, high-dimensional data [14, 24, 41, 42, 57, 60], while being parameter-efﬁcient interpretation of a given signal in various scenarios.
In particular, several works have attempted to exploit CNRs to interpret video signals [5, 23, 42, 57] by learning a neural network f : R 3 → R 3 with f ( x, y, t ) =
( r, g, b ) and exhibited their potential as a succinct representation of videos, as well as providing numerous applications including video generative modeling [42, 57], video compression [5, 59], and video super-resolution [7]. They a r X i v : . 06823v [ c s .
C V ] O c t
[Figure]
observe that conventional CNR architectures [40, 46] often fail to encode large-scale videos due to their complex temporal dynamics accompanied by large spatial variations, but the problem can be remarkably mitigated by designing CNR architectures specialized for videos.
For instance, Chen et al.
[5] proposes a CNR structure that focuses on the continuous modeling of the video signal only along the temporal dimension, allowing for more radical variations along spatial axes; it exhibits a comparable encoding quality to existing powerful video codecs ( e.g ., H.264 [51], HEVC [43]) while enjoying lots of intriguing properties ( e.g ., denoising and video frame interpolation).
However, CNRs suffer from a severe compute-inefﬁciency, 2 limiting their scalability to encode realworld, large-scale videos despite their advantages.
To alleviate this issue, several works [26, 34, 37] have proposed new CNR architectures by separating a CNR f into two parts; f
= h φ ◦ g θ for a coordinate-to-latent mapping g θ ( x, y, t ) =
z and a latent-to-RGB mapping h φ ( z ) =
( r, g, b ) .
They construct g θ as an embedding function deﬁned with latent grids U θ in which the shape resembles the grid interpretation of a given signal ( e.g ., a 2D array of C -dimensional latent codes U θ ∈
R
H
× W × C for image pixels) rather than as a neural network.
These approaches have shown a promise in compute-efﬁciency due to the strong locality induced by a grid structure of U θ ; however, they result in another problem: these architectures severely sacriﬁce the parameter-efﬁciency since the parameter size of θ can be very large, growing proportionally to both the input coordinate dimension and the signal resolution.
In this paper, we focus on developing video CNRs that are the best of both worlds: achieving high-quality encoding and the compute-/parameter-efﬁciency simultaneously.
Contribution.
We introduce neural video representations with learnable positional features (NVP), a novel CNR for videos.
NVP avoids requiring a single giant full-dimensional 3D array in g θ by presenting learnable positional features that effectively amortize a given video as “2D and 3D” latent grids with succinct parameters.
Speciﬁcally, we decompose the coordinate-to-latent mapping as
[Equation]
, for θ := ( θ xy , θ xt , θ yt , θ xyt ) , where we present two types of latent grids for constructing these mappings (see Figure 2)
◦
Latent keyframes : We ﬁrst design “image-like” 2D latent grids U
θ xy , U θ xt , U θ yt for g θ
xy , g θ xt , g θ yt (respectively) that learn the representative video contents across each spatio-temporal axis and dramatically improve the parameter efﬁciency of NVP.
◦ Sparse positional features : We then introduce a “video-like” 3D latent grid U θ xyt for g θ xyt , whose size is much smaller than the original video pixels, but effectively encodes video details locally. Measured
NVIDIA , NeRV hours encode
[Figure]
Moreover, we propose a compute-/memory-efﬁcient compression procedure to further reduce the parameter θ by incorporating existing image and video codecs, e.g ., JPEG [49] for images and
HEVC [43] for videos, respectively.
In particular, we treat 2D and 3D latent grids like the image or video pixels and utilize powerful compression pipelines for them.
Our compression scheme does not require any re-training of trained parameters, which signiﬁcantly increases compute-efﬁciency to prior approaches to compressing CNR parameters but remarkably the encoding quality.
We also remark that such a compression approach is not applicable to the hashing-based latent grid of the prior method [34], while ours is “collision-free” and maintains the video- or image-like structures.
Finally, for the choice of h φ , we suggest using a modulated network (with respect to the temporal coordinate) to improve the encoding quality of videos that contain dynamic motions.
We verify the effectiveness of our method on the popular UVG benchmark [32].
In particular, NVP achieves the peak signal-to-noise ratio (PSNR; higher is better) metric of 34.57 in 5 minutes (with a single NVIDIA V100 32GB GPU): it is achieved > 2 times faster, even with using > 8 times fewer parameters than the state-of-the-art on compute-efﬁciency that reaches 34.07 in 10 minutes.
Moreover, compared with prior arts on encoding quality, our method improves the learned perceptual image patch similarity (LPIPS [58]; lower is better) as 0.145 → 0.102 ( + 29.7%) with a similar number of parameters while requiring ∼ 72.5% less training time.
We also show numerous compelling properties of NVP, e.g .,
video inpainting, video frame interpolation, super-resolution, compression, and consistent frame-wise encoding results without deviating quality.
Related work
Coordinate-based neural representations.
Coordinate-based neural representations (CNRs), also known as implicit neural representations or neural ﬁelds, have emerged as a new paradigm for representing complex, continuous signals.
They propose to encode signals through a neural network, typically a multilayer perceptron (MLP) combined with high-frequency sinusoidal activations [40] or
Gaussian activations [9].
Prior works have focused on utilizing neural ﬁelds on various complicated data, e.g ., gigapixel images [29, 34], 2D videos [5, 42, 57], 3D static scenes, [30, 33, 35], and 3D dynamics scenes [23, 39, 52].
In particular, most approaches have focused on constructing CNR architectures for encoding 3D scenes [3, 15, 47] and exhibited how employing specialized prior knowledge for a given signal domain in the architecture can remarkably boost the encoding quality.
Despite these successes, extending CNRs for videos is yet under-explored.
In this paper, we aim to move toward developing a CNR for videos by exploiting their unique temporal properties.
Hybrid CNRs.
Rather than solely designing a neural network of coordinate-to-RGB mapping, hybrid CNRs incorporate learnable latent codes that follow a grid structure, e.g ., image CNRs combined with 2D latent spatial grids [6, 31], and 3D scene (or shape) CNRs with latent cubic grids [4, 8, 19, 26, 29, 37].
Speciﬁcally, they compute a latent vector using the grid-structured latent code and pass it through a neural network to compute the signal output at a given input coordinate.
Such approaches have shown signiﬁcant efﬁciencies in training time and encoding quality due to the powerful locality induced by grid-shaped latent codes.
However, the number of parameters required for latent grid-based representations easily grows proportionally to the input coordinate dimension or data resolution, limiting the scalability of hybrid CNRs.
Remarkably, some of the recent approaches have exhibited this inefﬁciency can be signiﬁcantly mitigated by considering multi-level (or progressive) structures for latent grids [26, 29, 44, 45].
While prior works primarily focus on encoding images or 3D scenes, we aim to design parameter-efﬁcient hybrid CNRs for videos.
NVP: Neural video representations with learnable positional features
We ﬁrst formulate our problem setup as follows.
Given a video signal v :=
( f 1 , f 2 , . . .
, f T ) consisting of T video frames, the goal is to ﬁnd a compact neural representation f w with parameters w , from which the original video v can be reconstructed with high quality.
Here, the quality can be deﬁned using various distortion metrics, e.g ., peak signal-to-noise ratio (PSNR) [16] and LPIPS [58], for evaluating a reconstruction quality and a perceptual similarity, respectively.
To achieve this goal, we take an approach based on coordinate-based neural representations (CNRs)— a paradigm where each datum ( e.g ., video) is parameterized as a neural network of coordinate mapping.
In particular, we aim to represent the given video using a neural network f w : R 3 → R 3 , which maps the space-time coordinates ( x, y, t ) of the video to corresponding RGB values ( r, g, b ) , where f w is optimized with reconstruction objectives, e.g ., mean-squared error.
Such an approach has signiﬁcant potential, as CNRs have shown to encode other continuous, complex signals ( e.g ., 3D scenes) [40, 46] compactly while enjoying lots of intriguing properties, e.g ., super-resolution [6] and denoising [5].
However, CNRs have suffered from tremendous time costs for training, and even in the case of videos, it is difﬁcult to achieve high-quality encodings if one utilizes conventional CNR architectures that overlook the complex spatio-temporal dynamics of videos [5].
Our contribution lies in resolving these issues by designing “learnable positional features” that succinctly encode a video as latent codes with high quality and keeping their compute-/parameter-efﬁciency intact.
In the rest of this section, we provide a detailed description of each component in NVP.
In Section 3.1, we explain the architecture of NVP.
We then describe our compression procedure in Section 3.2.
3.1 Architecture
We design our video CNR f w as a composition of two functions with a parameterization w :=
( θ, φ ) : a coordinate-to-latent mapping g θ and a latent-to-RGB mapping h φ .
Here, we decompose the coordinate-to-latent-mapping as g θ =
g θ xy × g θ xt
×
g θ yt
× g θ xyt with g θ ( x, y, t ) =
( z xy , z xt , z yt , z xyt ) (for θ :=
( θ xy , θ xt , θ yt , θ xyt ) ), where each g θ xy , g θ xt , g θ yt is formalized with image-like 2D latent spatial grids U θ xy , U θ xt , U θ yt (respectively) and g θ xyt is designed with a video-like sparse 3D latent grid U θ xyt .
We then present the latent-to-RGB mapping h φ ( z xy , z xt , z yt , z xyt ) =
( r, g, b ) to be a multi-layer perceptrion (MLP) modulated by another neural network.
To explain our architecture, we assume all the input coordinate ( x, y, t ) of g θ (and f w ) is in [0 , 1] 3 ⊂ R 3 without loss of generality.
Learnable latent keyframes.
At a high level, learnable latent keyframes U
θ xy , U θ xt , U θ yt are imagelike 2D latent grids learned to capture the common representative contents in a given video v across each t -, y -, x -axis, respectively.
For a given input coordinate ( x, y, t ) , we compute latent vectors z xy , z xt , z yt from U θ
xy , U θ xt , U θ yt individually.
We explain our keyframe only with U θ yt by letting U :
= U yt for simplicity, but note that other keyframes U θ xy , U θ xt operate in the similar manner.
Formally, U is L 2D spatial grids of C -dimensional latent codes u ij , whose resolution is H l × W l :
[Equation]
, U L ) , U
[Equation]
lij
[Equation] for l = 1 , . . .
, L, u ij ∈ R C for 1 ≤ i ≤ H l , 1 ≤ j ≤ W l . Here, the keyframe follows an L -level multi-resolution structure, i.e ., for each level l , the height H l and the width W l become different as H l = (cid:98) γ l − 1 H 1 (cid:99) and W l = (cid:98) γ l − 1 W 1 (cid:99) with ﬁxed γ > 1 and
H 1 , W 1 > 0 , where (cid:98)·(cid:99) indicates the ﬂoor function of the input.
Since U =
U θ yt is shared over the x -axis, we compute the latent vector z yt :=
( z 1 yt , . .
z L yt ) by considering only the value of y and t at a given coordinate ( x, y, t ) .
Speciﬁcally, for l = 1 , . . .
, L , each z l yt is a linearly interpolated vector of four vectors in the spatial grid U l , where the indices of these vectors are chosen as the closest ones to the relative position of the input coordinate ( y, t ) ∈ [0 , 1] 2 : [Equation] l = 1 , . . . [Equation]
L
[Equation]
, where lerp indicates a linear interpolation operation at the input coordinate between given vectors.
Note that we learn the keyframe as the latent codes, unlike conventional approaches that specify the keyframe in a deterministic manner from T video frames ( f 1 , f 2 , . . .
, f T ) ; it encourages to capture the representative contents of the video over each spatio-temporal direction better.
We also remark that our architecture involves two keyframes U θ xt , U θ yt that are considered across spatial axes.
Considering these keyframes may not be beneﬁcial in the RGB space as the spatial variation of video pixels is often large.
However, in our approach, these keyframes are learned under a more ﬂexible, continuous latent space, and thus the representative frames can even be found in these spatial directions in such a space while encoding the RGB outputs of the video accurately.
Finally, recall that U θ
xy , U θ xt , U θ yt consist of multi-resolution spatial grids, i.e ., the resolution of spatial grids in each latent keyframe grows from coarse to ﬁne.
Since natural scenes often include repeating patterns in various scales, e.g ., a scene of ﬂowers of different sizes, this multi-resolution architecture promotes learning common patterns with reduced memory and computation costs, which is also validated in Müller et al.
Sparse positional features.
Given a space-time coordinate ( x, y, t ) , we compute the latent vector z xyt with U θ xyt that represents the local details of the video at this input position.
Here, U θ xyt :
= ( u ijk ) ∈
R H
× W × S × D is a 3D sparse grid of D -dimensional latent codes, i.e ., the 3D grid size
H × W × S is much smaller than the size of the video pixels of a 3D RGB grid:
[Equation]
for 1 ≤ i ≤ H, 1 ≤ j ≤ W, 1 ≤ k ≤ S.
To evaluate the latent vector z xyt , we concatenate h × w × s latent codes in U θ xyt that their indices are near the relative position of the input ( x, y, t ) :
[Equation]
, u m + h − 1 ,n + w − 1 ,k + s − 1 ) where h, w, s > 0 are given as hyperparameters.
The locality of U θ xyt as 3D latent codes dramatically alleviates the compute-inefﬁciency in ﬁtting videos, in contrast to conventional CNRs where the entire parameters are shared (as a neural network) for arbitrary input coordinates ( x, y, t ) and thus require a signiﬁcant training cost.
Moreover, recall that we construct U θ xyt as a sparse 3D grid of latent codes; remarkably, U θ xyt efﬁciently captures the video details even if the size is smaller than the number of video pixels since the common contents of a given video are effectively encoded with the latent keyframes U θ xy , U θ xt , U θ yt .
Note that we design U θ xyt as a sparse 3D grid; each single u ijk should represent a wide area of videos solely without concatenation.
As the single latent vector may lack expressive power to represent such a wide range and may result in a non-smooth transition as the CNR output.
Hence, we mitigate this issue by concatenating multiple vectors near each other (see Figure 10 in Section 4.3).
Instead of directly selecting near latent codes from U θ xyt , one may consider upsampling of U θ xyt using linear interpolation before selecting the close latent codes at a given coordinate.
Such an interpolation further helps each latent code to learn smoother representations and also generalizes to representing video frames at unseen coordinates during training.
Meanwhile, this upsampling requires more computing time compared to the computational cost of other modules in NVP, and thus faces a trade-off between the smoothness and compute-efﬁciency in training (see Table 4 in Section 4.3).
Modulated implicit function.
With the latent vector z : =
[ z xy , z xt , z yt , z xyt ] evaluated from g θ , a naïve design choice of the latent-to-RGB mapping h φ is to utilize a MLP that maps z to the corresponding RGB output ( r, g, b ) .
However, if a video contains temporally dynamic motions, we found such a simple MLP architecture occasionally lacks expressive power and can be difﬁcult to capture the complex dynamics of the given video, even with the large network size of h φ .
To circumvent this issue, we design h φ to be a K -layer MLP (coined as a synthesizer network) modulated by another modulator network [31]: where the latent vector z and the time coordinate t are passed through the modulator and the synthesizer, respectively.
Here, the modulator network utilizes piecewise linear activations ( e.g ., ReLU), where the synthesizer uses sinusoidal activations.
Speciﬁcally, an RGB output ( r, g, b ) of the latent vector z (from ( x, y, t )) is computed as follows:
[Equation]
where A k , b k are weights and biases of k -th layer of the synthesizer, z k is k -th hidden feature of the modulator, and (cid:12) denotes an element-wise product.
It helps to achieve high-quality encoding rapidly in early training iterations and often at the convergence than a naive MLP (See Table 3 for details).
indicates applying the method without the corresponding compression scheme.
We report the BPP values of NeRV without compressing parameters if the encoding time is ≤ 1 hour since the NeRV’s compression requires a longer time.
On the other hand, the compression procedure of NVP only takes less than 1 minute, but for a fair comparison, we do not apply it to NVP as well whenever NeRV is not compressed.
[Table]
3.2 Compression procedure
Recall that we aim to ﬁnd “compact” video CNRs; several works have focused on reducing the number of coordinate-based neural representations parameters (or bits) after training while maintaining their performance.
In particular, they have relied on exploiting existing well-known techniques for neural network compression, e.g ., exploiting magnitude pruning [5, 21] or quantization [5, 59], and exhibited considerable results.
However, these approaches mainly involve a re-training of CNR parameters, requiring severe computation costs, and thus are not suitable for practical scenarios.
Instead, we propose a compression pipeline for NVP, which does not require re-training, yet signiﬁcantly reduces the number of bits while preserving the video quality.
Our main idea is to incorporate existing image and video codecs that have shown their promises for the compression of given pixels.
In particular, we focus on compressing keyframes U θ
xy , U θ xt , U θ yt , and sparse positional features U θ xyt , as the parameter size of the modulated implicit function h φ is neglectable compared with those.
Speciﬁcally, we quantize U θ xyt
and U
θ xy , U θ xt , U θ yt as 3D/2D grids of 8-bit latent codes and regard them as video and image pixel grids, where the number of the channel becomes the dimension of latent codes.
Based on these interpretations, we compress these latent codes by utilizing existing video and image codecs, e.g ., HEVC [43] for videos and JPEG [49] for images.
Intriguingly, we found this procedure can signiﬁcantly reduce the parameters while notably maintaining the video quality without any ﬁne-tuning of the latent-to-RGB mapping h φ (See Section 4.3).
Experiments
We verify the effectiveness of our framework on UVG-HD [32], a representative benchmark for evaluating video encodings.
Experimental results demonstrate that our neural video representations with learnable positional features (NVP) simultaneously improves the overall performance by (a) alleviating a compute-inefﬁciency in training, (b) achieving high-quality video encoding, and (c) maintaining parameter-efﬁciency.
We also show applications of our NVP, including video inpainting and spatio-temporal interpolation.
Finally, we conduct ablation studies to validate each component.
[Figure]
Evaluation.
We follow similar setups on prior work [5] proposing coordinate-based neural representations (CNRs) for videos.
All reported numbers are averaged over 7 videos in UVG-HD: Beauty,
Bosphorus, HoneyBee, Jockey, ReadySetGo, ShakeNDry, and Yachtride, along with the standard deviations unless otherwise speciﬁed.
We also use the Big Buck Bunny video, which is used in
NeRV [5].
For quantitative evaluation, we use the following metrics: peak signal-to-noise ratio (PSNR) for reconstruction quality, LPIPS [58], FLIP [2], and SSIM [50] for perceptual similarity, where all metrics are evaluated in a frame-wise manner and averaged over the whole video.
We evaluate these metrics on different bits-per-pixel (BPP; lower is better) to evaluate the parameter efﬁciency; see Appendix A.1 for more description of the evaluation.
Implementation details.
All main experiments, including baselines, are processed with a single
GPU (NVIDIA V100 32GB) and 28 instances from a virtual CPU (Intel ® Xeon ® Platinum
CPU @ 2.70GHz), where it takes at most ∼ 11 hours to run our method and ∼ 2 days to run other baselines.
Moreover, we denote NVP-S and NVP-L as the model with latent code dimensions of sparse positional features to be 2 and 4, respectively; see Appendix A.2 for more details.
Baselines.
We compare our method with SIREN [40], and FFN [46], which are well-known signalagnostic CNR architectures, Instant-ngp [34] for state-of-the-art CNRs on compute-efﬁciency, and
NeRV [5], which is a CNR specialized for videos.
For all of the baseline methods, we follow their reported experimental setups.
In particular, for NeRV [5], we use two conﬁgurations provided in the ofﬁcial implementation: NeRV-S and NeRV-L for a small and a large model, respectively.
See
Appendix B for a detailed description of baseline methods.
4.1 Main results
Figure 1, Figure 3, and Table 1 summarize quantitative and qualitative results of NVP and baselines.
Remarkably, as shown in Figure 1, NVP can accurately capture dynamic motions and high-frequency details of a video, e.g ., the legs of a running horse, while prior state-of-the-art CNRs fail to achieve and show a blurry artifact.
We also emphasize such a high-quality encoding is accomplished in “less than 1 minute”, which supports the superior compute-efﬁciency of NVP in training.
Moreover, Table 1 veriﬁes the effectiveness of NVP with quantitative evaluations, which outperforms all other baselines at varying encoding times from ∼ 5 minutes to > 40 hours.
In particular, NVP signiﬁcantly improves LPIPS compared with previous methods, demonstrating how the encoded videos are perceptually similar to ground-truth videos.
Such a result is also conﬁrmed in Figure 3;
NeRV shows a distortion that some pixels signiﬁcantly deviate from the ground-truth outputs, while our method does not suffer from such artifacts.
We also note that the variance of NVP is relatively small compared with other baselines, which shows the robustness of videos with diverse scenes and motion.
See Appendix C and D for video-wise results and discussion on decoding time, respectively.
[Figure]
[Figure] [Figure]
4.2 Applications
In this section we provide several applications of our method, NVP, as video CNRs.
For better, playable illustrations and qualitative results, please refer to our project page.
Video inpainting.
Intriguingly, our method has the capability of video inpainting, i.e ., the desired moving object in the video can be naturally removed by capturing shared video contents with learnable keyframes.
Figure 4 visualizes the illustration of inpainting results from NVP; as shown in this ﬁgure, one can see the car is removed where such parts are ﬁlled with a natural background.
Video frame interpolation.
Since video CNRs approximate videos as temporally continuous signals, they should interpolate among two different frames at an arbitrary time, even if such a frame does not exist in the training dataset.
To validate the interpolation capability of NVP, we provide the quantitative results on Big Buck Bunny sequences; our method shows better interpolation results measured with various metrics, such as PSNR and LPIPS.
Video super-
resolution.
We remark that NVP encodes a given video as a spatio-temporally continuous signal.
Thus, our method can interpolate the frames across spatial directions, i.e ., frame-wise super-resolution.
Figure 5 exhibits how well NVP smoothly interpolates video frames across spatial directions while preserving the sharp edges, compared with naïve upsampling methods.
Video compression.
Recall that one of the major advantages of CNRs is their succinct encoding to represent a given signal; one may consider utilizing CNRs for video compression [5, 11, 12].
To verify the potential of our method on video compression, we compare the quality of compressed videos from NVP with the ones from the current state-of-the-art video codecs.
As shown in Figure 6, compressed videos from NVP show the comparable reconstruction quality (measured with PSNR metrics) while outperforming perceptual similarity (measured with LPIPS metrics).
4.3 Ablation studies
Effect of architecture components.
To verify the effectiveness of each component, we train our model with all the videos in UVG-HD by removing each component while maintaining the total number of parameters, then measure PSNR metrics from these models.
Table 3 summarizes the effect of three different architecture components.
Without any of the components consisting of our positional features, the reconstruction quality gets dramatically worse, which validates how NVP
[Figure] [Table]
[Figure]
[Table]
[Figure]
[Figure] [Figure]
succinctly encodes a given video as latent codes.
We also note that the modulation not only improves the ﬁnal encoding quality but also notably achieves high-quality encoding in its early training epochs.
Compression procedure.
To validate the effectiveness of our compression scheme, we compare the encoding quality of (a) NVP with our compression scheme and (b) NVP compressed through magnitude-based pruning.
Figure 7 shows the proposed compression pipeline outperforms conventional magnitude-based pruning under various BPP values.
We also remark that our compression method does not require re-training and is thus much more time-efﬁcient.
Analysis of non-temporal keyframes.
Recall that we additionally design keyframes across spatial directions, unlike conventional approaches that designate the keyframe over only the temporal direction.
To validate the effect of such keyframes, we compare NVP with (a) NVP without spatial keyframes and (b) NVP without all of the keyframes in Figure 8, where the number of parameters is equally set for a fair comparison.
While utilizing latent learnable keyframes only over temporal direction is already fairly effective for high-quality encoding, one can observe the consideration of keyframes across other directions provides a further improvement.
Consistent frame-wise encoding quality.
Existing keyframe-based compression approaches often suffer from inconsistent encoding quality: the frame-wise quality of the compressed video highly depends on whether it is the designated keyframe or not.
In contrast, NVP learns the keyframes and does not have this problem.
Figure 9 validates the result: our method exhibits consistent encoding performance while conventional popular video codecs show several peaks that the reconstruction quality (measured with PSNR metrics) highly deviates from others.
Effect of the concatenation of latent codes in sparse positional features.
To validate the effectiveness of design choice on extracting latent features from sparse positional features U θ xyt , we compare the reconstructions from NVP with and without concatenation of U θ xyt .
As shown in Figure 10, the concatenation of latent codes u ijk in U θ xyt indeed mitigates non-smooth transitions between latent codes and captures sharp details in a given video better.
In particular, without the concatenation, it results in undesirable artifacts ( e.g ., showing discontinuous borders), validating our concatenation scheme for constructing latent representations from sparse positional features.
Effect of upsampling of sparse positional features.
We also examine the effect of upsampling of the sparse positional features U θ xyt .
Figure 11 shows the result: linear interpolation of U θ xyt exhibits more smooth patterns for unseen coordinates during training.
Meanwhile, we note that the upsampling requires 1.61 times more training time per iteration due to the additional computation bottleneck (see
Table 4); however, regardless of upsampling, we remark that NVP still achieves notable computeefﬁciency compared with prior state-of-the-art methods (such as Chen et al.
[Figure] [Figure]
[Table]
Discussion and conclusion
We proposed NVP, a new coordinate-based neural representation (CNR) to encode videos as succinct latent codes.
Our main idea is to decompose a video into “image-like” and ”video-like” structures to learn coordinate-to-latent mapping efﬁciently.
Extensive experiments have veriﬁed the effectiveness of NVP on all the parameter-/compute-efﬁciency and the encoding quality.
We hope our method will facilitate various future research directions in the CNR area.
Limitations and future works.
Each video contains different scenes and motions so that it can be either static or dynamic, yet we utilize the same hyperparameters and architectures for encoding any video.
Although such a video-agnostic design is fairly effective and outperforms prior works, we believe the video-wise consideration of the architecture and hyperparameter can remarkably boost the performance further.
Moreover, we have shown the potential of utilizing powerful image and video codes for compressing latent codes in NVP; extending such codecs to be specialized for the compression of latent codes should be an interesting direction.
Negative social impacts.
A side effect of CNRs is their potential unexpected behavior on encoding; they may cause undesirable artifacts in representing the given signal but are challenging to predict due to the under-explored behavior of training CNRs.
Furthermore, in the case of representing videos, the encoded videos may suffer from severe distortions and conceivably cause ethical problems.
In this respect, such behaviors should be extensively and carefully investigated and mitigated to exploit
CNRs as the standard for encoding videos in real-world situations.
Acknowledgments and Disclosure of Funding
We would like to thank Younggyo Seo, Jihoon Tack, Jongheon Jeong, Sukmin Yun, Jongjin Park,
Junsu Kim, Seong Hyeon Park, Seojin Kim, Changyeon Kim, Jaehyun Nam, and anonymous reviewers for their helpful feedbacks and discussions.
We also appreciate Max Ehrlich for providing the exact results of prior video compression methods.
This work was mainly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2021-0-02068, Artiﬁcial
Intelligence Innovation Hub; No.2019-0-00075, Artiﬁcial Intelligence Graduate School Program (KAIST); No.2019-0-01906, Artiﬁcial Intelligence Graduate School Program (POSTECH)).
This research was partly supported by the Challengeable Future Defense Technology Research and
Development Program (No.915027201) of Agency for Defense Development in 2022.
This work was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2022R1F1A1075067).
[-• SIREN [40], which uses high frequency sine activations ( i.e ., sin( ω 0 z ) with ω 
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