Prior-aware and Context-guided Group Sampling for Active Probabilistic Subsampling
Authors: Beomgu Kang
Hyunseok Seo
Venue: ICLR 2026 Poster (2026)
Keywords: Subsampling
Active acquisition
Accelerated MRI
Hyperspectral imaging
Top-k sampling
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Subsampling significantly reduces the number of measurements, thereby streamlining data processing and transfer overhead, and shortening acquisition time across diverse real-world applications. The recently introduced Active Deep Probabilistic Subsampling (A-DPS) approach jointly optimizes both the subsampling pattern and the downstream task model, enabling instance- and subject-specific sampling trajectories and effective adaptation to new data at inference time. However, this approach does not fully leverage valuable dataset priors and relies on top-1 sampling, which can impede the optimization process. Herein, we enhance A-DPS by integrating a deterministic (fixed) prior-informed sampling pattern derived from the training dataset, along with group-based sampling via top-k sampling, to achieve more robust optimization—method we call Prior-aware and context-guided Group-based Active DPS (PGA-DPS). We also provide a theoretical analysis supporting improved optimization via group sampling, and validate this with empirical results. We evaluated PGA-DPS on three tasks: classification, image reconstruction, and segmentation, using the MNIST, CIFAR-10, fastMRI knee, and hyperspectral AeroRIT datasets, respectively. In every case, PGA-DPS outperformed A-DPS, DPS, and all other sampling methods.

Published as a conference paper at ICLR 2026
PRIOR-AWARE AND CONTEXT-GUIDED GROUP SAM- PLING FOR ACTIVE PROBABILISTIC SUBSAMPLING
Beomgu Kang, Hyunseok Seo Department of Artificial Intelligence, Korea University, Seoul, Republic of Korea bokang1 @korea ac. kr, sech@korea ac.
ABSTRACT
Subsampling significantly reduces the number of measurements, thereby stream- lining data processing and transfer overhead, and shortening acquisition time across diverse real-world applications. The recently introduced Active Deep Prob- abilistic Subsampling (A-DPS) approach jointly optimizes both the subsampling pattern and the downstream task model, enabling instance- and subject-specific sampling trajectories and effective adaptation to new data inference time. How- ever, this approach does not fully leverage valuable dataset priors and relies on top-1 sampling, which can impede the optimization process. Herein, we enhance A-DPS by integrating deterministic (fixed) prior-informed sampling pattern de- rived from the training dataset, along with group- based sampling via top-k sam- pling, to achieve more robust optimization-a method we call Prior-aware and context-guided Group-based Active DPS (PGA-DPS). We also provide a theoret- ical analysis supporting improved optimization via group sampling, and validate this with empirical results. We evaluated PGA-DPS on three tasks: classification, image reconstruction, and segmentation, using the MNIST, CIFAR-10. 10, fastMRI knee, and hyperspectral AeroRIT datasets, respectively. In every case, PGA-DPS outperformed A-DPS, DPS, and all other sampling methods. Our code available at https:: /tttt:///tttti hub. com/ 99Kagg/ Baanng//GADDS PGAADP.
INTRODUCTION
Modern technologies generate massive datasets that can require lengthy acquisition time and hinder real-time onboard processing. Many real-world applications, including Magnetic Resonance Imag- ing (MRI) (Ye, 2019), computed tomography (CT) imaging (Chen et al., 2008), ultrasound imaging (Huijben et al., 2020b), digital micromirror device (Baraniuk, 2007), seismic surveying (Herrmann et al., 2012), and hyperspectral imaging (Sun & Du, 2019), highlight the importance of reducing imaging data volume. Therefore, strategic sampling not only reduces data volume and preserves essential information for efficient transfer and processing but also accelerates acquisition, a critical factor in medical imaging.
Compressed sensing (CS) was developed as subsampling strategy to overcome the Nyquist- Shannon limits on the sampling rates required for perfect signal reconstruction (Donoho, 2006; Eldar & Kutyniok, 2012). CS has been widely adopted across various applications and has demon- strated significant impact (Lustig et al., 2007; Baraniuk & Steeghs, 2007; Yu Wang, 2009; Martín al., 2014; Lorintiu et al., 2015; Han al., 2016). Although CS exploits the inherent signal struc- tures, such as sparsity, it does not take into account the information relevant to the downstream task during the sampling process. Bridging the gap between modality- and task-specific knowledge and the sampling process has proven challenging.
Recently, subsampling techniques customized for specific data distributions and downstream tasks have been proposed with advances deep learning, offering learned yet fixed sampling patterns (Huijben et al., 2020a; Weiss et al., 2020; Shen al., 2020; Sherry et al., 2020; Zhang et al., 2020; Aggarwal & Jacob, 2020; Mou et al., 2021; Yang et al., 2025). These approaches optimize sam- pling pattern based on the average data distribution in the training set, which may not provide op- timal results for individual instances. To address this limitation, active sampling was introduced,
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Published as a conference paper at ICLR 2026
where new points adaptively selected based on previously acquired samples, iterating until the required target number of samples is obtained (Zhang et al., 2019; Jin et al., 2019; Bakker et al,, 2020: Pineda et al., 2020; Van Gorp et al., 2021; Tian et al., 2025). Active sampling produces sampling trajectory that adapts to each test instance and incorporates newly acquired data dynam- ically. This is particularly valuable in medical imaging, where each patient's unique physiological condition demands individualized acquisition trajectories.
Although active subsampling provides instance-specific sampling patterns and enables effective adaptation to new data, boosting downstream task performance, its sampling strategy still has room for improvement. Through iterative top-1 sampling guided by previously selected samples, active sampling leverages inter-sample relationships to optimize the sampling model and minimizes re- dundant information. However, it fails to fully exploit the rich prior knowledge embedded in the training dataset. Moreover, relying on top-1 sampling leads to sub-optimal optimization (Huijben et al., 2020a).
In this work, we enhance Active Deep Probabilistic Subsampling (A-DPS) architecture by incor- porating deterministic (fixed) subsampling based on prior knowledge of the training data with group sampling to achieve more robust optimization (Fig. 1). We call this approach Prior-aware and context-guided Group-based Active Deep Probabilistic Subsampling (PGA-DPS). We demon- strate that PGA-DPS exploits training-date priors via deterministic sampling and reinforces this with anstance-adaptive group sampling, resulting in a smoother loss landscape and more stable optimiza- tion. We evaluated PGA-DPS the MNIST dataset (LeCun al., 1998), the CIFAR-10 10 dataset (Krizhevsky et al., 2009), the fastMRI knee dataset (Zbontar et al., 2018), and the hyperspectral AeToRIT dataset (Rangnekar al., 2020). Across classification, image reconstruction, and segmen- tation tasks, PGA-DPS outperforms all other state-of-the-art sampling methods.
RELATED WORK
Recent works have proposed learning-based subsampling techniques tailored to data types and downstream tasks. In the field of MRI, Learning-based Optimization of the Under-sampling Pat- tErn (LOUPE) was developed to simultaneously optimize the subsampling pattern and reconstruct the image, addressing two core challenges of compressed sensing (Bahadir et al., 2020). LOUPE learns the sampling mask by relaxing the non difffeerrentaalee threshold operation, which is similar to the Gumbel- trick used in Deep Probabilistic Subsampling (DPS) (Huijben al., 2020a). The target sampling ratio is enforced by an LI sparsity penalty on sampling mask within the loss function. Additionally, a stochastic greedy algorithm has been applied MRI to obtain the sampling pattern that minimizes the reconstruction loss (Sanchez et al., 2020). However, greedy algorithm- based methods require pre-trained reconstruction capable of handling any subsampling pattern to thoroughly evaluate the loss.
In hyperspectral imaging (HSI), band selection techniques are widely used to identify a small in- formative subset of spectral bands and reduce spectral redundancy. Self seff-Representation Learning with Sparse ID-Operational Autoencoder (SRL-SOA) employs a sparse autoencoder model to learn sparse representation using Taylor-series expansion of non-linear transformation (Ahishali al., 2022). However, this does not incorporate the downstream task model for band selection. Greedy Spectral Selection (GSS) adopts a greedy algorithm: it first performs filter-based interband redun- dancy analysis, then trains a Convolutional Neural Network (CNN) to assess classification perfor- mance of the chosen bands (Morales et al., 2021). On the other hand, CNN based on Bandwise- independent convolution and Hard thresholding (BHCNN) jointly optimizes band selection and the classification by applying a hard threshold mask via straight-through estimator (Feng al., 2020). Although this allows joint optimization, gradients for non-selected bands are ignored, which can hinder the discovery of other informative bands during training. Furthermore, the aforementioned task-aware band selection methods are designed for classification, which may not provide optimal spectral bands for segmentation tasks.
An active sampling strategy for MRI k-space acquisition uses adversarial neural network to dis- tinguish between sampled and unsampled lines in the Fourier space (Zhang et al., 2019). The ad- varsarial network identifies the k-space line that appears most realistically fake and selects it for acquisition; this process repeats until the desired number of lines is obtained. However, this ap- proach processes k-space data directly, which limits its applicability MR image undersampling.
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Full Sample(FS)
Sub-sampled(SS)
A-DPS
PGA-DPS (our)
DPS
(Ps:As)
4
Classification Digit
PPS-top-Pa
(K)
fo
Prior logits
DPS: Deep Probabilistic subsampling
DPS-top-As
(A)
k space
Reconstructed image
Hyperspectral imaging
Segmentation
Rediance
FS
SS
FS
SS
400410
650860
890S100
FS
(B)
(C)
bend (nm)
Figure 1: (A) A schematic overview of the proposed Prior-aware and Group-based Active DPS (PGA-DPS) applied to classification task on the MNIST dataset. PGA-DPS uses learned prior logits (d1), for a fixed sampling mask and then acquires new samples in grouped, active iterations. Here, Ps and As stand for portions prior and active sampling respectively. For example, DPS picks samples in step, A-DPS over 31 iterations, and PGA-DPS in just 3 iterations. (B) An example of an MRI reconstruction task. (C) An example of an HSI segmentation task.
Reinforcement learning (RL) has also been explored for active acquisition, applying greedy and modified e-greedy policies to actively acquire optimal sampling masks (Pineda et al., 2020; Bakker al., 2020). However, RL-based techniques require pretrained reconstruction network that can handle variety of sampling patterns. To address this issue, Active DPS (A-DPS) jointly optimizes both the sampling mask and the associated reconstruction network (Van Gorp et al., 2021). Building on A-DPS, the proposed Prior-aware and Group-based Active DPS (PGA-DPS) improves optimiza- tion robustness and fully leverages prior knowledge embedded in the training data.
METHOD
3.1 TASK-ADAPTIVE SURSAMPLING FRAMEWORK
We aim to find an optimal subsampling strategy A C {0, given input signal x E RR for
specific task i, such that the performance of the task is maintained using fewer input samples.
N
min 4.0
8 (0,
subject to
Σ
A AA=M
where A E EA
(1)
(0, (Ax)
(2)
where f is task model that predicts the task from the input signal æ, 0 is parameters of the model, and is the target number of subsamples. The proportion of selected samples can be represented 100 M/N%. In general, neural networks widely adopted for
by the sampling ratio task models, such as classification, segmentation, reconstruction, detection, and more; however, backpropagation from the loss function hindered by the non-differentiable nature of sampling. This issue was alleviated using the Gumbel-Softmax reparameterization trick introduced in Deep Probabilistic Subsampling (DPS).
3.2 DPS: DEEP PROBABILISTIC SUBSAMPLING
DPS proposed an end-to-end deep learning framework that jointly optimizes both the subsampling
strategy and the downstream task model (Huijben et al., 2020b). During training, DPS learns un- normalized logits Φ, which are used to generate subsampling mask probability P (AlØ) from
categorical distribution with N classes:
Categorical
exp(d.) Σ explo,)
E E(1, (1,...,NN) The

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A-DPS
PGA-DPS
DPS
A-DPS
PGA-DPS
DPS
Aclive
Active
Fixed
Fixed
Image space sub-sampling for classification task on MNIST dataset
k space sub- sub-sampling for reconstruction task on fastMRI knee dataset
Figure 2: An illustration of active sampling strategy for A-DPS and PGA-DPS, whereas a fixed (deterministic) masking pattern is used for DPS.
Gumbel-mas trick enables efficient sampling from categorical distribution (Gumbel, 1954; Mad- dison al., 2):
A = {
if E arg max Gø,
(3)
otherwise
Go. = + + Gumbel(o.). i {1....,N} N}
(4)
where E RV is an unnormalized logit vector composed of o; and G is vector of i.dd noise samples, Gū drawn from a Gumbel distribution Gumbel(O, 1). However, since the arg max function is non-differentiable and thus unsuitable for backpropagation, DPS employs the Gumbel- Softmax trick by relaxing the max operation into a differentiable softmax function as follows (Jang et al., 2017; Maddison et al., 2017):
V = V sosotmar, (Go)
(5)
where 7 is temperature parameter that controls the degree of relaxation, enabling gradients to be distributed across ditliiidimeniioall logits when 7 > during training. addition, as the temper- ature decreases r - O, sof soflmar, can anneal into categorical distribution. Although tuning the relaxation with 7 is crucial for managing the varianee trade-off of the gradient estimator (Tucker et al., 2017), the DPS architecture has been shown to perform effectively with a fixed temperature during training (T = 2).
In addition, the Gumbel-max trick can be extended to the Gumbel top-k trick to efficiently select the most probable samples, rather than just the single tighest-probabilig one (Kool et al., 2019; Plötz & Roth, 2018).
A = arg top (Ø + G) k
(6)
DPS introduces two variants for selecting h samples: DPS-top-1, which sequentially samples from independent categorical distributions each with own trainable logits-and and DPS-top-k: which selects all A samples simultancously using single shared logit for greater parameter efficiency. Although DPS-top-1 is more expressive, the DPS-top-k approach showed improved performance.
Similarly, Active Deep Probabilistic Subsampling (A-DPS) introduces active sampling that uses contextual information from previously selected samples to guide subsequent selection, allowing adaptation to new data (Van Gorp et al., 2021). In A-DPS, samples chosen iteratively by applying DPS-top-1 at every step.
A arg top { (wi-1 + + j 1= (wi-1+
g'), 0
where j denotes the iteration; w C O) is cumulative mask that assigns minus infinity to previously selected elements, ensuring they are excluded after re-normalization; Φi R and G E N are and G for jth sample, respectively; gd is sampling network in jth iteration that encodes the current task context based on the samples selected so far; and fo is a differentiable model that generates the current task prediction. The context is built using analysis-b--snnthest approach, where the task (synthesis) module guides the sampling (analysis). A-DPS, losses are accumulated over all iterations, and the network is updated in semi-greedy manner.
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3.3 PGA-DPS: PRIOR-AWARE AND GROUP-BASED ACTIVE DPS
PGA-DPS initiates with a deterministic subsampling pattern and then iteratively acquires additional samples through active sampling (Fig. 2). The deterministic pattern drawn from the training data's prior is followed by active sampling that exploits each new input's 's contextual information, thereby combining global data prior with input specific context.
Moreover, PGA-DPS uses DPS-top-k to select samples in groups for active sampling, rather than DPS-top-1 in A-DPS, enabling achieve smaller effective Lipschitz constant. We analyze group sampling enabled by DPS-top-A in terms of the loss, which captures the Lipschitzness of the loss and reflects the smoothness of the optimization landscape. The proof is available Appendix A.
Theorem 1.
............ be (The effect of group sampling on the Lipschitzness of the loss). Let f1, f2....,, task models, where each function fj has a corresponding Lipschitz constants L5 for 1,2..... ...,,. ,. In DPS-top-I, task functions are required for each inpul sample In, whereas DPS-rop-k defines a single task function Sk over group of k samples. The Lipschitzness of the loss function for each DPS-top-1 and DPS-top-k as follows:
(x))
II Lr |aj xill?, f
(..)))...))
[=oss -1 - =1f(==))) fa(F1, xz) S Lb || x|| Here, x² E R is the fully sampled input signal (unsampled signal = 0) E R. is the sampled input signal, and Dy is the 7th sample. If the Lipschitz constant of task model at each iteration Lj 2 1,
L II Lr sup, LONSDDS (x))] S sup, [LoosSpps..p
Neural networks typically have Lipschitz constants much greater than one, except in the trivial near-identity case (Malherbe & Vayatis, 2017; Bartlett et al., 2018; Latorre et al., 2020; Shi et al., 2022). Because our task of classification, image reconstruction (from k-space to image), and seg- mentation, are far from identity mappings, DPS-top-k exhibits smaller effective Lipschitz constant than DPS-top-1, whose effective constant is the product of multiple Lipschitz constants. Moreover, the same analysis can apply to the Lipschitz constants of gradient loss LoVsll Consequently, PGA-DPS creates smoother latent space, resulting in more stable and efficient optimization (Vir- maux & Scaman, 2018; Berkenkamp et al., 2017; Liu al., 2022; Gouk et al., 2021; Santurkar et al., 2018). This theoretical analysis aligns with previous experimental results that Top-k sampling outperformed Top-1 sampling in DPS (Huijben al., 2020a).
EXPERIMENTS
4.1 MNIST CLASSIFICATION
4.1.1 EXPERIMENT SETUP
We evaluated the classification performance under pixel subsampling using the MNIST dataset (Le- Cun et al., 1998). The 70,000 grayscale images of 28 28 pixels, representing handwritten digits from 0 and 9, were split into train, validation, and test sets with ratio of 5:1:1, respectively. We compare the proposed PGA-DPS method with DPS and A-DPS across various sampling ratios, rang- ing from I % to 8% with the increment of 1 %. Furthermore, also report the reference performance obtained using all samples (100%).
4.1.2 TASK MODEL
A multi layer perceptron (MLP) with layers is used for the classification network fe(.). The MNIST images are flattened and masked according to the subsampling pattern before being fed into the network. The sampling network g² (.) of an LSTM (Long Short- Thort-Term Memory) followed by a two-layer MLP, which encodes the current task context and generates the corresponding sampling
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mask. Both the classification network and sampling network are simultaneously trained using categorical cross-entropy loss. In addition, the trainable logits of size 784 (Ø1) are included in the network for DPS and PGA-DPS to provide deterministic sampling pattern. Detailed model architecture and training settings are provided the Appendix B.1.
In PGA-DPS, the proportions of prior (deterministic) sampling and active sampling fixed to 60 and 20 %. Here, the Ps and As denote the proportions of prior and active sampling, respectively. (Ps, As)=(60, 20) implies that 60% of the target samples selected by prior sampling, and the remaining samples (40%) are acquired over two active group sampling iterations of 20% each.
4.1.3 RESULTS
The classification accuracy test set is shown in Table 1. PGA-DPS outperforms both DPS and A-DPS across all sampling ratios, with the largest gain at the low sampling ratios. The active sampling method leverages previously selected samples for adapting its sampling pattern, which is particularly effective under extreme subsampling conditions. A-DPS showed strong performance when sampling ratio (r) is below 4%, whereas DPS works better when more samples available. This likely arises because A-DPS trains a separate classifier for each sampled pixel, inflating its Lipschitz constant (as discussed in Theorem 1).
Table The classification accuracy on the MNIST test set (10,000 samples) for various subsampling ratios (r). Each sampling strategy was repeated across six independent runs.
Sampling ratio: (%)
Sampling Model
3
5
7
100
DPS
63.5
83.6
91.5
95.2
96.4
97.1
97.3
97.6
98.2
A-DPS
64.6
85.2
92.2
95.3
96.1
96.6
97.1
97.2
PGA-DPS
68.8
86.9
93.9
95.8
96.7
97.2
97.5
97.7
4.2
CIFAR-10 CLASSIFICATION
4.2.1
EXPERIMENT SETUP
We evaluated pixel-level subsampling for classification using the CIFAR-IO dataset (Krizhevsky al., 2009), which contains 60,000 color images of size 32 32 across 10 classes. Of these, 50,000 images were used for training and validation, and 10,000 for testing. The training split was further divided into training and validation set at a 9:1 ratio. We compared the proposed PGA-DPS, DPS and A-DPS methods across sampling ratios ranging from 2% to 20% in increments of 2%. The reference performance using all samples (100 %) also reported.
4.2.2 TASK MODEL
For the classification model fo).), we employed a four-layer convolutional neural network (CNN) followed by three MLP layers. The CIFAR- images are first masked according the subsampling pattern and then fed into the network. We employed the same sampling network architecture and the same cross-entropy loss function in the MNIST classification experiments. The detailed model architecture and training settings are provided in the Appendix B.2. In PGA-DPS, the proportions of prior sampling and active sampling are fixed 10 and 20 %, respectively.
Table The classification accuracy on the CIFAR-10 10 test set (10,000 samples) for various subsam- pling ratios (r). Each sampling strategy repeated across six independent runs.
Sampling ratio (%)
Sampling Model
4
6
8
10
12
14
16
18
20
100
DPS
38.6
44.5
43.4
44.1
46.1
46.5
49.2
50.5
52.1
54.3
96.3
A-DPS
52.9
61.0
65.8
67.4
70.4
69.6
70.7
69.5
70.0
68.3
PGA-DPS
54.3
63.2
68.6
70.8
74.7
78.1
78.6
79.8
81.3
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4.2.3 RESULTS
Table 2 shows that the proposed PGA-DPS outperforms both DPS and A-DPS across all sampling ratios. Because CIFAR-10 classification is substantially more challenging than MNIST, the perfor- mance gains are larger across the entire range. Unlike the MNIST classification task, A-DPS exhibits consistently strong performance relative to DPS for all ratios. This behavior is likely attributable to the lower Lipschitz constant of CNNs compared to MLPs used in the MNIST experiments (Shi et al., 2022), which makes the optimization landscape easier to navigate. However, beyond certain num- ber of samples (r = 14 %), the classification accuracy A-DPS decreased, likely due to an inflated Lipschitz constant, similar what was observed in the MNIST classification task.
4.3
MRI RECONSTRUCTION
4.3.1
EXPERIMENT SETUP
To evaluate the performance of k-space subsampling, we tested on the single-coil knee RAW ac- quisitions from the fastMRI dataset (Zbontar et al., 2018). A total of 13,000 images, excluding the outer slices, were split into an 8:2:3 ratio for train, validation, and test, respectively. All slices were cropped to central 208 208 pixels and normalized to [0, 1]. Vertical Cartesian binary masks (M) were used for all sampling models, where one column line corresponds to acquiring one phase- encoding line. We simulated the partially acquired k-space by applying the Cartesian binary mask to fully sampled k-space:
Y= F MFX
where F.F-1 are the forward and inverse Fourier transforms, respectively: Y E RNNN is the image from subsampled k-space; X E RNXN is the ground truth image from fully sampled k- space; and |-| denotes the magnitude operation. Following the previous study's ss setup (Van Gorp et al., 2021), 1), we take the magnitude of complex-valued to simplify the image reconstruction.
4.3.2 TASK MODEL.
For the reconstruction task fo(.), a deep unfolded proximal gradient method is employed to recon- struet the original image X from the partially acquired measurement Y (Mardani et al., 2018), 8), by unrolling iterations of the proximal gradient algorithm into a feed-forward neural network:
X d++ = P (x* aV Y YF---MFMX F-IMXX)
(10)
where Py denotes the proximal neural network incorporating the image prior regularizer (t), and a the step size. The sampling network (-) consists of 3-layer CNN, followed by global average pooling, LSTM, and single MLP, in sequence. In this way, the current reconstruction result encoded into the LSTM to generate logits (ø), which are used to select the subsequent (active) sample. The reconstruction model and training details are provided in the Appendix B.3.
We compare PGA-DPS to other sampling methods, namely, low-pass, variable density sampling (VDS) (Lustig al., 2007), greedy mask selection (Sanchez al., 2020), LOUPE (Bahadir et al., 2020), DPS, and A-DPS. In the loss-pass method, lines nearest to the DC (k-space origin) compo- nents are selected; in VDS, sampling density decays with distance from the k-space origin, concen- trating the samples centrally and tapering off toward the periphery. In the greedy mask strategy, the mask pattern is optimized using stochastic greedy algorithm (Sanchez al., 2020), implemented via the NESTA solver (Becker et al., 2011). Afterwards, the corresponding proximal gradient net- work was trained using the fixed optimal mask obtained from the greedy algorithm (Greedy Prox.).
4.3.3 RESULTS
To assess the influence of the sampling hyperparameters (Ps, As), we conducted an ablation study using their various combinations. Table demonstrates the MR reconstruction performance on the hold-out test set, evaluated using three metrics: normalized mean square error (NMSE), peak signal- to-noise ratio (PSNR), and structural similarity index (SSIM). Reconstruction performance shows an overall increasing trend with higher As (i.e., larger k in top-k sampling), across various levels of prior sampling (Ps), even without the use of prior-aware deterministic sampling, which is equivalent

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to A-DPS with group sampling. This trend is consistent with the theoretical explanation proposed in Theorem 1. However, the improvement plateaus beyond an As of 15-20% or even declines slightly, presumably due to the reduced rate of active sampling. While PGA-DPS shows slight performance variation across (Ps, As) configurations, outperforms A-DPS in most cases.
We found the (30%, 30%) configuration of (Ps, As) to be the optimal and fixed it for further MRI reconstruction analysis. Furthermore, this optimal configuration generalizes well across different sampling ratios of k-space lines M 15, 20, 30, and 35 (Table in the Appendix). The performance gain is particularly notable in the low-measurement regime, where the number of k-space lines is small, further demonstrating the robustness of our method under limited data conditions.
Table 3: Average results over 10 runs the hold-out test set of size 208 x 208 pixels for an acceleration factor (M- 26, r = 12.5%), using PGA-DPS across various Ps and As.
As 5%
10%
15%
20%
30%
40%
NMSE
0.0398
0.0393
0.0389
0.0373
0.0376
0.0387
Ps 0%
PSNR
25.4
25.4
25.5
25.7
25.6
25.5
SSIM
0.576
0.581
0.584
0.598
0.591
0.585
NMSE
0.0388
0.0393
0.0378
0.0370
0.0359
0.0359
Ps 30%
PSNR
25.5
25.4
25.6
25.8
25.9
25.9
SSIM
0.588
0.585
0.597
0.618
0.621
0.619
NMSE
0.0387
0.0377
0.0372
0.0364
0.0366
0.0367
Py = 50%
PSNR
25.6
25.6
25.7
25.9
25.8
25.8
SSIM
0.592
0.598
0.603
0.615
0.610
0.611
NMSE
0.0370
0.0377
0.0368
0.0375
0,0371
P 70%
PSNR
25.7
25.7
25.8
25.7
25.7
SSIM
0.596
0.600
0.606
0.601
0.600
As shown in Table 4, the proposed PGA-DPS significantly outperforms all other sampling strategies across all evaluation metrics. The example reconstruction from masks generated by PGA-DPS, A-DPS, DPS, and other sampling methods are shown in the Appendix (Fig. 3).
Since DPS optimizes its mask to perform well average, it heavily concentrates on DC (low- frequency) lines, that capture overall structure of the input data (Fig. 2). contrast, PGA-DPS and A-DPS select more samples farther from the DC region, capturing richer structural details. Note that A-DPS always begins at the center line, whereas PGA-DPS starts with a mix of central and peripheral lines, achieving a more balanced representation of frequency components.
4.4 MRI RECONSTRUCTION WITH ACTIVE BASELINES
4.4.1 EXPERIMENT SETUP
To further validate the effectiveness of our method, conducted additional comparison against reinforcement learning (RL)-based sampling strategies: Evaluator Policy (Zhang et al., 2019) and Data-Specific Double Deep Q-Networks (DS-DDQN) (Pineda et al., 2020). To en- sure compatibility with the publicly available DS-DDQN checkpoints, we applied the same pre- processing procedures used in their original work. In addition, the trained checkpoints were used for DPS (DPS 16lines Oseed Pineda) and A-DPS (ADPS 16lines Oseed Pineda). We adopt the train- validation-test split protocol from (Van Gorp et al., 2021), yielding 34,742 training, 1,785 validation, and 1,851 testing images. Each input corresponds to k-space volume of size 368x640. For eval- uation, reconstruction scores are computed over the central 320x320 region, excluding peripheral background areas. PGA-DPS was trained for 5 epochs with batch size of 1, following the training scheme provided in A-DPS (Van Gorp et al., 2021). The Ps and As ratios were both set 30%.
4.4.2 RESULTS
Table 5 presents the MR reconstruction results the hold-out test set with acceleration factor of We adopt the Scenario- setting, in which 30 CiooCaaibbationn Signal (ACS) lines are fixed, and the remaining 16 target samples are selected. PGA-DPS outperforms all other sampling methods
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Table 4: Average results 10 runs the hold-out test set of size 208x208 pixels for acceler- ation factor of 8 (M- 26, r = 12.5%) compared to other sampling methods.
Sampling Model
Low pass
VDS
Greedy Prox.
LOUPE
DPS
A-DPS
PGA-DPS
NMSE
0.0462
0.0471
0.0425
0.0465
0.0408
0.0398
0.0359
PSNR
24.5
24.5
25.0
25.1
25.3
25.4
25.9
SSIM
0.511
0.533
0.536
0.574
0.571
0.576
0.621
under this setting. Notably, the overall PSNR and SSIM achieved in this experiment is substantially higher than that reported in our previous MRI study using a smaller matrix size (208x208), reflecting the benefits of using higher-resolution k-space data with abundant ACS lines.
Table 5: Results on the hold-out test set of size 368 x 640 pixels for an acceleration factor of 8
(M- = 46, r 12.5%, ACS = 30) compared to RL approaches.
Sampling Method
NMSE
PSNR
SSIM
Evaluator policy (Zhang et al., 2019)
0.0398
28.8
0.610
DS-DDQN (Pineda et al., 2020)
0.0370
29.2
0.623
DPS (Huijben et al., 2020a)
0.0360
30.1
0.650
A-DPS (Van Gorp et al., 2021)
0.0342
30.2
0.654
PGA-DPS (Proposed)
0.0331
30.5
0.668
4.5 HYPERSPECTRAL IMAGE (HSI) SEGMENTATION
4.5.1 EXPERIMENT SETUP
To analyze the generalizability of PGA-DPS, we evaluated its performance on hyperspectral band selection for segmentation. We used the AetoRIT dataset (Rangnekar et al., 2020), which consists of aerial images with hyperspectral bands from 400 to 900 nm in 10 nm increments, resulting in a total of 51 spectral bands. Following the original study's split, 1920 3968 image the left 1920 x 1728 for training, the next 1920 x 512 for validation, and the final 1920 x 1728 for testing. We extracted 64 x 64 patches with 50% overlap from the training set and non-overlapping patches for validation and test sets. The segmentation labels include five classes (1) roads, (2) buildings, (3) vegetation, (4) cars, and (5) water.
divided into
4.5.2 TASK MODEL.
For the segmentation network fo(-),
residual U-Net consisting of 6 ResNet blocks following the pix2pix design (Isola et al., 2017; Zhu et al., 20: this architecture is referred to as Res-U-net in the AeroRIT study (Rangnekar et al., 2020). The sampling network g²(+) consists of 4-layer CNN, with each layer followed by Batch normalization and ReLU activation. The output of the CNN is aggregated into feature vector via global average pooling, which is then fed an LSTM and single-layer MLP to generate logits.
The categorical cross-entropy loss is computed for 5 classes and the model with the highest mean in- tersection over union (mIOU) on the validation set is selected for further evaluation. Detailed model architecture and training settings are provided in the Appendix B.4. In PGA-DPS, the proportions of prior (deterministic) sampling ( (Ps) and active sampling (As) were 80% and 20%, respectively.
Three different DPS methods (DPS, A-DPS, and PGA-DPS) are implemented and compare to the conventional methods including uniform sampling, SRI-SOA (Self-Repressnnttion Learning with Sparse ID-Operational Autoencoder) (Ahishali et al., 2022), and GSS (Greedy Spectral Selection) (Morales et al., 202 l). In the uniform strategy, equidistant spectral bands are selected. In SRL-SOA, the polynomial order of the Taylor series expansion used to estimate the original signal using the autoencoder is set to 3. In the GSS approach, classification is performed the center pixel of x patch. For comparison, we also implemented the reference method 'All-bands', which does not band selection and utilizes all 51 hyperspectral images.

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4.5.3 RESULTS
Table shows segmentation performance using three metries: MPCA (mean per-class accuracy), mIOU (mean Intersection over Union), and mDICE (mean Sørensen- Dice coefficient). PGA-DPS outperformed all other methods, achieving performance comparable to that of using all 51 bands, while enabling over 10-fold acceleration. A-DPS produces less reliable segmentation maps, likely because the complexity of the segmentation makes joint optimization of the sampling strategy and multiple task models difficult. To preserve optimization stability, PGA-DPS limits active sampling at 20%. Example segmentation maps from subsampled bands selected by All-bands, PGA-DPS, A-DPS, DPS, and other band selection methods are shown in the Appendix (Fig. 4).
Table 6: Average segmentation results over 10 runs the hold-out AeroRIT test (3,127 patch samples) for band selection (using 5 bands, i.e. r z 9.8%), compared to other approaches.
Band Selection Model
All bands (Ref)
Uniform
SRL-SOA
GSS
DPS
A-DPS
PGA-DPS
MPCA (1)
88.36
80.59
83.68
77.91
85.75
65.55
86.37
mIOU (f)
0.7037
0.5992
0.6160
0.6220
0.6703
0.5181
0.6752
mDICE (1)
0.8063
0.6937
0.7476
0.7144
0.7732
0.6158
0.7803
5 CONCLUSION
We developed scalable, stable active subsampling technique, called Prior-aware and Group-based Active DPS (PGA-DPS), that integrates context-guided group sampling and deterministic (fixed) subsampling based on training-data prior. PGA-DPS not only provides theoretical analysis for the stable optimization of group sampling, enabled by DPS-top-k: rather than DPS-top-1, but also shows consistent and improved performance compared to conventional A-DPS. We demonstrated image reconstruction, and
the effectiveness of PGA-DPS across three diverse masks-classificallee segmentation usinn the MNIST, CIFAR-10 -0,, fastMRI knee, and AeroRIT datasets, outperforming all other sampling methods. Since top-k sampling and prior-aware deterministic sampling can be easily applied to various sampling tasks, PGA-DPS may serve as a powerful tool for improving performance in real-world applications where acquisition cost and inference efficiency are critical, such as CT, ultrasound, and radar systems.
6 LIMITATION & FUTURE WORK
Although PGA-DPS excels at generating subsampling strategies for diverse tasks, one possible lim- itation lies in selecting the hyperparameters associated with the proportion of fixed and active sub- sampling, denoted as Ps and As, respectively. The optimal sampling portion differs depending on the downstream task, task model, and sampling ratio. We observed that an active sampling ratio (As) range of 20-30% provides the best trade-off between the benefit of top-k sampling and the total budget allocated active sampling, which narrows the search space for optimal configurations.
To determine an appropriate prior-sampling ratio (Ps), we recommend using the performance dis- crepancy between DPS and A-DPS as an empirical indicator of the underlying Lipschitz character- istics of the task. Specifically, if DPS consistently outperforms A-DPS under a given configuration, this suggests that the optimization landscape exhibits a larger effective Lipschitz constant-implyinng that a higher Ps would be beneficial. Conversely, if A-DPS achieves superior performance, the land- scape is likely smoother, in which case a smaller Ps is preferable.
While optimal hyperparameter (Ps, As) ranges are suggested, automatically tuning them (Bergstra et al., 1; Feurer & Hutter, 2019; Bischl et al., 2023) could enhance the robustness of the proposed method. Future research may explore joint optimization of the active sampling hyperparameters (Ps, As), the subsampling trajectory, and the downstream task model.
We demonstrate that using fixed temperature yields robust results (Appendix D); however, tuning or annealing the temperature could further enhance DPS- based methods. A more comprehensive investigation of temperature scheduling therefore represents a promising avenue for future work.
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ACKNOWLEDGMENTS
This work was supported. in part, by the Institute of Information & Communications Technology Planning & (itiriomniIyy--TRCCiioimommi Technology Research Center) grant funded by the and by the National Research Founda-
Korea (MST))(TP--2222-RR tion of Korea(NRF) grant funded by the Korea
REPRODUCIBILITY STATEMENT
The experimental settings and models used in our work are described in the Experimental Setup sections of each task. The task models and baseline approaches are explained in detail in the Task Model section. Additional implementation details are provided the Appendix.
ETHICS STATEMENT
We used large language models (LLM) solely for line-level language editing, including grammar correction and minor phrasing refinements, during the preparation of this paper. LLMs were not involved in any technical aspects of the work.
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APPENDIX
A PROOF
In this Appendix, we prove the Theorem I in Method. We provide proof for the effect of DPS- sampling on the Lipschitzness the loss.
Theorem 1. Let S1, , fk be task models at jth iteration, where each function fj has cor- responding Lipschitz constants I,j for j .,,,..., The DPS-top-l, k task functions are required for each input sample zg, whereas DPS-top-k defines single task function f& over group of k samples. Lipschitzness of the loss function for each DPS-top-1 is as follows:
[osspps up -1f(=)))
II Lr 1| xl1?, f= f (f((z)))
(z)) 11fx(()))))))))))))))){()))))[ fx(=))1 fa 11f((=))))
xx - Lb || x01
Here, x² E RN is the fully sampled input signal, E H. is the sampled input signal (unsampled signal 0), and v, is the nhhh sample. the Lipschitz constant of task model each iteration Lj 2 1,
L S II L,
sup, [[Losspps (2)1l I sup, pp (x)]]
Proof. The Lipschitzness of the loss function for DPS-top-1 first iteration is
Ilf(=)) fi(x1)11 < L1 ||x" =11l
The Lipschitzness of the loss function for DPS-top-1 jth iteration is
< Lj || =z
= Lı [ - fz -
L - || 13-1|1 ||
By the principle of mathematical induction,
(z] - (xx)))
II L, ||= -r1ll
The Lipschitz constant is II, L, for (os) On the other hand, the Lipschitzness of the loss function for DPS-top-k
[[oospppsap (=)] [Ife(=") fx(=))1 < Lx 1| 111x==xx0] x||
The Lipschitz constant of the loss function for DPS-top-k is simply Lt- Therefore, if the Lipschitz constant of task model each iteration L, 1,
L
L, sup, |Loosppss.op- (x)] sup, || 1o
B MODEL ARCHITECTURE AND TRAINING DETAILS
We adopt the same architectures and training strategies used in A-DPS for MNIST classification and MRI reconstruction tasks (Van Gorp et al., 2021). 1). All experiments are run on a single NVIDIA RTX 3090 GPU.
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B. MNIST CLASSIFICATION
The classification network fo(-) consists of 5-layer MLP with 784, 256, 128, 128, and 10 nodes, respectively. Each layer was followed by leaky ReL.U activation with a negative slope of 0.2 and the last layer followed by softmax activation that output probabilities of class, dropout rate of 30% is also applied to the first three layers.
The sampling network g(-) consists of an LSTM (Long Short-Term Memory) with one hidden layer of size 128, followed by two MLPs with 256 and 784 nodes, respectively. A leaky ReLU activation with a negative slope of 0.2 and a dropout rate of 30% are applied after the first MLP.
The categorical cross- cross-entropy loss was minimized using the Adam optimizer (Kingma & Ba, 2014) with the learning rate of 2 x 10-4 (31 0.9, B2 = 0.999, and = 10-7). In addition, the trainable logits, of size 784 (nn. Parammeerrs))) are also updated with learning rate of 2 x 10-3 for DPS and PGA-DPS. The optimization was run for 100 epochs with batch size of 256.
B.2 CIFAR-10 CLASSIFICATION
The classification network fo(-) consists of four convolutional layers with channel sizes of 32, 64, and 128, respectively, and kernel size of 3. Each layer is followed by batch normalization, ReLU activation function, and 2 2 max pooling operation. The resulting 128-channel fea- ture map is then flatten and fed into an MLP composed Linear(256,1288 (-8))-RLLL--nneeeee (18,,
The sampling network g(-) consists of an LSTM (Long Short-Term Memory) with one hidden layer of size 128, followed by two MLPs with 256 and 1024 nodes, respectively. A leaky ReLU activation with a negative slope of 0.2 and a dropout rate of 30% are applied after the first MLP.
The categorical cross-entropy loss minimized using the Adam optimizer with the learning rate of 2 x 10 In addition, the trainable logits, of size 1024 Panammmtmt,r,)) are also updated with learning rate of 2 10-3 for DPS and PGA-DPS. The optimization run for 50 epochs with batch size of 128.
B.3 MRI RECONSTRUCTION
The proximal neural network Py consists of four convolutional layers with channel size of 16, 16,1 16, and I, respectively, and a kernel size of 3 x 3. Each layer is followed by a ReLU activation function except for the final layer. For the image prior regularizer (v²), single 3 x 3 convolutional layer is used. The proximal gradient method is unrolled for three iterations (k=3).
The adversarial loss (Ledig et al., 2017), combined with mean square error (MSE), used to reconstruct visually plausible MR images, by training a discriminator network that distinguishes the real and reconstructed images. In addition, the discriminator feature loss between the real and reconstructed images was employed.
The sampling network g-)-) consists of sequence of layers: Conv2d(1,16), ReLU, Conv2d(16.32), ReL.,, Conv2d(32,64), ReI.U, Average Pooling, Flatten, LSTM(64), and a single-layer MLP(64,208). All convolutional layers have kernel size of 3 3. The MLP converts the output of the LSTM (encoded context) to the logits of size 208.
The discriminator network is consists of a sequence of layers: Conv2d(1,64), Leak)R)L Conv2d(64.64)
Lea.yReLU(0.2), Conv2d(64,64)), LeakyRel.U(0.2), Average Pooling, Dropout(0.4) single-layer MLP (64,1), and Sigmoid. All convolutional layers have a ker- nel size of 3 x 3 and stride 2.
The total loss is computed as a weighted sum of three losses: mean squared error (MSE), adversarial loss, and the discriminator feature loss, with respective weights of 1, x 10 and 10-7
The network is updated using the Adam optimizer (Kingma & Ba, 2014) with the learning rate of 2 x 10-4 (31 0.9, &2 = 0.999, and 1e 7). In addition. the trainable logits, of size 208 (nn, Pam.Paramtter))) are also updated with a learning rate of 2 x 10 3 for DPS and PGA-DPS. The optimization was for 10 epochs with batch size of 2.
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B.4 HYPERSPECTRAL IMAGE SEGMENTATION
For the segmentation network fo(-), we use residual U-Net consisting of 6 ResNet blocks, as pro- posed in the pix2pix (Isola et al., 2017; Zhu et al., 2017). The input channel is set to 51, correspond- ing to the total number of hyperspectral bands, and the output channel is set to 6, corresponding to the number of classes including the undefined class. The number the filters in the last convolution layer is set to 64, and tow downsampling operations applied.
The sampling network g²(+) consists of a sequence of layers: Conv2d(6,32), BN, ReLU, Conv2d(32,64), BN, ReLu, Conv2d(64, BN, ReLU, Conv2d(128,2500 BN, ReLU, Average Pooling, Flatten, LSSTM(256), and a single-layer MLP(256,51), where BN denotes bach normaliza- tion. All convolutional layers have kernel size of 3 3. The last MLP converts the output of the LSTM (encoded context) to the logits of size 51.
In PGA-DPS, the proportions of prior (deterministic) sampling (N) and active sampling (M) were 80% and 20%, respectively, resulting in two group sampling iterations.
The network is updated using the Adam optimizer (Kingma & Ba, 2014) with the learning rate of 10-4 (31 = 0.9, 82 0.999, and le 7), while the learning rate of 2 x 10-4 is used for DPS and GSS. In addition, the trainable logits, of size 51 )arameetttrs)) are also updated with learning rate of for DPS and PGA-DPS. The optimization was run for 60 epochs with a batch size of 100.
C RESULTS
C.I MNIST CLASSIFICATION
We evaluated multiple Ps values under an As of 20% and multiple As values under Ps of 60%. Table shows that PA-DPS outperforms the baselines in almost all configurations, although the optimal configuration shifts slightly across sampling ratios.
Table 7:
The classification accuracy on the MNIST test set (10,000 samples) for various subsampling ratios (r) using various configurations of PGA-DPS (Ps,As). Each sampling strategy was repeated across six independent runs.
Sampling ratio: r (%)
Sampling Model
2
3
4
5
6
7
100
DPS
63.5
83.6
91.5
95.2
96.4
97.1
97.3
97.6
98.2
A-DPS
64.6
85.2
92.2
95.3
96.1
96.6
97.1
97.2
PGA-DPS (80,20)
69.1
86.0
93.9
95.8
96.8
97.3
97.6
97.9
PGA-DPS (60,20)
68.8
86.9
93.9
95.8
96.7
97.2
97.5
97.7
PGA-DPS (40,20)
67.8
86.8
93.6
95.9
96.7
97.3
97.4
97.6
PGA-DPS (20,20)
66.8
85.9
93.2
95.6
96.4
97.0
97.2
97.5
PGA-DPS (60,5)
68.8
87.1
93.7
95.8
96.5
97.0
97.2
97.6
PGA-DPS (60,10)
68.8
87.1
93.8
95.7
96.7
97.2
97.4
97.7
PGA-DPS (60,15)
68.8
87.6
94.2
95.8
96.6
97.2
97.5
97.7
PGA-DPS (60,25)
68.8
87.0
93.8
95.8
96.7
97.2
97.5
97.7
PGA-DPS (60,30)
68.3
87.0
93.9
95.7
96.7
97.2
97.5
97.7
C.2 MRI RECONSTRUCTION
Figure 3 shows example reconstruction from masks generated by PGA-DPS, A-DPS, DPS, and other sampling methods. Notably, PGA-DPS selects samples farthest from the DC, capturing fine- grained details. PGA-DPS exhibits the farthest average mask distance from the DC (11.8), versas 10.2 (A-DPS), 8.8 (DPS), 10.8 (LOUPE), 8.1 (Greedy Prox.), and 11.3 (VDS). Despite prioritizing gigh-frequency components, PGA-DPS also samples adequately near DC, demonstrating its superior reconstruction performance with higher SSIM values.
17

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Published as a conference paper at ICLR 2026
Reference
PGA-DPS
A-DPS
DPS
LOUPE
Greedy Prox.
VDS
SSM
PSNR D. 7277
27.78
1.6670
26.66
0.66.77
26.56
0.6664
25.94
0.6625
26.04 0. 5898
24,62
Sampling mask
1044
0
104
0
0
0
Figure 3: Three examples of subsampling masks (r = 12.5%) and the corresponding reconstructed MR images obtained from PGA-DPS, A-DPS, and DPS. Results are compared against reference images reconstructed from fully sampled k-space data.
To evaluate the robustness and general applicability of the proposed method, we tested whether the selected optimal configuration (Ps, As) (30%, 30%), identified from analysis with k-space lines M = 26, generalizes well across different sampling ratios by conducting experiments with varying values of M, i.e., k-space lines M 15, 20, 30, and 35, corresponding acceleration rates r 7.2%. 9.6%, 14.4%, and 16.8%, respectively. As shown in Table 8, PGA-DPS outperforms DPS and A- DPS across various numbers of k-space lines, with particularly large margin when the number of k-space lines is small.
Table 8: Average results over 5 runs on the hold-out test set of size 208 208 pixels for various acceleration factors = M/N, N 208), compared to the DPS and A-DPS methods.
Method
Metric M = 15
30
35
NMSE
0.0517
0.0448
0.0354
0.0325
DPS
PSNR
23.9
24.7
26.0
26.5
SSIM
0.476
0.528
0.623
0.660
NMSE
0.0571
0.0497
0.0360
0.0333
A-DPS
PSNR
23.3
24.2
25.9
26.4
SSIM
0.444
0.513
0.613
0.647
NMSE
0.0472
0.0402
0.0325
0.0304
PGA-DPS
PSNR
24.4
25.3
26.4
26.9
(30%, 30%)
SSIM
0.505
0.568
0.657
0.690
C.3 HYPERSPECTRAL IMAGE SEGMENTATION
Figure 4 shows example segmentation maps from subsampled bands selected by All-bands, PGA-
DPS, A-DPS, DPS, and other band selection methods.
D ABLATION STUDY ON TEMPERATURE IN DPS ARCHITECTURE
We fixed the temperature to during training for DPS, A-DPS, and PGA-DPS. However, tuning the relaxation parameter critical for balancing the bias-variance trade-off of the gradient estimator and may lead to further improvements.
To assess this, we conducted additional MR reconstruction experiments using various fixed tem- perature values. As shown in Table 9, the reconstruction performance largely insensitive to temperature values. Nonetheless, a fixed temperature of yielded the best overall results, suggest- ing that temperature optimization could provide marginal additional improvements.
18

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Published as a conference paper at ICLR 2026
5 bands
All bands (51)
PGA-DPS
A-DPS
DPS
GSS
SLR-SOA
Uniform
Figure 4: Two example segmentation maps estimated using 5 bands selected from PGA-DPS, A- DPS, DPS, and other band selection methods (r Rs 9.8%). Results are compared against reference segmentation map estimated using all 51 spectral bands.
Table 9: Average results over 5 runs on the hold-out test set (208 x 208 pixels) for acceleration factor of 8 (M 26, r 12.5%), evaluated across various fixed temperatures using PGA-DPS.
0.5
1.0
2.0
3.0
5.0
10.0
NMSE
0.0354
0.0354
0.0350
0.0355
0.0349
0.0353
PSNR
26.00
26.00
26.05
25.97
26.08
26.02
SSIM
0.620
0.624
0.625
0.619
0.627
0.625
We also evaluated temperature annealing, defined as, mar(2.0, x where denotes the training epoch. As shown in Table 10, different annealing schedules produced noticeably different performance. Consequently, using a fixed temperature provides sufficiently robust and stable results in our setting, consistent with what has been found to work well in practice (Huijben et al., 2020a; Van Gorp et al., 2021). Nevertheless, a more comprehensive investigation temperature annealing within DPS remains promising direction for future work.
Table 10: Average results over 5 runs on the hold-out test set (208 x 208 pixels) for acceleration factor (M 26, = 12.5%), evaluated across various temperature annealing strategies (T = max(2.0, T ("") using PGA-DPS.
y= 0.1
0.2
0.3
0.4
0.5
NMSE
0.0378
0.0362
0.0381
0.0364
0.0367
T=5
PSNR
25.7
25.9
25.6
25.9
25.8
SSIM
0.582
0.606
0.584
0.604
0.599
NMSE
0.0389
0.0353
0.0379
0.0361
0.0378
T=10
PSNR
25.6
26.00
25.68
25.9
25.7
SSIM
0.581
0.621
0.586
0.607
0.585
19


Reviews:
[{"review_id": "ztctPwozbO", "reviewer": "Reviewer_4uGe", "summary": "The paper proposes PGA-DPS, a method that integrates a fixed prior sampling mask with group-based active sampling. The proposed approach builds upon DPS and A-DPS. It is evaluated across three tasks: MNIST, MRI reconstruction, and hyperspectral image segmentation.", "questions": "- How would the performance change if model selection were based on validation performance (best checkpoint) rather than the final training epoch?\n\n- What is the rationale behind using different image resolutions (208x208 vs. 320x320) across MRI experiments?\n\n- How sensitive is the proposed approach to Ps or As settings in MINST and segmentation tasks?\n\n- Since the choice of Ps and As ratios is crucial, what is the justification for determining these values?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Extensive experiments are conducted across three tasks.\n\n- The paper is well-written and easy to follow.\n\n- The proposed method is supported by theoretical analysis.\n\n- The approach is an effective variant of the existing DPS-based methods.", "weaknesses": "- For all experiments, the number of training epochs is fixed according to the implementation details. It is unclear how the performance would change if the best-performing checkpoint were selected instead of the final epoch model.\n\n- In the MRI reconstruction experiments, one setup crops the slices to 208x208, while another uses 320x320 images. The reason for this inconsistency is not explained.\n\n- The ratios for the fixed prior (Ps) and active sampling (As) are central to the proposed method but are heuristically chosen for each task. While the authors present results across multiple Ps and As settings for the MRI reconstruction task, similar analyses are missing for the classification and segmentation tasks. The segmentation task uses (80%, 20%), which differs from MRI, and the MNIST configuration also varies. The search space for these ratios is large, but no principled optimization strategy is provided.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "NqidESUz2d", "reviewer": "Reviewer_yF5c", "summary": "The main idea of this paper is to augment Deep Probabilisitic Subsampling (DPS) for task adaptive subsampling with Active Deep Probabilistic Subsampling method (A-DPS). The main idea behind the DPS method is to use Gumbel-softmax trick for back-propagation to estimate the gradients. \n\nIn this paper, the proposed method first performs the deterministic subsampling from the training data and then performs the A-DPS method for contextually selecting more samples. Also, another modification proposed is to use DPS-K for sampling instead of DPS-1 in the A-DPS step.\n\nEmpirical results on MNIST and MRI datasets show significant improvements over existing baselines.", "questions": "1. How does this method compare against Attention guided methods [1]?\n\n2. Expand on section 3.3.  Also, is Theorem 1 a known result or new contribution?\n\n3. How sensitive is the method to the fixed temperature parameter \n\n4. Can the hyperparameters P_s and A_s (proportions of prior and active sampling) be learned during training instead of fixed?\n\n5. How does the prior-informed deterministic mask compare to purely learned or data-driven static masks in terms of interpretability and robustness?\n\n6. How does the choice of task model (classification vs. reconstruction) affect the optimal proportion of prior vs. active samples?\n\n\nReferences:\n\n[1] Shankaranarayana, Sharath M., et al. \"Deep Attention-guided Adaptive Subsampling.\" arXiv preprint arXiv:2510.12376 (2025).\n\nTypos:\n\nLine 017: impedes -> impede\nLine 280: accrucay -> accuracy\nLine 479: DSP-1 -> DPS-1", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. Empirical results show that the usefulness of the proposed method. Significant gains on MNIST and MRI reconstruction dataset.\n\n2. The method is benchmarked against a wide range of alternatives—including greedy algorithms, learned masks (LOUPE), RL methods, and spectral selection approaches proposed for other domains.", "weaknesses": "1. The core algorithm is a combination of already published ideas: deterministic mask learning (training-set prior as used in DPS and LOUPE), sequential active sampling (A-DPS), and top-k/group sampling (DPS-top-k, Gumbel-top-k) in a straightforward manner.\n\n2. The tuning of how many samples come from the prior mask versus active sampling (Ps/As) is hand-picked for different tasks, and the contributions are hyperparameter-dependent.\n\n3. The prior sampling part is not clear, and the key details are hidden away in appendix.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RojHDmrKVq", "reviewer": "Reviewer_9EHq", "summary": "This paper proposes Prior-aware and Context-guided Group-based Active Deep Probabilistic Subsampling (PGA-DPS), which enhances Active Deep Probabilistic Subsampling (A-DPS) by incorporating two key innovations: (1) integrating deterministic prior-informed sampling patterns derived from training data statistics with instance-specific active sampling; (2) introducing DPS-top-k group sampling to replace sequential top-1 sampling. The authors provide theoretical analysis showing that group sampling achieves smaller effective Lipschitz constants, leading to smoother optimization landscapes. Experiments on MNIST classification, fastMRI reconstruction, and hyperspectral segmentation demonstrate that PGA-DPS outperforms existing sampling methods across all evaluation metrics.", "questions": "1. Annotation dependency of prior sampling: Prior sampling requires complete training data annotations. How is this handled in annotation-scarce scenarios? How to update prior sampling patterns when new data continuously arrives?\n\n2. Hyperparameter sensitivity: The (Ps, As) ratios vary significantly across tasks. Is there an automatic selection strategy?\n\nOthers can be seen in Weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The dual sampling strategy combining deterministic priors with adaptive active sampling is well-motivated and novel. While group sampling is not entirely new, its application and theoretical analysis in this context show originality.\n\n2. The method is technically sound with solid implementation. The theoretical analysis (Theorem 1 on Lipschitz constants) provides valuable insights into optimization stability. The experimental design covers three diverse domains, demonstrating method generality.\n\n3. The paper is well-structured with clear method description and reasonable figure presentations.", "weaknesses": "1. Questionable practical relevance: The MNIST pixel-level sampling has limited real-world significance as pixel acquisition costs are identical and downsampling doesn't provide substantial practical benefits. For MRI and HSI tasks, while acceleration is mentioned, detailed time cost analysis and end-to-end system evaluation are missing.\n\n2. Incomplete experimental evaluation: All experiments lack 100% data sampling baselines, making it impossible to assess performance degradation at different sampling rates. This significantly undermines the assessment of the method's practical value.\n\n3. Limited dataset scale: MNIST is too simple to validate method scalability. With sufficient computational resources, evaluation on CIFAR-10/100 or larger datasets would strengthen the claims. While fastMRI and AeroRIT are more realistic, their scales remain relatively limited.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)