LotteryCodec: Searching the Implicit Representation in a Random Network for Low-Complexity Image Compression
Authors: Haotian Wu
Gongpu Chen
Pier Luigi Dragotti
Deniz Gunduz
Venue: ICML 2025 spotlightposter (2025)
Keywords: Implicit neural representation
source coding
overfitted image compression
lottery codec hypothesis
low-complexity image codec.
Primary area: applications->computer_vision

Abstract: We introduce and validate the lottery codec hypothesis, which states that untrained subnetworks within randomly initialized networks can serve as synthesis networks for overfitted image compression, achieving rate-distortion (RD) performance comparable to trained networks. This hypothesis leads to a new paradigm for image compression by encoding image statistics into the network substructure. Building on this hypothesis, we propose LotteryCodec, which overfits a binary mask to an individual image, leveraging an over-parameterized and randomly initialized network shared by the encoder and the decoder. To address over-parameterization challenges and streamline subnetwork search, we develop a rewind modulation mechanism that improves the RD performance. LotteryCodec outperforms VTM and sets a new state-of-the-art in single-image compression. LotteryCodec also enables adaptive decoding complexity through adjustable mask ratios, offering flexible compression solutions for diverse device constraints and application requirements.

LotteryCodec: Codec: Searching the Implicit Representation in a Random Network for Low-Complexity Image Compression
Haotian Wu Gongpu Chen
Pier Luigi Dragotti
Deniz Gündüzz
Abstract
19.1 in [%] (t)
COOL-CHICV2
AE-based codec Overfitted Codec LotteryCodec
We introduce and validate the lottery codec hy- pothesis, which states that untrained subnetworks within randomly initialized networks can serve as synthesis networks for overfitted image compres- sion, achieving rate-distortion (RD) performance comparable trained networks. This hypothe- sis leads to a new paradigm for image compres- sion by encoding image statistics into the network substructure. Building this hypothesis, we propose LotteryCodec, which overfits binary mask to an individual image, leveraging an over- parameterized and randomly initialized network shared by the encoder and the decoder. To address over averpaaramttriization challenges and streamline subnetwork search, we develop rewind mod- ulation mechanism that improves the RD per- formance. LotteryCodec outperforms VTM and sets new state-of the-arr in single-image com- pression. LotteryCodec also enables adaptive de- coding complexity through adjustable mask ra- tios, offering flexible compression solutions for diverse device constraints and application require- ments. Project page: https: htt////ddvvd...../ hot.ubbio///etterooodoee
BD-rate vs VTM- VTM-19.1
10
EVC.S
CST
EVC-M
VTM 19.1
EVC-
C3 adapt.
-10
LotteryCodec (ours)
MLC
Better
MLIC+
-20
10a
10a
10a
10
Decoding complexity [MACs/pixel] (1)
Figure 1. Rate-distortion performance (BD-rate) vs. decoding com- plexity on CLIC2020 dataset. LotteryCodes achieves a superior and adaptable RD trade-off than other codecs.
(AE)-based neural codecs often suffer from high decoding complexity and large number of network parameters, which limit their practical deployment on resource-constrained de- vices (Jiang al., 2023; Wang et al., 2023). In addition, they require training on extremely large datasets to ensure robust performance across diverse image distributions resources that are not always available. Addressing these issues to develop low-complexity and robust codecs with competitive rate- dittodistottion (RD) performance remains a critical open challenge (Yang et al., 2023).
1. Introduction
Traditional image/video compression algorithms rely on meticulously designed linear transforms. Recently, conven- tional methods have been increasingly challenged by emerg- ing (earning-based codees that replace analysis and synthesis transforms in classical codecs with neural networks (Ballé et al., 2018; Cheng et al., 2020a; He et al., 2022), While achieving impressive performance gains, these autoencoder
Implicit neural representations (INRs) (Sitzmann et al., 2020) has emerged as promising signal representation technique that leverages lightweight multi-layer percep- trons (MLPs) to directly parameterize continuous functions. INRs have demonstrated impressive performance vari- ous modalities and tasks, including modaality-annoste rep- resentation (Shi et al., 2024). 3D reconstruction (Atzmon & Lipman, 2020), and view synthesis (Mildenhall al., 2021), and have been extended to multi-instance settings via modulation mechanisms (Mehta et al., 2021). Quantiz- ing the overfitted network yields a signal compressor. For image compression, a lightweight neural network can over- fit single image by mapping pixel coordinates to their
'Department of Electrical and Electronic Engineering, Impe- rial College London, London SW7 2AZ, U.K.. Correspondence to: Gongpu Chen <gongpu.chen www.pp..hhnneeeriiiii.a @iieerral...c...k Haotian Wu <haotian. wul 1 ac.kr.al.ac..k>..
Proceedings of the ndnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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LotteryCodee: Scarching the Implicit Representation in a Random Network for Low- Compleiyyyy Image Compression
corresponding intensities. Building on this idea, the first INR-based overfitted image codec, COIN, was proposed in (Dupont et al., 2021). Later, the COOL-CHIC series codecs (Ladune et al., 2023; Leguay et al., 2023) and C3 (Kim et al., 2024) further enhanced the RD performance, outperforming widely used codecs such as BPG (Bellard, 2015), HEVC (Sullivan et al., 2012), and VCC (Bross et al., 2021a), while maintaining low decoding complexity.
Encoding
Dinery mest
Modulation vector
Disimeenn
Decoding
Ramsoom seed
Intaliation
Despite significant advances, wfte-of-the-art overfitted im- age codecs still fall short of the RD performance of com- petitive classical codecs such as VTM (Bross et al., 2021b). Further improvements are challenging because achieving higher reconstruction fidelity typically necessitates larger networks, which significantly increases the compression rate. In addition, most overfitted codecs rely on fixed net- work architectures for range of images, limiting their RD performance and adaptability. We thus anticipate a new paradigm, one that can balance the increasing cost of net- work complexity with representation capability while en- abling an adaptive architecture for individual images.
retwork
Superieak Natwvrr
Peesrstaction
Figure 2. Illustration of LotteryCodes scheme: the source image is encoded into a binary mask and latent modulations. During decoding, the receiver initializes a common random network and uses a modulated subnetwork to reconstruct the source image.
studies (Pensia et al., 2020; da Cunha et al., 2022) suggest that any target network of width tu and depth 4a can be approximated by pruning a random network that is factor O (1og((mr4a) wider and twice as deep, suggesting that suf- ficiently peraaataateeeddd randomly initialized networks contain some 'winning tickets' even without training. (2) Empirical evidence: extensive experiments conducted in this paper evaluate the hypothesis, and the results consistently support its validity.
This work is inspired by two key findings: initialized neural network can act as a handcrafted prior, encoding significant image statisties and prior informa- tion within its network structure (Ulyanov et al., 2018) and (2) over- parameterized neural networks contain high- performing untrained subnetworks (Ramanujan et al., 2020). These insights motivate us to propose the lottery codec hy- pothesis. Specifically, consider a well-trained overfitted image codec gw(z) (z), which represents image S neural network parameterized by W, with a latent representation its input. After quantization and entropy coding, the decoder reconstructs the image as S = 9w- (2) Next, con- sider an over- pree-parameterized, randomly initialized network IW', along with a learned binary mask r' E {0. 1) II''l and a latent z', where W'| denotes the number of parameters of gw The source image is reconstrueted via a subnet- work of gw as S' = ow (Z'), where O represents the Hadamard product, identifying the subnetwork. We propose the following hypothesis:
(1) a randomly
The proposed lottery codec hypothesis highlights the poten- tial of searching untrained but well-performing subnetworks as overfitted image codecs. While theoretical works and ex- periments demonstrate that sufficiently over-parameterized networks can contain untrained subnetworks that match the performance of well-trained networks, precise guidelines on the required level of veerparraettriizaioon, such as specific architectural depth or configurations, remain unclear for reliably obtaining 'winning ticket'.
Based on the above hypothesis, we propose a novel overfit- ted image compression scheme, called LotteryCodec (see Fig. 2). This method utilizes a randomly initialized network as the synthesis network and learns binary mask with la- tent modulations the code. With a predefined random seed, network parameters are eliminated from transmissions; instead, it is sufficient to transmit only the binary mask and latent variables for the decoder to reconstruct the image.
Lottery codec hypothesis. Let d denote a distortion func- tion and H the entropy function. For any overfitted image codec (w) there exists a pair (r',z') as the 'winning tickets' within a sufficiently over-parameterized and ran- domly initialized network gw, satisfying W'| > [W], such that d(S.S') S S() and H22))= = (2).
To address the challenges of over- pereraaaatttiiztiionn and sub- network search, we propose a rewind modulation mecha- nism that introduces image information during the subnet- work search, simplifying the process and enhancing the RD performance. To the best of our knowledge, the proposed LotteryCodec is the first overfitted image codec to surpass the RD performance of VTM while maintaining low de- coding complexity. Furthermore, LotteryCodec sets a new state-off of -ae--of-thhhae the for overfitted neural codecs obtained from a single image. Its adaptive masking strategy enables flexible
Note that the equality H(2)) (2) implies that the num- ber of bits required to represent E' and å after entropy cod- ing is the same. We conjecture this hypothesis to hold for the following reasons: (1) Theoretical justification: prior
In this paper, variables with a hat notation, such as 2, represent their quantized counterparts.
2

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LotteryCodee: Scarching the Implicit Representation in a Random Network for Low-Complexity Image Compression
Qi A
Qi A
Qi A
z
W
D
F
M
W - r Wo
S
S
S
(a). AE-based neural codec
(b). Overfitted neural codec
(c). LotteryCodec
Figure 3. Operational structure of different compression schemes. (a) AE-based neural codees: source image S is processed through pair of encoder and decoder. (b) Overfitted neural codecs: S is fitted by parameters {W, 2) via a fitting operation F. (c) LotteryCodec: is fitted by parameters {r, z). identifying subnetwork in randomly initialized network, with masking operations M.
model complexity adjustment based on varying mask ratios, balancing computational cost and performance, shown in Fig. 1.
2023), comprises a pair of encoding network & and decod- ing network D, jointly optimized over large dataset. A source image S is encoded by & into a latent representation 2, which is then compressed into R bits by quantization and entropy coding. At the decoder side, the quantized latent representation 2 is first recovered and then used to reconstruct the source image. Resulting average distortion is D Es [d(S, D(2)),, where d denotes the distortion metric, and the compression rate I is given by:
The contributions of this work are summarized as follows:
We propose and experimentally verify the lottery codec hypothesis, which suggests that subnetwork within a randomly initialized neural network can directly serve as a well-performing synthesis network for overfitted image compression. This hypothesis introduces new paradigm for INR-based image compression, empha- sizing the potential of encoding image statistics into the structure of a randomly initialized network.
R = Es
[- logg PQ(E(S)) (2)]
(I)
where Q represents quantization operations. Although AE- based approaches achieve competitive performance, their decoding complexity is typically high due to reliance on large and complex architectures for robust latent representa- tions (see Fig. 1).
We propose a novel LotteryCodec scheme, which over- fits randomly initialized neural network to the source image by learning a binary mask and modulation vec- tors. To alleviate over-parameterizztion and simplify subnetwork search, a rewind modulation mechanism is introduced, significantly improving the RD perfor- mance.
Overfitted neural codecs. Overfitting parametric function to each single image offers an alternative, where quantized function parameters serve as the compressed representation. A low-complexity network is often sufficient since gener- alization is not required. COIN (Dupont et al., 2021) pio- neered this by training lightweight MLP to map pixel co- ordinates to RGB values. Quantized parameters are entropy- coded into a bitstream for decoding. COIN+ (Dupont et al., 2022a) improved generalization with meta-learning. How- ever, COIN's RD performance remains limited despite low complexity and remarkable generalization. Subsequently, the COMBINER series (Guo et al., 2023; He et al., 2024) introduces variational INRs and leverages relative entropy coding for RD-optimized compression.
We show by extensive experiments that LotteryCodec achieves state-of-the-an performance among overfitted image codees designed for single-image compression at reduced computational cost. Additionally, Lot- teryCodec can adjust its decoding complexity by vary- ing the mask ratio, thus providing flexible solutions for diverse computational and performance needs.
2. Related work
2.1. Neural data compression
A significant advancement came with COOL-CHIC (Ladune et al., 2023), which improves RD performance by integrating latent representation and an entropy model while maintaining a low decoding complexity. As illustrated in Fig. 3b, COOL-CHIC jointly trains parametric function Iw with a latent vector z as the input to overfit S. Simi- larly to COIN, both W and z are compressed into R bits through quantization and entropy coding. During decoding, the quantized network and latent vector are used recon-
Currently, there are two main paradigms for neural data compression (see Fig. 3): AE-based and overfitted neural codecs, both designed to balance the trade-off between the distortion and the rate (Cover, 1999).
AE-based neural codecs. As illustrated in Fig. 3a, an AE-based neural codec, e.g., (Ballé et al., 2018; Cheng et al., 2020a; He al., 2022; Jiang et al., 2023; Wang et al.,
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LotteryCodec: Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
Bitstream
ARM parameters
learnable modulation
ModNet
seed & mask
2
BEB 63455
ARM
ModNet
Entrayy Decodimg
Modulation
1xt Conv
Com
1xt Conv
MxT Con
context
Entropy model
Decoded modulation latent
SuperMask network
Figure 4. Illustration of the image decoding process in LotteryCodec. The ARM parameters & are first retrieved to regress the latent modulations 2. Subsequently. the binary mask r initialization seed configure the synthesis network, while the modulation model parameters 0 are decoded to generate the modulations from & to guide the synthesis network to reconstruct the image.
struct the image via the mapping $ 9w (2). This results in average distortion D Es-p, [d(S, Fw (2)) at rate
biases. This LTH-based video representation method hances expressiveness but increases complexity.
Recently, Malach et al. (2020) theoretically proved the SLTH for fully connected networks with ReLU activations, showing that any target network can be approximated by pruning sufficiently over-parameterizee random network of polynomial size relative the target network. Orseau et al. (2020) and Pensia et al. (2020) relaxed the assumptions and improved these bounds to logarithmic order, which is later extended into convolutional neural networks (CNNs) in (da Cunha et al., 2022).
R = Es-p, logg Po (2) logg p( W) R2j
(2)
where F denotes the operations that overfit (W, z) parame- ters to the specific input S. (-) the estimated distribu- tion with estimation model s.. In practice, entropy coding of å relies on lightweight auto-regressive entropy model (ARM) ri for distribution estimation. In (2), Rg represents the extra bit overhead due the transmission of this model parameters.
3. LotteryCodec
Extensions like COOL-CHICV2 (Leguay et al., 2023), C3 (Kim et al., 2024; Ballé et al., 2024), and COOL-CHICV3 (Blard et al., 2024) further enhance the RD performance with advanced architectures and techniques, including soft- rounding, Kumaraswamy noise, and conditional entropy models. These advancements allow COOL-CHIC to outper- form widely used codecs such as BPG and HEVC.
Inspired by the lottery codec hypothesis, propose Lot- teryCodec, a novel image compression paradigm that en- codes images by identifying structured subnetworks within randomly initialized network. The detailed pseudocode for the method is provided in Appendix E.
3.1. Workflow
2.2. Lottery ticket hypothesis
Encoder. As depicted in Fig 3(c), given an over- parameterized network gw, with randomly initialized pa- rameters Wo, each image S is overfitted using subnetwork of gw. by learning a binary mask 7 and latent representa- tion z, such that the subnetwork groWo well reconstruct S using 2. The quantized latent å and binary mask T then compressed via entropy coding, producing bitstream rep- resentation of S. Additional mechanisms, such as ARM re and the modulation model ModNet fo. are incorporated to further enhance the RD performance, as will be elaborated on later.
Frankle & Carbin (2019) introduced the lottery ticket hy- pothesis (LTH), stating that randomly initialized, dense neural network contains a subnetwork that can match the test accuracy of the full network with equivalent training. Zhou et al. (2019) found that 'winning tickets' (i.e., masked subnetworks) can outperform random initialization without training, while Ramanujan al. (2020) extended the idea by showing that even untrained subnetworks can achieve near state-of-ther the-art performance, a phenomenon referred to as the strong lottery ticket hypothesis (SLTH). Building on these ideas, Choi et al. (2023) applied LTH to video rep- resentation with multiple supermask overlays and unpruned
Decoder. As shown in Fig. 4, the decoder begins by ini-

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LotteryCodec: Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
Conv
U 2
1x1 Conv
U2
1xt Conv
1x1 Conv
Up
Upsampu
ModNet
1x1
fo(-)
i
rewind
modulations
Concatenate
Concatonate
Concatonato
lightweight
M
M2
Ms
Lt
M
Entropy model
Tipl
aaaca
62455
Modulation operatioe pprrations
Modulation operations
Modulation operations
Concatenate
(x, y)
Coordinate
Masked layer
layer
Masked layer
Masked layer
R, G,G.B
SuperMask network
gröwo (-)
Figure 5. Illustration of the ModNet and SuperMask networks: SuperMask network maps pixel coordinates to RGB values by identifying subnetworks within randomly initialized network, guided by modulations generated by the ModNet using input Solid red lines indicate active weights, while dashed lines represent masked weights. The weights of the SuperMask network remain frozen during training: only the binary mask r ModNet parameters are learned.
tializing the neural network Dwo using the same random seed as the encoder. Next, the binary mask 7 is extracted identify subnetwork growo and the ARM parameters e are retrieved decode the latent modulation vector 2. Finally, modulation model fa is retrieved and applied to modulate the image generation process based on 2 as:
hard-rounding is applied during inference. Notably, the loss function (4) excludes the rate terms associated with eb, 0, and т, as their contribution the overall bit rate is minimal due their lightweight architectures. practice, these parameters quantized and entropy-coder codedd using non-learned distribution after the optimization process is completed, contributing to the final bitstream.
S(x) growo x)),
Overall, the LotteryCodec bitstream consists of four parts: the ARM parameters v learnable latent modulations modulation model parameters 0, and the binary mask T. Hence, the total compression rate is given by
where denotes the pixel coordinate vector of the im- age. The distortion of LotteryCodec is then measured by D = Es-p. d(S.,) S)] The decoding complexity remains low because grow. is a lightweight network. Moreover, LotteryCodec offers flexible decoding complexity by allow- ing adjustable mask ratios, which dynamically control the active size of the synthesis network.
Es
Po ((T)+ + Rg Roj
RD cost optimization. To balance the rate-distoree dire-rittotinn trade- off, LotteryCodec trained to fit a parameter set, denoted by Ω A [z, db, 0, 7}, with the goal of minimizing the following loss function (i.e., the RD cost):
where Rg and R3 denote the rate contributed by the trans- mission of quantized ModNet and ARM. As shown in Eqs. (2) and (5), the rate of overfitted codecs depends on (2, &. W). while the rate of our method is determined by (2, w, T, 0). According to the Lottery Codec Hypothesis,
((22) = d(S, Irowo (f)( + AR(2),
(4)
our bit cost for å and & matches that of standard overfitted codecs. While each quantized parameter in W typically requires more than 13 bits, our binary mask 7 uses up to bits per entry. Despite its higher dimensionality. T con- tributes significantly less to the total rate. Moreover, since Ô is lightweight, the combined rate of and 0 remains lower
where R(2) represents the compression rate contributed by à, and is a hyperparameter that controls the trade-off between distortion and rate. During training, z undergoes soft-rounding with varying Kumaraswamy noise, whereas
5

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LotteryCodee: Scarching the Implicit Representation in a Random Network for Low-Complexity Image Compression
than that of W, resulting in improved compression effi ciency. Note also that is transmitted in lossless fashion as it does not need to be quantized. In practice, both and i are entropy-coded using offline- trainee models or a static distribution.
and 2F different frequencies, hence M 2FP. The phase vector is defined as yp _ {0, Pr,,........................ ...,, 2T -1)/P/ For each phase, the frequency vector is defined as w [Wlow: Whigh where Wlow =
1} and Whigh = {1, (1, F.) denote low-frequency and high- frequency bases, respectively. Each element Am of A (1) is sampled from:
3.2. Winning a lottery codec
The design of LotteryCodec incorporates four key archi- tectural components: SuperMask network (fw,@r), Mod- Net (fa), latent modulation (z), and ARM (rw)). As shown in Fig. 5, the SuperMask network groWo is a high- performing subnetwork that maps pixel coordinates RGB values, obtained by applying the learned mask the over- parameterized network gWo Specifically, gro com- prises L, masked linear layers, with each masked linear layer followed by modulation operations. The ModNet fe includes an upsampling operation and (L,-1) convolutional layers with 1 1 kernel to generate hierarchical modulation vectors for each layer of groW, from the retrieved 2. This design significantly simplifies the subnetwork search while improving the RD performance. The latent modulation is set of learnable vectors that serve as primary compres- sion component, while the ARM (rw) is an auto-regressive entropy model commonly used to compress latent repre- sentation z in overfitted codecs (Ladune et al., 2023), with architecture detailed in Appendix A.
(1) mm. ~ U (-1
6 M AMEETTN (mn)))
V
d M > -= m,
(b
SuperMask network. We introduce a learnable matrix P to identify the subnetwork grsW., defined by mask т, that minimizes the loss function. Matrix P shares the same dimensions Wo, with each element representing score of the corresponding weight in Wo. During training, the randomly initialized Wo remains frozen while only P is updated. The top ra of weights with the highest scores across all layers are activated, while the remaining weights are set to zero.
More formally, let DO)) & {01 of nodes for the i-th masked linear layer with da nodes. The output of the k-th neuron in the i-th layer with the modulation function m(.) can then be written as:
(uf".....
(0) ...... Ug denote the values
d:-1 Σ This wki
Fourier initialization. Initialization plays critical role in the SLTH problem to ensure the efficient identification of "winning tickets" (Ramanujan et al., 2020). In our Lot- teryCodec, parameters Wo are initialized using a Fourier initialization approach. This design is based on two main considerations: (1) From an INR perspective, the Fourier reparametrization method can address the low-frequency bias of MLPs and enhance INR with richer textures (Shi et al., 2024); (2) From an SLTH point of view, this initial- ization ensures the network retains rich sign information (Zhou et al., 2019; Oh et al., 2025) while maintaining con- stant variance between inputs and outputs (Glorot & Bengio, 2010; He et al., 2016).
( ok a
(i- 1 (i- D (nlost-11))
mtus
(7)
(6-1) where is the activation function and wkj is the weight connecting the k-th neuron in i-th layer to the j-th neuron of the (i - 1)-th layer. The mask function returning the binary mask Tk.j
(i-1) if the score Pkj for the weight is among the top r.% highest values, and (i-1) 0 otherwise. Using the chain rule of TR.j
(i-1) h (P) is defined as: Tk.j
(6-1)
(i-1)
gradient, the gradient of the loss L with respect to Pkj can be estimated by a ttraight-hhooug gradient estimator:
Specifically, the weight matrix of the i-th MLP layer, denoted by wii [ is re-parameterized as weighted combination of fixed Fourier bases:
ac 0p
ac deg 1
whi w
11-1)
mio (1-1)))) &
(1-1)
1)
~
duyy (i)
do
Sky
(8)
kg
(i (1))
(6)
The above formula holds because Tk.j (i-1) is a non-decreasing
(6-1) function of Pkj The activation probability Pkj then be updated as:
(i-1)
where (1) E RRd. is the coefficient matrix, and (1)) E R d represents a set of M Fourier bases. Each element ((9 of (i)) (the m-th row and n--ollumn) is defined using distinct frequency and phase as
can
(f-1) (6-1) (i-1) + Pij Pkj
(0) = cos(w,,.. (2) + pm),
-askj
askj
where (i) aO) ..... dd is a positional sequence uni- formly sampled from [-T, T]. and w and y are the fre- quency and phase vectors. We adopt P different phases
(8)
where a is the learning rate. When activation or deactivation swaps occur, the loss decreases for the mini-batch, according to (Ramanujan et al., 2020; Wortsman et al., 2019).
6

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LotteryCodee: Scarching the Implicit Representation in a Random Network for Low- Low-Complexity Image Compression
Claater
IOENE C2 WA
Lulley 1:3
(120
Fata (152111)
C4
(a)
(b)
(c)
(d)
Figure 6. Experimental verification of the lottery codec hypothesii, where C3-lottery (Ne, d) refers to the scheme using over- parameterized network with N, hidden layers and d dimensions per layer. (a) RD curve and BD rate for different over- paramtterizzainn configurations. (b) BD-rate versus different mask ratios. (c)-(d) BD-rate over varying width and depth configurations.
Rewind modulation mechanism. In practice, directly searching for a well-performing subnetwork from gwo re- quires a deep, wide random network, leading to high com- pression and computational costs. To address this, we intro- duce ModNet fe to generate modulations to simplify sub- network search and improve the RD performance. Specif- ically, fe takes the quantized latent modulation å as in- put, where z & {zz, Z2. Z2...... ..... b comprises L learnable HW multi-resolution vectors, with each 2i E Z being learnable vector. In fe. 2 is first upsampled using trans- pose convolutional operations as in (Blard et al., 2024), producing Uo- = [uı; u ur. E Z where each u, e Upsample(2i) E z"W The resultant Un is then pro- cessed through convolutional layers as: U; - (U;1)),
layers while preserving high-level features. Note that the proposed LotteryCodec scheme with its rewind modulation mechanism serves general framework, allowing for al- ternative modulation operations, such as FiLM (Perez et al., 2018), which are discussed in Appendix D.4.
4. Experimental results
We evaluate our model on the Kodak (24 images) (Kodak, 1991) and CLIC2020 (41 images) (Toderici et al., 2020) datasets. The mask ratio is selected from [0.1, 0.9]. Lot- teryCodec is compared with classical codecs (VTM-19.1 (Bross et al., 2021a), HEVC (Sullivan et al., 2012)), AE- based neural codecs (CST (Cheng et al., 2020b), EVC (Wang et al., 2023), MIJC+ (Jiang et al., 2023)), and other overfitted image codecs (including C3 (Kim et al., 2024) and COOL-CHIC (Leguay et al., 2023)). The peak signal- to-noise ratio (PSNR) on RGB channels and BD-rate (Gisle, 2001) are used to evaluate the RD performance. The evalua- tion details and additional experiments, including ablation study and visualizations, are presented in the Appendix F.
i = 1,... Le - 1. Here, f64) and U, denote the operation and output of the i-th layer of ModNet, respectively.
Inspired by (Mehta al., 2021; Perez al., 2018; Zhou et al., 2019; Oh et al., 2025) and to leverage the network structure to encode the source image, we propose rewind strategy to modulate the synthesis process by concatenating compensational structural information in a rewind fashion. The modulation vector for the i-th layer of the synthesis network groW, is defined as:
4.1. Verification of the lottery codec hypothesis
We first validate the lottery codec hypothesis through a series of experiments on the first 10 images of the Kodak dataset. We implement the C3 scheme with a 16-dimensional ARM as the baseline. For comparison, we search for subnet- work within a randomly initialized network and replace the well rell-trained synthesis network in C3 with this subnetwork, keeping all other components unchanged. This method is referred to as the C3-Lottery scheme. See Appendix B.4 for more details.
M; Concatenate(Uu,c -1,-2..... -i) (10)
where vectors Uj's from ModNet are concatenated in re- verse order to facilitate the search for high-performing subnetwork.
The modulation operation concatenates M1 with the inter- mediate layer output of groW,. Consequently, the output of each masked linear layer after modulations is given by:
Fig. 6 presents the RD trade-off across varying net- work depths and widths. The results demonstrate that when the randomly initialized network is sufficiently over- parameterized, the C3-Lottery scheme successfully identi- fies subnetwork and an associated latent representation that achieves the same level of distortion as C3, but at a lower bitrate. In particular, Fig. 6a presents PSNR versus the rate
G m (Fi) Concatenate(MI, Fi).
(11)
where F; represents the output of the i-th layer of froWo. and G is the output after corresponding modulation opera- tions. Intuitively, this concatenation enriches the structure of the SuperMask network with both sign and magnitude in- formation, allowing for the reactivation of features in deeper
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LotteryCodee: Searching the Implicit Representation in a Random Network for Low-Complexity Image Compression
Butter
5D vs 1 978-3211 Busto
getter
13
FSUR
Mosling % of NOghtAT
24
03
65
03
64
C9
67
EDvir of LezeryCace:
(b)
(c)
Figure 7. Performance LotteryCodce and other schemes. (a) RD curve and BD rate on Kodak dataset. (b) RD curve and BD rate on CLIC2020 dataset. (c) BD-rate and decoding complexity across different mask ratios Kodak dataset.
contributed by 2, demonstrating that RD performance (in terms of the PSNR-rate curve and BD-rate) improves as the network width increases. In particular, when depth N₂- 4,
improvements are also observed from Fig. 7b over C3 (-5 (-5.99% BD-rate), C3-adpt (-2.00% BD-rate) and COOL- CHIC v2 25.5% BD-rate), respectively. From experi- ments on both the Kodak and CLIC2020 datasets, the Lot- teryCodec scheme demonstrates state-of-the-arr RD per- formance among current overfitted codecs. To the best of our knowledge, LotteryCodec the first neural codec to surpass VTM in RD performance while maintaining low decoding complexity, establishing it as the state-of-the-art for single-imaç image compression. Like other overfitted codecs, LotteryCodec
the C3-Lottery scheme matches or even surpasses the per- formance of well-trained C3 baselines for width d 2 64. Additional results for different depth settings can be found in Appendix B.4. Fig. 6b illustrates the impact of the mask ra- tio on performance, revealing that the optimal LotteryCoder is achieved mask ratio of approximately 50%. Intu- itively, this occurs because 50% mask ratio maximizes the entropy of the network structure, allowing more infor- mation to be encoded into the structure. Figs. 6c and 6d indicate that increasing both the depth and the width of the random network can significantly enhance RD performance. Furthermore, employing adaptive mask ratios for different images could further boost performance.
Codec still falls short of state-of-the-ar AE-based neural codecs such as MLIC+ in RD performance. But it achieves a BD-rate over VTM that is comparable to MLIC, with only a +2.33% gap. As shown in Fig. 1, LotteryCodee demonstrates a significant advantage over MLIC+ in terms of decoding complexity, requiring two orders of magnitude fewer decoding operations. Further discussion complex- ity is provided later.
4.2. RD performance of the LotteryCoder
We then compare the RD performance of LotteryCodec with the existing methods. As shown in Fig. 7a, LotteryCodec outperforms VTM and significantly surpasses other over- fitted codecs on the Kodak dataset, achieving BDDrate re- ductions of -6.4% over C3 and -3.73% over its adaptive variant, C3-adapt (relative to VTM-19.1). One of the sub- stantial performance gains occurs in the low-bpp regime, where network parameters dominate the compression rate in an overfitted codec. By contrast, LotteryCodec achieves lower rate by compressing binary mask instead of real- valued parameters, resulting in superior RD performance (more details are provided in Appendix B.5). Additional MS-SSIM evaluations are provided in the appendix (see Fig. 13). where LotteryCodec closely approaches ELIC and has a +10.72% BD-rate gap (versus VTM-19.1) compared to MLIC+.
4.3. The mask ratio and decoding complexity
The impact of the mask ratio is examined in Fig. 7c, which illustrates the performance of LotteryCodec under different mask ratios. As expected, the decoding complexity de- creases linearly as the mask ratio increases, since masking more weights reduces the overall computation required by the network. However, RD performance does not follow monotonic trend with respect the mask ratio. Interest- ingly, with the introduction of the rewind modulation, the optimal mask ratio for LotteryCodee to achieve the best BD-rate is around 20%, different from 50% observed in Fig, 6. Intuitively, decreasing the mask ratio from 50% to 20% significantly reduces the number of possible subnetworks, demonstrating that rewind modulation effectively simplifies the subnetwork search process while maintaining strong compression performance.
Fig. 7b shows the results the CLIC2020 dataset, where LotteryCodec demonstrates an even greater advantage. In particular, the performance gain over VTM-19.1 reaches up to 9..7%% (see Appendix B.5 for details). Consistent
Additionally, Fig. 7c demonstrates that LotteryCodec can flexibly balance RD performance and decoding complexity, allowing for adaptable trade-offs based on specific require-
8

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LotteryCodee: Scarching the Implicit Representation in a Random Network for Low-Complexity Image Compression
ments. Notably, even with high mask ratio of 80%, which results in low decoding complexity, LotteryCodec still out- performs the C3 baseline scheme. More detailed ablation studies and additional experiments on varying mask ratios are presented in Appendix B.5
gies exist, such meta-learning, mixed-precision training, and neural architecture search. In partieular, LotteryCodec also opens the door to parallel encoding of overfitted codecs by reparameterizing distinct network learning processes into a batch of mask learning processes.
more comprehensive comparison of decoding complexity between Lottery and other neural codecs is presented in Fig. and Fig. 10a. In particular, compared to most AE- based schemes, LotteryCodec achieves similar superior RD performance with at least an order of magnitude fewer MACs. For more advanced codecs like ELIC and MLIC+, while LodteryCodec does not exceed their RD performance, reduces MACs by over two orders of magnitude while maintaining acceptable quality. Compared to other over- fitted image codecs, such as the COOL-CHIC/C3 family, LotteryCodec achieves better RD performance with lower decoding complexity.
Future work. As a novel paradigm in image compression, LotteryCodec opens several avenues for future research, First, its performance and efficiency could be further opti- mized by incorporating advanced strategies, such those proposed in (Kim al., 2024; Ladune et al., 2024). Sec- ond, LotteryCodec can be extended as flexible alternative for video coding. By sharing modulation across adjacent groups of frames (GoF) and applying distinct masks, it can also encode temporal information into the network struc- ture. Moreover, video coding enables adaptive mask ratio selection across GoF, offering greater flexibility in both com- putational complexity and rate control. Its low decoding complexity positions LotteryCodec as a promising approach for real-world neural compression applications, enabling efficient deployment in resource-constrane environments.
Notably, the current figure shows the theoretical minimum decoding complexity, excluding masked operations. This lower bound can be approached with sparsity-aware libraries (e.g.. TVM (Chen al., 2018), cuSparse (Naumov et al., 2010), DeepSparse (Kurtz al., 2020)) on compatible hard- ware. For comprehensive analysis, we also report real coding times using structured pruning (see Tables 7 and 8 in the appendix). Additionally, we provide both theoretical upper and lower bounds on decoding complexity, corre- sponding to unpruned and active operations, respectively, with practical complexity lying in between. As shown in Fig. 11, even without pruning. LotteryCodec outperforms C3 in BD-rate with similar complexity.
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
Acknowledgments
This work received funding from the UKRT for the projects INFORMED-AI AI (EP/Y028732/1) and AI-R (ERC Consol- idator Grant, EP/XX00006/1).
5. Conclusion and future work
This paper introduces and validates the lottery codec hypoth- esis, which proposes new paradigm for image compres- sion: encoding images into structures of randomly initial- ized networks. Building on this hypothesis, we propose LotteryCodec, novel overfitted codec that compresses an image into modulation vectors and a binary mask for an over-parameterized, randomly initialized network. The proposed LotteryCodec achieves state-of of-the-art RD perfor- mance among existing overfitted codecs while maintaining adaptive and low decoding complexity. Our work advances the field of overfitted image compression by addressing the critical challenge of achieving high compression efficiency with minimal computational cost.
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LotteryCodec:
Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
Appendix
A. Quantization and entropy coding methods
For compression, the latent modulation z and network parameters 0, & are quantized into 2, 0 and vi respectively, and subsequently entropy-coded into bitstream, using standard methods, as in (Kim al., 2024; Ladune al.. 2024). More details can be seen in the Table
A.1. Latent modulation
Quantization. Similar (Kim et al., 2024), we adopt two-stage quantization aware optimization approach for optimizing During the training stage, is learned in continuous space for discrete optimization, with quantization approximated using Kumaraswamy noise. This soft-rounding technique ensures that the quantization process remains differentiable with respect to z. In the inference stage, uniform quantization with hard-rounding is applied to as:
(T(Z)) Q(z),
Training Stage
(12)
Training Stage I & Inference Stage,
where Sy denotes soft-rounding operation with temperature T, Q represents hard-rounding, and Ukam is the Kumaraswamy noise term. The temperature and noise strengths are controlled to shape the Kumaraswamy distribution, transitioning from a peaked form (low noise) at the beginning the training stage to a uniform distribution by end.
Entropy coding. Similar to (Ballé et al., 2018; Ladune al., 2023; Minnen et al., 2018), we introduce factorized auto- regressive model ro to estimate the distribution of 2, which is necessary in the entropy coding algorithm. The distribution of each latent element of 2s, (the j-th element of 2,) is conditioned on C' spatially neighboring elements CLj 2 as:
Ps (2) = II
Po (
(13)
1
where (2) modeled by an integrated Laplace distribution as
(o((s_//11)) = A4. g(2)d2.
(14)
-0.5
The expectation and scale parameters are estimated via context elements as g L(Mig o..), where Pig. rw (c..).
With this estimated distribution 2, the range coding algorithm is used (range-coder in PyPI), as (Kim et al., 2024) 2, to compress 2. The resulting rate contributed by is then given by:
R(2) loga (2)
Σ i.j
loga Pa (2tg)cij)
(15)
A.2. Model compression
The parameters of ModNet and ARM are essential for decoding and are therefore compressed. Specifically, we first quantize db 0 using a scalar quantizer Q(, A) with step size A as:
i Q(0, Ao), and Q Ag).
(16)
The quantized parameters Ô and & are then entropy-coded, where the discrete distribution of each quantized parameter modeled by a continuous Laplace distribution. Specifically, the probability of quantized parameter from 0 (similarly for v)) given by:
0.40.5
p(O.) = -0.5
g())d with g L(0, (tt.dvv())))))
(17)
where g follows Laplace distribution with zero mean and standard deviation stddev (0) of the quantized parameters.
AA optimized C++ implementation is open-sourced on COOL-CHIC project page.
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LotteryCodee: Scarching the Implicit Representation in Random Network for Low-Complexity Image Compression
Then, the total rate contribution from both ARM and ModNet can be expressed as:
RMLP Rg R
Σ
logz p(0.) + Σ log2 p (())).
(18)
A greedy search over quantization steps selects optimal Ao and A by minimizing the following rate-distortion cost: min D(S, (ro. (fo(2), x)) XR, Ag.A.
(19)
where is the same as that in Eqn. (5).
B. Implementation details.
B.1. Baseline choices
LotteryCodec is compared against classical codecs, including VTM (Bross et al., 2021a) and HEVC (Sullivan et al., 2012), as well as autoencoder-basee neural codecs: CST (Cheng et al., 2020b) (a competitive neural codec), EVC (Wang et al., 2023) (optimized RD performance with low decoding complexity), and MLIC+ (Jiang et al., 2023) (one of the state-of-the-art neural codec). Additionally, we compare with overfitted INR-based codecs such as C3 (Kim et al., 2024) (state-of-the-nne overfitted image codec) and COOL-CHICV2 (Leguay et al., 2023) (an optimized version of COOL-CHIC version). We measure PSNR on RGB channels and quantify RD performance using the BD-rate metric (Gisle, 2001). The baseline results were obtained using their official implementations directly using the reported results (C3, MLIC+) from their papers. For VTM, we use the CompressAl library (Bégaint et al., 2020) for an updated VTM-19.1 (YUV 10 bits) version, where code and datapoints are provided on our project website.
B.2. Datasets
Unless specified otherwise, we use the Kodak dataset and CLIC2020 professional validation sets for evaluation. Specifically, the Kodak dataset consists of 24 images, each with resolution of 512 x 768. The CLIC2020 professional validation set includes 41 images with resolutions ranging from 439 x 720 to 1370 x 2048.
B.3. Model architecture
We provide the detailed architecture setting for the proposed LotteryCodec scheme in Table 1.
For the ARM model with c contextual elements as input, denoted as ARM-c model, there are three linear or 1 x 1 convolutional layer, followed by GELU activation functions, with input and output dimension given (c x c) - GELU + 2). For the proposed LotteryCodec, we employ c {8, 16, 24, 32).
(c c) > GELU
The ModNet model, using L-dimensional latent modulation as the input, comprising L, layers (L, 4 and L 7 in this paper), the input and output dimension are given as: (7 x d) GELU + (d 3) - GELU + (3 x 3). For the proposed LotteryCodec, we employ c e {32, 48} for Kodak and CLIC2020 dataset.
For the SuperMask model using pixel coordinates as the input, comprising L, = 4 layers, the input and output dimension
are given as: (2 x 32) GELU + ([32 + 3) x 24) - GELU + ([24 + 3 + 3] x 16) - ([16 + + 3 + d] x 3) + Tanh.
To optimize the RD performance, can further add 3 x 3 convolutional operation in ModNet: (7 d) + GELU + (dx3) - GELU + (3x3) - GELU + (3x where the last two output are concatenated as the first modulation input. As result, the SuperMask mapping becomes: (2x - GELU + ([32 ([32+3+3] 24) GELU - ([24333++3) 16) +
([16 3 3 + d] x 3). This additional modification can be omitted if lower complexity is prioritized.
B.4. over-paramettrization experiments
This section outlines the detailed experimental settings of Section 4.1.
Section. 4.1 trains over-parameterized models with varying mask ratios (10% 20%, 30%, 50% 70%, 90%) and different E {2e- - 2, 1e - 2, 5c 3, 1e 3. - 4, 2e - 4} to compute the BD rate, which yields 36 models for each image. Considering extensive experiments, we use the first 10 images Kodak dataset to compare the average performance, which indicates that each point in the figure corresponds to an average performance of 360 well-trained INR models.
Datasets.
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LotteryCodec: Searching the Implicit Representation in a Random Network for Low-Complexity Image Compression
Hyper parameter
Initial values
Final values
Values of À
[2e
le
5e
le
5e
2e
Quantization Stage
Number of encoding steps Learning rate 3
10
10-2
0
Scheduler for learning rate
Cosine scheduler
Temperature T for soft rounding
0.3
0.1
Noise strength a for Kumaraswamy noise
2.0
1.0
Scheduler for Soft-rounding and Kumaraswamy noise
Linear scheduler
Quantization Stage II
Number encoding steps
10a
Learning rate
10-4
10
Decay learning rate if loss has not improved for this many steps
40
Decay factor
0.8 10" 10-4 4
Temperature T for soft rounding
Architecture - Latent modulations
Values
Number of latent vectors L Initialization of
7
Architecture ModNet
Values
Output channels the 1 x 1 convolutions
(48, 3) vs. (32, 3}
Number of 3 residual convolutions
{1} vs [2]
Architecture Entropy model
Alternttve widths of the 3 layers residual convolutions (ARM-c) Activation function
c E (8/16/24/32) GELU
Log-scale of Laplace is shifted before exp Scale parameter of Laplace is clipped to Architecture SuperMask network
4
[10 2, 150]
Values
Output dimensions of MLP layers
{32, 24, 16,
Mask ratios
{0.1, 0.9) with 0.05 intervals
Initialization of MLP
FFN initialization
FFN initialization phase number P
32
FFN initialization low/high frequency number F Initialization of score matrix P Learning rate for P Scheduler
64/64
Kaiming uniform initialization 0.1
Cosine scheduler
Table Hyper-parameter settings
Model architecture As illustrated in Fig. 8, we replace the synthesis network of C3 with an paraparameterize network, denoted as C3-Lottery. We present architecture with different over-parraeetrizzaionnn levels, in Table 3 and Table 4.
For fair comparison, we employ the same ARM model for the C3 in Section 4.1 the target network. To ensure fair evaluation of our hypothesis, only the synthesis network is replaced while all other components are kept unchanged for both schemes, as seen in Fig. 8.
Fast implementation. Given that LotteryCodes requires adaptive adjustments to mask ratios and model architectures across images, which may incur extra computational costs, we provide recommended configuration in Table 2 that achieves near state-of-the-art performance with less adaptation and faster training.
We also provide additional experimental results on the impact of increasing the depth of the over- wver-paraeeterizer network, as shown in Fig. 9. Specifically, Fig. 9a and Fig. 9b present the PSNR vs. rate term of 2 (bpp) and the corresponding BD-rate performance for randomly initialized networks with hidden dimensions of 48 and 64, respectively. We observe that, in both cases, a deeper network generally increases the likelihood of finding a winning lottery
More experimental results.
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LotteryCodec: Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
Architecture ModNet
Values
Output channels of the 1 x convolutions
{ 488, 3)
Number of 3 x 3 residual convolutions
{2}
Architecture Entropy model
Alternative widths of the 3 layers residual 1
x convolutions (ARM-c)
C E {16/24)
SuperMask network
Values
Mask ratios
(0.15, 0.4] with 0.05 intervals
Table Fast implementation of LotteryCodee
Over paner-aarrrmtttteedddd network
randomly initialized
ARM
C3-Lottery
VS.
Sel Goty
322 CaM
model
Cone
C3-baseline
Trainable sythesis network
Figure 8. Illustration of the experiments in Section 4.1: the synthesis network is replaced with a randomly initialized over-parameterized network, where only binary mask is learned, while all other components remain unchanged for fair comparison.
ticket, leading to improved RD performance. Notably, for = 64, lower distortion achieved with fewer layers.
C3-Lottery model
C3-Lottery (4, (4)
C3-Lottery (4,
C3-Lottery (4,64)
C3-Lottery (4, 128) (7, 128)
Masked linear layers
(7, 24)
(7, 37)
(7, 64) (64, 64) x 4,
(24, 24) x 4
(32, 32) x 4
(128, 128) x 4
(24, 3)
(32, 3)
(64, 3)
(128, 3)
Baseline C3
(7, 18;; (18, 3): (3, 3); (3, 3)
Table 3. Going wider: Model architectures (input-output channels) for over-parameterizzaion experiments, where all models employ an auto-segressive entropy model (ARM-16). The mask ratios for the experiments (0.1, 0.3, 0.5, 0.7, 0.9).
C3-Lottery model
C3-Lottery (1,48)
C3-Lottery (2,48)
C3-Lottery (4,48) (7, 48)
C3-Lottery (6,48) (7, 48)
C3-Lottery (8,48)
Masked linear layers
(7, 48)
(7, 48)
(7, 48)
(48, 48) x
(48, 48) x 2
(48, 48) x 4,
(48, 48) x 6
(48, 48) x
(48, 3)
(48, 3)
(48, 3)
(48, 3)
(48, 3)
C3-Lottery model
O61-1
O61-2
O61-4
O61-6 (7, 64)
O61-8
Masked linear layers
(7, 48)
(7, 64)
(7, 64)
(7, 64)
(64, 64) x
(64, 64) x
(64, 64) x 4,
(64, 64) x 6
(64, 64) x
(64, 3)
(64, 3)
(64, 3)
(64, 3)
(64, 3)
Baseline C3
(7, 18); (18, (3, 3); (3,3)
Table Going deeper: Model architectures (input-output channels) for prerpearamttriization experiments, where all models employ auto-regressive entropy model (ARM-16). The mask ratios for the experiments are (0.3, 0.5, 0.7).
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LotteryCodee: Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
PSWR (68)
PSNR (d8))
race
BD
C3 10400
30-
Cliettery (8.44)
censtre
Cslattery I534)
Lattery 16.60
C3 Lottery (4,4)
CDtateryy 14,40)
brselire
Chisttery (2,40)
Chitteery (340)
CS4attary 12.48)
15
Citctiary (266)
0.0
65
1.
12
26
0.2
0.1
12
Date (xpp) 14)
Date (ppp) (1)
(8)
(b)
Figure 9. Verification the lottery codec hypothesis across varying network depths when hidden dimension and 64.
BD-rate vs VTM-19.11 in [%)] (4)
AE based codec Overfitted codec
BD-rate vs VTM-199 19.19..1 In (%) (L)
COOL-CHICV2
AE Ei-based codec Overfitted Codec LotteryCodec
20
C3
LatteryCodec
adapt.
CST
10
EVC-S
CST
EVC-M
EVC
LotteryCodec (ours)
EVC-L
EVC-L
C3 adapt.
-10
ELIC
LotteryCadec (aurs)
MLIC
MLIC+
MLIC
-10
-20
10a
10
105
109
10a
10
Decoding complexity (MACs/pixel] (4)
Decoding complexity [MACs/pixel] (4)
(a) Kodak
(b) CLIC2020
Figure Performance of LotteryCodec (mask ratios E [0.15 0.05 : 0.9) across different decoding complexities (a) BD-rate across different decoding complexities Kodak dataset. (h) BD-rate across different decoding complexities the CLIC2020 dataset.
B.5. More experiments: BD rate vs. decoding complexity
We report the BD-rate (vs. VTM 19.1) on the Kodak and CLIC dataset in Fig. 10. We note that VTM configurations vary between implementations (Kim et al., 2024; Blard et al., 2024), and the BD-rate computation depends on both configurations and datapoints. For a fair and more aligned comparison, we update VTM baseline into VTM-19 19.1 from CompressAl (Bégaint al., 2020) and recompute BD-rates for all codecs under similar settings. also open-resourced all above baselines and datapoints in our project page for future alignment.
Due to computational constraints, the optimal BD-rate is evaluated (1e-2,5e 1e-3 5e-4, 2e 1e-1). Other datapoints in Fig. (especially CLIC2020) are trained with a narrower range [0.15, 0.45]. yet LotteryCodec still achieves strong performance. Further optimized RD-complexity trade-off's are ex- pected with broader mask ratio selection (see our updates on the project page). Detailed datapoints, lambda, and complexity are provided on our project page.
ratio [0.15, 0.9] and À
B.6. Theoretical vs. practical decoding complexity
The current figure reports the theoretical minimum decoding complexity, excluding the multiplication operations of masked parameters, an evaluation approach also adopted in (Han et al., 2015a;b). This lower bound can be approached with aparsity-aware libraries (e.g., TVM (Chen al., 2018), cuSparse (Naumov et al., 2010), DeepSparse (Kurtz al., 2020) on
17

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LotteryCodee: Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
BD-rate vs VTM-19.1 in (% (4)
VTM-19.1 11.19.. in (%) (4)
VTM19.1
5
C3 adapt.
BD-rate vs VTM-
VTM19.1
-5
C3 adapt.
LotteryCodec (ours)
LotteryCodec
$60
104
-190
104
Decoding complexity [MACs/pixel] (1)
Decoding complexity [MACs/pixel] (4)
(a) Kodak
(b) CLIC2020
Figure Flexible complexity region Kodak and CLIC2020, where the dashed region is achievable varying the mask ratios.
$2.40
Fourier initalization
Kaiming normal
Kaiming
0.00354
Kaiming
Kaiming nomal
Fourier Inttalizztionn
0.00354
$2.50
PSNR (dB)
RD-J RD-Loss with
22.00
0,00:33
020244
32.10
20000
25800
33300
45000
2200
20003
3000
40000
<5000
50000
55066
Step number
Step number
(a)
(b)
Figure Ablation study on initialization methods: (a) PSNR performance vs. coding step. (b) RD performance vs. coding step. The model is evaluated every 10 coding steps, and the best-performing model at each step is plotted. Results are presented for kodim01 as an example.
appropriate hardware. We adopt this metric because practical MACs per pixel and runtime for unstructured sparse networks highly dependent implementatiion-seeiii engineering factors, making fair comparisons difficult conduct.
For a comprehensive analysis, report real coding times using simple structured pruning strategy (see Tables 7 8), highlighting LotteryCodec's efficiency, especially on high-resolution images. Additionally, we also provide both theoretical upper and lower bounds on decoding complexity: the upper bound accounts for all operations without pruning, while the lower bound considers only active components. Practical complexity lies between these bounds, depending on implementation. As shown Fig. 11, even without pruning, LotteryCodec achieves better BD-rate than C3 scheme, with comparable complexity.
C. Qualitative analysis
Justification of Lottery Codec Hypothesis (LCH). Although rigorous bound supporting the LCH is not available, we can provide a rough validation based on existing proofs for Strong Lottery Tickets Hypothesis (SLTH). Suppose a codec gw (z) is overfitted to an image S, resulting in distortion a. According to SLTH, for any > O, there exists a subnetwork within sufficiently wer-parameterized network gw,, defined by supermask т, such that d(gw (z), gw (2)) c. Thus,
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LotteryCodec: Scarching the Implicit Representation in Random Network for Low-Complexity Image Compression
reconstructing the image S using ow (z) results in distortion of most a Now, we can further decrease the distortion by optimizing the latent vector set of z' satisfying H (zz)) (2), along with the supermask т. Since be made arbitrarily small, it is highly likely that can find a pair of (r's z²) such that (w (z') S a.
intuitively justify why the proposed LotteryCodec outperforms previous overfitted codecs in terms of the rate- aate-distortion performance. The rate formulations for overfitted codecs and our LotteryCodec are given in Eqs. (2) and (5), respectively. They show that the rate of overfitted codecs depends on {2. 4 W), while our method is determined by {2, vi r, B). According to LCH, to achieve the same level of distortion, we can find a pair of (2) such that the bit cost for 2 and e is equal to that of overfitted codecs. While each quantized parameter in W typically requires over 13 bits, our binary mask uses just bit per entry. Despite its higher dimensionality, contributes significantly less to the total rate. Moreover, since 0 is lightweight, the combined rate of and 0 remains lower than that of W, resulting in a lower compression rate and improved RD performance.
Intuition Behind the Advantages of LotteryCodee. Based on the LCH,
D. A Ablation studies
D.1. Impact of each component in LotteryCodec
To clarify the impact of each component in our design, we conduct an ablation study on each component. As shown in Table below, removing the Supermask network and using only the modulation network increases BD-rate by +12.45%, highlighting the importance of the random network. Removing ModNet and directly feeding z into the random network (with different overparameterizatton configurations) results in performance drop of up + +4.99% due to high overparameterization costs. Additional ablation studies and visualizations of other components are provided in Table 6.
I LotteryCodec
w/o SuperMask
Random network w/o ModNet: (4, 4,32)/ (4, 48)/ 64) -1..02% + 11.98% + 14.99%
+12.45%
Table 5. Change BD-rate due removal of individual components from LotteryCodee, ARM dimension
D.2. MS-SSIM distortion metric
In addition, we evaluate LotteryCodee against baseline methods in terms of MS-SSIM distortion on the Kodak dataset, as shown in Fig. 13. Specifically, we train our method with an MS-SSIM loss with À E (3e-1, 1e, 3.3e2, 2.2e-, -2 le=²), achieves up -43.39% BD-rate reduction over VTM-19.1, closely approaching ELIC and showing +10.41% BD-rate gap compared to MIIC+
22
20
MS-SSIM (dB) (f)
18
16
14
MLIC+
12
ELIC
LotteryCodec
VTM-19.1
10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Rate (bpp)
Figure 13, Rate-distortion performance for MS-SSIM metric.
19

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LotteryCodee: Scarching the Implicit Representation in a Random Network for Low-Complexity Image Compression
D.3. Other initialization methods
We conduct different initialization methods, the overall BD performance is presented in Table 6. To simplify the validation, here we employ the same training steps of 60000 in Stage I and 6000 for Stage II for all schemes. We also present the PSNR performance and loss values during the coding process in Fig. 12. We can observe that the Fourier initialization employed can enhance the performance and coding process.
Model Variant
BD rate vs. LutteryCodee
Coder scheme
0.055
Kaiming nonnal initialization (He 2016)
+1.55%5
Signel Kaiming inirialization (Ramanujan
+0.6395
FIlM modulatin methods (Peres et al., 2018)
42.21%
Scure Score-based same layer masking algorichm (Ramumujan et al., 2020)
+1.77%
NoRF positicnal encuding module (Mildenhall et al., 2021)
Not work well
initialization 2016)
Not
Gumble-solmaa for mask raño learning (Miles Mikolajzzyk, 2020; Dupont al. 20226)
Not work well
Bernoulli-hased masking algarithm (Zhou et al., 2019)
Not work well
Table 6. Ablation study on different mechanisms, conducted on the first 10 Kodak images using an ARM-16 model and a mask ratio of 20%, where À E (2e -2 1e_ee=2,000 53 le 33 2e 2e- ). A higher BD rate indicates worse RD performance, and "Not work well" signifies lack of robustness and unsatisfactory results
D.4. Other Modulation methods
Cafe
Weigeedd
Markne Uinar
Mark Blosk
Raparinak
Layer
(x,))
Layer
Superbausk
(4)
Figure 14. Different alternative modulation methods of the LotteryCodec. (a). A FilM-based modulation approach. (b). Concatenation- based approach
Note that LotteryCodec is flexible framework that supports various modulation methods. We also implement a FiLM-based modulation (Perez et al., 2018), as shown in Fig. 14 (a), whose performance presented in the Table 6. Interestingly, experiments show that additive bias alone achieves competitive performance, although falls short of the proposed concatenation-basee method. This approach, however, provides the potential of reducing inference complexity and exploring alternative modulation strategies in future research.
D.5. Alternative masking learning approach
This section presents various trials we explored. While some did not yield satisfactory results, we include them for completeness and future reference. Specifically, to achieve adaptive mask ratio, employed Gumbel-Softmax scheme for dynamically controlling the pruning rate, following (Miles & Mikolajezyk, 2020; Dupont et al., 2022b), but it did not produce satisfactory results. A similar Bernoulli-bar based approach, as in (Zhou et al., 2019), also underperformed compared to the current LotteryCodec. Additionally, we evaluated a mask learning algorithm applying fixed pruning rate across each layer (Ramanujan et al., 2020), which resulted in worse performance. Lastly, positional encoding, similar to (Shi et al., 2024), did not yield performance gains the context of overfitted codees.
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LotteryCodee: Scarching the Implicit Representation in a Random Network for Low-Complexity Image Compression
D.6. Coding latency across various resolutions
We present the coding cost of various schemes in Table 7, and report resolution-dependent coding costs in Table 8. The proposed method shows scalability to tithrsiighhresolutionn images, albeit with increased coding time. An additional example of 2K image encoding is shown in Table 9. Overall, our method has slightly higher encoding time than other overfitted codecs due to additional gradient-based mask learning, but it offers greater flexibility and faster decoding. Notably, the lottery codec hypothesis provides potential for parallel encoding by re-parameterizing distinct network optimizations into batch-wise mask learning, highlighting its advantage scalability for efficient large-scale image encoding.
All of these results are based on unoptimized code and current hardware, which can be significantly improved with proper engineering optimization. For example, we can accelerate inference via ONNX and DeepSparse libraries reduce the decoding time 20 80 on CPU. Additional techniques (Blard al., 2024), such symmetric/separable kernels, filter-based upsampling, and wavefront decoding, can further enhance the speed of overfitted codecs.
Models
Encoding time
Decoding time
VTM 19.1
85.53 (8)
352.52 (ms)
EVC (S/M/L)
20.23/ 22/33/2.21////// .35 (ms)
18.82/23. 23.73/
/32.56 733.73/32.6
(ms)
MLIC+
205.60 (ms)
271.31 (ms)
LotteryCodec (d 8/16/24) C3 C3 12/18/24)
13.86/14.64/14.992 (sec/Ik steps)
261.33 //////27.58///..8 (ms)
13.10/18.98/14.22 (sec/1k steps)
272.15/284.67 /295.03 (ms)
Table 7. Coding time for Kodak images on NVIDIA L40S (GPU) and Intel Xeon Platinum 8358 (CPU) with masking ratio of 0.8 under structured pruning. Orange indicates GPU computation; blue indicates CPU computation.
LotteryCodec vs. C3
Lottery Codec vs. C3 vs. MLIC+
Input resolution
GPU Encoding
CPU Decoding
Peak Memory usuage during the training (GB)
(sec/1k steps)
(ms)
512 x 512
10.71 vs. 10.43
232.46 vs. 228.43
0.56 vs. 0.31 vs. 1.98
1024 x 1024
56.81 vs. 38.54
565.22 vs. 576.51
2.15 vs. 1.24 vs. 3.61
1536 x 1536
136.81 vs. 84.79
984.01 vs. 1086.92
4.82 vs. 2.78 vs. 9.15
2048 x 2048
257.93 vs. 155.02
1595.86 vs. 1807.35
8.53 vs. 4.95 vs. 24.37
2560 x 2560
407.68 vs. 237.45
3003.24 vs. 3269.02
13.36 vs. 7.72 vs. OM
3840 x 2160
446.09 vs. 301.56
4014.21 vs. 4216.11
16.89 vs. 9.84 vs. OM
Table Encoding time for images across different resolutions, where mask ratio 0.8 and ARM model of d 16 are employed. OM mcans out of memory (> 32 GB).
Training steps
Training time (s)
hpp
PSNR (dB)
5k
678
0.24
36.51
10k
1347
0.22
36.92
20k
2685
0.21
37.02
30k
4026
0.20
37.10
50k
6733
0.199
37.14
Table Encoding cost for 2K image (size 1292 1945), "davide-ragusa-716 in CLIC2020 with optimal result PSNR 37. 18 hpp 0.196" (d = 24, ratio 0.2, peak memory 5.64 G), where 10-20k steps can yield descent performance.
E. Pseudocode for the algorithm
This section provides detailed encoding and decoding algorithm of LotteryCodec, as shown in Algorithm 1 and Algorithm 2.
F. Visualization
Compression Cost. This section visualizes the compression cost of each component in the bitstream of LotteryCodec. As shown in Fig. 15, thanks to the introduction of ModNet, bit cost of the binary mask can be minimal, particularly for
21

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LotteryCodec: Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
26
nete share each componeent 154
Nodilation
ATN NedRas
Dinory IISSA
C2-
(h)
Figure Visualization of compression cost distribution across the rate within the LotteryCodec scheme using a ARM-24 model a mask ratio of 0.2: (a) Rate share of compression cost on the Kodak. (h) Rate share of compression cost the CLIC2020.
mask ratio
1000%
0%
ARM
ModNltt
SuperMask network
304-8
part
2014
Decoding complexity (MACsipioel)
Figure 16. Decoding complexity of each component in LotteryCodec, where ARM-d denotes ARM model with a hidden dimension of d.
hesherone images like those in the CLIC2020 dataset, where the same network used with a lower hpp contribution from binary mask. As bpp increases, modulation bit cost rises, allowing finer image details to be preserved within the given bit budget. Since the network architecture is fixed, then the relative bit cost (%) contribution from the network and binary mask decreases bpp increases.
Decoding Complexity Analysis. To illustrate the adaptive complexity advantage, we visualize the decoding complexity of each component in the LotteryCodec scheme in Fig. 16. The SuperMask network contributes significantly to the total decoding complexity, which can be adaptively controlled via different mask ratios, enabling flexible complexity management across various regimes. Specifically, for LotteryCodec using ARM-8, 8, the SuperMask accounts for more than 60% of the total complexity, demonstrating its remarkable adaptability and efficiency, particularly in low-bpp regimes.
Effect modulations different SuperMask layers. We visualize the effect of different modulations from each ModNet layer in Fig. 17, where we employ three-layer ModNet and four-layer SuperMask network. When considering the mask ratio: lower mask ratio tends require complex modulations to aid the LotteryCodec search the subnetwork, which is reflected in the increased variability of signs and entropy, leading stronger representational ability, The variability of signs also indicates greater dependence on the randomly initialized network, especially with a low mask ratio. At lower mask ratios and lower compression rates, the ModNet output also exhibits more complex distribution. demonstrating the utilization of the random network for representation.
Additionally, the shallow ModNet layers play a more crucial role, as they are directly connected the deeper SuperMask
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LotteryCodee Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
Mod
Mod
Mod
Mod
27.34 08/0.0751
d./1.41
Mod
Mod
Mod
0.8/ 40.45 dB/ 1.42
(a)
(b)
Figure 17. Visualization of ModNet outputs and their effects in LotteryCodec scheme, where 0.2/27.34 /0.0751 represent reconstruction with 0.2 mask ratio, 27.34 PSNR, and 0.0751 bpp. Mod represents the visualization of the i-th layer of ModNet. The first shows reconstructions with all but the selected latent outputs set to zero, while the second row displays the averaged feature outputs, upscaled to match the resolution of the reconstructed image. Visualizations are provided for both low bit-rate (a) and high bit- (b) scenarios.
layers without rewinding, significantly influencing the synthesis process. contrast, the deeper ModNet layers provide coarser information, such as lighting and overall structure, which is repeatedly fed into different layers in rewind fashion.
Effect of different input latent modulations. We also visualize the effect of the input latent modulations in Fig. 18. As shown in the figure, observe that the highest resolution latent grid primarily captures luminance and structural details of the image, while lower resolution latent grids provide complementary information for the overall image reconstruction.
Effect of latent modulations across different bit rates. Comparing Fig. 18 (a) and Fig. 18 (b), we observe that in low-bpp scenarios, lower-resolution modulations play dominant role in reconstruction, while higher-resolution modulations contribute minimally. This highlights an RD trade-off, where lower-resolution modulations prioritize rate efficiency at the cost of higher distortion. Conversely, high-bpp scenarios, reconstruction is primarily influenced by higherorosolutton modulations, capturing finer image details.
Effect of different mask ratios. Comparing a mask ratio of 0.2 with 0.8, we observe that a lower mask ratio distributes more details across each layer of modulation (from 2ı 27), allowing the synthesis process to utilize richer structural information. In contrast, at higher mask ratio of 0.8, the generation process is predominantly influenced by high-resolution latent representations, with less contribution from lower-resolution modulations.
Interpretation of the design. From the above visualizations, we interpret modulation as additional "bias", where concatenating neurons with a learned weight mask is equivalent to adding flexible bias to the subsequent layers. This design demonstrates that the SuperMask network aims to encode images into the network structure, while ModNet introduces a flexible "adaptive bias" to enhance representation flexibility. As shown in Fig. 17, modulation outputs from different ModNet layers contribute varying compensatory information for image reconstruction.
23

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LotteryCodec: Scarching the Implicit Representation in Random Network for Low-Complexity Image Compression
Algorithm 1 Encoding stage of the LotteryCodec
Source image S, coordinate vector x, random seed e, learning rates for mask scores (P), 3 for modulations (z), and networks (ModNet 0and ARM vt). cosine scheduler for learning rate for Stage and II: C, C2.
Input:
linear scheduler for soft-rounding temperature and Kumaraswamy noise strength for Stage and II: 41, l2.
Greedy search for quantization step: g.
Output: Bits stream of z, vi 0, T: by, by, ba, br.
1: Wo = AB,
II Fourier initialization for g(:) based on e Kaiming uniform initialization
2: P 24x
3: for the i-th step within the Stage do
4: т 1((P), ! growo
I/ Configure network by masking k% weights based P I/ Quantization caaatization-aware aware training I/ Modulate the reconstruction I/ Compute the RD cost loss function
5: â (z) + Ugums
6: S Drowo (fo(2),
7: [ D(S, AR (2),
8:
+ P aVpL,
N Update the scores for mask Update latent modulations I/ Update ModNet // Update ARM // Update learning rate 11 Update noise strength
9: z + z BV,
8
11:
BV
12: Ci i), C1 (B,
13: T T= (T, i), Ukum 1 (Ukum:
14: end for
15: for the i-th step within the Stage II do
16:
T -h(P), = growe
// Mask k% weights based on updated P Hard rounding I/ Modulate the reconstruction I/ Compute the RD cost loss // Update the scores for mask // Update latent modulations I/ Update ModNet // Update ARM Update learning rate Update noise strength
17:
& = Q(z).
S growo (f).
19:
[ D(S XR (2),
20:
P +- P aVpL.
21:
z + B.,
22:
0 - BVGL,
23:
S + + LV
a Ca(a, i), 3 (2(
T 12 (T),
i), Ukam L2 (u
26: end for
27: by A(Q(z))
// Bit stream of after quantization and entropy coding // Bit stream of after entropy coding // Search for a optimal quantization step for networks Bit stream of 8 after quantization and entropy coding // Bit stream of vp after quantization and entropy coding
28: b, = A(T)
29: Ag, A C(O, 15)
30: by = A(Q(B, Ao))
31: b. A(Q(U,
Algorithm 2 Decoding stage of the LotteryCodec
Input: Coordinate vector random seed e, Bits stream: by. b ba. by. Output: Reconstruction of image S.
1: Wo = AB,
I/ Fourier initialization for g based on a given seed e. If Entropy decode mask and configure SuperMask network locally I/ Entropy decode and de-quantize parameters &p and // Entropy decode z // Reconstruct the source image
2: 7 = A(b,), 9 = wro
3: J = Q(A(by)), ((A(b)))
4: = A(fs, bz).
5: S growo x)).
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LotteryCodee Searching the Implicit Representation in Random Network for Low-Complexity Image Compression
0.2/ dB/ 0.0751
0.8/27.33 dB/ 0.0787
(a)
0.2/ 40.84 1B/
0.8/ 40.45044440 1.42
(b)
Figure 18. Visualization of the LotteryCodec scheme using kodim19 example, where 0.2/27.34/0.077 represent reconstruction with a 0.2 mask ratio, 27.34 PSNR, and 0.0751 bpp. From left to right: reconstructed image followed by latent modulations Z₁ to Zy, arranged from high low resolution. The first row shows reconstractions where all but latent the raw latents, upscaled to match the output resolution. (a). Reconstruction and visualization at a low bit-rate (around 0.078 bpp). (b). Reconstruction and visualization at high bit-rate (around 1.41 bpp).
zero. The second row displays
25


Reviews:
[{"review_id": "boTNIV2OHW", "reviewer": "Reviewer_W9j1", "summary": "The paper introduces the Lottery Codec hypothesis based on the Lottery Ticket hypothesis and implements an image codec, LotteryCodec, which achieves strong performance and outperforms the best INR-based image codec while maintaining low complexity.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the valuable comments and recommending two interesting papers. We will add (a) proper discussions of both papers, and (b) suggested ablation studies and tables to the revised manuscript.\n\nFor a discussion of Choi et al. (2023), please refer to our response to Reviewer [ynP1]. Regarding Mehta et al. (2021), while their dual-MLP framework also uses a modulation and synthesis network, it targets multi-instance representation **rather than compression**. Key differences include: (1) our synthesis network is based on the Lottery Ticket Hypothesis; and (2) our ModNet introduces rewind modulation to the synthesis network via concatenation for greater flexibility. Additional ablations over different modulation methods can be seen in Table 4 and Fig. 12 of our original paper.\n\nResponses to the remaining comments:\n\n* Modifications for clarification: ”As shown in Eqs. (2) and (5), the rate of overfitted codecs depends on $\\{\\hat{z}, \\hat{\\psi}, \\hat{W}\\}$, while the rate of our method is determined by $\\{\\hat{z}, \\hat{\\psi}, \\tau, \\hat{\\theta}\\}$. According to Lottery Codec Hypothesis (LCH), our bit cost for $\\hat{z}$ and $\\hat{\\psi}$ matches that of standard overfitted codecs. While each quantized parameter in $\\hat{W}$ typically requires over 13 bits, our binary mask $\\tau$ uses just 1 bit per entry. Despite its higher dimensionality, $\\tau$ contributes significantly less rate. Moreover, since $\\hat{\\theta}$ is lightweight, the combined rate of $\\tau$ and $\\hat{\\theta}$ remains lower than that of $\\hat{W}$, resulting in improved compression efficiency.“\n\n* Ablation study. We conducted additional ablation studies to assess the contribution of each component. See **Table 3.1** and its discussion in our response to Reviewer [itee]. \n\n* Coding speed. We report coding speed for different baselines and resolutions in **Table 4.2**  (response to Reviewer [ynP1]) and **Table 2.1** (response to Reviewer [bWTB]). \n\n*  Detailed BD-rate results are provided and will be included in the manuscript:\n\n### **Table 1.1. Detailed BD-rate data points**\n| Dataset| LotteryCodec |C3|MLIC+|CST|COOL-CHIC v2|\n|-|-|-|-|-|-|\n|Kodak|-3.64%|+3.24%|-13.19%|3.78%|31.65%|\n|CLIC2020| -5.89%|-2.85%|-12.56%|11.70%| 29.30%|\n*  We will cite the C3 source in the revised manuscript. We would also like to clarify that using either a re-implementated or the original C3 code does not affect the validation of the LCH. The goal of the experiment (Fig. 6) is to demonstrate that, in an overfitted codec setting, the synthesis network can be replaced by a subnetwork of a randomly initialized network while maintaining comparable distortion performance. To ensure a fair comparison, only the synthesis network is replaced, with all other components kept identical to the target overfitted codec structure (see Fig. 8).\n\nAnswers to questions:\n* Q1. The current figure reports theoretical minimum complexity, excluding the effect of masked parameters (similar evaluations can be seen in [1-2]). This theoretical lower bound can be approached using sparsity-aware implementations (cuSparse/DeepSparse) on compatible hardware. We adopt this metric to estimate the decoding complexity because both practical MACs and run-time for unstructured sparse networks are heavily influenced by many engineering factors. Thanks to the reviewer’s suggestion, we have decided to also report coding time with a simple structured pruning strategy (see **Tables 2.1** of response to Reviewer [bWTB]), showing our decoding efficiency, especially on high-resolution images. Additionally, we provide both theoretical upper and lower bounds on complexity (**Table 1.2**), where the upper bound includes all operations without any pruning. The practical complexity lies between these bounds, depending on its implementation. Note that compared to the C3 baseline, even a unpruned LotteryCodec can achieve better BD results (-0.1% vs. 3.24%) with comparable complexity (2822 vs. 2626). We will revise the figure using a dashed region to clearly illustrate this range and clarify it in Fig. 1 and Fig. 14 as well. By presenting both the theoretical complexity and the measured run-times, we aim to offer a comprehensive evaluation of our flexible decoding complexity. \n\n   [1]. Han, Song, et al. \"Learning both weights and connections for efficient neural network\"\n \n    [2]. Han, Song, et al. \"Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding\"\n\n### **Table 1.2 Flexible BD-rate vs. MACs/pixel region over Kodak**\n| **BD-rate** |-3.64%|-1.8%|-0.1%|\n|-|-|-|-|\n|**Lower-bound (Optimal)**| 3083| 2513| 2022|\n|**Upper-bound (Non-pruned)**| 3732|3112|2822|\n* Q2. Experiments in Figs. 7(a)-(b) do not impose such constraints, where model architectures follow their original papers. \n* Q3. Our network is roughly half the size of C3, and our entropy model uses $d = \\{8, 16, 24, 32\\}$ vs. C3 ($d = \\{12, 18, 24\\}$). (Table 1 in our paper for more details)", "claims_and_evidence": "Some claims are not clearly elaborated: For example, in line 260, why can LotteryCodec achieve a lower overall rate compared to overfitted codecs?", "methods_and_evaluation_criteria": "- The proposed methods and evaluation criteria are reasonable. The implementation based on the Lottery hypothesis is simple yet effective. It is lightweight while remaining comparable to SOTA models. The evaluation datasets follow common practice in the field.\n- More ablation studies would be helpful. For example, the use of latent variables as modulation vectors differs significantly from C3, where many techniques originate. The authors should compare the performance of the proposed model with modulation removed to clarify whether the performance gain comes from modulation or the lottery ticket-based masking network.\n- The actual encoding/decoding time is not provided. The real runtime of the model is an important factor for the practical application of the proposed codec.", "theoretical_claims": "The work is more of an application rather than a theoretical contribution, with few theoretical claims. The only issue is that the reason why LotteryCodec outperforms overfitted codecs is not well elaborated (line 260).", "experimental_designs_or_analyses": "The experiments designs and analyses are valid. For example, different hyper-parameters (mask ratio) are used for validating the hypothesis.", "relation_to_broader_scientific_literature": "The work is mainly related to the neural compression literature, but also the INR’s one. It proposed a new SOTA INR-based image codec.", "essential_references_not_discussed": "Lottery ticket hypothesis has been used for video representation/compression, which is highly related to INR-based image compression: \n\"Choi, Hee Min, et al. \"Is overfitting necessary for implicit video representation?\"\n\nThe proposed model is also highly similar with:\nMehta, Ishit, et al. \"Modulated periodic activations for generalizable local functional representations.\"", "other_strengths_and_weaknesses": "Overall, I find the work novel and of high quality. The lottery ticket-based codec is lightweight and achieves SOTA performance. The experiments provide a thorough evaluation of the method.", "other_comments_or_suggestions": "- It will be better if the BD-rate results are provided in a table as well. \n- Line 699: C3 is actually open-sourced: https://github.com/google-deepmind/c3_neural_compression \n- The authors should consider comparing the encoding/decoding speed with baseline models.", "questions_for_authors": "- Does the reported MACs/pixel include the masked parameters?\n- In Figures 7a and 7b, is the setting always < 2K MACs/pixel?\n- Both the proposed model and C3 use a set of adaptive settings. In the main experiments (e.g., Figure 7), does the proposed model always use a network and entropy model size that is not larger than C3?", "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": "eqRej6x7MQ", "reviewer": "Reviewer_bWTB", "summary": "The paper presents LotteryCodec, a new method for single-image compression that builds on the idea that large, randomly initialized neural networks contain subnetworks capable of matching the performance of fully trained networks. Concretely, instead of training and transmitting all synthesis network parameters for each image, LotteryCodec transmits only a binary mask (to identify a subnetwork inside a frozen, random network) and a small latent representation. This approach encodes the image’s statistics primarily into the network’s structure (the mask) rather than its weights.\n\nA key contribution is the “lottery codec hypothesis”, which posits that for any standard, overfitted compression model, there exists a subnetwork within a sufficiently large, randomly initialized neural network that can reconstruct the image to a similar distortion at the same or lower bit-rate. The authors reinforce this concept with a “rewind modulation” mechanism that merges a learned latent representation with hierarchical modulations at multiple layers, helping the subnetwork capture image details more effectively.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for valuable comments. We first respond to the reviewer's main concerns:\n* W1: Proof of Lottery Codec Hypothesis (LCH). Although a rigorous bound supporting the LCH is not available, we can provide a rough validation based on existing proofs for the Strong Lottery Tickets Hypothesis (SLTH). Suppose a codec $g_{{W}}({z})$ is overfitted to an image $S$ with distortion $\\sigma$. According to SLTH, for any $\\epsilon>0$, there exists a subnetwork within a sufficiently overparameterized network $g_{W'}$, defined by a supermask $\\tau$, such that $d(g_{{W}}({z}),g_{{W'}\\odot \\tau}({z})) \\le \\epsilon$ (suppose $d$ is a  distortion evaluated pixel by pixel). Thus, reconstructing the image $S$ using $g_{{W'}\\odot \\tau}({z})$ results in a distortion of at most $\\sigma+\\epsilon$. Now, we can further decrease the distortion by optimizing the latent vector over a set of $z'$ satisfying $H(z')=H(z)$, along with the supermask $\\tau$. Since $\\epsilon$ can be made arbitrarily small, it is highly likely that we can find a pair of $(\\tau',z')$ such that $d(S,g_{{W'}\\odot \\tau'}({z'}))\\le \\sigma$.\n* W2: We will add the following discussion about the encoding time: \"LotteryCodec’s low and flexible decoding cost is particularly beneficial in multi-user streaming scenarios, where encoding can be done once and offline, to support many users decoding the same content. While high encoding complexity remains a key bottleneck for all overfitted codecs, including ours, potential acceleration strategies include meta-learning, mixed-precision training, and neural architecture search. Notably, LotteryCodec also enables parallel encoding for overfitted codec by reparameterizing distinct network learning processes into a batch of mask learning process.\"\n* W3: To address the reviewer's concern about ultra-high-resolution images, we provide **Table 2.1** to detail the training and inference cost across various resolutions (with mask ratio $0.8$ and ARM model of $d=16$). An additional example of 2K image encoding is shown in **Table 3.2** (responses to Reviewer itee).\n* W4: We will add the following paragraph to discuss the potential extension to video compression: \"LotteryCodec can be extended as a flexible alternative for video coding. By sharing modulation across adjacent groups of frames (GoF) and applying distinct/weighted masks, it can additionally encode temporal information into the network structure, potentially yielding a lower bit cost. Moreover, video coding enables adaptive mask ratio selection across GoF, offering greater flexibility in both computational complexity and rate control.\"\n### **Table 2.1: Encoding time for different images. OM means out of memory ($>32$ GB).**\n| Input Resolution  | GPU Encoding (sec/1k steps): LotteryCodec vs. C3 | CPU Decoding (ms): LotteryCodec vs. C3 | Encoding Peak Memory Usage (GB): LotteryCodec vs. C3 vs. MLIC+ |\n|--|--|---|--|\n| 512 × 512| 10.71 vs. 10.43| 232.46 vs. 228.43 | 0.56 vs. 0.31 vs. 1.98 |\n| 1024 × 1024| 56.81 vs. 38.54| 565.22 vs. 576.51 | 2.15 vs. 1.24 vs. 3.61 |\n| 1536 × 1536| 136.81 vs. 84.79| 984.01 vs. 1086.92| 4.82 vs. 2.78 vs. 9.15 |\n| 2048 × 2048| 257.93 vs. 155.02|1595.86 vs. 1807.35 | 8.53 vs. 4.95 vs. 24.37 |\n| 2560 × 2560| 407.68 vs. 237.45| 3003.24 vs. 3269.02 | 13.36 vs. 7.72 vs. OM |\n| 3840 × 2160  | 446.09 vs. 301.56   | 4014.21 vs. 4216.11 | 16.89 vs. 9.84 vs. OM |\n\nResponses to questions:\n\n* Q1\\&2: We refer the reviewer to Fig. 13 in Appendix E, which details the cost of each component. In the high-rate regime, the total cost of $\\psi$, $\\theta$, and $\\tau$ accounts for less than 5\\%. The binary mask $\\tau$ is compressed via range coding (range-coder on PyPI) with a static distribution.\n* Q3: To validate the lottery codec hypothesis, the (4,128) setting suffices.  While wider networks (e.g., 4-256) can reduce distortion without increasing the bit cost for $z$ (hence can validate the hypothesis), they also raise the bit cost for the mask $\\tau$ and introduce greater training overhead, which often reduces overall compression efficiency. (An example of different configuration results can be seen in last column of **Table. 3.1** for Reviewer itee). This motivates us to design the modulation mechanism.\n* Q4. See our response to W1.\n* Q5\\&6. We present the coding cost of various schemes in **Table 4.2** of our response to Reviewer ynP1, and report resolution-dependent coding costs in **Table 2.1** above. The proposed method shows scalability to ultra-high-resolution images, albeit with increased coding time. Note that, significant speedups can be achieved through engineering and hardware optimizations. For example, we can accelerate the method via ONNX/DeepSparse library to reduce the decoding time into $20–80$ ms on a CPU. Additional techniques, such as symmetric/separable kernels, filter-based upsampling, and wavefront decoding, can further enhance the speed of overfitted codecs.", "claims_and_evidence": "Overall, the main claims in the paper are supported by consistent empirical evidence and ablation studies. However, as with many works extending the “lottery ticket” idea, there is no fully rigorous proof of the underlying “lottery codec hypothesis”. While the authors reference existing theory on the strong lottery ticket hypothesis, the paper itself relies on empirical demonstrations rather than a formal proof.", "methods_and_evaluation_criteria": "Yes. The paper targets the domain of single-image compression, a space where it is standard practice to evaluate models on well-established datasets like Kodak and CLIC. The authors adopt widely used, transparent metrics—PSNR for measuring distortion and BD-rate to compare rate–distortion trade-offs. They also report decoding complexity in terms of multiply-accumulate (MAC) operations per pixel, which directly addresses deployment feasibility on resource-constrained hardware.", "theoretical_claims": "There is no detailed derivation or proof in the submission.", "experimental_designs_or_analyses": "The experiments in the paper are generally designed and analyzed in a manner consistent with standard practices in neural image compression, and they align with expectations for single-image compression research. Here are the main observations regarding experimental soundness:  \n- They use popular datasets (Kodak and CLIC2020) and standard metrics (PSNR, BD-rate, MACs/pixel) for evaluation.  \n- They compare LotteryCodec with traditional codecs (e.g., VTM, HEVC) and overfitted approaches (e.g., C3, COOL-CHIC).  \n- They vary the rate–distortion parameter and mask ratios to explore how performance scales with different network depths and widths.  \n- They perform ablations on initialization, modulation methods, and architecture to highlight each component’s contribution.", "relation_to_broader_scientific_literature": "The paper builds on the lottery ticket hypothesis (Frankle & Carbin, 2019) by applying it to image compression. It leverages ideas from overfitted codecs (e.g., COIN, COOL-CHIC, C3) to encode images with minimal parameters. The work also incorporates insights on untrained subnetworks (Ramanujan et al., 2020) and uses Fourier initialization to mitigate low-frequency bias in MLPs. Overall, it integrates established concepts from compression, deep learning, and network pruning to reduce decoding complexity while maintaining high performance.", "essential_references_not_discussed": "No essential references are omitted.", "other_strengths_and_weaknesses": "**Strengths**\n- Leverages the lottery ticket hypothesis to utilize untrained subnetworks for image compression.\n- Achieves state-of-the-art rate–distortion performance while drastically lowering the number of operations at decoding time.\n- Adjustable mask ratios allow the method to balance compression performance with computational cost.\n\n**Weaknesses**\n- Lacks a formal theoretical proof or detailed bounds, relying mainly on empirical evidence.\n- The per-image optimization required for encoding may result in high encoding times, which is not fully addressed.\n- Searching for an optimal subnetwork in a highly over-parameterized network might become challenging for ultra-high-resolution images.\n- The method is demonstrated for single-image compression, with limited discussion on extending it to video or other signals.", "other_comments_or_suggestions": "- Consider adding a dedicated paragraph (or section) discussing the limitations of per-image optimization speed, especially in practical scenarios.\n- Including a brief discussion on potential extensions to video or multi-view compression could help contextualize broader applications.", "questions_for_authors": "1. In line 215–219 (right column), the paper states that the loss function (4) omits the rate terms for ψ, θ, and τ because their lightweight architectures contribute negligibly to the overall bit rate. Could you provide empirical evidence—such as detailed bit consumption measurements for each of these components—to support this claim?\n\n2. Regarding the binary mask, is its overhead significant, and how is the mask data compressed in practice?\n\n3. For network architecture, why is the maximum network width set to 128? What would be the impact of increasing the width further (e.g., to 256 or 512)? For instance, if a 50% mask ratio with a (4,128) network achieves the best performance, what outcome would you expect if a 25% mask ratio is used with a (4,256) network?\n\n4. Could you provide more formal insights or theoretical bounds to support the lottery codec hypothesis beyond the empirical results?\n\n5. What are the computational costs or encoding times for the per-image optimization process, and how do these compare with existing overfitted codecs and autoencoder-based codecs? Clarification on encoding speed is important for assessing the method's real-world practicality.\n\n6. How does the proposed approach scale to ultra-high-resolution images (e.g., 4K or 8K), particularly in terms of memory usage and the complexity of subnetwork search?", "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": "vNf1iwvpWM", "reviewer": "Reviewer_itee", "summary": "This paper introduces LotteryCodec, a novel, low-complexity image compression scheme based on overfitting. LotteryCodec effectively overfits a binary mask of an over-parameterized, randomly initialized network to an image, achieving high-performance compression. To enhance its performance, techniques such as Fourier initialization and rewind modulation are proposed. Extensive experimental results demonstrate LotteryCodec's high compression ratio and low decoding complexity.\n\n## update after rebuttal\n\nAs discussed below, I maintain my positive score.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer's valuable comments. Our responses to the reviewer's main concerns are as follows:\n\n* Encoding/decoding complexity. Practical encoding/decoding time and peak memory usage across images with various resolutions are reported in **Table 2.1** (see our response to **Reviewer bWTB**), with additional coding speed results reported in **Table 4.2** (response to **Reviewer ynP1**) and **Table 3.2** (this response). All of these results are based on **unoptimized research code** and current hardware, which can be significantly improved with proper engineering optimization (e.g., C API, optimized wavefront decoding). Overall, our method has a slightly longer encoding time than other overfitted codecs due to additional gradient-based mask learning process, but it offers greater flexibility and faster decoding. Notably, the lottery codec hypothesis (LCH) can provide **potential for parallel encoding** by re-parameterizing distinct network optimization into batch-wise mask learning, highlighting its advantage of scalability for efficient large-scale image encoding.\n\n* Qualitative analysis. In addition to experimental evidence, we provide a rough analysis of the LCH to explain why it is likely to hold (see our response to **Reviewer bWTB**). Based on the LCH, we can intuitively justify why the proposed LotteryCodec outperforms previous overfitted codecs in terms of rate-distortion performance. The rate formulations for overfitted codecs and our LotteryCodec are given in Eqs. (2) and (5), respectively. They show that the rate of overfitted codecs depends on $\\{\\hat{z}, \\hat{\\psi}, \\hat{W}\\}$, while our method is determined by $\\{\\hat{z}, \\hat{\\psi}, \\tau, \\hat{\\theta}\\}$. According to LCH, to achieve the same level of distortion, we can find a pair of $(\\hat{z},\\tau)$ such that the bit cost for $\\hat{z}$ and $\\hat{\\psi}$ is equal to that of overfitted codecs. While each quantized parameter in $\\hat{W}$ typically requires over 13 bits, our binary mask $\\tau$ uses just 1 bit per entry. Despite its higher dimensionality, $\\tau$ contributes significantly less to the total rate. Moreover, since $\\hat{\\theta}$ is lightweight, the combined rate of $\\tau$ and $\\hat{\\theta}$ remains lower than that of $\\hat{W}$, resulting in a lower compression rate and improved RD performance.\n\n* Ablation study. We conducted additional ablation studies to clarify the impact of each component in our design. As shown in **Table 3.1** below, removing the Supermask network and using only the modulation network increases BD-rate by +12.45%, highlighting the importance of the random network. Removing ModNet and directly feeding ${z}$ into the random network (with different overparameterization configurations) results in a performance drop of up to +14.99% due to high overparameterization costs. Additional ablation studies and visualizations of other components are provided in Table 4 of Appendix C in our original  paper.    \n\n### **Table 3.1 BD-rate change due to removal of individual components from LotteryCodec**\n\n| LotteryCodec | w/o SuperMask | Random network w/o ModNet: (4,32)/(4,48)/(4,64)         |\n|--------------|---------------|----------------------------------------------------------|\n| 0            | **+12.45%**       | **+13.02% / +11.98% / +14.99%**                          |\n\n### **Table 3.2 Encoding cost for a 2K image as an example**  \n*(Size: 1292 × 1945, “davide-ragusa-716” in CLIC2020, optimal PSNR: 37.18 at bpp 0.196, $d=24$, ratio=0.2, peak memory: 5.64 GB)*  \n*(10–20k steps can yield decent performance)*\n\n| Training Steps | Training Time (s) | bpp   | PSNR (dB) |\n|----------------|-------------------|-------|-----------|\n| 5k             | 678               | 0.24  | 36.51     |\n| 10k            | 1347              | 0.22  | 36.92     |\n| 20k            | 2685              | 0.21  | 37.02     |\n| 30k            | 4026              | 0.20  | 37.10     |\n| 50k            | 6733              | 0.199 | 37.14     |", "claims_and_evidence": "I have no concern on this part.", "methods_and_evaluation_criteria": "I have no concern on this part.", "theoretical_claims": "I have no concern on this part.", "experimental_designs_or_analyses": "1. While LotteryCodec achieves low decoding MACs, MACs alone do not fully represent decoding complexity. In practice, factors such as peak memory usage and, especially, decoding speed play crucial roles in determining complexity. A comparison with other schemes (e.g., C3, EVC, and ELIC) on these factors would provide a more comprehensive understanding.\n\n2. Beyond decoding complexity, encoding complexity also requires clarification. Compared to other overfitted image codecs (e.g., C3 or COOL-CHIC), does LotteryCodec require more or less encoding time?", "relation_to_broader_scientific_literature": "I have no concern on this part.", "essential_references_not_discussed": "I have no concern on this part.", "other_strengths_and_weaknesses": "Strengths : \n\n1. The idea of overfitting a binary mask of an over-parameterized, randomly initialized network to an image is novel, introducing a new paradigm for overfitted image compression.\n\n2. Experimental results effectively validate the LotteryCodec hypothesis\n\n3. The compression performance is excellent for a low-complexity overfitted image codec.\n\n\nWeakness :\n\n1. The discussion on complexity is insufficient, as noted in 'Experimental Designs and Analyses'.\n\n2. While experiments support the LotteryCodec hypothesis, the paper lacks a qualitative analysis explaining why LotteryCodec is superior to previous overfitted codecs like C3.\n\n3. Compared to C3, LotteryCodec differs in both the synthesis network and ModNet. An ablation study on removing ModNet could help clarify the impact of each modification.", "other_comments_or_suggestions": "I have no other comments.", "questions_for_authors": "I have no additional questions.", "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": "hiVlxexnAQ", "reviewer": "Reviewer_ynP1", "summary": "This paper investigate the lottery ticket hypothesis for implicit representation based image compression.  \n\nIt proposes to overfits a binary mask and modulation vectors to the source image, and then leverages a randomly initialized neural network to generate the reconstruction.  \n\nThe proposed LotteryCodec achieves state-of-the-art performance among overfitted image codecs designed for single-image compression at a reduced computational cost.   \n\nAdditionally, LotteryCodec can adjust its decoding complexity by varying the mask ratio, providing flexible solutions for diverse computational and performance needs.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer’s valuable comments and for highlighting Choi’s ICML 2023 paper. Our detailed responses to each comment are as follows:    \n* (1). Following the suggestion, we have conducted additional MS-SSIM experiments on the Kodak dataset. The results, presented in **Table 4.1**, demonstrate that our method consistently outperforms VTM, achieving up to a **-43.81%** reduction in **BD-rate**, closely matching ELIC's performance. We note that previous overfitted codecs only focus on PSNR, and direct MS-SSIM optimization is unstable for those baselines (as reported in C3 and its extension work (Fig. 6 and line 3 in [1])). \n\n    [1]. Ballé, Jona, et al. ``Good, Cheap, and Fast: Overfitted Image Compression with Wasserstein Distortion.'' \n### **Table 4.1 MS-SSIM / bpp performance on Kodak dataset**\n|  | MS-SSIM1 / bpp1 | MS-SSIM2 / bpp2 | MS-SSIM3 / bpp3 | MS-SSIM4 / bpp4 | **BD-rate vs. VTM (%)** |\n|---------------|----------------------|----------------------|----------------------|----------------------|----------|\n|VTM|13.10 / 0.212| 14.31 / 0.287|16.75 / 0.492|18.56 / 0.704| 0|\n|LotteryCodec|13.85 / 0.153| 16.78 / 0.275| 19.46 / 0.473 | 22.70 / 0.853| -43.81|\n|ELIC|12.22 / 0.091| 15.86 / 0.215| 18.83 / 0.394 | 21.67 / 0.667 |-44.60|\n|MLIC+|14.91 / 0.148|16.53 / 0.214|18.20 / 0.307|19.77 / 0.425|-52.75|\n* (2-3). We have compared the encoding (NVIDIA L40S) and decoding latency of LotteryCodec and its BD-rate against other alternatives (see **Table 4.2** with a structured pruning over masking ratio of 0.8). Additional latency results across resolutions are reported in **Tables 2.1 (Reviewer bWTB**) and an coding exmaple is given in **Table 3.2** (**Reviewer itee**). Given the fast decoding speed of overfitted codecs, we evaluate all overfitted codecs on an Intel Xeon CPU. Overall, our method achieves faster decoding with slightly higher encoding time, compared with other overfitted codecs. Additional analysis is provided in our response to **Reviewer itee**. We want to note that real-world latency is affected by many uncontrollable factors in a lab setting and can be significantly reduced through various optimization techniques, making fair coding speed comparisons difficult. For example, [2] reported that Cool-chic achieves a 100ms latency using a C API for binary arithmetic coding, while our implementation is slower due to the lack of such optimization. Nonetheless, we recognize the importance of real-world latency and provide these evaluations for a practical perspective. To ensure fairness, all reported results are based on **same** unoptimized decoding implementations, with **no** methods using C API optimizations. We expect **similar speedups** across all methods with these techniques.\n\n  [2] Blard, Théophile, et al. \"Overfitted image coding at reduced complexity.\" 2024.\n### **Table 4.2  Coding time for Kodak images**\n| Models | Encoding time | Decoding time  | BD rate   |\n|-|-|-|-|\n|**Traditional codec**|**CPU (s)**|**CPU (ms)**| -|\n| VTM|85.53|352.52|0|\n| **AE-based codec**| **GPU (ms)**|**GPU (ms)**|-|\n| EVC (S/M/L)| 20.23/32.21/51.35|18.82/23.73/32.56|3.3% / -0.8% / -1.9%|\n|MLIC+|205.60| 271.31|-13.19%|\n|**Overfitted codec**|**GPU(sec / 1k steps)**| **CPU (ms)**  |-|\n|LotteryCodec (d=8/16/24)|13.86/14.64/14.92|261.3/267.5/278.3| -3.64% |\n|C3 (d=12/18/24)|13.10/13.98/14.32|272.1/284.6/295.0|+3.24%|\n* (4). We have conducted extensive additional ablation studies in the rebuttal (as shown in these tables) and will include visualizations of these results to support our analysis in our revised manuscript, such as (a). impact of each component (**Tables 3.1** from  **Reviewer itee** ) and (b). training latency vs. performance (**Tables 3.2** from **Reviewer itee**), (c) visual comparison for MS-SSIM results (**Table 4.1** here). For clarity, here we provide the corresponding numerical results in tabular form in the above rebuttal. \n* (5). We will add a discussion over Choi et al.’s ICML 2023 paper in our revised manuscript. Here, we highlight the **key differences** between their approach and ours: While both studies leverage the Lottery Ticket Hypothesis (LTH) for INRs, Choi et al. apply LTH to video representation using image-wise encoding with multiple supermask overlays and unpruned biases, boosting representation at the cost of increased complexity and bit rate. In contrast, our LotteryCodec adopts a pixel-wise model and focuses on low-complexity image compression problem. We introduce mechanisms such as Fourier initialization and Rewind modulation to enhance rate-distortion performance, distinguishing our approach from Choi’s. Although Choi’s method is a novel contribution to video representation, it still falls short of state-of-the-art compression techniques. We will also add one paragraph to discuss the potential extension of our work for video compression (see response to **Reviewer bwTB** for more details).\n* (6). We have proofread the manuscript again and corrected the typos.", "claims_and_evidence": "Yes. The manuscript is well written and logical.", "methods_and_evaluation_criteria": "(1) Only bpp-PSNR is compared. It is suggested to add MS-SSIM as evaluation metric.  \n\n(2) MACs/pixel is not a reliable metric for the real running complexity of neural networks.  For neural applications, IO might occupy most of the latency. The decoding pipeline of the proposed method is more complex than the original INRs, as shown in figure 4. It is better to compare the latency with baseline INRs C3 on a BD-rate decoding latency curve.   \n\n(3) Encoding latency should be compared with baseline C3.", "theoretical_claims": "No theoretical claims.", "experimental_designs_or_analyses": "The experiment is well designed, and the anlysis is clear and thorough.", "relation_to_broader_scientific_literature": "Related to many lottery ticket papers, which are already properly discussed in the manuscript.", "essential_references_not_discussed": "Missing important citations: Is overfitting necessary for implicit video representation? ICML 2023  \n\n(5) This previous icml paper investigates the same topic of lottery hypothesis for implicit representation. The difference should be properly discussed.", "other_strengths_and_weaknesses": "None.", "other_comments_or_suggestions": "L178, networt", "questions_for_authors": "This is a good paper regarding ideas.   \n\nThere are some concerns regarding experiments and metrics, listed as (1-5) in previous sections. I am ready to increase the score if my concerns can be solved.", "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:

Meta-review: This manuscript propose a compression method using lottery ticket scheme, per-scene optimization based on implicit neural representation. The algorithm improved modulation mechanisms leading to better RD performances compared to VTM and baselines.

All the reviewers agreed the novelty and the soundness of this paper. Reviewer W9j1 found the algorithm is desinged to be lightweight and take a sota position.  Reviewers bWTB, itee admit that an idea of this paper adequately utilizes the lottery ticket hypothesis on compression problems. Moreover, all the reviewers noticed that the proposed algorithm lowers computational complexity. The remaining concerns about (1) unreliable metric as MAC/pix, (2) credit on previous researches, and (3) clarities  were well resolved after a rebuttal period. After rebuttal phase, all reviewers were satisfied responses from authors and converged to the acceptance of this paper to ICML.

Therefore, I recommend the acceptance of this paper for publication.
Decision: Accept (spotlight poster)