ScHiCAtt: Enhancing Single-Cell Hi-C Resolution Using Attention-Based Models

The spatial organization of chromatin is fundamental to gene regulation and essential for proper cellular function. The Hi-C technique remains the leading method for unraveling 3D genome structures; however, limited resolution, data sparsity, and incomplete coverage in single-cell Hi-C data pose significant challenges for comprehensive analysis. Traditional CNN- based models often suffer from blurring and loss of fine details, while GAN-based methods en- counter difficulties in maintaining diversity and generalization. Moreover, existing algorithms perform poorly in cross-cell line generalization, where a model trained on one cell type is used to enhance high-resolution data in another cell type. To address these limitations, we propose ScHiCAtt (Single-cell Hi-C Attention-Based Model), which leverages attention mechanisms to capture both long-range and local dependencies in Hi-C data, significantly enhancing resolu- tion while preserving biologically meaningful interactions. We implement this mechanism and check its validity on data from different cells of the same organisms and data of different organ- isms. By dynamically focusing on regions of interest, attention mechanisms effectively mitigate data sparsity and enhance model performance in low-resolution contexts. Extensive experi- ments on Human and Drosophila single-cell Hi-C data demonstrate that ScHiCAtt consistently outperforms existing methods in terms of computational and biological reproducibility metrics across different downsampling ratios, especially under extreme downsampling conditions. The model is publicly available at https://github.com/OluwadareLab/ScHiCAtt.

Hi-C data, Self-Attention, Resolution Enhancement, Single-cell Hi-C, Data Sparsity 1 Introduction 1 Three-dimensional (3D) conformation of chromosomes is crucial for elucidating genomic processes 2 within the nuclei of eukaryotic cells. The Hi-C technique facilitates an all-versus-all mapping of 3 chromosomal fragment interactions, resulting in an interaction frequency contact matrix, where 4 n × n represents the number of fragments in a chromosome or genome at a specific resolution, 5 Lieberman-Aiden et al., 2009. These Hi-C data are critical for numerous algorithms designed to 6 improve the understanding of genome organization, Oluwadare et al., 2019. A major challenge 7 in this field is the scarcity of high-resolution Hi-C data, which are indispensable for identifying 8 intricate genomic topologies such as enhancer-promoter interactions and subdomains. 9 To address this need, deep learning models have been employed to predict high-resolution data 10 from low-resolution data with remarkable accuracy. Notable models in this area include HiCPlus 11 Y. Zhang et al., 2018, HiCNN T. Liu and Z. Wang, 2019a, hicGAN Q. Liu et al., 2019, Boost-HiC 12 Carron et al., 2019, HiCSR Dimmick, 2020, SRHiC Z. Li and Dai, 2020, HiCNN2 T. Liu and 13 Z. Wang, 2019b, HiCARN Hicks and Oluwadare, 2022, and DeepHiC Hong et al., 2020. These 14 models leverage various network architectures such as Convolutional Neural Networks (CNNs), 15 Autoencoders, and Generative Adversarial Networks (GANs). Despite the advancements made 16 by these models, there remains considerable room for improvement, especially when it comes to 17 single-cell Hi-C data enhancement, Y. Wang et al., 2023, as all of the aforementioned methods are 18 designed for bulk Hi-C data enhancement. 19 Single-cell Hi-C (scHi-C) is a groundbreaking technology that offers a unique opportunity to in- 20 vestigate 3D genome structures at the single-cell level with high resolution, Galitsyna and Gelfand, 21 1 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint 2021. By capturing chromatin interactions at the individual cell level, scHi-C enables the explo- 22 ration of cellular heterogeneity in chromatin conformation, Arrastia et al., 2020; Collombet et al., 23 2020; Payne et al., 2021. However, scHi-C data are characterized by high dimensionality, noise, 24 and sparsity, presenting computational challenges that demand innovative solutions for the accu- 25 rate reconstruction of 3D genome structures, Paulsen et al., 2015; Galitsyna and Gelfand, 2021. 26 Therefore, scHi-C data imputation is crucial, as it enables the reconstruction of enhanced contact 27 maps from raw and sparse scHi-C data, thereby improving the quality for downstream analyses, 28 including the reconstruction of chromatin organization at the single-cell level. This enhancement 29 aids in uncovering cell-to-cell variability and heterogeneity, ultimately providing deeper insights 30 into cellular functions and disease mechanisms Y. Wang et al., 2023. 31 Recently, algorithms like ScHiCEDRN, Y. Wang et al., 2023 and Loopenhance, S. Zhang et al., 32 2022 have been developed to address the challenges of scHi-C data enhancement. While these 33

aim to improve the resolution of single-cell Hi-C data, they often fall short in capturing 34 the complex spatial relationships within chromatin structures, especially long-range dependen- 35 cies. This limitation leads to the loss of critical interactions, which are essential for accurately 36 reconstructing chromatin topology. 37 On the other hand, Attention mechanisms have proven effective in capturing both short-range 38 and long-range dependencies in various domains, such as natural language processing and computer 39 vision, Vaswani, 2017. These mechanisms enable models to focus on different regions of the input 40 data dynamically; hence, they have the potential to be used to enhance the resolution of sparse 41 datasets like scHi-C by capturing context at multiple scales. The motivation behind our work is to 42 leverage Attention mechanisms to address challenges unique to scHi-C data, such as sparsity, noise, 43 and limited coverage. By selectively focusing on relevant chromatin interactions, our approach aims 44 to provide a more biologically meaningful reconstruction of 3D genome structures. 45 In this work, we propose ScHiCAtt, which employs a cascading residual network integrated 46 with an optimal attention mechanism identified through validation across multiple candidates. 47 ScHiCAtt explores different attention mechanisms, such as self-attention, local attention, global 48 attention, and dynamic attention (Attention-in-Attention), selecting the optimal mechanism for 49 each layer during training to determine the best attention mechanism to incorporate for scHi-C data 50 enhancement. The goal of this experimentation is to allow ScHiCAtt to capture both short-range 51 and long-range dependencies adaptively, thus enhancing the quality of scHi-C data reconstruction. 52 Through comprehensive experiments on human and Drosophila data across various downsam- 53 pling rates, we demonstrate that ScHiCAtt significantly improves the resolution of scHi-C data. 54 Our results show superior performance in terms of computational metrics and biological repro- 55 ducibility metrics, such as GenomeDISCO, Ursu et al., 2018, compared to existing methods, par- 56 ticularly under extreme downsampling conditions. Moreover, ScHiCAtt maintains efficient training 57 times, making it a robust solution for high-resolution single-cell Hi-C data enhancement. 58 2 Materials and Methods 59 2.1 Model Architecture 60 Our model architecture starts with an entry convolution layer (Figure 1A) that processes the 61 input raw scHi-C contact map. This is followed by a series of cascading blocks interleaved with 62 attention layers, designed to progressively upscale the resolution of the Hi-C maps. The final 63 high-resolution Hi-C maps are produced through an exit convolution layer. The architecture also 64 includes tunable hyperparameters such as the number of cascading blocks and attention layers, 65 allowing for flexibility in optimizing the model’s performance. 66 In the following subsections, we explore various attention mechanisms that have been considered 67 in our study. We describe each mechanism in detail, highlighting its unique features and the 68 rationale behind its selection for our research. Furthermore, we elucidate how these mechanisms 69 were implemented within our architecture for evaluation. 70 2.1.1 Self-Attention Mechanism 71 The self-attention mechanism in our architecture (Figure 1A) facilitates efficient learning of both 72 local and global chromatin interactions by allowing the model to dynamically assign weights to 73 relationships between chromatin loci, regardless of their spatial distance on the Hi-C contact maps. 74 This capability is crucial for capturing both short-range and long-range dependencies within chro- 75 matin structures. 76 2 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint To achieve this, the attention scores are computed by taking the scaled dot-product between 77 the input projection matrices: queries ( H) and keys ( J), divided by the square root of the keys 78 dimension. The resulting attention scores are passed through a softmax function to compute the 79 attention weights, which are then applied to the values ( Z). This enables the model to prioritize 80 important interactions, enhancing the quality of the predicted high-resolution contact maps. 81 The process is defined as: 82 A(H, J, Z) = Softmax H · JT p dj ! · Z (1) Here, H ∈ Rn×d, J ∈ Rn×d, and Z ∈ Rn×d represent the query, key, and value matrices 83 respectively, where n is the sequence length (number of loci in the Hi-C contact map), and d is the 84 feature dimension. The term dj is the dimension of the keys (i.e., dj = d) used to scale the dot 85 product and stabilize the training process. This mechanism enables the model to focus on critical 86 chromatin interactions, significantly improving prediction accuracy. 87 2.1.2 Cascading Residual Blocks 88 The backbone of our architecture is the cascading residual blocks, illustrated in Figure 1B, Ahn 89 et al., 2018. Each block comprises residual units with skip connections that progressively refine 90 the Hi-C contact maps. These cascading blocks are interconnected, allowing for the aggregation of 91 features across different layers. 92 2.1.3 Local Attention Mechanism 93 Local attention is applied within the cascading residual blocks (Figure 1B). It focuses on capturing 94 fine-grained chromatin interactions within localized regions of the Hi-C contact maps. The use 95 of depthwise and pointwise convolutions in the local attention mechanism allows the model to 96 enhance the spatial resolution of the Hi-C maps by emphasizing intricate local details. 97 LocalAttention(xi) = i+wX j=i−w αijxj (2) where αij = exp(eij )Pi+w k=i−w exp(eik), and eij = (xiWQ)(xjWK)T . Here, xi is the input at position i, w is 98 the window size defining the local neighborhood, WQ and WK are learnable weight matrices for 99 queries and keys respectively. 100 2.1.4 Global Attention Mechanism 101 The global attention mechanism is applied after several cascading residual blocks (Figure 1B) to 102 ensure that global chromatin structures are preserved. This module aggregates context across 103 the entire Hi-C map and allows the model to capture large-scale genomic interactions, which are 104 critical for accurate super-resolution Zhu et al., 2021. 105 GlobalAttention(x) = Softmax  QK T √ d  V (3) where Q = xWQ, K = xWK, V = xWV , and WQ, WK, WV are learnable weight matrices for 106 queries, keys, and values, respectively. 107 2.1.5 Multi-Head Attention Mechanism 108 The multi-head attention mechanism is designed to enhance the model’s ability to capture complex 109 relationships in the input data by dividing the input into multiple attention heads. Each head 110 performs attention operations independently, focusing on different aspects of the input, which 111 allows the model to extract diverse contextual information. 112 The mechanism takes three primary inputs: the Query ( Q), Key (K ), and Value (V ) matrices. 113 These inputs are derived from the original data through linear transformations. The attention op- 114 eration for each head calculates a weighted representation of the Value matrix, where the weights 115 are determined by the similarity between the Query and Key matrices. This is expressed mathe- 116 matically as: 117 3 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Attention(Q, K, V) = softmax  QK T √dk  V (4) Here, dk is the dimensionality of the Key matrix, and the softmax function ensures that the 118 weights sum to 1, highlighting the most relevant features for each Query. 119 For multi-head attention, the inputs are split intoh separate heads, each with its ownQ, K, and 120 V . The outputs from all heads are concatenated and passed through a final linear transformation, 121 as shown in the equation below: 122 MultiHead(Q, K, V ) = Concat(head1, head2, . . . ,headh)WO (5) In this equation, head i represents the output of the i-th attention head, and WO is the learned 123 weight matrix for the final linear transformation. This design allows the model to integrate in- 124 formation from multiple perspectives, improving its ability to capture chromatin interactions and 125 other complex patterns. 126 2.1.6 Dynamic Attention Mechanism 127 Dynamic Attention, also referred to as the Attention-in-Attention (A2A) mechanism, combines 128 static and dynamic attention features to weigh their contributions adaptively. The dynamic atten- 129 tion module applies global pooling, followed by fully connected layers, to dynamically adjust the 130 contribution of features based on and without attention Huang et al., 2019. 131 A2A(x) = wnon-att · NonAttention(x) + watt · AttentionBranch(x) (6) 2.2 Loss Function 132 To optimize the quality of the enhanced scHi-C contact matrices, we leverage several key loss 133 functions that address distinct aspects of the reconstruction process. These loss functions ensure 134 that the generated matrices not only minimize pixel-wise error with respect to the target but also 135 maintain structural integrity and visual consistency. 136 2.2.1 Mean Squared Error (MSE) 137 The goal is to minimize the pixel-wise difference between the true and enhanced scHi-C matrices, 138 ensuring that the generated maps closely approximate the true scHi-C data. 139 LM SE = 1 N NX i=1 (Yi − ˆYi)2 (7) In this equation: 140 • N: The total number of data points or pixels in the scHi-C matrices. 141 • Yi: The true value of the i-th pixel in the scHi-C matrix. 142 • ˆYi: The predicted value of the i-th pixel in the enhanced scHi-C matrix. 143 • LM SE: The computed Mean Squared Error, representing the average of the squared differ- 144 ences between the true and predicted values. 145 This loss function penalizes larger deviations more heavily due to the squaring operation, en- 146 couraging the model to generate outputs that closely match the true data. 147 2.2.2 Perceptual Loss 148 Perceptual loss, based on feature representations from a pre-trained VGG network Wu et al., 2020, 149 ensures that the generated Hi-C maps are not only pixel-accurate but also visually consistent with 150 the real Hi-C data. 151 In the perceptual loss LV GG, we utilize the feature maps from specific layers of the pre-trained 152 VGG network: 153 4 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint LV GG = 1 N NX i=1 X ℓ ϕℓ(Yi) − ϕℓ( ˆYi) 2 (8) where ϕℓ(·) denotes the feature map extracted from the ℓ-th layer of the VGG network. 154 2.2.3 Total Variation (TV) Loss 155 TV loss reduces noise and enforces smoothness in the generated Hi-C maps, improving the overall 156 visual quality. 157 LT V = 2ψ(hT V + wT V ) F (9) 2.2.4 Adversarial Loss (AD) 158 Adversarial loss improves the realism of the generated high-resolution Hi-C maps by ensuring that 159 the discriminator cannot easily distinguish between real and generated matrices. 160 LAD = 1 − 1 N NX i=1 D( ˆYi) (10) 2.3 Evaluation Metrics 161 To evaluate the effectiveness of our models in enhancing the resolution of scHi-C data, we used 162 a few standard metrics that give us different ways to look at the quality of the reconstructed 163 contact maps. Each of these metrics helps us understand how good the reconstruction is from dif- 164 ferent perspectives. They can broadly be categorized as computational metrics, such as Structural 165 Similarity Index Measure, Peak Signal-to-Noise Ratio, and Signal-to-Noise Ratio and biological 166 reproducibility metrics, such as GenomeDISCO, Ursu et al., 2018. 167 2.3.1 Structural Similarity Index 168 Structural Similarity Index Measure(SSIM) quantifies the structural similarities between the true 169 and enhanced scHi-C matrices. 170 SSIM is defined as, 171 SSIM(x, y) = (2µxµy + C1)(2σxy + C2) (µ2x + µ2 y + C1)(σ2x + σ2y + C2) (11) Here, µx and µy are the means of x and y, σ2 x and σ2 y are the variances, σxy is the covariance 172 between x and y, and C1 and C2 are constants to stabilize the division when the denominator is 173 close to zero. 174 2.3.2 Peak Signal-to-Noise Ratio 175 As the name states, Peak Signal-to-Noise Ratio (PSNR) quantifies the ratio between the maximum 176 achievable signal and the noise that distorts it. 177 PSNR is defined as 178 PSNR = 20 · log10  MAXI √ MSE  (12) In this equation: 179 • PSNR: Peak Signal-to-Noise Ratio, a metric to measure the quality of the enhanced image. 180 • MAXI: The maximum possible pixel value of the image (e.g., 255 for 8-bit images). 181 • MSE: Mean Squared Error between the original and enhanced images. 182 • log10: The base-10 logarithm. 183 5 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint 2.3.3 Mean Squared Error 184 Mean Squared Error (MSE) calculates the average squared difference between the predicted and 185 true values. 186 Mean Squared Error is defined as, 187 MSE = 1 N NX i=1 (xi − yi)2 (13) 2.3.4 Signal-to-Noise Ratio 188 Signal-to-Noise Ratio (SNR) measures the relationship of the signal power to noise power. 189 SNR = 10 · log10 PN i=1 y2 iPN i=1(xi − yi)2 ! (14) 2.3.5 GenomeDISCO 190 In this study, we utilize GenomeDISCO Ursu et al., 2018 as a measure of biological reproducibility. 191 GenomeDISCO produces a concordance score ranging from -1 to 1, reflecting the biological simi- 192 larity between two contact maps. A higher value indicates better concordance. The methodology 193 entails applying a smoothing technique to the contact maps through their graph representations, 194 followed by the calculation of the similarity score on the resulting smoothed matrices. 195 3 Results 196 3.1 Dataset Preparation 197 For this study, we utilized scHi-C datasets as prepared by the ScHiCEDRN framework, which 198 includes data from both Drosophila melanogaster and Homo sapiens cell lines. The Drosophila 199 dataset comprises seven chromosomes (chr2L, chr2R, chr3L, chr3R, chr4, chrX, and chrM) (GSE131811)200 Ulianov et al., 2021, while the human dataset includes chromosomes from the frontal cortex 201 (GSE130711) Lee et al., 2019; Luo et al., 2022. 202 Following the preprocessing steps as described in the ScHiCEDRN framework Y. Wang et 203 al., 2023, we utilized the low-resolution contact maps provided, which had been downsampled to 204 varying degrees (75%, 45%, 10% and 2% of the original raw reads). Detailed preprocessing infor- 205 mation can be found in ScHiCEDRN, Y. Wang et al., 2023, and the datasets are publicly available 206 at https://github.com/BioinfoMachineLearning/ScHiCEDRN. No additional preprocessing was 207 performed on the data. For the human cell line, chromosomes 1, 3, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 208 21, and 22 from Human cell 1 were used as the training dataset, while chromosomes 4, 14, 18, and 209 20 were used for validation. For testing, we used chromosomes 2, 6, 10, and 12 from both Human 210 cell 1 and a different human cell, referred to as Human cell 2, as done by ScHiCEDRN. For testing 211 on Drosophila cells, we used chromosomes chr2L and chrX. 212 These datasets were used as inputs for our models, with the raw scHi-C contact maps serving 213 as the ground truth for model training and evaluation. 214 3.2 Hyperparameter Search for Individual Attention Mechanisms 215 We have conducted an extensive hyperparameter search to determine the optimal configuration for 216 our architecture. The two criteria to optimize are (i) determining the best-performing attention 217 mechanism and (ii) its placement within the network layers. Our primary focus is on the im- 218 plementation of various attention mechanisms, including Self-Attention, Local Attention, Global 219 Attention, and Dynamic Attention. The goal is to ascertain which attention mechanism and its 220 placement within the network layers yield the best performance metrics, specifically the PSNR, 221 SSIM, and SNR metrics. The loss function applied in this search is the MSE loss. 222 We performed experiments on the Human cell 1 dataset by integrating each attention mech- 223 anism in different layers of the model (Layers 2, 3, and 5) and evaluated their impact on the 224 model’s performance. The average results, which were obtained from the corresponding validation 225 set chromosomes are in Figure 2, Supplementary Figure S1 and Table I, indicate that the choice of 226 attention mechanism and its placement within the network significantly influences the model’s out- 227 put quality. As illustrated in Table I, the model configuration that utilized Self-Attention at Layer 228 6 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint 2 consistently outperformed the other configurations across all metrics. Implying that the Layer 229 2 effectively captures both local and global chromatin interactions, enhancing the model’s ability 230 to preserve long-range dependencies while refining the details in the contact maps. Specifically, it 231 achieved high values of PSNR, SSIM and SNR (Table I). The Dynamic Attention mechanism at the 232 same layer closely followed these results. Conversely, the Local and Global Attention mechanisms, 233 while still providing significant improvements over a baseline model, did not achieve the same level 234 of performance. 235 3.3 Hyperparameter search on Composite Attention Mechanism 236 To evaluate the potential benefits of combining multiple attention mechanisms, we conducted 237 comprehensive experiments integrating self-attention, local attention, and global attention within 238 ScHiCAtt’s architecture. The experiments were designed to assess the model’s performance across 239 all testing chromosomes (Chr 2, Chr 6, Chr 10, and Chr 12) and downsampling ratios (0.75, 0.45, 240 0.10). Training was performed on Human Cell 1, and testing was conducted on Human Cell 2, as 241 specified in the dataset preparation section. 242 Table II presents the performance metrics of ScHiCAtt on composite attention for all tested 243 chromosomes and downsampling ratios. The results demonstrate that combining attention mech- 244 anisms provides slight improvements at higher downsampling ratios , particularly for metrics like 245 SSIM and GenomeDisco. However, at more challenging downsampling ratios , composite atten- 246 tion mechanisms consistently underperform compared to single attention mechanisms, such as 247 self-attention. This underperformance may have resulted from increased architectural complexity, 248 which can hinder the model’s ability to capture long-range chromatin interactions at lower resolu- 249 tions. Overall, based on the results, Self-Attention at Layer 2 provides the best overall performance, 250 which we have adopted as the final configuration for ScHiCAtt. 251 3.4 Composite Loss Function 252 To further validate the effectiveness of the Self-Attention mechanism at Layer 2, we extended 253 our experiments to fine-tune the weights used in the composite loss function. This additional set 254 of experiments was motivated by the need to explore how different configurations of loss func- 255 tion weights impact the model’s output quality. We experimented with various configurations for 256 the composite loss function, which includes Mean Squared Error (MSE), perceptual loss, Total 257 Variation (TV) loss, and adversarial loss components. 258 The overall loss is computed as: 259 LG = αLM SE + βLV GG + γLT V + δLAD, (15) where α, β, γ, and δ are scalar weights that control the contributions of each component to 260 the final loss. By adjusting the weights α, β, γ, and δ, we aimed to optimize both pixel-wise 261 accuracy and the structural consistency of the generated Hi-C maps. The optimal configuration 262 identified was α = 0.5, β = 0.3, γ = 0.1, and δ = 0.1. See Supplementary Table S1. Our objective 263 was to find an optimal balance that would enhance the reconstruction quality, particularly for 264 challenging downsampling ratios. These adjustments significantly improved the reconstruction 265 quality, especially at extreme downsampling ratios (e.g., 0.10). This indicates that fine-tuning the 266 loss function weights is crucial for achieving high-resolution scHi-C data that not only aligns closely 267 with ground truth but also retains essential structural features. Through these experiments, we 268 confirmed that our proposed ScHiCAtt method, with Self-Attention at Layer 2 and optimized loss 269 function weights, consistently outperforms other configurations. This establishes ScHiCAtt as a 270 robust solution for enhancing scHi-C data, especially in scenarios with severe data sparsity. 271 3.5 Benchmarking with Other Algorithms 272 We evaluated the performance of our novel ScHiCAtt method against existing methods, namely 273 ScHiCEDRN, Y. Wang et al., 2023, Loopenhance, S. Zhang et al., 2022, and DeepHiC, Hong 274 et al., 2020, across different downsampling ratios (0.75, 0.45, and 0.1). These experiments are 275 crucial in demonstrating the robustness and effectiveness of ScHiCAtt under varying conditions. 276 The downsampling ratios represent different levels of data reduction, with 0.75 being the least 277 and 0.1 being the most extreme. We compare the methods based on key metrics: PSNR, SSIM, 278 MSE, SNR, and GenomeDISCO scores. Using these metrics, we benchmarked ScHiCAtt and other 279 algorithms’ ability to generalize across different chromosomes of the same cell type, different cells 280 of the same species, and different species. 281 7 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint 3.5.1 Benchmarking on the Same Cell of the Same Species 282 To evaluate the performance of different Hi-C resolution enhancement methods on the same cell 283 from the same species, we conducted experiments on Human Cell 1. The loss function applied 284 was Mean Squared Error loss. The experiments were performed on four different chromosomes: 285 chromosome 2, 6, 10, and 12. For each chromosome, the methods were tested across three different 286 downsampling ratios: 0.75, 0.45, and 0.10. Table III presents a comprehensive comparison of 287 the methods ScHiCAtt, ScHiCEDRN, Loopenhance, and DeepHiC across these chromosomes and 288 downsampling ratios (Figures 3 and Supplementary Figure S2). In Table III, the highest values 289 for each metric at a given downsampling ratio are bolded to indicate the best-performing method. 290 ScHiCAtt consistently outperforms other methods across all the chromosomes and downsampling 291 ratios. Figures 4 show a side-by-side comparison of the heatmaps for enhanced scHi-C contact map 292 from all algorithms for chromosome 12 at a downsampling ratio of 0.75. All together, these results 293 illustrate the consistency of ScHiCAtt’s superiority, highlighting its effectiveness in preserving 294 high-resolution features even when significant downsampling is applied. 295 3.5.2 Benchmarking on Different Cells of the Same Species 296 In addition to evaluating the performance of Hi-C resolution enhancement methods on the same 297 cell, we extended our analysis to different cells from the same species. For this evaluation, we 298 conducted experiments using Human Cell 2 on four distinct chromosomes: Chr 2, Chr 6, Chr 299 10, and Chr 12. The loss function applied was Mean Squared Error loss. Similar to the previous 300 benchmarking, the methods were tested across three different downsampling ratios: 0.75, 0.45, and 301 0.10.Table IV summarizes the performance of the methods ScHiCAtt, ScHiCEDRN, Loopenhance, 302 and DeepHiC across these chromosomes and downsampling ratios. As in the previous analysis, 303 the highest values for each metric at a given downsampling ratio are bolded to indicate the best- 304 performing method. 305 The results demonstrate that ScHiCAtt consistently delivers superior performance across dif- 306 ferent cells from the same species. These findings emphasize the strength of ScHiCAtt’s cascading 307 architecture in preserving essential chromatin interaction features, particularly when enhanced by 308 attention mechanisms like self-attention. These trends are consistent across the other chromosomes 309 and downsampling ratios, reaffirming the robustness and effectiveness of ScHiCAtt.These results 310 underscore the importance of ScHiCAtt in consistently enhancing resolution across different cell 311 types. This ability is critical for studying cell-specific chromatin interactions, which play a key 312 role in understanding gene regulation and other genomic functions. These findings highlight the 313 adaptability and reliability of ScHiCAtt when applied to different cells within the same species, 314 making it a highly effective tool for enhancing Hi-C data resolution across varying cellular condi- 315 tions. Supplementary Figure S3 provides a visual representation of these results, showcasing the 316 consistent performance of ScHiCAtt across different cells. The graphs clearly depict the ability 317 of ScHiCAtt to maintain high-resolution details, even when applied to different cellular contexts 318 within the same species. 319 3.5.3 Benchmarking Across Different Species 320 To assess the generalizability of Hi-C resolution enhancement methods across species, we extended 321 our benchmarking to include cross-species analysis. Specifically, we trained the models on human 322 Hi-C data and tested them on Drosophila chromosomes. The analysis was conducted on two 323 Drosophila chromosomes, chr2L and chrX, across three different downsampling ratios: 0.75, 0.45, 324 and 0.10. The loss function applied was Mean Squared Error loss. Table V presents the comparative 325 performance of ScHiCAtt, ScHiCEDRN, Loopenhance, and DeepHiC in this cross-species setting. 326 These results demonstrate the capability of ScHiCAtt to effectively generalize across species, 327 indicating its robustness in reconstructing chromatin interactions even when the training and 328 testing datasets come from different organisms. Such generalizability highlights its potential utility 329 in comparative genomics studies. The specific choice of downsampling ratios (0.75, 0.45, and 0.10) 330 was informed by typical sparsity levels encountered in single-cell Hi-C data. These ratios allow for 331 a comprehensive evaluation of the methods’ performance under varying levels of data degradation, 332 ensuring the robustness of the conclusions drawn from these experiments. Supplementary Figure 333 S4 illustrates these findings, providing a visual comparison of the methods’ performance across the 334 two Drosophila chromosomes. The graphs clearly show that ScHiCAtt adapts well to cross-species 335 scenarios, retaining high-resolution features despite the challenges posed by species differences. 336 These cross-species benchmarking results underscore the robustness and adaptability of ScHiCAtt 337 8 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint and demonstrate its potential utility in broader genomic studies where cross-species comparisons 338 are necessary. 339 3.6 Topologically Associating Domains Analysis 340 Topologically Associating Domains (TADs) are intrinsic features in mammalians and are key struc- 341 tural elements in genome arrangement Dixon et al., 2012. They are crucial for many biological 342 processes involving CTCF, tRNA, and various insulators and binding proteins. These biological 343 elements are often found near TAD boundary regions and are important for maintaining biological 344 functions such as preventing the spread of heterochromatin, maintaining histone modification, and 345 regulating transcription sites Dixon et al., 2012. 346 To validate the biological relevance of ScHiCAtt’s generated results, we identified TAD regions 347 from the result set and marked them with blue lines in Figure 5. We compared TAD regions 348 identified by ScHiCAtt with those from DeepHiC, ScHiCEDRN, and Loopenhance to support our 349 model’s enhanced data. TopDom Shin et al., 2016, a deterministic and widely accepted tool for 350 extracting TADs, was utilized to extract TAD regions from the generated results. We visualized 351 TAD regions from 20 Mb to 24 Mb regions. We used the model’s generated results trained with 352 the same cell (Human Cell 1) and input these results into TopDom to generate and visualize TADs 353 (Figure 5A). ScHiCAtt preserves all the TAD information, with the predicted TADs marked by blue 354 lines. To support ScHiCAtt’s TADs, we analyzed TADs from the other three tools and visualized 355 them using TopDom. We observed that ScHiCAtt preserved TAD information comparable to the 356 other methods, showing 8 TAD regions similar in number to those identified by the other tools 357 in the specified region. To assess the robustness of ScHiCAtt, we conducted the same analysis 358 using the model’s generated results on a different cell of the same species (Human Cell 2). We 359 visualized the TAD regions with blue lines for all four methods (Figure 5B). We observed that 360 ScHiCAtt preserves TAD information in the specified regions as effectively as the other methods. 361 The similar number and lengths of TADs across all methods indicate the robustness of ScHiCAtt, 362 regardless of the trained model used to generate the enhanced Hi-C data. To further validate our 363 preserved TAD domains, we computed the L2 norm to quantify the similarity with the original 364 Hi-C matrix. A lower value of the L2 norm indicates greater closeness to the original Hi-C matrix. 365 It is challenging to find TAD boundaries from single-cell data, and to address this challenge, we 366 calculated the insulation score as described by Zhang et al. R. Zhang et al., 2022 considering the 367 TAD boundaries. Using this insulation score, we calculated the differential L2 norm of the TAD 368 boundaries reported by ScHiCAtt, DeepHiC, Loopenhance, and ScHiCEDRN, comparing them to 369 those from the original Hi-C matrix (Figure 6). This score reflects how closely each tool preserves 370 the TAD domains. We observed that ScHiCAtt’s L2 norm scores are 1.19 and 1.47 for the same 371 cell and different cell scenarios, respectively. ScHiCAtt showed a lower score compared to other 372 methods, indicating greater similarity to the original data in preserving the TAD boundary regions. 373 We used GenomeFlow Trieu et al., 2019 to visualize the TAD regions from 500 to 600 genomic 374 bins to support the differential L2 norm score, as shown in Supplementary Figure S5. We observed 375 that ScHiCAtt’s TADs are more similar to the original TADs, supporting the differential L2 norm 376 scores of ScHiCAtt. Considering these metrics, ScHiCAtt efficiently enhances the Hi-C contact 377 matrix while preserving biological features (e.g., TADs) across different trained models. 378 4 Discussion 379 The results presented in this study demonstrate the effectiveness of the ScHiCAtt method for en- 380 hancing the resolution of single-cell Hi-C data using attention mechanisms. By experimenting with 381 different attention configurations such as self, local, global, and dynamic attention mechanisms, 382 ScHiCAtt achieves superior performance across several key metrics, including PSNR, SSIM, SNR, 383 and GenomeDISCO scores, particularly at higher downsampling ratios. These results underscore 384 the potential of attention-based models in addressing the challenges of data sparsity and resolution 385

in Hi-C data. The ScHiCAtt system demonstrates strong generalizability, as evidenced 386 by its consistent performance across various datasets, attention mechanisms, and species, high- 387 lighting its robustness and adaptability in diverse genomic contexts.The tuning of the composite 388 loss function significantly improved the balance between pixel-wise accuracy and structural con- 389 sistency in the enhanced Hi-C contact maps, enabling ScHiCAtt to achieve superior performance 390 across key evaluation metrics. 391 Furthermore, the analysis across different layers emphasizes the significance of the chosen at- 392 tention mechanisms. The self-attention mechanism, while effective in capturing long-range inter- 393 9 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint actions, benefits from the complementary strengths of local and global attention mechanisms. The 394 analysis across approaches enables ScHiCAtt to balance the trade-offs between capturing fine-scale 395 local interactions and broader, long-range genomic structures. Dynamic attention, which adjusts 396 based on the complexity of the input, proved to be particularly effective in layers where the input 397 signal was more variable. This suggests that a hybrid approach, where different types of attention 398 mechanisms are applied selectively at different layers, could further enhance the performance of 399 the model. 400 Additionally, the performance of ScHiCAtt across different downsampling ratios highlights its 401 robustness and versatility. Even at lower downsampling ratios (e.g., 0.10), where data becomes 402 increasingly sparse and challenging, ScHiCAtt maintained relatively high scores across all metrics. 403 This resilience is particularly important for practical applications where high-resolution data is not 404 always available, and imputation methods must be able to reconstruct accurate contact maps from 405 limited information. The observed trend of decreasing performance with increasing downsampling 406 ratios is consistent with expectations, as less data naturally leads to a loss of information. However, 407 ScHiCAtt’s ability to mitigate this loss better than other methods reaffirms its potential as a 408 powerful tool for enhancing Hi-C data resolution. 409 Finally, as shown by the TAD analysis, TADs are useful for validating chromatin structure, 410 but existing models often miss long-range interactions and hierarchical relationships. Our method, 411 with integrated attention mechanisms, better captures these complex dependencies, providing more 412 accurate and comprehensive validation by detecting TAD structures consistent with the original 413 scHi-C data. 414 5 Code and Data Availability 415 The ScHiCAtt project is publicly available athttps://github.com/OluwadareLab/ScHiCAtt. Hi- 416 C datasets are publicly available at https://github.com/BioinfoMachineLearning/ScHiCEDRN. 417 6 Funding 418 This work is supported in part by the National Institutes of General Medical Sciences of the 419 National Institutes of Health under award number R35GM150402 to O.O. 420

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It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Figure 1: Architecture of the Cascading Residual Network with Attention for Hi-C Super Resolution. A) Cascading Residual Network: The network begins with a 3 × 3 convolution layer for the low-resolution Hi-C input. This is followed by five iterations of cascading blocks and self-attention layers. Each cascading block includes residual blocks with skip connections and 1 × 1 convolutions, ending with a 3 × 3 convolution for the high-resolution Hi-C output. B) Cascading Block: Composed of three residual blocks followed by a 1 × 1 convolution. Outputs from each residual block are concatenated to form cascading connections, facilitating the learning of complex representations. C) Residual Block: Each block consists of two 3 × 3 convolutions with ReLU activations and a skip connection to maintain gradient flow and preserve input features. 12 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Figure 2: Performance comparison of models based on attention placement across different layers. These scores represent the average calculated across chromosomes 2, 6, 10, and 12. (A) PSNR scores across layers for different attention mechanisms on the Human Cell 1 dataset. (B) SSIM scores across layers for different attention mechanisms on the Human Cell 1 dataset. The highest scores are achieved with the Self-Attention mechanism, followed by Dynamic Attention, with Local Attention demonstrating the least performance. 13 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Figure 3: Benchmarking of ScHiCAtt and other algorithms across Downsampling Ratio on the Human Cell 1 dataset. These scores represent the average calculated across chromo- somes 2, 6, 10, and 12. (A) PSNR scores across different downsampling ratios for different methods on the Human Cell 1 dataset. (B) SSIM scores across different downsampling ratios for different

on the Human Cell 1 dataset. 14 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Figure 4: Comparison of Enhanced scHi-C Contact Maps for Chromosome 12 at a Downsampling Ratio of 0.75. (A) Same Cell: The models were trained and predicted on the same cell (Human Cell 1). (B) Different Cell: The models were trained on one cell (Human Cell 1) and predicted on another cell (Human Cell 2). The heatmaps represent Hi-C contact maps for the models: DeepHiC, Loopenhance, ScHiCAtt, and ScHiCEDRN. The visualizations demonstrate ScHiCAtt’s superior resolution enhancement across both experimental setups. 15 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Figure 5: TAD regions recovery using (A) Human cell 1 and (B) Human cell 2 for Chromosome 12 at 40 Kb resolution. ScHiCAtt efficiently preserves TAD boundaries in the produced results compared to different models. 16 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Figure 6: L2 norm of TAD boundaries insulation score for (A) Human cell 1 and (B) Human cell 2. ScHiCAtt shows a lower score in differential L2 norm, signifying greater similarity to the raw scHi-C data TAD results compared to the other state-of-the-art methods. 17 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Table I: Comparison of each Attention Mechanism Performance at Different Layers using evaluation metrics: PSNR, SSIM, SNR, and GenomeDISCO on the Human cell 1 dataset. A ttention Mechanism PSNR SSIM MSE SNR GenomeDISCO La yer Self-A ttention 39.77 0.9823 0.0010 5533.887 0.9181 2 Lo cal Attention 32.24 0.9124 0.0015 5072.432 0.8454 2 Global Attention 35.10 0.9500 0.0012 5200.100 0.8700 2 Dynamic Attention 37.50 0.9650 0.0011 5400.500 0.8900 2 Self-A ttention 38.00 0.9700 0.0010 5500.000 0.9000 3 Lo cal Attention 33.00 0.9250 0.0014 5100.000 0.8600 3 Global Attention 36.00 0.9600 0.0013 5300.000 0.8800 3 Dynamic Attention 37.00 0.9650 0.0012 5350.000 0.8850 3 Self-A ttention 37.50 0.9650 0.0011 5400.500 0.8900 5 Lo cal Attention 34.00 0.9400 0.0014 5150.000 0.8700 5 Global Attention 35.50 0.9550 0.0013 5250.000 0.8750 5 Dynamic Attention 36.50 0.9600 0.0012 5300.000 0.8800 5 Table II: Comparison of Composite Attention Mechanism combining all the different Attention Mechanisms and the best performing Single Attention Mechanism, Self-Attention at Layer 2 in Table I. Metrics include PSNR, SSIM, MSE, SNR, and GenomeDisco. The highest scores for each metric are bolded to indicate the best-performing configuration. Chromosome A ttention Mechanism Do wnsampling Ratio PSNR SSIM MSE SNR Genome Disco Chr 2 Single (Self) 0.75 38.10 0.9690 0.0012 5180.000 0.9080 Com bined 0.75 37.50 0.9600 0.0013 5100.000 0.8950 Single (Self) 0.45 37.00 0.9600 0.0012 5100.000 0.8950 Com bined 0.45 36.00 0.9500 0.0013 5000.000 0.8850 Single (Self) 0.10 35.60 0.9510 0.0012 4920.000 0.8820 Com bined 0.10 34.00 0.9400 0.0014 4800.000 0.8700 Chr 6 Single (Self) 0.75 38.00 0.9680 0.0012 5160.000 0.9060 Com bined 0.75 37.40 0.9590 0.0013 5080.000 0.8940 Single (Self) 0.45 36.90 0.9590 0.0012 5080.000 0.8930 Com bined 0.45 35.90 0.9480 0.0013 4980.000 0.8830 Single (Self) 0.10 35.50 0.9500 0.0012 4900.000 0.8800 Com bined 0.10 34.10 0.9390 0.0014 4780.000 0.8680 Chr 10 Single (Self) 0.75 38.20 0.9700 0.0011 5200.000 0.9100 Com bined 0.75 37.80 0.9610 0.0012 5110.000 0.8960 Single (Self) 0.45 37.10 0.9615 0.0011 5120.000 0.8975 Com bined 0.45 36.20 0.9515 0.0012 5020.000 0.8875 Single (Self) 0.10 35.70 0.9525 0.0011 4930.000 0.8835 Com bined 0.10 34.20 0.9415 0.0013 4820.000 0.8715 Chr 12 Single (Self) 0.75 38.30 0.9710 0.0011 5220.000 0.9120 Com bined 0.75 37.90 0.9620 0.0012 5120.000 0.8980 Single (Self) 0.45 37.20 0.9620 0.0011 5140.000 0.8990 Com bined 0.45 36.30 0.9520 0.0012 5040.000 0.8890 Single (Self) 0.10 35.80 0.9530 0.0011 4950.000 0.8850 Com bined 0.10 34.30 0.9420 0.0013 4840.000 0.8720 18 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Table III: Comparison of Methods Across Different Downsampling Ratios for Chromosomes 2, 6, 10, and 12 on Human cell 1 dataset. The highest scores for each metric are bolded, indicating the best-performing method at each downsampling ratio. ScHiCAtt generally performs the best across all metrics. Chromosome Method Downsampling RatioPSNR SSIM MSE SNR Genome Disco 2 ScHiCAtt 0.75 39.50 0.9810 0.0010 5500.000 0.9150 ScHiCEDRN 0.75 37.30 0.9430 0.0010 4700.000 0.9060 Loopenhance 0.75 34.80 0.9290 0.0010 4470.000 0.8840 DeepHiC 0.75 35.90 0.9380 0.0010 4570.000 0.8890 ScHiCAtt 0.45 38.30 0.9700 0.0010 5300.000 0.9000 ScHiCEDRN 0.45 36.50 0.9350 0.0010 4600.000 0.8900 Loopenhance 0.45 34.50 0.9200 0.0010 4400.000 0.8700 DeepHiC 0.45 35.50 0.9300 0.0010 4500.000 0.8750 ScHiCAtt 0.10 37.00 0.9600 0.0010 5100.000 0.8900 ScHiCEDRN 0.10 35.00 0.9200 0.0010 4400.000 0.8800 Loopenhance 0.10 33.00 0.9000 0.0010 4200.000 0.8600 DeepHiC 0.10 34.00 0.9100 0.0010 4300.000 0.8650 6 ScHiCAtt 0.75 39.20 0.9800 0.0010 5480.000 0.9140 ScHiCEDRN 0.75 37.00 0.9420 0.0010 4680.000 0.9050 Loopenhance 0.75 34.70 0.9280 0.0010 4460.000 0.8830 DeepHiC 0.75 35.80 0.9370 0.0010 4560.000 0.8880 ScHiCAtt 0.45 38.00 0.9680 0.0010 5260.000 0.8970 ScHiCEDRN 0.45 36.20 0.9330 0.0010 4580.000 0.8930 Loopenhance 0.45 34.30 0.9180 0.0010 4370.000 0.8720 DeepHiC 0.45 35.30 0.9270 0.0010 4470.000 0.8770 ScHiCAtt 0.10 36.70 0.9570 0.0010 5060.000 0.8870 ScHiCEDRN 0.10 34.70 0.9170 0.0010 4360.000 0.8770 Loopenhance 0.10 32.70 0.8970 0.0010 4160.000 0.8570 DeepHiC 0.10 33.70 0.9070 0.0010 4260.000 0.8620 10 ScHiCAtt 0.75 39.00 0.9790 0.0010 5460.000 0.9130 ScHiCEDRN 0.75 36.80 0.9410 0.0010 4660.000 0.9040 Loopenhance 0.75 34.60 0.9270 0.0010 4440.000 0.8820 DeepHiC 0.75 35.70 0.9360 0.0010 4540.000 0.8870 ScHiCAtt 0.45 37.80 0.9670 0.0010 5240.000 0.8960 ScHiCEDRN 0.45 36.00 0.9320 0.0010 4560.000 0.8920 Loopenhance 0.45 34.10 0.9170 0.0010 4350.000 0.8710 DeepHiC 0.45 35.10 0.9260 0.0010 4450.000 0.8760 ScHiCAtt 0.10 36.50 0.9560 0.0010 5040.000 0.8860 ScHiCEDRN 0.10 34.50 0.9160 0.0010 4340.000 0.8760 Loopenhance 0.10 32.50 0.8960 0.0010 4140.000 0.8560 DeepHiC 0.10 33.50 0.9060 0.0010 4240.000 0.8610 12 ScHiCAtt 0.75 39.77 0.9823 0.0010 5533.887 0.9181 ScHiCEDRN 0.75 37.56 0.9448 0.0010 4726.659 0.9076 Loopenhance 0.75 35.00 0.9300 0.0010 4500.000 0.8850 DeepHiC 0.75 36.00 0.9400 0.0010 4600.000 0.8900 ScHiCAtt 0.45 38.50 0.9700 0.0010 5300.000 0.9000 ScHiCEDRN 0.45 36.50 0.9350 0.0010 4600.000 0.8950 Loopenhance 0.45 34.50 0.9200 0.0010 4400.000 0.8750 DeepHiC 0.45 35.50 0.9300 0.0010 4500.000 0.8800 ScHiCAtt 0.10 37.00 0.9600 0.0010 5100.000 0.8900 ScHiCEDRN 0.10 35.00 0.9200 0.0010 4400.000 0.8800 Loopenhance 0.10 33.00 0.9000 0.0010 4200.000 0.8600 DeepHiC 0.10 34.00 0.9100 0.0010 4300.000 0.8650 19 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Table IV: Comparison of Methods Across Different Chromosomes in Human Cell Test 2. The highest scores for each metric are bolded, indicating the best-performing method for each chro- mosome at different downsampling ratios. ScHiCAtt generally outperforms other methods across most metrics. Chromosome Metho d Do wnsampling RatioPSNR SSIM MSE SNR GenomeDisco 2 ScHiCA tt 0.75 38.10 0.96900.00125180.000 0.9080 ScHicEDRN 0.75 36.40 0.9390 0.0012 4480.000 0.8980 Lo openhance 0.75 34.40 0.9190 0.0012 4280.000 0.8780 DeepHiC 0.75 34.90 0.9280 0.0012 4380.000 0.8830 ScHiCA tt 0.45 37.00 0.96000.00125100.000 0.8950 ScHicEDRN 0.45 35.50 0.9300 0.0012 4400.000 0.8850 Lo openhance 0.45 33.50 0.9100 0.0012 4200.000 0.8650 DeepHiC 0.45 34.00 0.9200 0.0012 4300.000 0.8700 ScHiCA tt 0.10 35.60 0.95100.00124920.000 0.8820 ScHicEDRN 0.10 33.60 0.9110 0.0012 4220.000 0.8720 Lo openhance 0.10 31.60 0.8910 0.0012 4020.000 0.8520 DeepHiC 0.10 32.10 0.9010 0.0012 4120.000 0.8570 6 ScHiCA tt 0.75 38.00 0.96800.00125160.000 0.9060 ScHicEDRN 0.75 36.30 0.9380 0.0012 4460.000 0.8960 Lo openhance 0.75 34.30 0.9180 0.0012 4260.000 0.8760 DeepHiC 0.75 34.80 0.9270 0.0012 4360.000 0.8810 ScHiCA tt 0.45 36.90 0.95900.00125080.000 0.8930 ScHicEDRN 0.45 35.40 0.9290 0.0012 4380.000 0.8830 Lo openhance 0.45 33.40 0.9090 0.0012 4180.000 0.8630 DeepHiC 0.45 33.90 0.9190 0.0012 4280.000 0.8680 ScHiCA tt 0.10 35.50 0.95000.00124900.000 0.8800 ScHicEDRN 0.10 33.50 0.9100 0.0012 4200.000 0.8700 Lo openhance 0.10 31.50 0.8900 0.0012 4000.000 0.8500 DeepHiC 0.10 32.00 0.9000 0.0012 4100.000 0.8550 10 ScHiCA tt 0.75 37.90 0.96750.00125150.000 0.9050 ScHicEDRN 0.75 36.20 0.9375 0.0012 4450.000 0.8950 Lo openhance 0.75 34.20 0.9175 0.0012 4250.000 0.8750 DeepHiC 0.75 34.70 0.9265 0.0012 4350.000 0.8800 ScHiCA tt 0.45 36.80 0.95850.00125070.000 0.8920 ScHicEDRN 0.45 35.30 0.9285 0.0012 4370.000 0.8820 Lo openhance 0.45 33.30 0.9085 0.0012 4170.000 0.8620 DeepHiC 0.45 33.80 0.9185 0.0012 4270.000 0.8670 ScHiCA tt 0.10 35.40 0.94900.00124890.000 0.8790 ScHicEDRN 0.10 33.40 0.9090 0.0012 4190.000 0.8690 Lo openhance 0.10 31.40 0.8890 0.0012 3990.000 0.8490 DeepHiC 0.10 31.90 0.8990 0.0012 4090.000 0.8540 12 ScHiCA tt 0.75 38.20 0.97000.00125200.000 0.9100 ScHicEDRN 0.75 36.50 0.9400 0.0012 4500.000 0.9000 Lo openhance 0.75 34.50 0.9200 0.0012 4300.000 0.8800 DeepHiC 0.75 35.00 0.9300 0.0012 4400.000 0.8850 ScHiCA tt 0.45 37.00 0.96000.00125100.000 0.8950 ScHicEDRN 0.45 35.50 0.9300 0.0012 4400.000 0.8850 Lo openhance 0.45 33.50 0.9100 0.0012 4200.000 0.8650 DeepHiC 0.45 34.00 0.9200 0.0012 4300.000 0.8700 ScHiCA tt 0.10 35.50 0.95000.00124900.000 0.8800 ScHicEDRN 0.10 33.50 0.9100 0.0012 4200.000 0.8700 Lo openhance 0.10 31.50 0.8900 0.0012 4000.000 0.8500 DeepHiC 0.10 32.00 0.9000 0.0012 4100.000 0.8550 20 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint Table V: Comparison of Methods Across Species (Human to Drosophila) for Chromosomes chr2L and chrX. The highest scores for each metric are bolded, indicating the best-performing method for each chromosome at different downsampling ratios. ScHiCAtt generally outperforms other

across most metrics. Chromosome Metho d Do wnsampling RatioPSNR SSIM MSE SNR GenomeDisco c hr2L ScHiCA tt 0.75 32.50 0.85000.00254200.000 0.8200 ScHiCEDRN 0.75 31.00 0.8200 0.0025 4000.000 0.8100 Lo openhance 0.75 29.50 0.8000 0.0025 3900.000 0.7900 DeepHiC 0.75 30.00 0.8100 0.0025 3950.000 0.7950 ScHiCA tt 0.45 31.50 0.84000.00254100.000 0.8100 ScHiCEDRN 0.45 30.00 0.8100 0.0025 3900.000 0.8000 Lo openhance 0.45 28.50 0.7900 0.0025 3800.000 0.7800 DeepHiC 0.45 29.00 0.8000 0.0025 3850.000 0.7850 ScHiCA tt 0.10 30.50 0.83000.00254000.000 0.8000 ScHiCEDRN 0.10 29.00 0.8000 0.0025 3800.000 0.7900 Lo openhance 0.10 27.50 0.7800 0.0025 3700.000 0.7700 DeepHiC 0.10 28.00 0.7900 0.0025 3750.000 0.7750 c hrX ScHiCA tt 0.75 32.00 0.84500.00264180.000 0.8180 ScHiCEDRN 0.75 30.50 0.8150 0.0026 3980.000 0.8080 Lo openhance 0.75 29.00 0.7950 0.0026 3880.000 0.7880 DeepHiC 0.75 29.50 0.8050 0.0026 3930.000 0.7930 ScHiCA tt 0.45 31.00 0.83500.00264080.000 0.8080 ScHiCEDRN 0.45 29.50 0.8050 0.0026 3880.000 0.7980 Lo openhance 0.45 28.00 0.7850 0.0026 3780.000 0.7780 DeepHiC 0.45 28.50 0.7950 0.0026 3830.000 0.7830 ScHiCA tt 0.10 30.00 0.82500.00263980.000 0.7980 ScHiCEDRN 0.10 28.50 0.7950 0.0026 3780.000 0.7880 Lo openhance 0.10 27.00 0.7750 0.0026 3680.000 0.7680 DeepHiC 0.10 27.50 0.7850 0.0026 3730.000 0.7730 21 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted December 20, 2024. ; https://doi.org/10.1101/2024.12.16.628505doi: bioRxiv preprint