Towards Croppable Implicit Neural Representations
Authors: Maor Ashkenazi
Eran Treister
Venue: NeurIPS 2024 poster (2024)
Keywords: Implicit Neural Representations
Implicit Functions
Deep Learning
Primary area: deep_learning_architectures
TL;DR: In this paper we present Local-Global INRs, a novel INR architecture that supports cropping encoded signals by design, ensuring a proportional weight decrease, without retraining.

Abstract: Implicit Neural Representations (INRs) have peaked interest in recent years due to their ability to encode natural signals using neural networks. While INRs allow for useful applications such as interpolating new coordinates and signal compression, their black-box nature makes it difficult to modify them post-training. In this paper we explore the idea of editable INRs, and specifically focus on the widely used cropping operation. To this end, we present Local-Global SIRENs - a novel INR architecture that supports cropping by design. Local-Global SIRENs are based on combining local and global feature extraction for signal encoding. What makes their design unique is the ability to effortlessly remove specific portions of an encoded signal, with a proportional weight decrease. This is achieved by eliminating the corresponding weights from the network, without the need for retraining. We further show how this architecture can be used to support the straightforward extension of previously encoded signals. Beyond signal editing, we examine how the Local-Global approach can accelerate training, enhance encoding of various signals, improve downstream performance, and be applied to modern INRs such as INCODE, highlighting its potential and flexibility. Code is available at https://github.com/maorash/Local-Global-INRs.

Towards Croppable Implicit Neural Representations
Maor Ashkenazi Ben-Gurion University of the Negev maorash@post. wwwp://oottttuuuu.ooooo agu.ac.il
Eran Treister Ben-Gurion University the Negev erantêcs www.:eccs.bu.cc.. ag.
Abstract
Implicit Neural Representations (INRs) have peaked interest in recent years due to their ability encode natural signals using neural networks. While INRs allow for useful applications such as interpolating new coordinates and signal compression, their black-box nature makes it difficult to modify them post-training. In this paper we explore the idea of editable INRs, and specifically focus on the widely used cropping operation. To this end, we present Local-Globe SIRENs novel INR architecture that supports cropping by design. Local-Global SIRENs are based on combining local and global feature extraction for signal encoding. What makes their design unique is the ability to effortlessly remove specific portions an encoded signal, with a proportional weight decrease. This is achieved by eliminating the corresponding weights from the network, without the need for retraining. We further show how this architecture can be used to support the straightforward extension of previously encoded signals. Beyond signal editing, we examine how the Local-Global approach can accelerate training, enhance encoding of various signals, improve downstream performance, and be applied to modern INRs such as INCODE, highlighting its potential and flexibility. Code available at httpps//gthhbb.ccmmmmmras/////// ooca://aooooaaooaaaaaoolllllaala ocal-Globall-NNRs
Introduction
Neural networks have proven to be an effective tool for learning representations of various natural signals. This advancement offers a paradigm of representing signal without explicitly defining The general idea behind an implicit neural representation (INR) is to model the signal as a prediction task from some coordinate system to the signal values that coordinate system. This is usually performed using a Multi-Layer Perceptron (MLP). composed of fully connected layers. Once trained, the signal has been implicitly encoded in the weights of the network. These implicit representations have been shown to be useful in various scenarios from interpolating values at new coordinates 22] through signal compression
and can be treated embeddings for downstream tasks [3.
Although INRs exhibit flexibility within their input space and are well-suited for tasks involving high- dimensional data, their black-box nature makes the encoded signal difficult modify post-training. A trivial strategy involves editing the original signal, followed by training a new INR to encode the modified signal. Another option fine-tuning the existing INR encode the modified signal, but requires preserving the INR size and architecture, which may not be ideal. Other methods attempted apply direct ransformations on the weight space modify the encoded signal [42 30).
In this paper, our primary focus is on the fundamental signal editing operation of cropping. We wish be able to remove parts of the encoded signal, with a proportional decrease of INR weights. Although not possible in previous approaches, in principle this should be obtained without any additional fine-tuning, since conceptually does require encoding additional information. As secondary task, we wish to extend an encoded signal effectively. This is not trivial in a simple setting, since encoding additional information may require increased capacity in terms of parameters, and altering the number of parameters makes it difficult to leverage previously encoded information.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

---

200
# of Parameters (K)
Local Parameters
100
Global Parameters
50
100
199K Parameters
80K Parameters
47.7K Parameters
% of Image Cropped
Figure 1:
Examples of cropping a Local-Global SIREN with 199k parameters. Plot on the right shows the number of parameters as function of cropped partitions in the encoded image.
As natural way to obtain our goals, we first partition the input signal space. The granularity of the partitioning will determine the ability to edit the INR with greater detail. straightforward approach involves training a compact INR for each partition of the signal. Subsequently, cropping and extending signals are simple.
crop specific partitions, one simply eliminates the INRs corresponding to those partitions. To extend INRs, new signal partitions can be seamlessly incorporated by training additional compact INRs on the new partitions, subsequently adding them the ensemble. Notably, this straightforward approach offers significant speed benefit. While requiring unique implementation, utilizing an ensemble of compact INRs for both encoding and reconstructing the signal is much more efficient than fully connected INR. Indeed, in KiloNeRF (35) 3D scene was encoded by adopting the INR- Per--er--Parttion approach, leading to notable improvements rendering times.
However, this partitioning approach lacks global context, resulting in increased reconstruction erro and undesired artifacts. In [5), this was solved using knowledge distillation. Initially, large INR was trained to encode the entire signal. Next, the encoded representation was distilled into the ensemble of compact INRs. While this approach facilitates rapid rendering. it involves a more intricate training process, demanding additional time to train both the full INR and the compact INRs.
In this work, we present a novel INR architecture based on the premise of combining both local and global context learning. Local features are learned via multiple compact local sub-networks, while global features are learned via larger sub-network. The features of the local and global networks interleaved throughout the forward pass, resulting in relatively high reconstruction accuracy, without additional training steps, while also gaining latency improvements due to the local feature learning. While these ideas can be applied to any MLP-basee INR, we focus on SIREN [38 for its quality and widespread popularity. We further explore INCODE 20.. a state-of-the-an (SOTA) INR, as potential baseline architecture. We summarize our contribution as follows:
We propose Local-Global SIRENs, novel INR architecture that supports cropping parts of the signal with proportional weight decrease, as depicted in Figure I all without retraining.
We analyze Local-Global SIRENS' inherent tradeoff between latency and accuracy by tuning the granularity of input space partitioning.
We show how Local-Global SIRENs can be leveraged to extend a previously encoded signal.
We apply the Local-Global architecture on INCODE and solve various downstream tasks, demonstrating the adaptability of our proposed approach.
We present cases where Local-Globe INRs improve upon the baseline INRs.
2
Related work
Implicit neural representations INRs have found applications in many diverse tasks such as image super resolution 8 31]. image inpainting (38, zero-shot image denoising (2I) image compression [1], image interpolation [ video encoding [6), camera pose estimation 45 and encoding the
weights neural networks [3]. Another work demonstrating the versatility INRs, [3] has shown that they can be treated as data points, utilizing their weights as latent vectors for downstream tasks. For 3D shapes, the works 28 T0
34 approached the task by formulating mapping from
3D coordinates to occupancy, Alternatively,
B3 has characterized the task as Signed Distance

---

Function (SDF). [39 expanded upon this concept by incorporating information related to object appearance. Based on these foundations, [2 predicted the density and color of points within a 5D coordinate system. This approach facilitated the incorporation of high-frequency details through
the use of positional encodings. A parallel concept, introduced by [38. utilizes sine non-linearities
to encapsulate high-frequecyy details. (00 extended upon this idea, by introducing a harmonizer
network tasked with modifying the properties of the nonlinearities. Alternatively, [II] leveraged multiscale representations, gradually incorporating finer features throughout the layers.
Editing neural representations The realm of editing INRs is still in early stages.
42
introduced methods for applying signal processing operators to INRs, involving high-order derivative computation graphs. Alternatively, [30] addressed the challenge of weight space symmetry by proposing an architecture tailored for learning within these spaces. This architecture can later be used directly edit the weights of a given network. Shifting to 3D scenes, (7] demonstrated scene editing through point cloud manipulation, while [17] introduced a learned color palette for dynamic color changes. Style transfer for INRs was explored by [16], while [43] focused on shape geometry modification, offering techniques for smoothing and deformation.
Input space partitioning Processing local regions by input space partitioning has shown promise in improved capturing of local details. [5] 27 proposed learning a local latent vector per partition. The former passed the latent vector as an input to the INR, while the latter used as input for a modulator function. Both have shown that when encoding scenes with intricate details, partitioning allows for finer detailed reconstruction. Similar ideas were presented in 40
g used multiple INRs, handling partitions of different resolutions, and [41] proposed an extension by clustering partitions based on shared patterns. Similar clustering methods where leveraged for 3D) face modeling [46] 47).
1 used an INR with sparse heads, corresponding to image partitions, to improve generalization. Partitioning was additionally used to enhance compression capabilities. Specifically, [14] proposed compression scheme, where preliminary partitioning step is performed on large scale signals. Similarly, employed a hierarchical tree structure, sharing parameters among similar partitions.
Partitioning has also been used to optimize latency. 37 accelerated training by employing multiscale coarse-to-fine INRs and dynamically selecting regions needing finer details. While compelling, this results in uneven weight distribution throughout partitions of the signal, hindering cropping with relative weight reduction. 225 accelerated convergence by partitioning the input signal space via se- mantic segmentation and training smaller INRs per segment. 23 accelerated INRs by independently learning each input dimension, which shares a resemblance to partitioning methods. Inspired by long 3D rendering time, [35 [5] offered alternative compact INR-per-pand perr-paartiionn approaches. As mentioned before, while these methods could apply to our case, we aim to avoid the extra full INR training step.
3 Method
3.1
Background
In its core, an INR is mapping function, F: X' + V. where X' C " is the input coordinate space, J C RT is the values space, and F a neural network. An RGB image, for example, corresponds to X C R² for pixel coordinates and y C RR3 for RGB values. A standard choice for F is MLP, meaning it is composed of series of fully connected linear layers, followed by non-linear activation functions. Before being passed to the network, the input coordinates undergo some transformation. In SIREN, the input coordinates are normalized, commonly to (-1,1), 1). and the activation functions are sine. A SIREN layer is defined by 1,(x) sin (w (W; x + b,)), where W., b, are the learned parameters of layer I, and w a hyperparameter representing the frequency of the sine wave.
3.2 Partitioning the signal
We begin by partitioning the signal, as cropping is achieved at the partition level. We assume the input coordinate space &' can be bounded by an n dimensional hyperrectangle, where the i-th dimension has boundaries [Bi B Each dimension is split into C, equally sized partitions, resulting in I C, non-overlapping partitions. The coordinate values are determined before partitioning and remain unaltered thereafter. Each of the partitions is indexed by coordinates, (Po, Pi,..., Pa-1) E N", where E P, S C.. This process is demonstrated Figure 2 point p with coordinates (Po. Pi..... ......PPa .p-11) is mapped to its respective partition by:
3

---

(1
B Po
B 1
))
Partition(p)
Pn-1
Ap
where A;
Bin Bunn represents the size of each partition in dimension i.
C;
3.3
Local-Global architecture
Our architecture is composed of Local Sub-Networks, each responsible for a specific partition, and Global Sub-Network, familiar with the entire signal. This de- sign facilitates simultancous extraction of local features using the former and global features using the latter. The Merge Operator is responsible for combining the intermediate local and global features throughout the architecture. Here, for example, we describe our ap- proach with SIREN the baseline INR, utilizing sine nonlinearities throughout the network. An overview of our proposed architecture is demonstrated in Figure
B min
A
B
B
A
B
Local sub-networks We employ multiple local sub- networks, each for specific partition without shared weights, for total of II C, net-networks. The lo- cal sub-networks are composed of SIREN layers, inter- leaved with the merge operator, described below. The final layer of each local sub-network outputs the parti- tion's 's values. Given an input point p, we pass it on to the local sub-network corresponding to Partition(p). Cropping is natively supported by eliminating entire local sub-networks. While similar to the idea of KiloNeRF, in Local-Global SIRENs we do not require additional pre-training knowledge distillation steps, significantly reducing overheads.
Figure Example of partitioning an image. This trivial example uses Co 3, Ci To achieve flexible cropping, one must choose larger partition factors.
Global sub-network While the local sub-networks are able to extract details of local patterns, they lack global context, resulting in subpar reconstruction accuracy compared to SIREN. This is demonstrated qualitatively in Figure 4 and quantitatively throughout our experiments. To remediate this, utilize an additional SIREN, termed the global sub-network. Its objective is to extract features that are crucial for the global context of the signal. The global features are subsequently combined with the local features through the merge operator. The global sub-network comprises compared to the local sub- networks; it does not output signal values but is used solely to augment the intermediate local features with global contextual information.
less layer
Merge operator The merge operator performed per coordinate, meaning that a coordinate's local features are only merged with the same coordinate's 's global features, upholding the definition of an INR. The merge operator consists (1) a concatenation operation, and (2) a linear layer with a subsequent activation function. The linear layer reduces the concatenated vector's 's size, to the hidden size of the local sub-networks. given by:
Merge(L, G) = (concat( GJ) W bbb
where L and G represent the local and global features, respectively. The term denotes the activation function, in our case, sine. W and are the weight matrix and bias term of the linear layer, respectively, and are shared throughout the network.
3.4 Cropping and extending signals
Cropping is achieved the partition level, meaning the precision of the cropping operation is directly influenced by the granularity of input space partitioning smaller partitions enable more precise cropping. Cropping involves identifying local sub-networks associated with the selected partitions for removal, and eliminating their weights. In our experiments, we show that for image encoding, using partitions 32 x 32 pixels results in respectable reconstruction accuracy, even surpassing the baseline INR. Recall that our objective for the cropping operation is to remove a number of weights proportionate to the removed segment of the signal, all without retraining. Since the weights of the global sub-network and the merge operator, collectively referred to as the

---

(b) Local Sub-Networks
Po
(Ro. Go. Bo)
Partition
(R,, Gy, B,)
P1
Po
SIREN Layer
Merge Operator
(Po. Pı) )= Input Batch
P
Global Sub Network
Figure 3: Illustration the Local-Globe SIREN architecture and inference flow for two image coor- dinates po: P1- The coordinates are passed through (a) the global sub-network and their partition's corresponding (b) local sub-network. Note that the coordinates are distinct elements in a batch, meaning that a coordinate's ' local features are only merged with the same coordinate's global features.
global weights, must be preserved, they should ideally encompass relatively small part of the overall architecture. Additionally, opting for a larger global sub-network increases training and inference times due the quadratic increase in the floating point operations associated with the fully connected layers. We found that allocating 5-15% of the parameters to the global weights is sufficient for achieving the desired reconstruction accuracy, while also facilitating accelerated training and inference speeds, given by the dominance of the local sub-networks in the architecture.
Extending encoded signal may also be achieved at the partition level. Since cannot exclude a learning stage, the process is achieved by including additional local sub-networks, corresponding to the newly encoded partitions, followed by fine- fine-tuning steps. As some partitions of the signal are already encoded, we use them to initialize the new weights. Similar to a mirror padding operation, at the signal's 's borders, copy the local sub-network's weight symmetrically. We show in Section 4.4 that this process allows improved encoding of concatenated partitions compared to alternatives.
3.5 Additional properties
An interesting attribute of our proposed architecture is its capability to balance between the accuracy of the reconstructed signal and the efficiency, terms of training and inference speeds, achieved by tuning the partition factors. Increasing the number of partitions reduces neuron interconnectivity thus enhancing speed, while reducing them results in more accurate encoding. This is explored naturally exploit cases
in Section 4.5 Another interesting finding is that the local sub-networks with significant differences between partitions. Consequently, our method manages to capture local details with fewer iterations. A qualitative example of this phenomenon provided in Section 4.2
3.6 Automatic partitioning and implementation
Our implementation offers either fixed or automatic signal partitioning configurations. With automatic partitioning. the purtition factors and sub-nelwork hidden dimensions are automatically determined based on the target partition size (c.g., 32 x 32 pixels in an image). This automatic approach reduces manual hyperparameter tuning and streamlines the training process of a Local-Global SIREN. Additional details are in Appendix
A We implement the local sub-networks using a custom locally connected (LC) layer, leveraging torch's batched matrix matrix-multipl. multiply operation-bmun, significantly outperforming a trivial implementation. During training, we use a batch containing the same number of sampled coordinates in each partition. If needed, to reconstruct only the requested partitions.
portion of the LC layer's 's weights
Limitations While Torch-bmm has been useful in our case, it is known to be unstable, in terms of latency, across different GPUs. addition, as cropping possible at the partition level, limited in terms of flexibility. However, the extensive experiments presented highlight our method's potential.
5

---

SIREN-per- SENN-per-Partiiinn Partition
Local Local-Global SIREN
29.64
31:11
30 74
32
9.34
27.40
28.60
29 09
31
SIREN
Initialization
250 Iterations
500 Iterations
750 Iterations
1000 Iterations
Figure 4: Encoded images throughout training iterations. PSNR values are at the top left of each image. Method names the left. Notice the artifacts in the SIREN-per-Partttion method and the reduced noise in our approach compared to SIREN. For extended qualitative results of various signals and cropping operations, refer https :/stte///teeeeeeeeeeeeeeeeeeeee google. wwtp:iie//iiiiieeeeeeeeeee -aaooccllllllaalll.o inns
Experiments
We evaluate our method on various signal encoding tasks and compare it to alternatives. To our knowledge, no other INR architecture supports cropping as we outlined carlier. Existing methods either necessitate an extra knowledge distillation step. or do not uniformly distribute weights across signal partitions, as in MINER 37 Thus, we compare our approach to an INR-per-Partition and full INR. We focus on SIREN as baseline, and later examine INCODE for various tasks. We use roughly the same network size when comparing methods. The full configuration and networks' size for experiments to method based on knowledge distillation is redundant. For completeness, Appendix C shows why an approach like 35 does not trivially improve image encoding, and Appendix D demonstrates limitations of hierarchical approach like MINER. in providing the discussed cropping capabilities.
Appendix B Since we manage to improve upon a full INR, comparing
We start with image, audio, video, and 3D shape encoding tasks. Local-Global SIRENs consistently outperform TRREN-per-Partinee granularity. Due to space constraints, 3D shape experiments are Appendix Next, we present how Local-Glohe Global SIRENs allow extending a previously encoded signal, explore the tradeoff between latency and accuracy when choosing the partitioning factors, and explore the effects of global weight ratios. We further apply our Local-Global approach on INCODE, evaluating it on image encoding and various downstream tasks, showcasing its potential for boosting downstream performance. To ensure fair comparison, we primarily followed the default omega values and learning rates from baseline methods. In some experiments, we made slight adjustments to the learning rate, ensuring that the selected values benefit all compared architectures. We the experiments multiple times a single Nvidia RTX3090. For most experiments, we report the mean Structural Similarity (SSIM) with the mean and standard deviation of the Peak Signal-to-Noise Ratio (PSNR), Additional ablation experiments are in Appendix
and surpass SIREN while facilitating cropping in relatively fine
4.1 Image encoding
We begin by evaluating our method image encoding tasks. Qualitative results visualizing the training process on the famous 512 x 512 Cameraman image, using partition factors Co 16, Ci = 16 are shown in Figure Next, from the DIV2K dataset [2], we have randomly selected subset of

---

25 images which were downsampled by factor of four before training. We have trained Local-Global SIRENs using both fixed and automatic partitioning configurations. For the fixed scheme, we set the partition factors to Co- = 16, C1 = 16, thus splitting images into partitions ranging from 21-32 pixels, with the global weights comprising 8% of the network. The automatic scheme used a target partition size of 32 x 32 pixels, automatically selecting partition factors, and the global weights accounted for roughly 11% of the network on average. Each network was trained for 2k iterations with a [ presents the mean SSIM and PSNR values on the DIV2K subset, demonstrating the efficacy Local-Global SIREN. These results indicate our approach significantly improves upon the SIREN-per- Per-Partiiionn baseline without requiring additional training steps.
learning rate of 5 10 Table
39.26
Table 1: Mean encoding results on 25 DIV2K images
using five random seeds per image. Automatic parti- tioning uses partition factors 11 I C. S 16 to ensure 32 x 32 pixel partitions. SPP, LGS stand for SIREN- per-Parition and Local-Global SIREN, respectively.
Ground Truth
SIREN- S-REN--er-Paaree Partition
Partition Factors
48
39, 94
Method
SSIM
PSNR (dB) f
SPP
(16, 16)
0.957
31.73 = 0.63
SPP
Auto
0.955
31.90 + 0.64
LGS (ours)
(16, 16)
0.968
33,94 + 0.64
Local-Global SIREN
SIREN
LGS (ours)
Auto
0.971
34.13 + 0.59
Figure 5: Encoded Bach audio clips. Mean PSNR values using 10 random seeds are on the top left of each figure.
SIREN
0.966
33.57 = 0.65
4.2
Audio encoding
We continue by evaluating our method on encoding audio clips, taken from 38
We encode the first 7 seconds of Bach's Cello Suite No. I: Prelude (Bach), and a 12 second clip of an actor counting 0-9 (Counting). We use a partitioning factor Co 32, allowing cropping in roughly 220 ms and 370 intervals, respectively. The global weights account for 10.5% of the network. We train each network for 1K iterations with learning rate of 10-1 Local-Global SIRENS significantly outperform other methods, as seen in Figure 5 The local sub-networks can exploit the heterogencous nature of audio partitions, showcasing less noise in silent regions, and noticeable improvement in accuracy. Due to space constraints, quantitative results for both clips are in Appendix G
4.3
Video encoding
Next, we evaluate our method on a video encod- ing task. We encode the 12 second cat video from (38), which has a spatial resolution of 512 x 512 and contains 300 frames. We use partition factors Co = 5, C1 = 8, C2 = 8, meaning we split the video in both the tem- poral and spatial dimensions. After training, the video can be cropped 2.4s intervals, of 64xc x4 pixels. The global weights take up 3.5% of the network. We train each network for 5k iterations with a learning rate of 10 10-4, Another useful property of Local-Global SIRENs is its lower memory bandwidth constraints, allowing more pixels to be sampled per training iteration when encoding these large signals. We provide results for sampling 38 10-4% of pixels, fol- lowing the original paper, and demonstrate the effect of sampling more. The mean SSIM and PSNR values, computed on all frames, are pre-
-Time
31 20
31.34
32.10
SIREN Partitatio (*)
32,20
32.47
33. 80
Local-Global SIREN (*)
Figure 6: Three frames of an encoded video. PSNR is at the top left of each frame.
7

---

sented in Table 2 Qualitative results of three frames is in Figure 6 While SIREN-per per-Partition achieves respectable results, artifacts remain apparent. Local-Glote Groaal SIREN significantly reduces these artifacts and captures details better than SIREN. Cropped video examples are in Appendix H
4.4 Extending encoded image
We present how Local-Global SIRENs allow extending a previously encoded signal. We start by encoding the top 512 256 pixels of the Cameraman image from Section 4.1] using a SIREN and Local-Global SIREN. both roughly 55% the size of the networks previously used. In our method, extending signal is done by adding new local sub-networks, corresponding to the novel partitions. followed by fine-tuning. Thus, we add 16 x 8 local sub-networks, We compare this strategy with (1) fine-tuning the smaller SIREN on the entire signal, and (2) training a new full-sized SIREN. Figure 7 shows that, unsurprisingly, our approach outperforms both methods, since it can scale up the number of parameters while leveraging previous knowledge. Notice how fine-tumie finettning the smaller SIREN stagnates fast, as it lacks capacity to encapsulate the entire signal. An extended plot is in Appendix
Table 2:
Mean video encoding results, using 10 random seeds. (*) next to method stands for sampling 2 (00%% of pixels in each iteration. SPP, LGS stand for SIREN SIREN-per- peee--errtioon and Local-Global SIREN, respectively.
Menn Squared Error (MSE)
Smaller SIREN (FT)
10
Local-Globul SIREN (FT)
SIREN (FS)
Method
SSIM
PSNR (dB) f
SPP
0,826
29.58 + 0.02
10
200
400
800
LGS (ours)
0.854
30.28 0.05
Iteration
SIREN
0.815
29.71 + 0.09
Figure 7: Log-scaled training MSE for extending previously encoded image, using 10 seeds. Our approach (green) outperforms alternatives. FT, FS stand for fine-tuning and from-scratch, respectively.
SPP
0.854
30.83 0.01
LGS (*) (ours)
0.888
31.91 + 0.02
4.5
Partitioning and global weights effects
There is an inherent tradeoff between latency and accuracy in Local-Global SIRENs, achieved by tuning the signal partition factors. To demonstrate the tradeoff, we encode the Cameraman image from Section
and the cat video from Section 4.3 using various partition factors. Results are in Table Note how enlarging the partition factors leads to faster training. while decreasing the partition factors enhances reconstruction accuracy, surpassing SIREN. We additionally explore the extreme case of setting the partition factors to in Appendix J Next. explore the effect of adjusting the ratio of global weights in the network. As shown Table 4 larger global weights do not significantly boost accuracy and sometimes have adverse effect.
Table 3: Effect of partitioning on latency and accuracy. Results averaged on 10 seeds.
Partition Factors
MSE
Train
Signal
Model
SSIM
PSNR (dB) t
(-10-4)
Time (s)
(2, 2)
11.2
0.946
32.59 = 0.52
74
(4, 4)
12.0
0.946
32.10 + 0.47
Local-Global SIREN (ours)
Image 512 x 512
(8, 8)
13.5
0.942
32.29 # 0.42
26
(16, 16)
15.3
0.934
32.00 + 0.39
22
(32, 32)
19.0
0.917
31.51 0.28
15
SIREN
18.4
0.914
31.17 0.68
(5, 4, 4)
32.8
0.862
30.95 + 0.07
386
Local-Global SIREN (ours)
Vidco 300 x 512 x 512
(5,
34.7
0.854
30.28 + 0.05
284
(5, 16, 16)
41.8
0.834
29.52 + 0.03
244
SIREN
43.4
0.815
29.71 0.09
2354

---

4.6 Local-Global INCODE
To further highlight the potential of the Local-Global approach, we examine the SOTA INCODE [20] INR as potential baseline. INCODE contains main MLP, harmonizer and task-specific network. For a Local-Global INCODE, we modify the main MLP as seen earlier. The harmonizer, which configures properties of the nonlinearities, is adapted output modulators for the local sub-networks, global sub-network and merge operator (i.e. scalars). Since the task-specific model (e.g., ResNet 18] is pre-trained and may remain frozen, do consider its weights -pp-ccici... We compare Local-Globs INCODE to INCODE and an INCODE-Per-Pariing
on the image encoding task from Section 4.1 with results shown Table 5 The global parameters constitute 15.5% of the network, with the harmonizer taking an additional 3%. We train each network for 2k iterations, with
learning rate of 10 3 for local weights and 5.5 10 for global weights.
Table 4: Encoding the Cameraman image (Sec- tion 4.1 and the cat video (Section 4.3) using differ- ent proportions of global weights, using 10 seeds.
Table 5: Mean encoding results 25 DIV2K images using five random seeds per image. We partition factors Co 8, C1 8. IPP, LGI stand for INCODE-pers Pere---e--aarttion and Local-Globh INCODE, respectively.
Global Weights (%)
PSNR 1 (dB)
Signal
SSIM
11.6%
0.934
32.00 + 0.39
Method
SSIM
PSNR (dB) 1
Image
22.9%
0.931
32.24 + 0.48
33.5%
0.925
32.06 # 0.41
IPP
0.963
36.42 + 0.10
LGI (ours)
0.974
39.03 # 0.16
3.5%
0.854
30.28 + 0.05
Video
INCODE
0.963
38.79 # 0.38
10.2%
0.850
30.04 + 0.07
30.01
0.904
29.81
0.881
31,23
31.01
GT
LG INCODE
INCODE
GT
LG INCODE
INCODE
32.37
0,866
32.26
0.864
Noisy Image
LG INCODE
INCODE
Figure 8: Local-Global (LG) INCODE applied to downstream tasks. Top-left: 4x image super- resolution, top-right: CT reconstruction, bottom: image denoising. Mean PSNR and SSIM values across 10 seeds are displayed in the top-left and top-right corners of each frame, respectively.
Downstream tasks INCODE showcased SOTA results various downstream tasks. We demon- strate our approach's ability to boost downstream performance by replicating key experiments from the original paper: image denoising, super-resolution, and CT reconstruction. Qualitative results are in Figure training configuration is in Appendix B.2 and full details and results are in Appendix K
Conclusions and future work
In this paper we introduced Local-Global INRs, a novel architecture extension designed to seamlessly support cropping operations with proportional weight decrease, without an additional pre-training or fine-tuning step. Local-Global INRs utilize both local and global contextual information, and have have surpassed alternative methods in terms of reconstruction accuracy. We further demonstrated how adjusting the signal partitioning allows for a balance between latency and the accuracy of reconstructed signal. Furthermore, we have showcased instances where Local-Global INRs outper- form the baseline INR's s reconstruction accuracy, illustrated their capability to extend a previously encoded signal, and demonstrated their use in enhancing downstream performance. We believe our

---

proposed method represents stride towards editable INRs and hope our findings will inspire further exploration into the design of INRs that inherently support modifications.
There are several directions for future work. Firstly, exploring additional architectural modifications, such alternative merge operators, to refine our method's s capabilities. Next, extending the Local- Global approach to INRs beyond MLP-based networks holds promise. Additionally, incorporating semantically meaningful partitions, as presented in [25], into our Local-Global architecture might further accelerate training and improve quality, Lastly, with Local-Global INRs representing each partition with a fixed amount of weights, there potential in leveraging these networks for partition- based downstream tasks within INRs, as an extension to ideas in [13.
Acknowledgements and disclosure of funding
The authors thank the Israeli Council for Higher Education (CHE) via the Data Science Research Center and the Lynn and William Frankel Center for Computer Science BGU.
References
[1] Arya Aftab, Alireza Morsali, and Shahrokh Ghaemmaghami. Multi-head relu implicit neural representation networks. In ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2510-2514. IEEE, 2022.
[2] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, July 2017.
[3] Maor Ashkenazi, Zohar Rimon, Ron Vainshtein, Shir Levi, Elad Richardson, Pinchas Mintz, and Eran Treister. NeRN: Learning neural representationn for neural networks. In The Eleventh International Conference Learning Representations, 2023.
[4] Mojtaba Bemana, Karol Myszkowski, Hans-Peter Seidel. and Tobias Ritschel. X-fields: Implicit neural view-, light- and time-image interpolation. ACM Transactions Graphics (Proc. SIGGRAPH Asia 2020), 39(6), 2020.
[5] Rohan Chabra, Jan E Lenssen, Eddy 1lg, Tanner Schmidt, Julian Straub, Steven Lovegrove, and Richard Newcombe. Deep local shapes: Learning local sdf priors for detailed 3d reconstruction. In European Conference on Computer Vision, pages 608-625. Springer, 2020.
[6] Hao Chen, Bo He, Hanyu Wang. Yixuan Ren, Ser Nam Lim, and Abhinav Shrivastava. Nerv: Neural representations for videos. Advances in Neural Information Processing Sys- tems, 34:21557-21568 2021.
[7] Jun-Kun Chen, Jipeng Lyu, and Yu-Xiong Wang. NeuralEditor: Editing neural radiance fields via manipulating point clouds. In CVPR, 2023.
[8] Yinbo Chen, Sifei Liu, and Xiaolong Wang. Learning continuous image representation with local implicit image function. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages (628-8638 2021.
[9] Zhang Chen, Yinda Zhang, Kyle Genova, Sean Fanello, Sofien Bouaziz, Christian Häne, Ruofei Du, Cem Keskin, Thomas Funkhouser, and Danhang Tang. Multiresolution deep implicit functions for 3d shape representation. In Proceedings of the IEFF/CVF International Conference on Computer Vision (ICCV), pages 13087-13096. October 2021.
[10] Zhiqin Chen and Hao Zhang. Learning implicit fields for generative shape modeling. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 5939-5948 2019.
[11] Yishun Dou, Zhong Zheng, Qiaoqiao Jin, and Bingbing Ni. Multiplicative fourier level of detail. In Proceedings of the IEEF/CVE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1808-1811 June 2023.
10

---

[12] Emilien Dupont, Adam Goliñski, Milad Alizadeh, Yee Whye Teh, and Arnaud Doucet. Coin: Compression with implicit neural representations. arXiv preprint arXiv:2103.03/23, 2021.
[13] Emilien Dupont, Hyunjik Kim, SM Eslami, Danilo Rezende, and Dan Rosenbaum. From data to functa: Your data point is function and you can treat it like one. arXiv preprint arXiv:2201. 12204, 2022.
[14] Emilien Dupont, Hrushikesh Loya, Milad Alizadeh, Adam Goliński, Yee Whye Teh and Amaad Doucet. Coin++: Neural compression across modalities. arXiv preprint arXiv:2201. 12904, 2022.
[15] Stefano Esposito, Daniele Baieri, Stefan Zellmann, André Hinkenjann, and Emanuele Rodola. Kiloneus: A versatile neural implicit surface representation for real-time rendering. arXiv preprint arXiv:2206.10885, 2022.
[16] Zhiwen Fan, Yifan Jiang. Peihao Wang, Xinyu Gong, Dejia Xu, and Zhangyang Wang. Unified implicit neural stylization. In European Conference on Computer Vision, pages 636-654. Springer, 2022.
[17] Bingchen Gong, Yuehao Wang, Xiaoguang Han, and Qi Dou. Recolomert: Layer decomposed radiance fields for efficient color editing of 3d scenes. arXiv preprint arXiv:2301.077 10795,, 2023.
[18] Kaiming Hc, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image 2015.
recognition. CoRR,
[19] Chiyu Max Jiang, Avneesh Sud, Ameesh Makadia, Jingwei Huang, Matthias Nießner, and Thomas Funkhouser. Local implicit grid representations for 3d scenes. In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), 2020.
[20] Amirhossein Kazerouni, Reza Azad, Alireza Hosseini, Dorit Merhof, and Ulas Bagci. Incode: Implicit neural conditioning with prior knowledge embeddings. In Proceedings of the IEEE/CVF Winter Conference Applications of Computer Vision, pages 1298-1307, 2024.
[21] Chaewon Kim, Jaeho Lee, and Jinwoo Shin. Zero-shot blind image denoising via implicit neural representations, 2022.
[22] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR), San Diega, CA. USA. 2015.
[23] Ruofan Liang, Hongyi Sun, and Nandita Vijaykumar. Coordx: Accelerating implicit neu- ral representation with a split MLP architecture. In International Conference on Learning Representations, 2022.
[24] David B Lindell, Dave Van Veen, Jeong Joon Park, and Gordon Wetzstein. Bacon: Band-limited coordinate networks for multiscale scene representation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 16252-16262, 2022.
[25] Ke Liu, Feng Liu, Haishuai Wang, Ning Ma, Jiajun Bu, and Bo Han. Partition speeds up learning implicit neural representations based exponential-increase hypothesis. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5474-5483, 2023.
[26] Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In International Conference Learning Representations, 2019.
[27] Ishit Mehta, Michaël Gharbi, Connelly Barnes, Eli Shechtman, Ravi Ramamoorthi, and Man- mohan Chandraker. Modulated periodic activations for generalizable local functional represen- tations. In Proceedings of the IEEE/CVF International Conference Computer Vision, pages 14223,, 2021.
[28] Lars Mescheder, Michael Occhsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. Occupancy networks: Learning 3d reconstruction in function space. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4460-4470, 2019.
[29] Ben Mildenhall, Pratul Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. 2020.
11

---

[30] Aviv Navon, Aviv Shamsian, Idan Achituve, Ethan Fetaya, Gal Chechik, and Haggai Maron. Equivariant architectures for learning in deep weight spaces, arXiv preprint arXiv:2301.12780 2023.
[31] Quan H Nguyen and William J Beksi. Single image super-resolution via a dual interactive implicit neural network. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 4936-4945, 2023.
[32] Ntumba Elie Nsampi, Adarsh Djeacoumar, Hans-Peter Seidel, Tobias Ritschel, and Thomas Leimkühler. Neural field convolutions by repeated differentiation. ACM Trans. Graph., 42(6),
Dec 2023.
[33] Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. Deepsdf: Learning continuous signed distance functions for shape representation. In Proceed- ings of the IEEE/CVF conference computer vision and pattern recognition, pages 165-174, 2019.
[34] Songyou Peng, Michael Niemeyer, Lars Mescheder, Mare Pollefeys, and Andreas Geiger. Convolutional occupancy networks. In European Conference Computer Vision, pages 523-540. Springer, 2020.
[35] Christian Reiser, Songyou Peng, Yiyi Liao, and Andreas Geiger. Kilonerf: Speeding up neural radiance fields with thousands of tiny mlps. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14335-14345, 2021.
[36] Vishwanath Saragadam, Daniel LeJeune, Jasper Tan, Guha Balakrishnan, Ashok Veeraraghavan, and Richard G Baraniuk. Wire: Wavelet implicit neural representations. In Conf. Computer Vision and Putlern Recognition, 2023.
[37] Vishwanath Saragadam, Jasper Tan, Guha Balakrishnan, Richard Baraniuk, and Ashok Veeraraghavan. Miner: Multiscale implicit neural representation. In European Conference Computer Vision, pages 31 318-333. Springer, 2022.
[38] Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. Im- plicit neural representations with periodic activation functions. Advances in neural information processing systems, 33:7462-7473, 2020.
[39] Vincent Sitzmann, Michael Zollhöfer, and Gordon Wetzstein. Scene representation networks: Continuous 3d-structure-awwrt neural scene representations, Advances in Neural Information Processing Systems, 32, 2019.
[40] Edgar Tretschk, Ayush Tewari, Vladislav Golyanik, Michael Zollhöfer, Carsten Stoll, and Chris- tian Theobalt. PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations. European Conference on Computer Vision (ECCV), 2020.
[41] Meng Wang, Yu-Shen Liu, Yue Gao, Kanle Shi, Yi Fang, and Zhizhong Han. Lp-dif: Learning local ppttern-specffic deep implicit function for 3d objects and scenes. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pages 21856- 21865. June 2023.
[42] Dejia Xu, Peihao Wang, Yifan Jiang, Zhiwen Fan, and Zhangyang Wang. Signal processing for implicit neural representations. In Advances in Neural Information Processing Systems (NeurIPS), 2022.
[43] Guandao Yang. Serge Belongie, Bharath Hariharan, and Vladlen Koltun. Geometry processing with neural fields. In Thirty-Fifth Conference on Neural Information Processing Systems, 2021.
[44] Runzhao Yang. Tine: Tree-structured implicit neural compression. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18517-18526. 2023.
[45] Lin Yen-Chen, Pete Florence, Jonathan T. Barron, Alberto Rodriguez, Phillip Isola, and Tsung- Yi Lin. iNeRF: Inverting neural radiance fields for pose estimation. In JEEE/RSJ International Conference Intelligent Robots and Systems (IROS), 2021.
12

---

[46] Mingwu Zheng, Hongyu Yang, Di Huang, and Liming Chen. Imface: A nonlinear 3d morphable face model with implicit neural representations. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20343-20352 2022.
[47] Mingwu Zheng, Haiyu Zhang, Hongyu Yang, Liming Chen, and Di Huang. Imface++: A sophisticated nonlinear 3d morphable face model with implicit neural representations. arXiv preprint arXiv:2312.04028 2023.
13

---

A Automatic partitioning
The automatic partitioning determines the hidden layer dimensions based on the target network size, global weights ratio, and the selected partition size. Pseudo-code is available below.
Algorithm 1 Automatic Partitioning
1: function AUTOMATICPARTIIN PTTOOAATCAARTTTONNNNCieeeLLLLLLL burgt_glooal__eiihtt_ffat tar-
get partition_ssiei size, signal resolution)
2: groups -- COMPUUZNNNNGGGOUUUSSssaa//rooo,L Sarget_pprtitionn size)
3: global_hiddens dime <- FiNDDDMENSSOO/argLLLoopppppppp X target
4:
global_ -- COMPUUTEEGLOAAALWWEECCCSSSSpp _iddeen dim)
5: lnget_local_weighee +- Larget_total_parmssss wliial
6:
local_hidden_dimg +- FINDDMMENSSOMarrreeLooLLLvvvvni groups)
7:
local_weights CONPUTTELOOCA.IWNIHTTSSooolll
groups)
8:
while belobal_weighte local weights not within 1% of target_ total params do
9:
if shobal_wwiight + _eigght > target_toole tttal_oll_______
_or_a_paaaaassssss params then
@lobal_hiddent dii + global_ londden_dmmm- 11: else
globel_hidden global hidden dim + global hidden dim end if
13:
global_weights +- CoMerTTG..oo...aaasrrsooo...ad end while
15:
16:
return local foldenn_dii- global_hideel
17:
end function
18: function CoMprTTETONGRRUUUXsiieeeeeettttt
pergittoatition_siize
// Calculates the number of partitions
19: end function
20: function
// Calculates global weights based on hidden dimension
21:
end function
22: function MAAPUUTELOCALLIIGGSSSSS hhiddddeennh groups)
// Calculates local weights based on hidden dimension and groups end function
23:
24: function FINDDIMENSION(uaree (weigt count, groups) Uses binary search find the optimal dimension
25: end function
14

---

B Complete experiment configuration
B.1
Configuration for SIREN-based experiments
The configuration for all SIREN-based experiments in the paper is outlined in Table 6 For image encoding, audio encoding, and video encoding, we employ an AdamW scheduler [26] with learning rates of 5 10-4, 10 and 10- respectively. We sample the entire signal in each iteration, when encoding images and audio. For videos, we sample portion of pixels, described Section 4.3
The network hidden sizes remain fixed across layers, with all networks comprising five layers.
Table 6: Configuration of experiments based SIREN. For the automatic partitioning, report the mean number of parameters. LGS and SPP denote Local-Global SIREN (ours) and SIREN-per- Partition, respectively.
Experiment Scction
Parameters
Hidden Sizes
Partition Factors
Method
Iters
Total
Local
Global
Local
Global
Co
C₁
C2
Section
SIREN
198.4k
198.4k
256
1k
Cameraman
SPP
200k
200k 175.9k
Ik
(grayscale)
LGS
198.9k
23k
84
16
16
1k
SIREN
198.9k
198.9k
256
2k
Section 4.
SPP
208. 1k
208. 1k
15
16
16
2k
DIV2K
SPP(Auto)
207.2k
207.2k
15-18
11-16
11-16
2k
(RGB)
LGS
199k
183.6k
15.4k
14
68
16
16
2k
LGS(Auto)
200k
180.4k
19.7k
14-17
69-86
11-16
11-16
SIREN
198.1k
198.1k
256
1k
Scction 22
Audio
SPP
203k
203k
45
LGS
198.2k
177k
20.7k
42
72
1k
SIREN
3.19M
3.19M
1030
5k
Section 4 Vidco
SPP
3.19M
3.19M
LGS
3.19M
3.08M
111k
55
180
8
8
5k
Section
SIREN
111k
(Half Image)
LGS
11lk
88k
23k
84
16
8
2k
Section
STREN
198.4k
198.45 4k
(Full Image)
LGS
198.9k
175.9k
23k
14
84
16
16
1k
LGS
198.7k
153.6k
45k
1k
S.5tion
LGS
197.5k
173.7k
23.8k
59
72
1k
Image
LGS
198.4k
174.5k
23.9k
29
82
8
8
1k
Partitioning
LGS
198.9k
175.9k
23k
14
84
16
16
1k
LGS
210.6k
201.8k
8.8k
S.5
LGS
3.18M
3.0SM
131k
111
180
4
5k
Vidco
LGS
3.19M
3.08M
111k
55
180
Partitioning
LGS
3,25M
3.15M
104k
27
180
16
16
5k
S.c
LGS
198.9k
175.9k
23k
Weights
LGS
199k
153.3k
45.7k
13
120
16
16
1k
Image
LGS
199k
132.4k
66.7k
12
146
16
16
1k
S.ction
LGS
3.19M
3.08M
11
55
180
8
8
5k
Weights
LGS
3.19M
2.87M
325.3k
53
318
8
5k
Video
SIREN
198.7k
198.7k
256
27k
Appendix
SPP
199,9k 9k
199.9k
18
27k
3D Shape
LGS
199.2k
179.7k
19.5k
17
27k
15

---

B.2 Configuration for INCODE-based experiments
The configuration for all INCODE experiments in the paper outlined in Table Following the original paper [20], we use the Adam optimizer [22] and a step-wise exponential learning rate scheduler across all experiments. For the DIV2K image encoding experiment, we use learning rate of 10-3 for INCODE and the local weights of Local-Global INCODE. When training a Local-Global INCODE, we roughly halve the learning rate for the global weights. For the downstream tasks, we adopt the learning rates from the official implementation: 9 10 for super-resolution, 1.5 10-1 for image denoising, and 2- 10-1 for CT reconstruction. In each training iteration, the entire image is sampled. All networks comprise five layers, except for Local-Global INCODE in CT reconstruction, where we use three layers. The network hidden sizes remain fixed across layers.
Table 7: Configuration of experiments based on INCODE. The pre-trained ResNet parameters are excluded as they remain frozen during training. LGI and IPP denote Local-Global INCODE (ours) and INCODE- Partition, respectively.
Experiment
Parameters
Hidden Sizes
Partition Factors
# Iters
Method
Section
Total
Local
Global
Local
Global
Co
C₂
C2
INCODE
205.3k
205.3k
256
2k
Section 4.6
IPP
208.9k
208.9k 166.8k
31
8
8
2k
DIV2K
LGI
205.2k
38.4k
28
96
8
2k
Section Super Res.
INCODE
205.3k
205.3k
256
2k
LGI
205.7k
181.3k
24.4k
6
2k
Section 4.6 Denoising
INCODE
201.9k
201.9k
256
1k
LGI
196.2k
159.4k
36,8k
80
82
2
400
Section 4.6 CT Recon.
INCODE
327.5k
327.5k
2k
LGI
328.1k
220k
108. 1k
230
300
1
2
2k
16

---

C Training with knowledge distillation
Training a compact INR for each partition in the signal straightforward approach for achieving the desired cropping and extension capabilities. However, as seen across all the experiments in the paper, the INR-per- per-Partition approach is subpar in terms of reconstruction accuracy and exhibits undesired artifacts in the reconstructed signal. Our approach solves this issue by learning both global and local contextual features, even surpassing the baseline INR accuracy. In methods based on NeRF (29.. such as
35 15,, this is solved using knowledge distillation. Initially, large NeRF is trained to encode the entire signal. Subsequently, the encoded representation distilled into an ensemble of compact NeRFs using novel rendered views from the large NeRF. While this approach facilitates rapid rendering, involves a more intricate training process, demanding additional time to train both the full NeRF and the compact NeRFs.
We aim to avoid this additional training step. However, for completeness, we explore similar approach for encoding images using SIREN. We trained full SIREN on the subset of 25 DIV2K images presented in Section 4.1 Next, for each trained SIREN, we decoded the image upsampled by x2 by sampling novel pixels between each two original pixels (e.g.. for an image of size 512 x 512, we sample intermediate novel pixels, resulting 1023 1023 image). Subsequently, we trained PRREN-perPPartttion using the original pixels and the novel pixels extracted from the full SIREN. The results are presented in Table Unfortunately, the reconstruction accuracy degrades in terms of both SSIM and PSNR when training using the novel pixels. We have tried various configurations, training iterations, checkpoint selection methods, loss weighting schemes, and general hyperparameter optimization; however, the results remained consistent and did not improve. Note that even if the results improved due to knowledge distillation, they would likely be bounded by a full SIREN, which
Loal-GGlobi SIRENs manage to surpass. We hypothesize that the methods in [35 [3] work due to the unique characteristic of NeRF, which is novel view rendering. Thus, these methods may not necessarily work other domains and INR architectures.
Table 8: Results for encoding 25 images from DIV2K. Each image is encoded using five random seeds.
Partition Factors
PSNR (dB)
Method
Distillation
SSIM f
SIREN Partition Perraatt-- SIREN- BIREN-per-Partitinn Partitioo
(16, 16)
X
0.955
31.90 - 0.64
(16, 16)
v
0.953
31.64 0.50
Local-Global SIREN (ours)
(16, 16)
0.971
34.13 0.59
SIREN
0.966
33.57 + 0.65
17

---

D Comparison with MINER
employs multiscale coarse-to-fine INRs, encoding the Laplacian pyramid signals. To enhance training speed, MINER dynamically selects regions needing finer details. While compelling. this approach results an uneven weight distribution throughout the signal partitions, preventing cropping with relative weight reduction. To illustrate this, we have selected an image from the DIV2K dataset and encoded with MINER and a Local-Global SIREN. The results are shown in Figure ? Consider the scenario where one wishes to crop the image's s boundary to center the person, as depicted in figure. The border constitutes approximately 29% of the entire image. With MINER, most of the image border is encoded using coarse INRs, which cannot be removed. Consequently, only 2.8% of the entire weights can be discarded. However, using a Local-Global SIREN,
MINER 37
discard the entire local weights corresponding to the border, reducing approximately 27% of the INR weights. This example highlights that while intriguing, MINER'S coarse-to fine approach cannot offer two technical advantages over MINER: first, MINER'S s implementation only supports signals with equal spatial dimensions (i.e., square-shaped images cubic 3D scenes); second, since MINER dynamically allocates weights to different signal areas, the overall parameter count is challenging to calibrate and varies significantly between signals of the
general solution for croppable INRs. Additionally, Local-Global SIRENs
size. Figure 10 illustrates this issue. This issue does not affect Local-Global SIRENs, as the weights are distributed equally, and the neural network structure is fixed.
Original Image
Area to Crop
MINER
Local-Global SIREN
PSNR: 38.87 dB 205.2K Parameters
PSNR: 43.83 dB 198.9K Parameters
Figure 9: Illustration of cropping image using MINER and Local-Global SIREN (ours). From left to right: (1) The original image, (2) The area to be cropped out of the encoded signal (roughly 29% of the image), (3) MINER reconstruction, with colors indicating the coarse-to-fine scale and weight distribution. Only 2.9% of MINER weights can be discarded, and (4) Local-Global SIREN reconstruction with uniform scale, allowing 27% of the INR weights to be discarded.
MINER Parameter Count
5
4-
2-
1-
150
200
250
300
Parameter Count (K)
Figure 10: MINER parameter count histogram when encoding subset of 25 images from the DIV2K dataset (as described in Section 4.1 with the exact configuration.
18

---

E
3D shape encoding
We evaluate our method on 3D shape encoding task using the Lucy data from the Stanford 3D Scanning Repository (T] We follow the data processing strategy presented in [36 and use the implementation from [2]] Points are sampled on a 512 512 x 512 grid. Values of are given to voxels within the object and 0 to voxels outside. We use partition factors Co = 8, C1 = 8, C2 8, 64 x 64 voxels. We assign local sub-networks only to non-empty partitions, and the global weights account for roughly 10% of the network. In each iteration we sample 10 voxels, and train each network for roughly 27k iterations (20 epochs) using learning rate of 10-2 and step-wise exponential learning rate scheduler. We measure the Intersection over Union (loU) between the encoded and original shape. Results are presented in Complete configuration is in Appendix B.I
meaning we split the grid into partitions
Figure 11
Ground Truth
SIREN-per-Partition IoU: 0.9909
Local-Global SIREN IoU: 0.9920
SIREN IoU: 0.9904
Figure 11: 3D shape encoding results. On the top of each column is the method name and achieved loU score. Notice how Local-Global SIREN (ours) captures finer details with fewer artifacts than other methods, while facilitating cropping the shape 64 64 64 partitions.
sttpp://graphics.staattto stanford. www.afforr..tt/ttttt////aaaomam
19

---

Additional ablation experiments
F11
Alternative merge operator
To highlight the importance of carefully crafting the merge operator, we explore an alternative, more efficient option. We utilize smaller linear layer, that processes only global features. The new operator is given by:
Ferge (L, G) L + o(G W b)..
(2)
Results in Table indeeaindicate that, while more efficient, the alternative operator incurs a significant drop in accuracy.
Table 9: Comparison of merge operators when encoding the 512 512 Cameraman image. The original FF operator is compared against the more efficient FC+Add. Both use partition factors Co 16, C₁ 16, with the global sub-network hidden dimension set to 84 and the local sub-network dimension set to 14, resulting in similar number of parameters. Averaged 10 seeds.
Merge
PSNR t
Train
SSIM
Operator
(dB)
Time (s)
Concat+FC FC+Add
0.934
32.00 + 0.39
22
0.901
30.21 = 0.48
20
F.2
Network depth
Our chosen merge operator adds learned layer. As a result, instead of T. layers, as in the original SIREN, our network can be seen having 2T layers. To emphasize that the improved accuracy is result of capturing both local and global contextual features, rather than depth, we train Si with additional hidden layers. The results are presented in Table I0
Table 10: Evaluating the effeets of increasing the network depth for the SIREN-pe ieee-errtiiion method when encoding the 512 512 Cameraman image. We partition factors Co 16, C₁ 16. and the results are averaged over random seeds. The findings suggest that the effectiveness of Global SIRENs is result of merging local and global contextual features, rather than the number nonlinearities in the architecture.
#
PSNR 1 (dB)
Method
SSIM
Params
Layers
SIREN- -ee---ee--Pree per-Partition
194K
10
0.902
31.24 0.36
SIREN WIREN-per-Be pper-Partttion
236K
10
0.916
31.67 + 0.59
Local-Globa SIREN (ours)
199K
5
0.934
32.00 + 0.39
20

---

G
Audio quantitative results
Table 11: Audio encoding results after 1k training iterations. Averaged on 10 seeds.
Audio Clip
Method
Co
MSE (-10-5) 5) +
PSNR (dB)
SIREN-per-Partitee Partition
32
12
39.26 0.30
Bach (7s)
Local-Global SIREN (ours)
32
3
45.18 + 0.99
SIREN
10
39.94 0.75
SIREN-per-Partinn Partttaan
32
75
31.24 = 0.19
Counting (12s)
Local-Global SIREN (ours)
32
48
33.18 + 0.34
SIREN
62
32.07 = 0.32
Table 12: Audio encoding results after 5k training iterations. Averaged on 10 seeds.
Audio Clip
Method
Co
MSE (-10-5) 5) 4
PSNR (dB)
SIREN-per-Paritoon Partttiion
32
2.4
46.20 = 0.34
Bach (7s)
Local-Global SIREN (ours)
32
0.8
50.83 0.55
SIREN
1.3
48.93 = 0.60
EIREN-per-Partiin Partition
32
44
33.56 0.08
Counting (12s)
Local-Global SIREN (ours)
32
28
35.56 + 0.42
SIREN
38
34.20 0.13
21

---

H
Video cropping examples
(a) Spatial cropping along the borders across all frames. Remaining parameters: 1.84M.
(b) Temporal cropping where frames of roughly 5(s) are removed. Remaining parameters: 1.96M.
(c) Combined temporal and spatial cropping, where frames of roughly 7(s) cropped in specific spatial areas. Remaining parameters: 2.5M.
(d) Random cropping across different frames and spatial areas. Remaining parameters: 1.65M.
Figure 12: Cropping a video encoded a Local-Global SIREN, containing 3.19M parameters, with different cropping strategies.
22

---

I
Encoded image extension
10
Mean Squared Frror (MSF)
Smaller SIREN (FT)
Local-Global SIREN (FT)
10-
SIREN (FS)
10"3
0
1000
2000
3000
4000
Iteration
Figure 13:
Log-scaled training MSE for extended a previously encoded image when significantly increasing training iterations, using seeds. We pre-train and fine-tune for 4k iterations.
Setting the partition factors to 1
While our Local-Global SIREN with partition factors of Vi, C, might appear similar to regular SIREN, is important to note that the two architectures are significantly different. In this extreme case, Local-Global SIREN still involves two networks with features intertwined throughout the forward pass. This intricate architecture affects performance, as seen Table [3] for the Cameraman image encoding task discussed previously. Additionally, setting Vi, C, is somewhat analogous to INCODE, where a small modulator network augments the features of a large network. Thus, it not surprising that Local-Global SIREN in this case achieves high reconstruction quality, even though it does not explicitly perform local feature learning.
Table 13: Effect of setting Co, C1 1 when encoding the Cameraman image. Averaged on 10 seeds.
Partition Factors
MSE
Train
Model
SSIM
PSNR (dB) t
(-10-1)
Time (s)
Local-Global SIREN (ours)
(1,
12.9
0.939
32.52 0.66
87
SIREN
18.4
0.914
31.17 # 0.68
34
23

---

K Downstream tasks with Local-Global INCODE
For all downstream tasks, we replicate the setup from 20 using the official code implementation. Qualitative results are in Figure Quanititative results are in Table Full network configuration is in Appendix|B22 [3.2] addition, Table [5] presents results from an extended super-resolution experiment on 4x downsampled versions of the DIV2K subset, as outlined in Section
Image Denoising We use an image from the DIV2K dataset 22, resized 512 288 x 3 pixels. To create noisy image simulating realistic sensor measurement, we apply readout and photon noise. Specifically, the mean photon count (r) set to 40, and the readout noise set to signal-to-non ratio of 2. Since the objective is to denoise the image using an INR, and we wish to focus on reconstruction accuracy, we choose coarse partition factors for Local-Global INCODE, specifically Co C1 2.
We use publicly available 256 256 CT lung image from the Kaggle Lung Nodule Analysis dataset P A sinogram is generated from the ground truth image using the radon transform with 180 projection measurements. The INRs aim to predict a reconstructed CT image from the sinogram data. To guide the model toward generating CT images with reduced artifacts, the loss function is computed between the sinograms of the INR's predicted output and the ground truth sinogram derived from the original image. Since the objective is learn representations that align with the underlying projection data, we focus only on reconstruction accuracy, and use partition factors Co 2, C1 = 1 for Docal-Global INCODE. This partitioning strategy vertically divides the image into two halves, with each partition containing one the lungs. As seen the experiments throughout the paper, coarser partitions enhance quality while finer ones improve cropping capabilities and latency.
CT Reconstruction
Image Super-Resole Resolution We first replicate the experiment from 20 using image from the DIV2K dataset [2] resized to 1344 x 2016xx 3 pixels. We train INCODE and Local-Global INCODE to encode a 4x downsampled version of the image. During evaluation, capabilities of INRs to generate the full resolution image. We use partition factors C. = 6, C1 8, splitting the image partitions 56 x 63 pixels. Finally. we extend this setup larger-scale experiment on the previously mentioned DIV2K subset, maintaining the same configuration.
the inherent interpolation
Table 14: Mean results for downstream tasks across 10 random seeds, replicated from 20
Task
Method
SSIM t
PSNR (dB) f
Local-Global INCODE 0.866
32.37 0.08
Image Denoising
INCODE
0.864
32.26 0.06
Local-Global INCODE INCODE
31.23 0.14
CT Reconstruction
31.01 0.14
Local-Global INCODE
0.904
30.01 # 0.11
Image Super-Resolution
INCODE
0.881
29.81 0.11
Table 15: Extended mean super-resolution results on a subset of 25 DIV2K images.
Task
Method
SSIM t
PSNR (dB)
Local-Globe INCODE
0.734 0.703
26.76
Image Super-Resolution
INCODE
26.68
http://uuunll.ggann-chlhaleeeeee
24

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
The abstract and introduction accurately reflect the key claims and contribu- tions of the paper. Claim (1) that our proposed architecture can remove sections of the encoded signal with a proportional INR weight decrease an inherent part of our proposed architecture, demonstrated in Figure Tand explained in Section [3.4 Claim (2) of accelerated training is quantified in Table 3 Clam (3) that our approach can enhance encoding over
Justification:
the baseline INR is evidenced throughout the signal encoding experiments (e.g. Table [. Claim (4) that our architecture supports extension of previously encoded signals is shown in Figure 7 Claim (5) of improved downstream performance is demonstrated in Figure and Table 14 Claim (6) that our technique can be applied to modern INRs like INCODE is validated in Section 4.6
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as it is clear that these goals are attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: We discuss the limitations of our proposed method, covering both implementa- tion details and design aspects, dedicated highlighted paragraph at the end of Section To demonstrate the robustness of our results, we report the number of random seeds used for each experiment. Additionally, we validate our approach across various domains and instances, providing confidence in of our conclusions. Furthermore, we investigate the trade-off between the number of partitions and the accuracy of the reconstructed signal, showing that while significantly increasing number of partitions reduces training time, it also degrades the quality of the reconstructed signal (see Table 3). Regarding privacy and fairness considerations, we believe these issues not specific to area of research, but rather general concerns applicable to the machine learning field as a whole.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model sell-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested few datasets with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be
25

---

used reliably to provide closed captions for online lectures because it fails to handle technical Jargon.
The authors should discuss the computational efficiency of the proposed algorithms
and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimess.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [NA]
Justification: We do not cover theoretical results our paper, but rather justify our design choices through various experimental scenarios.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
statement of any theorems. The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
All assumptions should be clearly stated or referenced
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should properly referenced.
4. Experimental Result Reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: We provide details the full training setup used for all experiments in Appendix B These details include the optimizer, learning rates, network architecture, number of training iterations, and other hyperparameter settings. Additionally, we have released the code implementation of our proposed architecture, the training loop, and evaluation code, along with detailed README file to allow others to and reproduce our results. The specific signals (images, audio, video, etc.) that were used for training our models are also included in the supplementary materials.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution a novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same datasct, provide access to the model. In general. releasing code and data is often
26

---

one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how replicate the results, access a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm.
(b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e.g.. a large language model), then there should either be way access this model for reproducing the results way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reprodueibility may be tricky in some cases, in which authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g.. to registered users), but it should be possible for other researchers have some path reproducing verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification: We have released the code implementation of our proposed architecture, the training loop, and evaluation code, along with detailed README file to allow others to run and reproduce our results. The specific signals (images, audio, video, etc.) that were used for training our models are also included in the supplementary materials.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.. ec/
mublic/guided aoglliicguuiles/oodeebbbbassssss Poodeeubmissiioooolo
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
7 7/nips. cc/ httec/ubblllggguuue wwwpc//ggieseseeee Sttp:///SoooSSSsssiooieeeee
seiobbmmiisioooooccy.. for more details.
The authors should provide instructions data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental Setting/Details
Question:
Does the paper specify all the training and test details (c.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
27

---

Justification: For each experiment, we provide the important details necessary to understand and appreciate the results. For instance, Section 4.1 outlines the partition factors, global weights ratios, partition size in pixels, number of images used, their sources, number of random seeds, learning rate, and number of training iterations. We follow a similar approach of including relevant experimental details across other sections as well. The complete training setup configurations and network hyperparameters used in all experiments are in Appendix B
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, or as supplemental material.
7. Experiment Statistical Significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer: [Yes]
Justification: We test method various types of signals, with each experiment being run multiple times, For images, we also experiment of subset of 25 images from DIV2K, where we encode each of the images multiple times. We PSNR as encoding quality metric throughout all experiments, and add the standard deviation as well as its mean (see Section for details, and all other tables for information on number of seeds and PSNR standard deviation, e.g, Table Table 12) Due to space constraints, we did not add the standard deviation for SSIM.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information on the puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: We specify at the beginning of Section 4 that all experiments were run single Nvidia RTX3090 GPU with 24GB of RAM. This indicates that replicating all our experiments requires more than 24GB of available RAM. In Section 4.5 we report the
28

---

training time for image and video encoding tasks. While runtimes for other tasks are omitted due space constraints, the video encoding task serves as an upper bound, being the largest signal encoded in the main paper.
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary failed experiments that didn't make into the paper).
9. Code Of Ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics teattps://neuriss.oom httppp/ccccccc..ttt/ccheeecieeae
Answer: [Yes]
Justification:
We have read through the code of ethics and confirm to it.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No. they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (c.g.. there a special consid- eration due to laws or regulations in their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: Our work focuses on advancing the technical capabilities of implicit neural representations for signal encoding and editing, which does not directly introduce novel societal impacts. However, we acknowledge that the responsible development and deploy- ment of machine learning technologies requires consideration of potential risks and ethical concerns, which is relevant to the field whole.
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to partieular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
29

---

11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: Our work does not release any pretrained models, generators, or scraped datasets that could pose risks of misuse. We utilize standard datasets for experiments, and cite the sources when introducing them in the paper. Therefore, we feel safeguards for responsible release are not applicable.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: In our paper, we credit the creators and original owners of any existing assets (code, data, models) that were utilized. When introducing the datasets used for experiments, such those detailed in Section 4.1 and Appendix E we cite the relevant sources they were taken from. Similarly, for any existing codebases or specific data samples used as foundation for our work, like the data samples mentioned Section 4.3 and Section 4.2] we cite the source and clearly state the licenses (e.g., MIT) under which they were originally released our supplementary material. Additionally, our released code package includes README file that explicitly lists the MIT license and provides credits for any third-party codebases incorporated into our implementation.
Guidelines:
The answer NA means that the paper does existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset used and, possible, include URI..
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (c.g.. website). the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, wwwpssspppeesteeeeeeeepe thcode. com datasets has curated licenses for some datasets. Their licensing guide can help determine the license dataset.
For existing datasets that are re- re-packaged, both the original license and the license of the derived asset (if has changed) should be provided. If this information is available online, the authors are encouraged to reach out to the asset's is creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
30

---

Answer: [Yes]
Justification: The relevant asset in our case is the code implementation, which can be used to recreate the experiments presented in the paper. The supplementary material, which includes the code, provides detailed documentation on the license and instructions on running the code.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: This paper does not involve crowdsourcing experiments or research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then much detail as possible should be included the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/teview based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification:Thin paper does not involve crowdsourcing experiments research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
31


Reviews:
[{"review_id": "Ua11r95CUm", "reviewer": "Reviewer_45rR", "summary": "This paper proposes a new INR architecture to admit easy cropping of the target datum to a certain partition, allowing one to save memory and inference cost without any retraining. Comparing with training a new INR for the target partition, the approach lets one utilize the global context as well. The idea is to train multiple local networks, and modulate their intermediate features with the features of a global network. Through experiments on image/audio/video encoding, the paper demonstrates that the method enjoys faster and more accurate fitting than training one INR per partition. Also, the paper shows that the method works when combined with many INR architectures, e.g., SIREN and INCODE.", "questions": "Please see the \"weakness.\"", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "- A notable strength of the proposed method is that it is very simple and easy to use, making it likely to be scalable and generally applicable. I believe that the method can also be combined well with the triplane-based neural fields or instant-ngp.\n\n- The method is also very clearly presented. In particular, Figure 3 is very effective in delivering how the proposed architecture works.\n\n- Lastly, I appreciate the fact that the paper provides experiments on many different modalities, from image to video.", "weaknesses": "- **Utility of croppability?** The key weakness of this paper is the motivation. Apart from \"saving storage & compute,\" the practical utility of having a croppable INR is unclear; will local-global INRs also be useful in performing any subsequent \"editing\" operations? I suspect that this is why authors provide section 4.4, where the authors \"extend\" the LGS to parameterize the larger image than the one originally considered. However, for such purposes, there are already other good meta-learning-based solutions such as [26]. I am not sure why the model should be croppable for such applications.\n\n- **Novelty & Ablations.** The proposed method bears much similarity with [26], which modulates the local model with another global model. The key difference here is how we modulate; this paper uses an extra linear layer to process the local+global features, while [26] uses multiplications (later works, such as functa, used addition). To fully understand what this paper contributes, there should be an explicit comparison with these similar methods as a baseline.\n\n- **Evaluation.** If I understood correctly, the evaluation is mostly based on how the model fits the seen coordinates. I wonder how these affect the generalizability of the learned signal to unseen coordinates. As this is one of the key strengths of having a global context, I have enough reasons to believe that LGS will work well. However, an explicit verification is needed.\n\n- **Hyperparameter tuning.** I wonder how the hyperparameters for the models and the baselines are selected. In particular, how were the values of \"omega\" and the learning rate selected? These two are quite critical in determining the fitting speed, so this point should be crystal clear.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear reviewer, thank you for the constructive feedback. We appreciate the time and effort. Please see our comments and additional results below.\n\n**Utility of croppability**\n\nThe utility of our method stems from the inspiration for editable INRs. We began with the fundamental cropping operation and demonstrated various other benefits. The primary goal is the ability to identify which neural network weights to remove based on the required target signal in a zero-shot manner. Our method offers several additional advantages, as detailed in the paper: **improved accuracy** over the alternative INR-per-partition method and the baseline INR, **faster convergence** in terms of iterations and latency, and **enhanced performance** on various downstream tasks such as CT reconstruction, super-resolution, and denoising. Additionally, we showed its adaptability across multiple modalities.\n\nRegarding more advanced editing operations, we believe our proposed architecture provides a foundation for more sophisticated per-partition editing operations and downstream tasks. Methods that directly manipulate the network’s weight space, such as [29], can leverage the inherent locality of our method.\n\nRegarding section 4.4 - We demonstrate that our method can be used for extending signals. However, it does not compete with other meta-learning solutions. Instead, it serves as a *complementary* method, as one can meta-learn a good initialization for Local-Global INRs and benefit from both. Note that the additional benefit of extending signals with our method lies in the ability to *enlarge the number of weights* to fit larger signals, which is not possible with meta-learning-based solutions that require learning a new initialization. The intuition is demonstrated in Figure 7, where the small SIREN reaches stagnation since the large signal requires more parameters to properly encode.\n\n**Novelty & Ablations**\n\nWhile the mentioned method bears a resemblance, it does not support cropping of the encoded signal with proportionate decrease in neural network weights, which is the main goal of our architecture. Although [26] improved encoding capabilities with a local-global approach, the network remains a fully-connected INR and thus cannot be modified as discussed. In contrast, our method  leverages an NN architecture that uniformly distributes weights across signal partitions, inherently supports removing unwanted weights, and lays the foundation for future extensions of per-partition editing over the weight space.\n\nOn the other hand, one might consider our Local-Global SIREN (LGS) as a potential replacement for [26]’s synthesizer. This idea closely resembles our proposed Local-Global INCODE (LGI). In LGI, we retain the harmonizer (similar to the modulator in [26]) and replace the composer network (similar to the synthesizer in [26]) with a Local-Global version. Since LGI improved both encoding quality and performance on various downstream tasks, we believe replacing the modulator in [26] with a LGS could also enhance the method.\n\nHaving said that, we provide a comparison with [26] on the DIV2K subset mentioned in our paper. We trained [26] with the default configuration in the official implementation. Since their implementation currently only supports square images, we used the seven 512x512 samples from the DIV2K subset. The methods were trained from scratch on a single image for 2k iterations, sampling all coordinates in each iteration. Note that [26] requires significantly more training iterations (>60k) to converge, while our LGI achieves better performance after only 2k iterations. *Additionally, [26] has 5.5 times the number of trainable parameters compared to ours.*\n\n| | [26] | SIREN| LGS| INCODE| LGI | [26] (64k iterations) |\n|-|-|-|-|-|-|-|\n|Average PSNR|23.85|32.18|32.88|37.85|**38.37**|35.21|\n|#Params|1.1M|199k|200k|205k|205k|1.1M|\n\n**Evaluation**\n\nWe follow the evaluation methods used in many previous INR architecture papers, focusing on various signal encoding capabilities. Towards the end of our paper, we present three downstream tasks where our Local-Global version outperforms the baseline.\nRegarding generalizability, this is a great point that we also addressed in the paper (Section 4.6). Specifically, we train an INCODE and a LGI on a 4x downsampled version of an image and then evaluate the SSIM/PSNR on the full-resolution image. This experiment replicates the one presented in [20]. To provide further evidence of our method's generalizability, we conducted this experiment on the entire DIV2K subset (25 images) mentioned in the paper. The results below show that the Local-Global approach manages to enhance generalization capabilities compared to the baseline INR.\n| Method| Mean PSNR | Mean SSIM |\n|-|-|-|\n|INCODE|26.68|0.703|\n|LGI|**26.76**|**0.734**|\n\n**Hyperparameters**\n\nTo ensure a fair comparison, we used the same omega values as in the original SIREN and INCODE implementations. For the LR, we primarily followed the default configurations from baseline methods. In some experiments, we made slight adjustments to the learning rate, ensuring that the selected LR benefits all compared architectures. We will emphasize these points in the final revision of the paper.\n\nFor the Local-Global configuration, hyperparameters are selected using our automatic partitioning logic. This logic determines hidden layer dimensions based on a target network size and target global weights ratios (please refer to the general comment for the pseudocode). Detailed experiment configurations and hyperparameters can be found in Appendices A.1 and A.2, as well as in the provided code implementation.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "CqkPem3jMR", "reviewer": "Reviewer_AXyi", "summary": "The paper proposes a method for learning patchwise INRs that are integrated with a global INR. The method is designed with cropping in mind, and this cropping can be achieved by pruning the relevant patchwise INR - similarly, cropping is limited to the pre-defined patches. This allows for novel post-training cropping, where the INR can be cropped in a way that reduces the number of model weights (and therefore the storage space). The method shows benefits beyond cropping - faster training time (or better visual quality at equal epochs). It is also flexible, and can be applied to various MLP-based INRs.", "questions": "What are the practical applications of this method? The main reason my score isn't higher is because I think the impact of this work is somewhat limited to more nice applications that might be of interest to those that study INR, but less so to the broader community.\n\nWhat does this reveal about the nature of INRs? It would also be nice if the paper revealed some deeper insights about INR in general.", "limitations": "Yes.", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "[S1] The paper is exceptionally easy to follow, with good reasoning/motivation, well-explained method, and experiments that support the claims of the paper. Last paragraph of the intro, Figure 1, and Figure 3 are especially good in this regard.\n\n[S2] While on face the applications seem limited, since the pruned parameters can be discarded, this method could be quite useful in the compression regime, where the MLP INR could be cropped by the end user and size would be reduced accordingly. The faster training time is also beneficial in this setting.\n\n[S3] The method has benefits beyond its target problem (cropping) - better quality with less training.\n\n[S4] The experiments are very thorough, proving the flexibility of the method with applications across multiple models and domains.\n\n[S5] The supplementary even goes beyond what's necessary to provide comparisons with e.g. KD for INR training.", "weaknesses": "The patch-based formulation is a little unsatisfying in the following ways.\n\n[W1] It doesn't reveal anything very new about the INRs themselves. Rather than discover pruneable parameters that correspond to cropping, or developing some objective that imparts some locality on the representation, the local vs. global distinction is very rigidly enforced as a prior.\n\n[W2] The image can only be cropped according to the pre-defined patches.\n\nSeparately, \n\n[W3] Partly connected to W1, the post-training editing is totally restricted to only cropping. This might have applications to compression, but is otherwise at this point more of a novelty, in the sense that it is not very practical.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear reviewer, thank you for the thoughtful feedback and insightful comments. We appreciate the time and effort. Please see our comments and additional results below.\n\n**Weaknesses:**\n\n**[W1]** We appreciate the reviewer’s observation regarding the rigid enforcement of the local-global distinction as a prior. This rigidity is indeed central to achieving zero-shot croppability in our method. While it may not reveal novel aspects of INRs themselves, our approach demonstrates that (1) combining local and global features serves as a robust prior, enhancing reconstruction quality compared to the INR-per-partition method, (2) the quadratic complexity of fully connected layers in INRs can be relaxed, and (3) there is potential for partition-based downstream tasks and editing. \n\n**[W2]** We agree that the current method only allows cropping according to predefined patches. As mentioned by reviewer *XqfY*, integrating semantic segmentation-based partitioning could address this limitation. Although this is beyond the scope of the current paper, we find it an exciting direction for future research.\n\n**[W3]** We acknowledge that post-training editing is currently limited to cropping. Our long-term vision is to expand this capability, enabling more sophisticated partition-based editing operations. We believe this work lays groundwork for future developments in editable INRs.\n\n**Questions:**\n\n**Practical Applications:** While our research is particularly relevant to those exploring INRs, we believe it also offers broader implications. By extending a baseline MLP-based INR with our local-global approach, we achieve enhanced quality and latency. This improvement can benefit various lines of work incorporating INRs, including image reconstruction, super-resolution, and potentially more complex tasks. In addition, we believe our work can be used for partition-based downstream tasks. For instance, while Functa [13] has shown the use of INRs for classification, our partition-based approach can be used for more complex tasks such as object detection (per-partition classification). Additionally, the locality of weights in our method could facilitate partition-based editing, with methods which directly operate over the weight space such as [29].\n\n**Insights about INRs:** While our work might not provide groundbreaking new insights into the nature of INRs, it demonstrates that integrating local and global features is a promising approach for improving reconstruction quality and reducing computational complexity. \n\nWe aim to lay foundations for future partition-based editing and inspire the development of INRs which are inherently editable.\n\nWe appreciate the reviewer’s feedback and hope that our comments help illustrate the potential impact and future directions of our work.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "G6Dawps22Q", "reviewer": "Reviewer_XqfY", "summary": "This paper proposes Local-Global SIRENs, which partition the space into different regions and fit each region with smaller local INRs, leading to croppable INR by cropping the weights relative to the local regions. The model further proposes to use local and global feature extraction to improve the fitting performance. The experiments show that their method supports cropping INRs for Image, Audio, Video and CT.", "questions": "1. Could you please discuss how to automatically partition the region with your method?\n2. Could you please discuss whether your method can be extended to semantic segmentation-based cropping?", "limitations": "The limitations and potential negative societal impact of their work have been discussed.", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The idea of using partition-based INRs for croppable INRs is novel. Croppable INRs are an interesting application for partition-based INRs.\n2. The paper is well-written and easy to follow.\n3. The cropping performance looks fancy and the fitting performance is slightly improved compared to SIREN due to the global feature extraction.", "weaknesses": "1. Cropping INRs is a natural property of partition-based INRs, which makes the contribution minor. \n2. While the authors mention their method supports automatic partitioning, they do not show the detailed implementation of how to automatically partition the space.\n3. Even though the authors have conducted an ablation study on partition factors, the range of experimented partition factors is not enough. I recommend the authors to try Partition\nFactors as low as (2,2) and as high as (512, 512) for the 512 * 512 images and show how the partition affects the fitting performance.\n4. Cropping based on simple grids may be impractical for real scenarios. I recommend the authors improve their method by implementing semantic segmentation-based cropping. See partition-based INRs with semantic segmentation [1].\n5. I am confused about the conclusion that enlarging the partition factors leads to faster training while decreasing the partition factors enhances reconstruction accuracy (line 293). Since SIREN is just your Local-Global SIREN with partition factors (1,1), if your conclusion is right, SIREN should have better performance than your LG SIREN. As pointed out in [1], partition should generally improve the fitting performance with larger partition factors. And please provide some explanation about why increasing the number of partitions enhances overall speed. \n\n[1] Liu, Ke, et al. \"Partition speeds up learning implicit neural representations based on exponential-increase hypothesis.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear reviewer, thank you for the constructive feedback and great reference. We appreciate the time and effort. Please see our comments and additional results below.\n\n**[W1] Contribution**\n\nWhile training an INR-per-partition does allow for cropping with a proportionate weight decrease, our extensive experiments across various modalities show that this method significantly degrades encoding quality and introduces unwanted artifacts. These artifacts are illustrated in Figures 4, 6, and 11, with quantitative results presented in Tables 1, 2, and 12. Our method not only addresses these issues but also **improves upon the baseline INR itself**. Local-Global INRs enable cropping capabilities while enhancing encoding quality and performance on downstream tasks.\n\nAlthough other INR-per-partition methods using larger or semantically-uniform partitions might improve over uniform partitions, they have two downsides: (1) They limit the flexibility of cropping. (2) Since the partitions are not fixed across various signals, future applications of partition-based downstream tasks become more difficult to achieve.\n\n**[W2/Q1] Automatic Partitioning**\n\nThe automatic partitioning process is described briefly in Section 3.6 and involves a straightforward approach. Given a target partition size (e.g., 32x32 image pixels) and a required global weight ratio (typically around 10%), we compute the partition factors through simple division and determine the hidden dimensions of sub-networks using binary search. The implementation is provided in the `compute_partitions.py` module. We will include the relevant pseudocode in the final revision of the paper (please see pseudocode in the general top comment).\n\n**[W3] Partition Factors Range**\n\nWe agree that extending the range of partition factors is valuable, though space constraints limited our initial revision. We have now included image encoding results for partition factors (2, 2), (32, 32), and (64, 64). The results are as follows:\n| Partition Factors | MSE (*10^-4) | SSIM | PSNR | Train Time (s) |\n|-------|----------|--------------|-------|---------|\n|(2,2)|**11.2**|**0.946**|**32.59 ± 0.52**|74|\n|(4,4)|12.0|**0.946**|32.10 ± 0.47|40|\n|(8,8)|13.5|0.942|32.29 ± 0.42|26|\n|(16,16)|15.3|0.934|32.00 ± 0.39|22|\n|(32,32)|19.0|0.917|31.51 ± 0.28|**15**|\n|(64,64)|31.9|0.868|29.56 ± 0.45|**15**|\n\nUsing larger partition factors, as the reviewer mentioned, is not feasible as there are not enough weights in the network to distribute among the partitions. Further increasing partition sizes would require expanding the network capacity beyond the typical 200k parameters used in previous literature for image encoding tasks. We will include these extended experiments in the final revision of the paper.\n\n**[W4/Q2] Segmentation-based Cropping**\n\nThank you for the suggestion. Implementing semantic segmentation-based cropping could indeed enhance the quality of our method by aligning partitions with meaningful image features. However, we believe integrating this approach into our current work is beyond the scope of this paper. We recognize that while semantic segmentation-based methods can improve the encoding quality and offer context-aware cropping, they may also limit cropping flexibility since only entire segments may be cropped (we briefly mentioned this in the first subsection of this rebuttal). We will definitely consider exploring this direction as part of our future research. Additionally, the paper you cited is highly relevant to our approach, and we will include it in both the related work and future work sections of our paper. \n\n**[W5] Quality-Latency Trade Off**\n\nThank you for highlighting this point. It is important to clarify that while SIREN with partition factors of (1,1) might appear similar to our Local-Global SIREN, the two architectures are **significantly different**. LG-SIREN with (1,1) still involves two networks with features intertwined throughout the forward pass. This intricate architecture affects performance, as seen for the image encoding task discussed above:\n\n| Method | MSE (*10^-4) | SSIM | PSNR | Train Time (s) |\n|-|-|-|-|-|\n|LG-SIREN (1,1)|**12.9**|**0.939**|**32.52 ± 0.66**|87|\n|SIREN|18.4|0.914|31.17 ± 0.68|34|\n\nAdditionally, the extreme case of (1,1) is somewhat analogous to INCODE, where a small modulator network augments the features of a large network. It is not surprising that LG-SIREN in this case achieves high reconstruction quality, even though it does not explicitly perform local feature learning. We will make sure that these distinctions are clearly presented in the revised paper.\n\nRegarding why larger partition factors enhances training speed, note that larger partition factors (i.e. *smaller partitions*) results in a *larger* amount of *smaller* local sub-networks, which means there is less interconnectivity between neurons in the entire architecture. This quadratically reduces the number of floating-point operations (FLOPs) in the linear layers, and allows for better parallelization, thereby speeding up training. We briefly mention the quadratic complexity of FLOPs in Section 3.4, but we agree that this point needs to be more explicit. We will make sure it is clear in the final revision of the paper.\n\nRegarding the observation made by [1], it seems like increasing the number of partitions is beneficial in terms of PSNR when using segmentation-based partitions (PoS), but this is not necessarily the case for a fixed grid (PoG) and SIREN, which is similar to our use-case. Also, please note that in our experiments, we explore a significantly larger number of partitions (from 2x2 up to 64x64 in the results above), and in Figure 6 in [1], the authors experiment with up to 12 partitions. It would be interesting to explore the effects of *significantly* increasing the number of partitions for PoS. We once again thank you for pointing our attention towards [1], this work is extremely interesting and relevant to our own.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We would like to express our sincere gratitude to all the reviewers for their valuable feedback and insightful comments. We have carefully addressed each point raised in the individual reviews and provided detailed responses in the corresponding review replies.

Additionally, we recognize that the details of the automatic partitioning method were not entirely clear in the initial submission. The automatic partitioning determines the hidden layer dimensions based on the target network size, global weights ratio, and the selected partition size. To clarify, we are providing the pseudocode for the automatic partitioning process below, which will be added to the revised paper:


	FUNCTION AutomaticPartitioning(target_total_params, target_global_weight_ratio, target_partition_size, signal_resolution):
		groups = ComputeNumGroups(signal_resolution, target_partition_size)
		
		// Compute global hidden dimension
		global_hidden_dim = FindDimension(target_total_params * target_global_weight_ratio)
		global_weights = ComputeGlobalWeights(global_hidden_dim)
		
		// Compute local hidden dimension
		target_local_weights = target_total_params - global_weights
		local_hidden_dim = FindDimension(target_local_weights, groups)
		local_weights = ComputeLocalWeights(llocal_hidden_dim, groups)
		
		// Adjust global weights to meet target ratio and total parameter count
		WHILE (global_weights + local_weights) NOT WITHIN 1% OF target_total_params:
			IF (global_weights + local_weights) > target_total_params:
				global_hidden_dim -= 1
			ELSE:
				global_hidden_dim += 1
			global_weights = ComputeGlobalWeights(global_hidden_dim)
		
		RETURN local_hidden_dim, global_hidden_dim

	// ComputeNumGroups: Calculates the number of partitions the signal is divided to, using simple division
	// ComputeGlobalWeights: Calculates the number of weights in the global network based on the given configuration
	// ComputeLocalWeights: Calculates the number of weights in local networks based on the given configuration
	// FindDimension: Uses binary search to find optimal hidden dimension given target weight count and network parameters.

Thank you,

The authors

Meta-review: The reviewers agreed that the paper is well written and showcases an interesting and effective method to perform cropping.  
There were some concerns initially about the motivation and evaluation of the method, but they were addressed adequately and all reviewers are in favour of accepting the paper.
Decision: Accept (poster)