11institutetext: University of Surrey 22institutetext: Adobe Research

# HyperNST: Hyper-Networks for Neural Style Transfer

Dan Ruta 11 Andrew Gilbert 11 Saeid Motiian 22 Baldo Faieta 22 Zhe Lin 22 John
Collomosse 1122

###### Abstract

We present HyperNST; a neural style transfer (NST) technique for the artistic
stylization of images, based on Hyper-networks and the StyleGAN2 architecture.
Our contribution is a novel method for inducing style transfer parameterized
by a metric space, pre-trained for style-based visual search (SBVS). We show
for the first time that such space may be used to drive NST, enabling the
application and interpolation of styles from an SBVS system. The technical
contribution is a hyper-network that predicts weight updates to a StyleGAN2
pre-trained over a diverse gamut of artistic content (portraits), tailoring
the style parameterization on a per-region basis using a semantic map of the
facial regions. We show HyperNST to exceed state of the art in content
preservation for our stylized content while retaining good style transfer
performance.

##  1 Introduction

Neural style transfer (NST) methods seek to transform an image to emulate a
given appearance or ‘style’ while holding the content or structure unchanged.
Efficient, stylistically diverse NST remains an open challenge. Feed-forward
NST methods are fast yet typically fail to represent a rich gamut of styles.
At the same time, optimization based approaches can take several seconds or
minutes at inference time, lacking the speed for practical, creative use.
Moreover, NST algorithms are often driven by one or more exemplar ‘style’
images, rather than an intuitive parameter space, impacting their
controllability as a creative tool.

In this work, we propose a fast feed-forward method for driving neural
stylization (NST) parameterized by a metric embedding for style
representation. Our approach is based upon a hyper-network trained to emit
weight updates to a StyleGAN2[13] model, trained on a large dataset of
artistic portraits (e.g. AAHQ [16]) in order to specialize it to the depiction
of the given target style. Our work is inspired by the recent StyleGAN-NADA
[5], in which a CLIP [20] objective is optimized by fine-tuning a pre-trained
StyleGAN2 model to induce NST. We extend this concept to a feed-forward
framework using a hyper-network to generate the weight updates. Furthermore,
we introduce the use of a metric parameter space (ALADIN [22]) originally
proposed for style driven visual search to condition the hyper-network
prediction (vs. CLIP in [5]) and adaptively drive this parameterization using
a semantic map derived from the source and target image. Without loss of
generality, our experiments focus on the challenging domain of facial
portraits driven using a semantic segmentation algorithm for this content
class. We show our method improves target image content retention versus the
state of the art while retaining comparable accuracy for diverse style
transfer from a single model – and despite using a hyper-network exhibiting
comparable inference speed to leading feed-forward NST [19]. Moreover, our
method exhibits good controllability; using a metric space for our style code
enables intuitive interpolation between diverse styles and region-level
controllability of those parameters. We adopt the recent ALADIN style code for
this purpose, raising the novel direction of unifying style based visual
search and stylization from a single representation.

##  2 Related Work

Neural Style Transfer (NST) The seminal work of Gatys et al. [6] enabled
artistic style transfer through neural models. This work demonstrates the
correlation between artistic style and features extracted from specific layers
in a pre-trained vision model. The AdaIN work [8] introduced parameterized
style transfer through first and second moment matching, via mean and standard
deviation values extracted from random target style images. MUNIT [9] explores
domain translation in images through the de-construction of images into
semantic content maps and global appearance codes. ALADIN [22] explored the
creation of a metric space modeling artistic style, across numerous areas of
style. The embedding space was trained in conjunction with AdaIN and a
modified version of the MUNIT model and weakly supervised contrastive learning
over the BAM-FG dataset. A follow-up work [21] studying multi-modal artistic
style representation expanded upon ALADIN, pushing the representation quality
further through a vision transformer model. CycleGAN also explored domain
transfer in images, but through learned model weight spaces, encoding pairwise
image translation functions into separate generators for each image domain.
Enforced by cyclic consistency, the translation quality between a pair of
image domains was high, at the cost of requiring bespoke models for each
domain translation to be trained. Using StyleGAN as a generator model,
Swapping Autoencoders [19] directly learn the embedding of images into a
StyleGAN generator’s weight space while simultaneously encoding a vector
representation of the visual appearance of an image externally. These models
separately focus on landscapes, buildings, bedrooms, or faces.

StyleGAN Inversion The evolution of the StyleGAN models [12, 13, 10] explore
generation of extremely realistic portrait images. They use weight modulation
based editing of visual appearance in the generated images. They also
undertake preliminary investigations into the inversion of existing images
into the GANs’ weight spaces for reconstruction. The work in e4e [26] includes
an undertaking of a deeper analysis of real image embedding into the StyleGAN
weight space, including the quality/editability tradeoff this imposes. Their
work enables multiple vectors of editability for images generated through
StyleGAN across several domains. Restyle [1] improves the reconstruction
quality of images embedded into the weight space by executing three fine-
tuning optimization steps at run-time. Also, using StyleGAN as target
generators, HyperStyle [2] embeds real portrait images into the weight space
with high fidelity. Similar to our approach, they use a hyper-network to
generate weight updates for StyleGAN, trained to infer weights to bridge the
gap between quick rough inversions and the fully detailed reference portrait
images. Strengths of this approach are the high reconstruction fidelity and
strong photorealistic editing control for portrait photos. They further
undertake some early explorations at domain adaptation for images by changing
StyleGAN checkpoints. However, the HyperStyle work focuses on photorealism and
does not enable region-based control or style space parameterization as we
propose in HyperNST.

Our approach is inspired by the StyleGAN-NADA [5] work, which explores style
transfer in the StyleGAN weight space through CLIP-based optimization. Though
effective, this incurs long-running optimization passes, which are impractical
for wide use. Moreover, this method has no built-in methods to effectively
embed real portrait images into the weight space for reconstruction and
editing. Recently, FaRL [28] undertakes representation learning of facial
images, through multi-modal vision-text data, with face segmentation models
that cope well with various visual appearances for portraits.

##  3 Methodology

Domain adaptation models like CycleGAN perform well at image translation,
where style features from a style image are correctly mapped to the matching
semantic features in a content image. A limitation of CycleGAN is that
transfer only between a single pair of image domains (styles) is possible.
Hypernetwork [7] models are used to predict the weights of a target model.
Such a hypernetwork can be conditioned on some input before inferring the
target model weights. Early experiments with a CycleGAN backbone yielded
promising results, especially when we re-framed the training process into a
more manageable task by learning weight offsets to a pre-trained checkpoint
rather than a from-scratch model. Motivated by these findings, we use a more
extensive, modern generator such as StyleGAN2 with weight updates predicted
using a hyper-network. This echoes the recent optimization based approach
StyleGAN-NADA which updates weights via fine-tuning for stylization rather
than hyper-network prediction. HyperStyle [2] uses a channel-wise mean shift
in the target generator, which significantly reduces the target number of
trainable weights into a practical range.

###  3.1 HyperNST Architecture

We compose the stylization pipeline of our model with a hyper-network set up
to generate weight deltas for a target frozen, pre-trained StyleGAN2 model.
Fig 1 shows an architecture diagram of HyperNST, showing the losses and the
conditioning process of the hyper-network upon the content image and
semantically arranged ALADIN style codes of the style image.

We direct the training to find a set of weight deltas for StyleGAN2, which can
generate the same image as the content image for reconstruction. We begin with
the GAN inversion, using e4e to reconstruct a given content portrait image
roughly. An encoder encodes this image into a tensor used by the hyper-network
weight generator modules along with style information to predict weight deltas
to apply to the frozen, pre-trained StyleGAN2. Stylization then occurs by
changing the style embedding in the hypernetwork conditioning.

###  3.2 Conditioning on style, and facial semantic regions

We further introduce conditioning on a target style image by injecting a style
representation embedding. We project the initial 16x16x512 encoding into
16x16x256, using ALADIN [22] codes to compose the other half of the 16x16x512
tensor. Each ALADIN code is a 1x256 vector representing the artistic style of
an image. We project semantically arranged ALADIN embeddings into a second
16x16x256, which we then concatenate together with the first to form the
16x16x512 tensor upon which the hypernetwork is conditioned.

Facial portraits are very heavily grounded in their semantic structure. We
therefore condition the stylization process on these semantic regions to
ensure that the content is maintained. We execute this using segmentation
masks extracted via FaRL [28].

To condition on semantic regions, we aim to use the ALADIN style code
representing only the style contained within a given semantic region. Given
that ALADIN codes can only be extracted from square or rectangular inputs, we
use the average ALADIN code extracted across several patches per semantic
region.

We use FaRL to compute the semantic regions, extract patches from the image
randomly, and use mean intersection over union (IoU) to ensure that patches
mainly cover pixels attributed to these respective semantic classes for each
region. The ALADIN codes from these patches are averaged to form the average
ALADIN code for a given semantic class. These average style codes are tiled
and re-arranged on a per-pixel basis to match the semantic segmentation maps
of the content image before they are projected by an encoder into the second
16x16x256 tensor, as above.

This projected 16x16x256 semantically arranged ALADIN tensor and the original
16x16x256 tensor encoded from the content image, are concatenated in the
channel dimension to 16x16x512, making up the final tensor which the
hypernetwork weight delta generating modules operate over.

Figure 1: Architecture diagram of our approach. Facial semantic segmentation
regions used in conditioning via ALADIN and guiding via patch co-occurence
discriminator a HyperStyle model into embedding a content portrait image into
an AAHQ+FFHQ trained StyleGAN2 model, and using ALADIN style codes to stylize
it towards the style of a style image. Blue modules represent frozen modules,
and orange modules represent modules included in the training. + represents
concatenation in the channels dimension. (A) represents the stylization pass
losses, and (B) represents the reconstruction pass losses. Not pictured for
clarity: the reconstruction pass uses the same semantic regions as the content
image for the 256x256x256 semantically arranged ALADIN conditioning.

###  3.3 HyperNST training process

We use three iterations per batch refining methodology during training. We
include a patch co-occurrence discriminator $D_{patch}$ to introduce a style
loss and an image-level discriminator $D$. The hypernetwork weight deltas
generator $H$ is conditioned on the encoded content images $E_{c}(c)$, and
ALADIN style codes arranged by the semantic segmentation mask of the content
image $M(x,E_{mask})$, seen in Eq 1.

$M(x,E_{mask})=E_{mask}\left(rearrange\left(\frac{\sum_{p=1}^{P}A(crop(x,SM_{x})_{p})}{P},SM_{c}\right)\right)$
(1)

$y(c,s)=G(\theta+H(M(s)^{\frown}E_{c}(c),A(s))))$ (2)

During training, two forward passes are executed, one for stylization (A) (Eq
2), and one for reconstruction (B). The reconstruction pass (B) loads content
images and their respective ALADIN style code arranged by the content image
semantic map and performs the original reconstruction code (Eq. 3). The
stylization pass (A) performs style transfer by loading the content images
$c$, and ALADIN style codes of other style images $s$. During stylization, the
generation is performed with the mixed features combined to create stylized
images, with the patch co-occurrence discriminator providing a learning signal
to train the stylization (Eq. 4). In this pass, the discriminator is also
trained, with the stylized images as fake, and the target style images as real
(Eq 5).

$\mathcal{L}_{rec}(c)=\left(c,y(c,c))\right)$ (3)

$\mathcal{L}_{pcd}(D_{patch})=\operatorname{\mathbb{E}}_{s\sim S,c\sim
C}\left[-log(D_{patch}(crops(s),crops(y(c,s))))\right]$ (4)

$\mathcal{L}_{disc}(c,s,D)=\operatorname{\mathbb{E}}_{s\sim S,c\sim
C}\left[-log(D(s,y(c,s))\right]$ (5)

where: $c$ is content image, $s$ is style image, $C$ are all content images,
$S$ are all style images, $\theta$ are the original StyleGAN2 weights, $H$ is
the hypernetwork weight delta generator, $G$ is the StyleGAN2 generator, $A$
is ALADIN, $P$ is number of patches per semantic region, $SM$ are pre-
extracted semantic segmentation masks, and ⌢ represents concatenation.

$\mathcal{L}=\lambda_{1}\mathcal{L}_{rec}+\lambda_{2}(\mathcal{L}_{disc}+\mathcal{L}_{pcd})$
(6)

The final loss is shown in Eq. 6, with Sec.4.3 describing ablations for the
$\lambda$ values.

###  3.4 Stylized target generator

The hypernetwork model is trained to infer weight delta values for weights in
a StyleGAN2 model, which acts as the generator. Given that we work in the
artistic style domain, we thus need the target generator to be able to model
the weight space of a generator already able to produce high quality highly
stylized images. We thus first fine-tune an FFHQ [11] StyleGAN2 model on the
Artstation Artistic Face (AAHQ) dataset [16]. Largely popular in research
centered around the facial images domain, the FFHQ dataset has been used by
the majority of reference papers targeting this domain. Given our exploration
into artistically manipulating the visual features of portrait images, we
further use this AAHQ dataset, which encompasses portraits from across a large
and varied corpus of artistic media. We continue to include FFHQ images, to
ensure we keep high quality modeling capabilities for features more often
found in photographic images than artistic renderings (like glasses and
beards) to ensure real world images can still be encoded well.

We first train our model simply for ALADIN conditioned reconstruction of the
AAHQ and FFHQ datasets for all layers, including the toRGB layers, which have
been shown to target textures and colors [2]. We then fine-tune this pre-
trained checkpoint with the goal of stylization, where we include the patch
co-occurrence training for guidance and ALADIN code swapping in conditioning
for style transfer.

During the stylization fine-tuning step, we freeze the content encoder and
train only the hypernetwork weight delta prediction modules. This is to
prevent the stylization signal from negatively affecting the model’s embedding
abilities to reconstruct real images with high accuracy.

We run the stylization fine-tuning only on the part of the target StyleGAN
layers. We find that the further into the StyleGAN2 model we apply stylization
fine-tuning, the more the stylization affects colorization rather than
textures and adjustments to the structure. We include the toRGB layers
originally omitted in HyperStyle for their texture adjustments, and we train
the weight deltas generation modules for layers 13 onward (out of 25). The
weight delta generation for layers before this are frozen after their initial
training, therefore still allowing reconstruction, but no more extended
training during the stylization stage. This ensures that the overall facial
structure of the images is not too greatly affected during stylization
training. Layer 13 is a sweet middle spot with the best balance between
stylization and retaining good face structure reconstruction. A visual example
of this phenomenon can be seen in Fig.3.

We further make changes to the patch co-occurrence discriminator. The Swapping
Autoencoders model generates images in 1024x1024 resolution, with a
discriminator operating over 8 patches of 128x128 dimensions. Our hypernetwork
model generates images with a resolution of 256x256 pixels, therefore, we
adjust our discriminator’s patch sizes to a lower size of 32x32.

###  3.5 Region mask driven patch discriminator

We also use facial semantic segmentation masks in the patch co-occurrence
discriminator, to provide a style signal separated by semantic region.

In the original discriminator, patches are extracted from across the entire
image at random. Instead, our process is repeated for each semantic class’
map. Patches are extracted at random, ensuring that the mean intersection over
union (IoU) mostly covers pixels attributed to the respective semantic class.
As in the original case, the losses from the patches are averaged to form the
style learning signal. However, instead of comparing the stylized patches with
patches randomly selected from the reference style image, we select patches
bound by the respective semantic region - e.g. style hair patches are matched
with stylized hair patches, background with background, face with face, etc.

####  3.5.1 Implementation

The semantic regions predicted by FaRL contain several regions which
individually cover only small areas in the pixel space. Given our use of the
regions as patches we extract for ALADIN and the patch co-occurrence
discriminator, we could not accurately use these small regions without the
patches mainly containing pixel data from the surrounding regions. Instead, we
group up the regions into 3 larger classes which typically cover larger areas
of a portrait: (1) Hair, (2) Face, and (3) Background. Due to overlap that
cannot be avoided, the Face region also contains eyes, noses, and lips.
Furthermore, some images do not contain hair, for which this semantic class is
not used. In the semantically driven patch co-occurrence loss, we use 3
patches for each region, totaling 9 patches.

##  4 Evaluation

Experiments generally required around 24 hours to converge. We ran our
experiments on a single NVIDIA RTX 3090 with 24GB of VRAM. The HyperNST
experiments were executed with a batch size of 1, which required around 22GB
of VRAM, due to the high number of weights needed in the hypernetwork
configuration.

###  4.1 Datasets

We create a test dataset for use in evaluation, using images from FFHQ [11],
and AAHQ [16]. We extract 100 random content images from FFHQ and 100 random
style images from AAHQ. Together, these result in 10’000 evaluation images,
when models are used to stylize all combinations.

We measure the content similarity using the two LPIPS variants (Alexnet [15],
and VGG [25]), and we measure the style similarity using SIFID.

LPIPS [27] evaluates the variance between two images based on perceptual
information better aligned to human perception compared to more traditional
statistics based methods. We use this LPIPS variation to compute the average
variation between each stylized image and its original content image. A lower
average variation value would indicate a more similar semantic structure,
therefore, a lower value is better.

Like Swapping Autoencoders, we employ the Single Image Fréchet Inception
Distance (SIFID) introduced in SinGAN [23]. This metric evaluates FID, but
uses only a single image at a time, which is most appropriate when evaluating
style transfer computed using a single source sample. A lower value indicates
better style transfer here.

Finally, we measure the time it takes to synthesize the stylized image in
seconds per image. A low inference time is essential for the practicality of a
model in real use cases. All timings were computed on an RTX 3090 GPU.

###  4.2 Baselines

To test the performance of our approach, we train 7 other methods on the FFHQ
and AAHQ datasets: Swapping Autoencoders [19], Gatys [6], ArtFlow [3], PAMA
[17], SANet [18], NNST [14], and ContraAST [4]. From these, Swapping
Autoencoders is the most closely related, as it also operates over a StyleGAN2
space, thus, we separate it from the other more traditional methods which do
not.

Table 1 shows the LPIPS, SIFID, and timing results computed for our own
HyperNST method, and the other methods we evaluate against. The results show
the superiority of HyperNST in retaining the most semantic structure in the
facial reconstructions, indicated by the lowest LPIPS value. Meanwhile, we
achieve comparable SIFID values (2.279) to Swapping AutoEncoders (1.948),
indicating a small gap in stylization quality. Only our HyperNST model can
embed a portrait into a model with semantic editing capabilities. Finally, the
inference time of our model is similar to other methods and low enough for
practical use of the model in real applications.

One disadvantage of the hypernetwork based approach is the current limitation
with how strongly the StyleGAN2 model can be fine-tuned. As per our findings
and the HyperStyle authors’, hyper-learning weight deltas for every individual
weight would be infeasible on current hardware (requiring over 3 billion
parameters for a StyleGAN2 model) - we are limited by the technology of our
time. So at best, we can aim to at most match a method where the model is
fully trained, the closest comparison being Swapping AutoEncoders. The
Swapping AutoEncoders model also fine-tunes a StyleGAN2 model. However, the
more straightforward training approach affords the luxury to fine-tune
individual weights in the generator, compared to the channel-wise mean shifts,
currently possible with a hyper-network on today’s hardware.

Model | LPIPS (Alexnet) | LPIPS (VGG) | SIFID | Time (s/img) | Interpolation | Editing
---|---|---|---|---|---|---
SAE [19] | 0.334500 | 0.4857 | 1.948 | 0.10 | ✓ | ✗
HyperNST (ours) | 0.000042 | 0.0017 | 2.279 | 0.35 | ✓ | ✓
Gatys [6] | 0.000164 | 0.0030 | 1.369 | 14.43 | ✗ | ✗
ArtFlow [3] | 0.000080 | 0.0022 | 1.347 | 0.32 | ✗ | ✗
PAMA [17] | 0.000109 | 0.0029 | 0.522 | 0.14 | ✓ | ✗
SANet [18] | 0.000180 | 0.0068 | 0.486 | 0.11 | ✓ | ✗
NNST [14] | 0.000149 | 0.0030 | 0.871 | 55.40 | ✗ | ✗
ContraAST [4] | 0.000133 | 0.0035 | 0.666 | 0.10 | ✗ | ✗
Table 1:  Overall results, comparing metrics for our model’s content, style,
and timing and the closest most similar model, Swapping AutoEncoders (top),
and some further, more traditional methods (bottom). All methods were trained
using AAHQ as the style dataset and FFHQ as the content dataset.

Nevertheless, hyper-network based NST is interesting to study, as such
limitations are temporary. Both model and hardware improvements with
subsequent works will reduce such limitations in time. We can compare hyper-
network approaches directly with fully-trained counterparts for the current
state of the art.

Figure 4 visualizes some style transfer results obtained with a Swapping
Autoencoders (SAE) model, re-trained with the AAHQ dataset. Figure 2 shows the
same visualization, obtained with HyperStyle. It is worth noting that the SAE
model generates 1024x1024 images, whereas the target StyleGAN2 model in the
hypernetwork setting uses a smaller, 256x256 version. Quality of stylization
is somewhat equivocal for these approaches; in most cases, the SAE results are
slightly more faithful in their style transfer accuracy but are less faithful
at retaining the semantic structure of the portraits vs. HyperNST. The SAE
model also has difficulty stylizing backgrounds.

Style loss strength | LPIPS (Alexnet) | LPIPS (VGG) | SIFID
---|---|---|---
0.5 | 0.001480 | 0.002657 | 3.312
1.0 | 0.001310 | 0.002626 | 2.590
2.0 | 0.000042 | 0.001688 | 2.279
5.0 | 0.000097 | 0.000191 | 2.463
10.0 | 0.000091 | 0.000222 | 2.571
Table 2: Ablation results for varying the style loss strength Figure 2: Qualitative HyperNST visualization of portrait style transfer. Figure 3: Representative visualization of the effect of choosing where in the target StyleGAN2 layers to start fine-tuning hyper-weight generators for. The left-most image is the reference content image, and the right-most is the reference style image. In the middle, from left to right, images represent visualizations for layers 3, 7, 13, 17, and 22. Figure 4: Baseline comparison to Swapping Autoencoders (re-trained with AAHQ), the closest work - a fully per-weight-trained model. Layer | LPIPS (Alexnet) | LPIPS (VGG) | SIFID
---|---|---|---
3 | 0.000140 | 0.00399 | 3.123
7 | 0.000190 | 0.00302 | 2.792
13 | 0.000042 | 0.00169 | 2.279
17 | 0.000153 | 0.00268 | 3.337
22 | 0.000042 | 0.00104 | 3.506
Table 3: Ablation results for varying the starting StyleGAN2 layer past which
layers are included in the stylization fine-tuning.

###  4.3 Ablations

Figure 5: Stylization comparison of HyperNST (1st pair), against Artflow
(2nd), NNST (3rd), Gatys et.al (4th), ContraAST (4th), SANet (5th), and PAMA
(6th)

We perform the stylization fine-tuning on only part of the StyleGAN2 layers’
hyper-weight generators. Out of 25 layers, we find layer 13 to be a good
balance between inducing style transfer and retaining semantic structure. The
earlier the target StyleGAN2 layers that hyper-weight generators get fine-
tuned for stylization, the stronger the emphasis on style is, therefore losing
structure reconstruction quality. Conversely, the later the starting layer is,
the less pronounced the stylization is, thereby focusing the training more on
the semantic reconstruction quality and instead just performing a color
transfer. Figure 3 shows a representative visualization of this effect, and
Tbl. 3 shows quantitative metrics. The images further to the left represent a
deeper fine-tuning of layers of style and losing structure. The images to the
right show a more shallow fine-tuning for style, retaining more structure from
the original content image. We targeted these specific layers, as these are
toRGB layers in the target StyleGAN2 layer, which are known to more
significantly affect color and texture.

Finally, we ablate the use of facial semantic region information in the model
and training pipeline. We explore the effect of including the semantic regions
as a conditioning signal in the pipeline (cond) and as a way to match region
types in the patch co-occurrence discriminator (loss). We populate the results
in Tbl4, showing the usefulness of these components.

Experiment | LPIPS (Alexnet) | LPIPS (VGG) | SIFID
---|---|---|---
Baseline (with both cond and loss) | 0.00004 | 0.0017 | 2.279
No mask cond and no mask loss | 0.00017 | 0.0024 | 2.892
No mask cond | 0.00012 | 0.0025 | 2.848
No mask loss | 0.00016 | 0.0026 | 3.438
Table 4: Ablation results for varying the facial semantic information used in
the architecture.

###  4.4 Downstream experiments

Figure 6: Visualization of style interpolation between a content image, and a
target style image. Note in this example, we show that a non-portrait style
image can also be used.

####  4.4.1 Style interpolation

In Figure 6, we visualize a controllability aspect of the stylization process
based on interpolations done in ALADIN style space. Basing the stylization
upon a metric style embedding space, it is possible to perform smooth
transitions between the style of a reference content image and a target style
image. We also show in this example that it is possible to perform stylization
using style images not containing portraits. In this case, the image-wide
ALADIN code is used instead of semantically arranged per-feature ALADIN codes.

Figure 7: Semantic face/portrait editing capabilities. The top two example
rows range across the age vector, the second two example rows show the smile
vector, and the third shows the pose rotation vector.

####  4.4.2 Semantic controlability

One advantage over the SAE model is the editable method of GAN inversion that
the HyperNST model uses. Coupled with InterFaceGAN [24], latent directions in
the StyleGAN2 weight space can be used to expose semantic controls over
portrait aspects such as age, pose, and facial expression. On top of the
artistic style aspects of the style transfer capabilities of HyperNST, these
semantic abilities offer a deeper level of artistic control over the editing
and generation of portraits. Figure 7 visualizes some style transfer examples,
where these latent directions are also used in tandem for more advanced
control. We show the smile, pose, and age vectors.

##  5 Conclusion

We explored a novel application of a class of models, hypernetworks, to the
task of style transfer. We explored the merits and drawbacks of such an
approach and what is currently possible. The hypernetwork approach is
excellent at maintaining high quality semantic structure and allows for
artistic controls, such as semantic editing and style-code-based stylization
interpolation.

The main limitation of the current implementation of hyper-weight prediction
is the very high VRAM consumption of such a model (22GB for a batch size of 1)
during training, forcing weight deltas to affect the target generator only on
a per-channel mean shifting basis. It is possible that the style transfer
quality could be pushed further with a larger batch size. For example, the
batch size used by Swapping Autoencoders is 16. This could be mitigated by
exploring smaller alternatives to StyleGAN2, or by implementing GPU
optimization tricks such as memory/compute tradeoff training approaches based
on gradient checkpointing. Such reductions in VRAM use could also afford an
increase in batch size, bringing the training more in line with previous
works, primarily affecting discriminators. A more promising direction could be
to more deeply analyse which layers can be omitted from training (i.e. need
not be updated by the hyper network). In this paper, we focused our attention
on the domain of human portraits. However, other domains would be equally
important to study, further generalizing this novel approach to neural
artistic stylization using more general semantic segmentation techniques or
larger semantically diverse models such as StyleGAN XL, once hardware evolves
to support hyper-network inference of larger models’ weights.

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Topological Signal Processing on Quantum Computers for Higher-Order Network Analysis

Caesnan M. G. Leditto
School of Physics and Astronomy, Monash University, Clayton, VIC 3168, Australia

Angus Southwell

Quantum for New South Wales, Haymarket, NSW 2000, Australia

Behnam Tonekaboni

Quantum Systems, Data61, CSIRO, Clayton, VIC 3168, Australia

Gregory A. L. White

School of Physics and Astronomy, Monash University, Clayton, VIC 3168, Australia
Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany

Muhammad Usman

Quantum Systems, Data61, CSIRO, Clayton, VIC 3168, Australia
School of Physics, The University of Melbourne, Parkville, VIC 3052, Australia
School of Physics and Astronomy, Monash University, Clayton, VIC 3168, Australia

Kavan Modi
Quantum for New South Wales, Haymarket, NSW 2000, Australia
School of Physics and Astronomy, Monash University, Clayton, VIC 3168, Australia

Predicting and analyzing global behaviour of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modelling complex systems using networks endowed with multiway interactions among nodes, known as higher-order networks. In this context, simplicial complexes are a class of higher-order networks that have received significant attention due to their topological structure and connections to Hodge theory. Topological signal processing (TSP) utilizes these connections to analyze and manipulate signals defined on non-Euclidean domains such as simplicial complexes. In this work, we present a general quantum algorithm for implementing filtering processes in TSP and describe its application to extracting network data based on the Hodge decomposition. We leverage pre-existing tools introduced in recent quantum algorithms for topological data analysis and combine them with spectral filtering techniques using the quantum singular value transformation framework. While this paper serves as a proof-of-concept, we obtain a super-polynomial improvement over the best known classical algorithms for TSP filtering processes, modulo some important caveats about encoding and retrieving the data from a quantum state. The proposed algorithm generalizes the applicability of tools from quantum topological data analysis to novel applications in analyzing high-dimensional complex systems.

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