Contrastive Learning with Adaptive Neighborhoods for Brain Age Prediction on 3D Stiffness Maps
Authors: Jakob Träuble
Lucy V Hiscox
Curtis Johnson
Carola-Bibiane Schönlieb
Gabriele S Kaminski Schierle
Angelica I Aviles-Rivero
Venue: Accepted by TMLR ()

Abstract: In the field of neuroimaging, accurate brain age prediction is pivotal for uncovering the complexities of brain aging and pinpointing early indicators of neurodegenerative conditions. Recent advancements in self-supervised learning, particularly in contrastive learning, have demonstrated greater robustness when dealing with complex datasets. However, current approaches often fall short in generalizing across non-uniformly distributed data, prevalent in medical imaging scenarios. To bridge this gap, we introduce a novel contrastive loss that adapts dynamically during the training process, focusing on the localized neighborhoods of samples. Moreover, we expand beyond traditional structural features by incorporating brain stiffness—a mechanical property previously underexplored yet promising due to its sensitiv- ity to age-related changes. This work presents the first application of self-supervised learning to brain mechanical properties, using compiled stiffness maps from various clinical studies to predict brain age. Our approach, featuring dynamic localized loss, consistently outperforms existing state-of-the-art methods, demonstrating superior performance and laying the way for new directions in brain aging research.

Published in Transactions on Machine Learning Research (10/2024)
Contrastive Learning with Adaptive Neighborhoods for Brain Age Prediction on 3D Stiffness Maps
Jakob Träuble
jnt27@com.ac. uk
University of Cambridge
Lucy Hiscox
FiscorI.&aardien ac. uk
Cardiff' University Brain Research Imaging Centre
Curtis Johnson University of Delawore
olj edu
Carola-Bibiane Schönlieb University of Cambridge
cbs31 10431@com.ac.. uk
Gabriele Kaminski Schierle University of Cambridge
gsk200ccmm.ac.k uk
Angelica Oviles-Rivero University of Cambridge
ai3230com.com uk
Reviewed on OpenReview: https: // net/ forum? oI2Tpa411P
Abstract
In the field of neuroimaging, accurate brain age prodiction is pivotal for uncovering the com- plexities of brain aging and pinpointing early indicators of neurodegenerative conditions. Recent advancements in selfsuuervised learning, particularly in contrastive learning, have demonstrated greater robustness when dealing with complex datasets. However, current approaches often fall short in gencralizing across non-uniformly distributed data, prevalent in medical imaging scenarios. To bridge this gap, we introduce a novel contrastive loss that adapts dynamically during the training process, focusing on the localized neighborhoods of samples. Moreover, we expand beyond traditional structural features by incorporating brain stiffness-4 mechanical property previously underexplored yet promising due to its sensitiv- ity to age-related changes. This work presents the first application of self-supervised learning to brain mechanical properties, using compiled stiffness maps from various clinical studies to predict brain age. Our approach, featuring dynamic localized loss, consistently outperforms existing seate-of-the-at methods, demonstrating superior performance and paving the way for now directions in brain aging rescarch.
1 Introduction
Aging causes significant changes in the structure and function of the brain. Magnetic Resonance Elastography (MRE) has recently emerged as non-invasive technique to measure mechanical brain properties (Hiscox et al., 2016), such as stiffness μt, that is, the resistance of a viscoclastic material to an applied harmonic force. Studies have shown a promising age sensitivity of whole-brain stifliess measurements (Hiscox et. al., 2021), surpassing established neuroimaging age biomarkers, such as volume measurements (Sack et al., 2011). With advancing MRE protocols, improvements resolution have enabled the study of stiffness changes localized brain regions, revealing regional age-related variability (Murphy et al., 2013; Arani al., 2015; Takamura al., 2020; Hiscox et al., 2018; Delgorio et al., 2021). Furthermore, clinical studies in patients
more

---

Published in Transactions on Machine Learning Research (10/2024)
Method
Contrastive Regression Loss
Rank-N-Contrast
L RmC - Ei Exzt log Ex,nes exp(81.1)
exp($k)
with Si.5 == (k & i, d(us. Une 2 d(us, UU)}
Y-Aware
Lu-aware = = Ei Kiyi
log
explos.a)
Ln Witt
App exp(es,1)
Threshold
Lthreshold
= = -i Ikass Σ. Bi
Wich
log
explai,))
rpek fwnn "man exp(sna))
Exponential
Ceep -- Ei Exys Σ, wi,t
With log
exp(x;
exp(s..((-w...))
Table 1: Overview of Contrastive Regression Losses. This details existing methods each employing distinct strategies to refine the contrastive learning process for regression tasks.
with neurodegenerative diseases have revealed stiffness alterations exceeding those observed in healthy aging (Murphy ct al., 2016; Hiscox et al., 2020a). However, current methods are limited region-wide averages and thus fail to exploit the rich information available in stiffness maps, which can be accessed through nonlinear relationships at voxel level.
Brain age prediction leverages neuroimaging data through machine learning by casting it as a regression problem, wherein models are trained on healthy samples to establish a baseline trajectory for aging. Regres- sion a statistical method used to predict a continuous outcome sutchme-suchh as age- on input data, in this case, brain imaging data. This approach is particularly promising for identifying deviations from normal aging processes that might indicate neurological conditions. This approach has traditionally been applicd to structural brain features using Te-weighted MRT (Baecker et al., 2021). More recently, the scope has expanded to include features obtained from resting-state IMRI, diffusion imaging and MRE are also being examined (Lund et al., 2022; Niu et al., 2020; Clements et al., 2023). Additionally, its potential in detecting and the prognosis of neurodegenerative disorders such as Alzheimer's Disease (AD) is gaining significant. at- tention (Lee et al., 2022). In parallel, modeling approaches have evolved from traditional regression methods to state-of-the-art self-supervised learning (Zha et al., 2024; Dufumier et al., 2021; Barbano et al., 2023). Inspired by advancements in computer vision, self-supervised learning techniques, particularly contrastive learning methods, have been effectively adapted for predicting brain age from structural MRT scans (Dufu- micr et al., 2021; Barbano et al., 2023). Contrastive learning, a technique that learns by comparing pairs of examples, enhances model performance by structuring the embedding space to bring samples with similar ages closer together and push dissimilar samples further apart.
Despite their potential, current methods often struggle with generalization, particularly across datasets characterized by non-uniform distributions. To address this limitation, we introduce a novel rastivve loss that specifically focuses on localized sample neighborhoods. This method is distinctively designed to adapt dynamically across different stages of training, thereby enhancing model performance where traditional approaches falter. Furthermore, considering the demonstrated age sensitivity of mechanical properties com- pared to structural brain properties, this study is pioneering. It represents the first application of contrastive learning to bruin stiffness maps, highlighting a new direction in neuroimaging research. Our contributions are summarized next.
We introduce a adaptive neighborhoods approach, specifically tailored for the framework of contrastive regression learning. Our new method is designed to address the major challenge of limited generalizability in medical image analysis, particularly within datasets characterized by non-uniform distributions. By concentrating on these challenging distributions, our approach not only enhances the robustness of the models but also performance.
We apply our hothod to brain stiffness maps, introducing a novel, age-sensitive modality for brain age prediction that offers insights into neurological aging processes.
To validate our novel contrastive regression loss, we have aggregatod the largest multi-study dataset of brain stiffness from healthy controls, enabling comprehensive and robust conditions. We conducted experiments and demonstrated higher performance than existing techniques.
2

---

Published in Transactions on Machine Learning Research (10/2024)
2
Related Work
Regression Task Regression is a statistical technique that establishes a relationship between a set of independent variables (X) and dependent variable (Y), through function f X Y. Regression specifically addresses contimuous variables, with Y taking values in R. Known for its robust effectiveness, regression has made significant impacts across various domains including (Fanelli et al., 2011; Sun et al., 2012; Lathuilière et al., 2019). Recent decades have seen a surge in research aimed at advancing deep regression techniques, significantly enhancing their performance and applicability- - for example, the works of that (Gao et al., 2018; Rothe et al., 2015; Li et al., 2021; Cao et al., 2020; Yang et al., 2021). Another interesting family of techniques, which is the focus of this work, falls within the contrastive learning family. This perspective is particularly interesting due to its ability to enhance learning by emphasizing differences between samples, thereby improving model robustness and gencralization (Zha et al., 2024; Barbano et al., 2023).
Contrastive Learning. To construct semantically rich and structured representations, contrastive learn- ing has become a widely adopted method for self-supervised representation learning. This technique involves difforentiating between similar (positive) and dissimilar (negative) pairs of data samples D2 and Ik, with the goal of adjusting the distances between representations in the embedding space bringing similar items closer and pushing dissimilar ones apart (Chen et al., 2020b; Khosla al., 2020). Contrastive learning initially gained popularity through its applications in computer vision, where it demonstrated significant improvements in tasks such as image classification and object detection. Early methods like SimCLR (Chen et al., 2020b) introduced simple yet effective framework that maximized agreement between differently augmented views of the same data sample. This approach utilized a contrastive loss function to bring repre- sentations of augmented pairs (positive pairs) closer while pushing apart representations ions of different samples (negative pairs). Building on these foundations, a notable advancement was the introduction of supervised contrastive learning (Khosla et al., 2020), which extended the contrastive loss to leverage label information, treating all samples with the same label as positives. This approach enhanced the performance of models by incorporating supervised information into the sule-supe learning framework.
As we shift focus from classification to regression problems, the distinction between positive and negative pairs transitions to a continuous spectrum. This shift necessitates the model's ability to discern varying degrees of similarity, represented as 8L,- = sim( sim( ticularly, we are interested in brain age prediction, which requires precise modeling of age-related changes in brain structure and function. In response to the challenge of integrating continuous labels such as age, recent advancements propose strategies such as the Y-Aware loss (Dufumier et al., 2021), which softens the boundary between positive and negative samples. Similarly, the work of that (Barbano et al., 2023) proposed the Threshold and Exponential losses, which adjust the strength of aligument and repulsion based on the similarity between continuous labels. Another work introduced the which employs a comparative ranking strategy among samples. This method ranks samples based on their similarity to a given anchor, creating a ranking-bass contimuous spectrum of positive and negative pairs.
beyond mere categorical differentiation. Par-
loss (Zha et al., 2024),
Curriculum Contrastive Learning. Curriculum learning, which introduces training samples in a pro- gressively challenging manner, has been effectively applied to contrastive learning to improve model gener- alization. In this context, simpler pairs of samples are presented early in training, with more difficult pairs introduced gradually. Chu et al. (Chu et al., 2021) propased CuCo, graph representation learning met hod that leverages curriculum contrastive learning to enhance performance on graph tasks. Similarly, Wang et al. (Wang et al., 2024) applied curriculum contrastive learning to self-supervised depth cstimation under adverse weather conditions, showing improved robustness in challenging environments. These approaches demonstrate that progressively increasing difficulty in sample pairs can help models learn more effectively in both graph and visual tasks, making curriculum contrastive learning a promising strategy for various domains.
3 Proposed Technique
This section details the proposed adaptive neighborhoods strategy, a novel approach within contrastive learning tailored for regression tasks. The primary objective of adaptive neighborhoods is to improve the
3

---

Published in Transactions on Machine Learning Research (10/2024)
model's generalization by progressively focusing on localized data neighborhoods in the embedding space. As training progresses, the number of repulsed samples is reduced, allowing the model to capture finer distinctions between samples, which is particularly important for handling non-uniform distributions in continuous regression tasks like brain age prediction. This approach enhances the model's ability to learn meaningful represenlations based on age-related similariiies, regardless of specific brain regions.
3.1 Problem Setup
The primary challenge in brain age modeling lies in accurately mapping sigh-dimessional brain imaging data to a continuous age variable. Traditional contrastive learning methods are limited in their capacity to handle the subtle variations in brain stiffness associated with aging due to their global approach. Our proposed technique introduces a dynamic, localized strategy, focusing on progressively capture age-related features effectively. Importantly, our adaptive neighborhoods method progressively reduces the number of repulsed samples during training, unlike static nearest-neighbor methods like NNCLR (Dwibedi et al., 2021). This adjustment, is critical for capturing the continuous nature of regression lasks, such as brain age prediction. Formally, in brain age modeling, our objective is to train a neural network capable of accurately mapping brain images E X' to their corresponding target ages E R, neural network capable of accurately mapping brain images, where X' S IR" represents the space of high-dimensional brain imaging data (e.g. stiffness maps). The model comprises two key components: a. feature encoder f : X 2, which transforms brain images into an embedding space Z Rd, and an age predictor g + E, tasked with estimating the age from these features.
3.2 Adaptive Neighborhoods
The adaptive neighborhoods technique is a cornerstone of our methodology, designed to optimize the con- trastive learning framework specifically for the regression tasks inherent in brain age modeling. This section outlines the detailed mechanics of this technique, including model components, operational processes, and algorithmic strategies.
To enhance the precision of contrastive learning, we introduce a adaptive neighborhoods approach that progressively explores varied scales within the embedding space, as depicted in Figure 1. This methodology systematically adjusts the selection of repulsion candidates, taking into account both their proximity and the evolutionary stage of training. The selection process for repulsod samples is defined by:
(N(a;, {Ix fepoch (2&) among the Nooo(ppoc)) nearest
neighbors of fepoch based on d(fepoch (IK), Sepoch Sepoch(x:)))
(1)
This expression delineates the set of samples subject to repulsion, identified by their distance d: Zx R+ Our approach progressively narrows the scope of nearest neighbors involved in the repulsion process, thereby focusing the learning increasingly localized neighborhoods within the embedding space. This adaptive mechanism is governed by two critical hyperparameters: the final count of nearest neighbors, Nub. final: representing the ultimate scope of repulsion at the end of training, and the decrement frequency, N N size: which specifies the interval of epochs for adjustments in the neighbor count, as detailed in Algorithm 1.
In datasots that show non-uniform distributions, espocially those with multi-modal characteristics, it is common to find some target areas oversampled and others undersampled. This scenario is typical in neu- roimaging datasets (see Fig. 3). Our dynamic localized strategy is designed to address this issue. It starts by segregating distinct groups and then the training objective evolves to focus exclusively those groups. This process is illustrated in Fig. 1. Our approach aims to reveal more coherent representations throughout the dataset.
Following the methodology proposed by (Barbano al., 2023), we utilize kernel functions to determine the degrees of positiveness, Wi,k K(y: y&) where 0 s w₁,k S 1, between pairs of samples. This metric is defined by the function K K(y;= yx) and reflects the age similarity between two samples. A higher value of
4

---

Published in Transactions on Machine Learning Research (10/2024)
EMBEDDING SPACE R
STIFFNESS MAPS
AGE
NN+b
fo
fx(x)
DyyLLockep
fe
fe(x)
y1
DECREASING REPULSED SAMPLES
EPOCHS
Nb
NNa
STIFFNESS MAPS
AGB
NNa
fe
fo(x)
Yi
Dynleettep
fe
fo(x))
Yj
Figure Graphical Illustratoon of Our Proposed Method. Throughout training (top to bottom), the re- pulsion progressively localized as the number of samples, selected as nearest neighbors, are gradually decreased. The circle radii correspond to the label values of the samples, with larger circles representing older samples and smaller circles corresponding to younger samples.
Algorithm Calculation of Number Nearest Neighbors N (epoch)
Require: NNetep size
max epochs A NNab, final 2 0
steps completed
current epoch
MK Migtop aize
total steps + nax epochs
KMotup uice
NN.b decrement per step-
batch size NKa,, disal
total steps
NN.b f- batch size - (NN,, decrement per step x steps completed)
NN.b f- max(NN.., NNan, rinal)
Wi, suggests that the samples are close age, prompting the algorithm to minimize the distance between their representations in the embedding space. Conversely, a lower value indicates significant age difference, thus leading increase in the distance between their embeddings.
Each sample z; in a batch is compared against every other sample 2s, with the embeddings being adjusted based on their relative age similarit The selection of nearest. neighbors for this comparison, N NNa (epoch), dynamically changes as the training progresses. Initially, a larger set of neighbors is considered to establish broad relationships. As training advances, this number is progrossively reduced focus on more immediate and relevant interactions, thus refining the learning towards localized features. The par-sample adaptive neighborhoods loss reads:
5

---

Published in Transactions on Machine Learning Research (10/2024)
Wi,k log Wi,t
exp($t,k) EMEeNo exp(s; (5 wi,))
Adap'N
This expression calculates the contribution of each sample pair to the overall loss. It normalizes these contributions by the sum of positiveness weights for all comparisons within the batch, adjusting the impact of each pair based on their age-related similarity. The softmax function is then applied to these normalized and adjusted similarity scores 8i,k, defined by 8: 2 x 2 + IR+, which are recalculated for each dynamically defined nearest neighbor set. What is the Intuition Behind Our Adaptive Noighborhoods? We address the challenge of non-uniform data distributions in neuroimaging datasels. Traditional learning models often fail adequately distinguish between different age groups when these groups are unevenly reprosented in the training data. Our approach refines this by adjusting emboddings dynamically. This is done via (2) that represents the per-sample loss function in contraslive learning framework, which aims to dynamically adjust the embeddings based on age-related similarities. The essence of this equation lies in its ability to modulate the degree of repulsion or attraction between samples within the same batch based on their age proximity, which is quantified by WA.k the positiveness weight. This formulation allows for adaptive learning where the focus is progressively shifted toward more challenging or informalive pairs, potentially those that are not well-aligned in age, thus encouraging the model to learn finer distinctions as training progresses.
The total loss AdapN is then calculated over all samples anchors:
C AdapN
Σ
La AdopN
Wi,k log Wiit
exp(s;R) En,ENN(a exp (t.(st,(11 wi,e)
(3)
This aggregated loss function is key for structuring the embedding space optimally, ensuring that samples with similar ages are located closer together while those with significant age differences are distanced. Such configuration not only enhances the accuracy of age prediction but also demonstrates the model's ability to learn icalll structured representations based on age-related palterns.
4
Experimental Results
This section details the complete set of experiments conducted to evaluate the proposed technique.
4.1
Data Description
We have assembled a dataset of 311 three-dimensional (3D) brain stiffness maps obtained from healthy control subjects (HC). These data were sourced from multiple clinical studies, all of which utilized highly similar Magnetic Resonance Elastography (MRE) protocols. This ensures consistency across the collected data. Although our dataset contains only 311 subjects, it represents one of the largest collections of brain stiffness maps, spanning a wide age range and offering a balanced distribution of male and female subjects. For detailed information on the individual studics and the data collection methods, plcase refer to Table All datasets were collected in accordance with ethical standards, under protocols approved by the respective local institutional review boards.
The age distribution of all samples from cach study is illustrated in Fig. 3. While age-related non-uniformity is evident in the dalaset, further variability in brain coverage, as shown in Appendix Fig. 7, adds complexily to our analysis of stiffness maps. Following this, stiffness maps, depicted in Fig. 2, were processed to enhance quality and uniformity. Initially, cach map underwent skull stripping using Frecsurfer (Fischl, 2012), step isolate the brain tissue from non-relevant anatomical structures. Subsequently, we applied a bias field correction to remove intensity gradients that could affect subsequent analyses.

---

Published in Transactions on Machine Learning Research (10/2024)
MECHANICAL PROPERTIES: STIEENESS MAP j
StauctuRal PROPERTIES: TI WEIGHTED IMAGE
AGE: 76
2.30
2.30
AGE: 61
AGE: 42
1030
AGE: 26
2.30
Figure 2: Comparison of Neuroimaging Modalities. Each row shows three orthogonal views (sagittal, coronal, and axial) of the brain images, highlighting the differences in mechanical and structural properties across different ages.
To address the issue of data heterogeneity across different studies, we performed affine registration of the images the MN1152 template. This registration was conducted at an isotropic resolution of mm3 using ANTs (Avants et al., 2009), ensuring consistent orientation and scale among all datasets. Finally, normalized the quantitative stilfness images, setting their mean to zero and slandard deviation to one across the dataset.
4.2 Evaluation Protocol
Our evaluation strategy involved 3D ResNNet-18 model (33.5M parameters). which pre-trained on the openBHB dataset (Dufumier et al., 2022), containing 5000 Ti 3D MRI brain images from multiple scanning sites, using the best reported method from the OpenBHB challenge (Dufumier et al., 2022). To enhance generalization to our stiffness dataset, we utilized quasi-raw images, ensuring uniform image pre- processing, and downsampled the structural MRI images to 2 mm3 isotropic resolution. We selected ResNet- 18, the smallest variant of the ResNet architecture, ResNet-18 18 underwent full fino-tuning (i.e. updating all weights) on our brain stiffness dataset, following an 80:20 train-test split, over 50 epochs and batch size of 32 using the Adam optimizer. This optimization
match the scale of our datasct. The pre-trained

---

Published in Transactions on Machine Learning Research (10/2024)
Table 2: Compilation of Dataset Information Across Multiple Studies: This table presents a detailed break- down of the datasets used in our analysis. The aggregated data encompasses diverse age range and a balanced gender ratio, facilitating a comprehensive evaluation of brain stiffness in healthy controls.
Study
Published In
#Subjects
Age [years]
Sex F.MM]
(Hiscox et al., 2020c)
134
23.4 + 4.0
78:56
2
(Bayly et al., 2021)
60
37.8 + 20.9
34:26
(Hiscox
et. al.,
12
69.4 + 2.4
6:6
2020b)
(Delgorio
al.,
68
69.3 + 5.8
49:19
2023)
(Sanjana et al., 2021;
37
49.1 + 16.6
16:21
Delgorio et al., 2022)
Total
311
41.0:121.9
183:12
20
Number of subjects
Study
15
2
10
5
0
10
Age (years)
Figure 3: Age Distribution of Participants from Multi-Site MR Elastography Studies. Contribution to the 311 healthy control (HC) stiffness brain maps of different clinical studics highlighted in color. The distribution bimodal, indicating two predominant age groups among the subjects.
included an initial learning rate of x 10-4, decreased by 0.9 every 10 epochs, and a weight decay of 5 10-5, Hyperparameters N and N Nttepssia were optimized via random search across 30 ilerations. Our implementation is based on Barbano et al. (Barbano et al., 2023). As contrastive learning frameworks SimCLR and NNCLR require data augmentations, Gaussian Noise was applied for these methods. Our models were trained using an NVIDIA A100-SXM-80GB GPU. Following the training the representations, employed Ridge Regression estimator (Barbano al., 2023) top of the frozen encoder to predict age. As evaluation metric, we calculated the mean absolute error (MAE) on the test set, averaging the results across five random seeds.
4.3 Results and Discussion
We begin by evaluating the represcntations of stiffness maps learned using our adaptive neighborhoods loss as in (3) with Manhattan distance, N N = 14 and N Nattppiie 1, selected via random search, against those using current state-offthe-art contrastive classification and regression losses.
Table illustrates the effectiveness of our proposed Dynamical Localized Repulsion approach in the context of brain age prediction from stiffness maps, as evidenced by the Mean Absolute Error (MAE) metric. No- tably, method significantly outperforms contrastive classification losses such as SimCLR (Chen et al.,
8

---

Published in Transactions on Machine Learning Research (10/2024)
Table 3: Representation comparison demonstrates the superior performance of our method over state-of-the- art contrastive classification and regression losses. The best result is in green
Contrastive Classification Loss
MAE [years]
SimCLR (Chen et al., 2020a)
9.600 + 1.701 8.526 + 1.442
NNCLR (Dwibodi et al., 2021)
Contrastive Regression Loss
(Zha et al., 2024)
5.266 + 0.587
Y-Aware (Dufumier et al., 2021; Barbano al., 2023)
3.852 + 0.212
Threshold (Barbano et al., 2023)
4.420 + 0.503
Exponential (Dufumier et. al., 2021; Barbano et al., 2023)
3.824 + 0.215
Adaptive Neighborhoods (Ours)
3.724 + 0.220
2020b) and NNCLR (Dwibedi al., 2021), which achieve higher MAEs of 9.600 + 1.701 and 8.526 + 1.442, respectively. When comparing our method to existing stale-of-the-art contrastive regression losses, our ap- proach demonstrates superior accuracy in predicting brain age. Upon careful examination, that Rank-N-Contrast (Zha et al., 2024) shows the highest MAE, suggesting it may be less adept at capturing the nuanced patterns within the data necessary for precise age prediction. Y-Aware and Exponential (Du- fumier et al., 2021; Barbano et al., 2023) losses show improvements over Krank-N-Contrast These hod appear to better align with the underlying age-related changes in brain stiffness but still fall short compared to our approach. Threshold (Barbano et al., 2023) loss offers a competitive performance, yet does not achieve the same level of accuracy as our method. This could indicate that while it handles some aspects of the data variability effectively, it might not fully capture the localized age-related changes our method does. Our proposed loss achieves the lowest MAE, underscoring its ability to more accurately model the age- related changes in brain stiffness. This suggests that our method's focus on localized sample neighborhoods and its dynamic adaptation during the training process significantly contribute to its improved performance.
can observe
To investigate the role of the distance norm for nearest neighbor selection of our adaptive neighborhoods approach, we conduct an ablation study, examining the impact of various distance norms on the model's performance, as detailed in Fig. 4a. The method shows robustness regarding the choice of distance norm. Our findings revcal that the Manhattan norm achieves the lowest MAE of 3. +.220 years, outperforming the Cosine (MAE- 3.748 + 0.142 years), Euclidean (MAE 3.806 + 0.154 years), and Chebyshev norm (MAE- = 3.842 + 0.196 years).
In addition to the primary evaluation of the contrastive regression loss, we conducted a comparison of different auxiliary loss functions to investigate their impact on the final performance. Specifically, we evaluated the Mean Squared Error (MSE), Mean Absolute Error (L1), Huber loss, and DEX loss (Rothe et al., 2015). For this experiment, the encoder was first trained using AdaanN- The trained encoder was then frozen, and a separate predictor trained on top of the fixed representations using the auxiliary loss function. The results, shown in Fig. 4b, indicate that the MSE loss performs best with a MAE of 3.724 + 0.220 years. Both L1 and Huber losses also showed strong performance, 3.795 + 0.254 years and 3.973 + 0.199 years respectively. However, the DEX loss performed significantly worse in this setup, producing a final MAE of 0.749 years, suggesting that traditional regression-based losses like MSE are better suited for this task when combined with the contrastive learning representations compared to classification-basse approaches like DEX.
Data augmentations play prominent role in other self-supervised learning methods, they often help mod- cls learn more robust and generalizable representations. In the context of brain imaging data, augmentation can be particularly important, but it must be applied with care due to the structural consistency of the data. To investigate this, we conducted an ablation study to explore the impact of various augmentations on the model's performance. Specifically, we applied four types of augmentations--Ne -Nise,, Cutout, Rotation, and ship-during training to examine how each one influences the learned representations and final predic- tions. The results, shown in Fig. 4c, indicate that Cutout provides the best performance with MAE of
9

---

Published in Transactions on Machine Learning Research (10/2024)
Chebyshev
DEX
Euclidean
Cosine
Huber
Manhatian
MSE
3.0
32
34
3.6 MAE [yeass]
3.8
4.0
42
3.0
3.5
4,0
4.5
5.0
5.5
6.0
6.5
MAE [years]
(a) Ablation study for different distance when selecting nearest neighbors shows Manhattan norm achieves lowest MAE.
(b) Ablation study for different regression losses shows MSE loss achieves lowest MAE compared to Huber, L11 and DEX.
Rotation
Flip
features projection
Noise
features wr projection
Cutout
None
MAE [ycars]
3.0
3.5
4.5
6.0
MAE [ycus]
(c) Ablation study for different augmentations reveals the Cutout method achieves the lowest MAE, outper- forming other augmentations.
(d) Ablation study for feature extraction shows feature extraction after non-linear projection mapping achieves lower MAE.
Figure 4: Ablation studies show the impact of distance norms, regression losses, augmentations, and pro- jection mapping on model performance, with the Manhattan norm, MSE loss, Cutont augmentation, and projection mapping achieving the best results, respectively.
3.667 years. This may be due to the fact that Cutout selectively masks parts of the brain images while preserving the overall structural integrity, allowing the model to focus the most informative areas without introducing significant. distortions. Noise also performed reasonably well, with MAF of 3.956 + 0.283 years, likely because it introduces minor variations that enhance the model's robustness. Flip resulted in a slightly higher MAE of 4.238 = 0.192 years. This augmentation appears to be less harmful than others, likely due the natural symmetries in brain anatomy. In contrast, rolation had the worst performance, significantly degrading the modcl's accuracy with MAE of 5.431 + 0.414 years. This likely because brain images are pre-registered during preprocessing to ensure consistent. orientation across subjects, meaning that rotation disrupts this careful alignment.
In previous self-supervised learning frameworks like SimCLR, features are first extracted and then trans- formed through a non-linear projection before computing the loss. Specifically, the encoder p: X' - H maps the input data x E to feature vectors H, where H C Rd the feature space. The projection function H + then maps these feature vectors to the embodding space. The overall function f X Z, which maps the input E X directly to the embedding E Z, the composition of the encoder p and the projection f(x) =p(())) To explore the impact of this projection step in framework,
10

---

Published in Transactions on Machine Learning Research (10/2024)
EPOCH =
EPOCH =
EPOCH = 21
74
300
105
EPOCH 30
EPOCH 40
EPOCH 50
123
422
-36
-35
60
25
50
15
1922
STUDY
AGE
30
45
60
90
Figure UMAP visualizations representations show model improvements throughout various learning stages. As epochs increase, the clusters become more distinct and separate, indicating a more defined representation of the underlying data features.
conducted an ablation study comparing model performance under two conditions: (1) when features are used in the same space as the loss (features w/ projection), i.e. f(x) is equivalent to p(x), meaning the embeddings directly correspond to the features, and (2) when features are computed before the projection step (features w/o projection), making the embeddings distinct from the features. The results, shown Fig. 4d, indicate that the model benefits from extracting the features after the projection layer, achieving a MAF of 3.724 + 0.220 years with the projection, compared to 4.323 + 0.216 years.
Following the ablation studies, turn attention to the evolution of the representations as the model learns across epochs. The UMAP embedding visualizations presented in Fig. 5 showcase the progressive refinement of the feature space through epochs 1, 6, 21, 30, 40 and 50. Initially, the representations are scattered and lack clear structure, indicating that the model is yet to learn distinct age-related patterns. As training progresses, we observe the emergence of more defined clusters, reflecting the model's increasing adeptness at capturing age-related variations in brain stiffness. By epoch 50, the embeddings show distinct, well-scparated groupings, suggesting that our method has achieved a better understanding of the underlying age-related features. These visualizations not only confirm the effectiveness of our adaptive neighborhoods approach but also offer intuitive insights into how contrastive learning can be harnessed for regression tasks in medical imaging.
11

---

Published in Transactions on Machine Learning Research (10/2024)
5 Conclusion
We introduced novel contrastive regression loss that adeptly prioritizes local regions within embedding spaces and dynamically adjusts these regions throughout the training process. By applying this method to brain stiffness maps obtained from Magnetic Resonance Elastography (MRE), we achieved superior pre- dictive performance in brain age estimation compared to established contrastive learning methods. This advancement not only demonstrates our model's efficacy but also underscores the potential of using localized dynamic adjustments the analysis of complex neuroimaging data. Significantly, our research marks the first opplication of self-superoised learning techniques to explore the mechanical properties of the brain, an area previously uncharled in the lilerature. The implications of this are profound, opening up new avenues for understanding the structural changes associated with aging and potentially other neurological conditions. However, while our proposed contrastive learning method shows strong predictive performance in brain age estimation, its validation remains limited to the domain of brain imaging. Broader testing across diverse datasets and comparison with other approaches, such as purely supervised learning, are needed to fully substantiate its generalizability. Thus, while promising, our method requires further exploration to confirm its broader applicability. Future work includes to extend our framework to include cohorts with neurological diseases, such as Alzheimer's and Parkinson's. This expansion expected to provide deeper insights into the progression and early diagnosis of these conditions, leveraging the detection capabilities of our model. Additionally, we aim to explore the integration of multimodal imaging data to enhance the robustness and accuracy of our predictions, potentially leading to breakthroughs in personalized medicine and neuroimaging analytics. Finally, as this is a first. strategy to leverage non-nearest, samples, we acknowledge that more advanced methods to introduce bias in the sampling strategy could be explored. This direction, including adaptive or more dynamic reweighting mechanisms, is an exciting area for future work.
Acknowledgments
JT acknowledges support from the Gates Cambridge Trust via the Gates Cambridge Scholarship. CJ ac- knowledges partial support from the National Institutes of Health grants RO1-AG058853 and U01-NS112120. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC advanced career fellowship EP BP/VV22428/LL EPSRC grants EP /P/0066045/ and EP JP/TT00553/L EP/N014588/11 EP E TO179961/, the Wellcome Innovator Awards (0/73////19/ / and 221633/ 221633/7/20/ ///20//2 CCMI and the Alan Turing Institute. GSKS acknowledges funding from the Wellcome Trust (065807/Z.) /Z) (203249 / 16/)), the UK Medical Research Council (MRC) MMR/K02292X/1) 1), ARUK (ARUK-PGO13-1) Michael J Fox Foundation (16238; 022159), and Infinitus China Ltd. LVH is supported by the Wellcome Trust (grant number: 226420/Z/22/42 AAR gratefully acknowledges funding from the Cambridge Centre for Data-Driven Discovery and Accelerate Programme for Scientific Discovery, made possible by a dona- tion from Schmidt Futures, ESPRC Digital Core Capability Award, and CMIH and CCLMI, University of Cambridge.
References
Arvin Arani, Matthew C Murphy, Kevin Glaser, Armando Manduca, David Lake, Scott A Kruse, Clifford R Jack Jr, Richard L Ehman, and John Huston 3rd. Measuring the effects of aging and sex on regional brain stiffness with mr elastography in healthy older adults. Newroimage, 111:59 64, 2015.
Brian B Avants, Nick Tustison, Gang Song, et al. Advanced normalization tools (ants). Insight j. 2(365): 1 35, 2009. 7
Lea Baccker, Rafael Garcia-Dias, Sandra Vieira, Cristina Scarpazza, and Andrea Mechelli. Machine learning for brain age prediction: Introduction to methods and clinical applications. EBioMedicine, 72, 2021. 2
Carlo Alberto Barbano, Benoit Dufumier, Edouard Duchesnay, Marco Grangetto, and Pictro Gori. Con- trastive learning for regression in multi-site brain age prediction. In 2023 IEEE 20th International Sym- posium on Biomedical Imaging (ISBI), pp. 1-4. IEFE, 2023. 2, 3, 4, 8, 9,
12

---

Published in Transactions on Machine Learning Research (10/2024)
Philip V Bayly, Ahmed Alshareef, Andrew K Knutsen, Kshitiz Upadhyay, Ruth J Okamoto, Aaron Carass, John A Butman, Daung I. Pham, Jerry I. Prince, KT Ramesh, et al. Mr imaging of human brain mechanics in vivo: new measurements to facilitate the development of computational models of brain injury, Annals of biomedical engineering, 49:2677-2692 2021.
Wenzhi Cao, Vahid Mirjalili, and Scbastian Raschka. Rank consistent ordinal regression for neural networks with application to age estimation. Pallern Recognition Lellers, 140:325 331, 2020. 3
Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. simple framework for contrastive learning of visual representations. In International conference on machine learning, pp. 1597-1607. PML.R,
2020a. 9
Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. simple framework for contrastive learning of visual representations. In International conference on machine learning, pp. 1597-1607. PMLR,
2020b. 3, 8
Guanyi Chu, Xiao Wang, Chuan Shi, and Xunqiang Jiang. Cuco: Graph representation with curriculum contrastive learning. In IJCAI, pp. 2300-2306, 2306, 2021.
Rebecca G Clements, Claudio Cesar Johnson. Mechanical property based brain age prediction using convolutional neural networks RioR pp. 2023 02, 2023. 2
Grace McIlvain, Austin J Brockmeier, and Curtis L
Peyton L Delgorio, Lucy V Hiscox, Ana M Daugherty, Faria Sanjana, Ryan T Pohlig, James M Ellison, Christopher R Martens, Hillary Schwarb, Matthew DJ McGarry, and Curtis L Johnson. Effect of aging on the viscoelastic properties of hippocampal subfields assessed with high-resolution mr elastography. Cerebral Cortez, 31 (6):)979 2811, 2021.
Peyton L Delgorio, Lucy Hiscox, Ana M Daugherty, Faria Sanjana, Grace Mcllvain, Ryan T Pohlig, Matthew DJ McGarry, Christopher R Martens, Hillary Schwarb, and Curtis L Johnson. Structure-function dissociations of human hippocampal subfield stilfness and memory performance. Journal of Newroscience, 42(42):7957-7966 2022. 8
Peyton L Delgorio, Lucy V Hiscox, Grace Mcllvain, Mary K Kramer, Alexa M Diano, Kyra Twohy, Alexis A Merritt, Matthew DJ McGarry, Hillary Schwarb, Ana M Daugherty, et al. Hippocampal sub- field viscoelasticity in amnestic mild cognitive impairment evaluated with mr elastography. Newrolmage: Clinical, 37:103327, 2023. 8
Benoit Dufumier, Pictro Gori, Julie Victor, Antoine Grigis, Michele Wessa, Paolo Brambilla, Pauline Favre, Mircea Polosan, Colm McDonald, Camille Marie Piguet, et al. Contrastive learning with continuous proxy meta-data for 3d mri classification. In Medical Image Computing and Computer Assisted Intervention- MICCAI 2021: 24th International Conference, Strasboury, France, September 27-October 1, 2021, Pro- ceedingg, Part II 24, pp. 58 68. Springer, 2021. 2, 3, 9, 15
Benoit Dufumier, Antoine Grigis, Julie Victor, Corentin Ambroise, Vincent Frouin, and Edouard Duchesnay. Openbhb: large-scale multi-site brain mri data-set for age prediction and debiasing. Neurolmage, 263: 119637, 2022. 7
Debidatta Dwibedi, Yusuf Aytar, Jonathan Tompson, Pierre Sermanet, and Andrew Zisserman. With a little help from my friends: Nearest-neighbor contrastive learning of visual representations. In Proceedings of the IEEE/CVE International Conference Computer Vision, pp. 9588-9599 2021. 4,
Gabriele Fanelli, Juergen Gall, and Luc Van Gool. Real time head pose estimation with random regression forests. In CVPR 2011, pp. 617-624. TEFE, 2011.
Bruce Fischl. Freesurfer. Neuroimage, 62 2012. 6
Bin-Bin Gao, Hong- Yu Zhou, Jianxin Wu, and Xin Geng. Age estimation using expectation of label distri- bution learning. In IJAA,, volume 1, pp. 3, 2018. 3
13

---

Published in Transactions on Machine Learning Research (10/2024)
Lucy V Hiscox, Curtis L Johnson, Eric Barnhill, Matt DJ McGarry, John Huston, Edwin JR Van Beek, John M Starr, and Neil Roberts. Magnetic resonance elastography (mre) of the human brain: technique, findings and clinical applications. Physics in Medicine & Biology, 61(24):R401, 2016. 1
Lucy V Hiscox, Curtis L. Johnson, Matthew DJ McGarry, Michael Perrins, Aimee Littlejohn, Edwin JR Boek, Neil Roberts, and John M Starr. High-rosolution magnetic resonance clastography reveals differences in subcortica ical gray matter viscoelasticity between young and healthy older adults. Neurobiology of aging, 65:158-167 2018. 1
Lucy V Hiscox, Curtis L Johnson, Matthew DJ McGarry, Helen Marshall, Craig W Ritchie, Edwin JR Van Beek, Neil Roberts, and John M Starr. Mechanical property alterations across the cerebral cortex due to alzheimer's disease. Brain Communiications, 2(1):fe2049 2020a. 2
Lucy Hiscox, Curtis L Johnson, Matthew DJ McGarry, Helen Marshall, Craig W Ritchic, Edwin JR Van Boek, Neil Roberts, and John M Starr. Mechanical property alterations across the cerebral cortex due to alzheimer's disease. Brain Communicattins, 2(1):fc2049, 2020b. 8
Lucy Hiscox, Matthew DJ McGarry, Hillary Schwarb, Elijah EW Van Houten, Ryan T Pohlig, Neil Roberts, Graham Huesmann, Agnieszka 7. Burzynska, Bradley P Sutton, Charles H Hillman, et al. Standard-space atlas of the viscoclastic properties of the human brain. Human brain mapping, 41(18):
5282 5300, 2020c.
Lucy V Hiscox, Hillary Schwarb, Matthew DJ McGarry, and Curtis Johnson. Aging brain mechanics: Progress and promise of magnetic resonance elastography. Neuroimage, 232:117888 2021.
Curtis I Johnson, Joseph L Holtrop, Matthew DJ McGarry, John B Weaver, Keith D Paulsen, John G Georgiadis, and Bradley P Sutton. 3d multislab, multishot acquisition for fast, whole-brate mr elastography with high signal-to-noise efficiency. Magnetic resonance in medicine, 71 (22):47774485, 2014. 16
Prannay Khosla, Piotr Teterwak, Chen Wang, Aaron Sarna, Yonglong Tian, Phillip Isola, Aaron Maschinot, Ce Liu, and Dilip Krishnan. Supervised contrastive learning. Advances in neural information processing systems, 33:18661-18677 2020. 3
Stéphane Lathuilière, Pablo Mesejo, Xavier Alaneda-Pineda, and Radu Horaud. A comprehensive analysis of deep regression. IEFE transactions on pottern analysis and machine intelligence, (2(9):2065-205) 2019.
3
Jeyoon Lee, Brian J Burkett, Hoon-Ki Min, Matthew Senjem, Emily S Lundt, Hugo Botha, Jonathan Graff-Radford, Leland R Barnard, Jeffrey Gunter, Christopher Schwarz, et al. Deep lcarning basod brain age prediction in normal aging and dementia. Nature Aging, 2(5):412 044:122-44,,4 2022. 2
Wanhua Li, Xiaoke Huang, Jiwen Lu, Jianjiang Feng, and Jie Zhou. Learning probabilistic ordinal embed- dings for uncertainty-aware regression. In Proceedings of the IEEE/CVT conference on computer vision and pattern recognition, pp. 13896-13905, 2021. 3
Martina J Lund, Dag Alnæs, Ann- G de Lange, Ole A Andreassen, Lars T Westlye, and Tobias Kaufmann. Brain age prediction using fmri network coupling in youths and associations with psychiatric symptoms. Neurolmage: Clinical, 33:102921, 2022. 2
Matthew C Murphy, John Huston III, Clifford R Jack Jr, Kevin J Glaser, Matthew L Senjem, Jun Chen, Armando Manduca, Joel P Felmlee, and Richard L Ehman. Measuring the characteristic topography of brain stiffness with magnetic resonance clastography. PloS one, 8(12):c81668, 2013. 1
Matthew C Murphy, David T Jones, Clifford R Jack Jr, Kevin J Glaser, Matthew L. Senjem, Armando Manduca, Joel P Felmlee, Rickey E Carter, Richard L Ehmaan, and John Huston III. Regional brain stiffness changes across the alzheimer's disease spectrum. Neurolmage: Clinical, 10:283-290 2016. 2
Xin Niu, Fengqing Zhang, John Kounios, and Hualou Liang. Improved prediction of brain age using multi- modal neuroimaging data. Human brain mapping, 41(6):1626-1644) 2020. 2
14

---

Published in Transactions on Machine Learning Research (10/2024)
Rasmus Rothe, Radu Timofte, and Luc Van Gool. Dex: Deep expectation of apparent age from single image. In Proceedings of the IEFE international conference on compuler vision workshops, pp. 10-15, 2015. 3,9
Ingolf Sack, Kaspar-Josche Streitberger, Dagmar Krefting, Friedemann Paul, and Jürgen Braun. The influ- ence of physiological aging and atrophy brain viscoclastic properties in humans. PloS one, 6(9):e2345,,
2011.
Faria Sanjana, Poyton L Delgorio, Lucy V Hiscox, Theodore M DeConne, Joshua C Hobson, Matthew L Cohen, Curtis I, Johnson, and Christopher R Martens. Blood lipid markers are associated with hippocam- pal viscoclastic properties and memory in humans. Journal of Cerebral Blood Flow & Metabolism, 41()):
1417 1427, 2021. 8
Min Sun, Pushmoet Kohli, and Jamic Shotton. Conditional regression forcsts for human pose estimation. In 2012 IEEE Conference on Computer Vision and Pallern Recognition, pp. 3394 3401. IEEE, 2012.
Tomohiro Takamura, Utaroh Motosugi, Yu Sasaki, Takashi Kakegawa, Kazuyuki Sato, Kevin J Glaser, Richard L Ehman, and Hiroshi Onishi. Influence of age on global and regional brain stiffness in young and middle-aged adults. Journal of Magnetic Resonance Imaging, 51 51(3):727-733, 2020.
Jiyuan Wang, Chunyu Lin, Lang Nie, Shujun Huang, Yao Zhao, Xing Pan, and Rui Ai. Weatherdepth: Curriculum contrastive learning for self-supervised depth estimation under adverse weather conditions. In 2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 4976-4982. IEEE, 2024. 3
Yuzhe Yang, Kaiwen Zha, Yingcong Chen, Hao Wang, and Dina Katabi. Delving into deep imbalanced regression. In International conference on machine learning, pp. 11842-11851. PMLR, 2021. 3
Kaiwen Zha, Peng Cao, Jeany Son, Yuzhe Yang, and Dina Katabi. Rank-n-contrase Learning continuous representations for regression. Advances in Neural Information Processing Systems, 36, 2024. 2, 3,
A Appendix
A.1 Influence of Sampling of Non-Nearest Neighbors
To study the effect of including farther examples at reduced rates, we introduce distance-basee weighting scheme for the non-ncarest samples. The weight Vi, assigned to cach non-ncarest neighbor is determined by the function:
1 di,t
(4)
where Y represents the normalized inverse distance between the anchor and the sample, and À is a hyper- parameter controlling the rate of decay in weighting for samples at greater distances. Thus, the repulsion term in 3 is expanded to all samples, and non-ncarest samples accordingly weighted. This formulation en- sures that as X increases, the contributions from farther negative samples diminish more rapidly. In the extreme case where + oc, only the nearest neighbors contribute to the loss 3. Conversely, when À = 0, the weighting bocomes uniform across all samples, recovering the exponential contrastive regression loss (Dufumier et al., 2021; Barbano et al., 2023). We performed an ablation study investigate the impact of different values of À on the model's performance, illustrated in Fig. 6. The results indicate that while we-ghithting the non-nearest samples provides some benefits, only configuration with intermediate value of À = marginally outperformed the approach of simply dropping non-ncarest samples yielding a MAE of 3.681 years. This suggests that re-weighting can help retain informative negative samples but has a limited overall impact on improving model generalization. Further exploration of more sophisticatod we-ghighting mechanisms could be beneficial future work.
15

---

Published in Transactions on Machine Learning Research (10/2024)
Negative Sumple Weight 10-x
2
10
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
MAE [years]
Figure 6: Ablation study for sampling of non-nearest neighbors.
A.2 Brain Coverage of Stiffness Maps
subject
25
20
0.70
0.75
0.50
0.35
3.30
0.95
1.00
suffness Brain Coverace [N]
Figure 7: Distribution of Brain Coverage in Stiffness Maps Across Studies. In Magnetic Resonance Elas- tography (MRF), achieving optimal brain coverage necessitates a balance between high spatial resolution, signal-to-noise ratio (SNR), and acceptable scan times (Johnson et al., 2014). The majority of existing brain MRE studies focus on deep brain structures, leading to limited coverage in certain areas. This limitation is illustrated here, where the brain coverage variability in our stiffness maps is visualized.
16

---

Published in Transactions on Machine Learning Research (10/2024)
Full coverage
95% coverage
90% coverage
80% coverage
Figure Examples of stiffness maps across spectrum of coverage percentages. Full coverage is shown alongside three reduced coverage cases: 95%, 90%, and 80%, respectively. As seen in Fig. 7, most of the data fall between 90% and full brain coverage.
17


Reviews:
[{"review_id": "PMf43ORnv0", "reviewer": "Reviewer_58LT", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. Few researches have attempted to improve contrastive learning by focusing on negative samples in loss functions. The proposed method pioneers negative sample selection in contrastive regression problems, which is intriguing.\n2. The intuition behind the method is well-aligned with the existing challenge of non-uniform data distributions in medical imaging.\n3. The formulation of the objective function is straightforward, and the idea is easy to follow.\n\nWeaknesses:\n1. Despite the fact that majority class instances may negatively affect the representation learning for minority class instances, directly dropping them seems to impact the generalization of the learned representations. For example, it has been shown that some hard negative instances are beneficial to contrastive learning [1]. Considering this, I believe reweighting the negative samples based on distance might be more effective than simply dropping them during training.\n2. The framework builds upon Contrastive Regression Loss (CRL) [2], with modifications in the sampling of negative pairs. In the experiments from [2], it was observed that CRL alone might not be sufficient to learn good representations, thus requiring auxiliary losses (such as L1) to support the learning process. I wonder if this is also the case for the objective function introduced in this paper.\n\n[1] Robinson, J., Chuang, C.Y., Sra, S. and Jegelka, S., 2021, January. CONTRASTIVE LEARNING WITH HARD NEGATIVE SAMPLES. In International Conference on Learning Representations (ICLR).\n\n[2] Zha, K., Cao, P., Son, J., Yang, Y. and Katabi, D., 2024. Rank-n-contrast: learning continuous representations for regression. Advances in Neural Information Processing Systems, 36.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper presents a novel approach for brain age prediction using contrastive regression techniques applied to brain stiffness maps. The proposed method, Dynamic Localized Repulsion, addresses the challenge of non-uniform data distributions in medical imaging, where the method gradually drops negative samples that are farther away from the anchor when calculating the contrastive objective. By focusing on localized neighborhoods during training, it reduces the effect of oversampled instance classes on the learning. The new contrastive objective is shown to improve the predictive power of models working with mechanical brain properties, which are highly sensitive to age-related changes.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "See Weaknesses Above.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "CmvQJ3zKRz", "reviewer": "Reviewer_TVUU", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n* The paper is the first application of self-supervised learning to brain mechanical properties.\n\nWeaknesses:\n* The paper does not demonstrate the importance of decreasing the number of repulsed samples during training. It is my understanding that this would recover a weighted Nearest-Neighbor Contrastive Learning of visual Representations (NNCLR) (Dwibedi et al., 2021).\n* The method contributions of this paper are not significant. The paper would be a better fit for a healthcare-focused conference or journal.\n* The search space for hyperparameters (e.g., initial learning rate and weight decay) is fixed for all methods. There is no detail for hyperparameter tuning for baselines while $NN_{nb,final}$ and $NN_{stepsize}$ are tuned via random search. Are baselines and the proposed method getting the same time and compute resources for hyperparameter tuning?\n\nDebidatta Dwibedi, Yusuf Aytar, Jonathan Tompson, Pierre Sermanet, Andrew Zisserman. With a Little Help From My Friends: Nearest-Neighbor Contrastive Learning of Visual Representations. In *Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)*, 2021.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes a k-nearest neighbors (KNN) based contrastive loss that decreases the number of repulsed samples during training. The paper is the first application of self-supervised learning to brain mechanical properties. The paper shows improved mean absolute error (MAE) for their proposed method compared to a few other contrastive regression losses but does not demonstrate the importance of decreasing the number of repulsed samples during training.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "* Consider adding NNCLR (Dwibedi et al., 2021) as a baseline.\n* Consider shrinking Figure 3. I do not think a plot of the distribution of ages should take up half a page.\n\nRequested Clarifications:\n* Why are MAE results bolded when intervals overlap? Are these statistically significant results?", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "YRA33eEZGW", "reviewer": "Reviewer_AVKh", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "This is a fairly applied study. \n\nStrengths:\n========\n- Demonstrates (for the first time) the effectiveness of brain stiffness maps for brain age regression, through a contrastive learning approach.\n- Aggregates the largest multi-study dataset of brain stiffness from healthy controls (5 sources for a total of 311 subjects).\n- The improved performance for brain age regression can be appreciated in neuroimaging and related subfields.\n\nWeakness:\n========\n- ~~On the other hand, the contribution in ML is limited; see below.~~\n- The presentation needs a revision.\n- The contribution to ML needs clarification and better positioning; see below.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose an epoch-adaptive contrastive loss for representation learning of 3D brain stiffness maps for age regression. The evaluation of contrastive losses is progressively restricted to more localized neighborhoods in the current embedding space, which the authors achieve by reducing the number of nearest neighbors considered in the summation. This is motivated by the need to improve robustness to non-uniformly sampled datasets, e.g., in terms of represented age ranges. Results demonstrate the efficacy of the approach, achieving improved MAE over 4 baselines from 3 recent studies.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "**Preamble:** My requests mainly concern the presentation, with only few technical remarks. I'm guessing the primary audience for this type of article are neuroimaging researchers and practitioners, some of whom are not necessarily ML experts. Towards publication in a recognized ML journal, I'm placing a greater emphasis on the precise phrasing of technical statements and their potential interpretations by non-experts.\n\nPositioning & Terminology:\n====================\n- \"Dynamic *localized* repulsion\" initially suggested to me that the proposed loss adapts to different brain parts to better utilize the *regional age-related variability* in 3D stiffness maps.\n  - Also in Section 3.1: [..] limited in their capacity to handle the subtle variations in brain stiffness [..] due to their global approach\n  - After reading the paper, I view the proposed approach as more of a curriculum contrastive learning approach; see:\n    - Chu, Guanyi, Xiao Wang, Chuan Shi, and Xunqiang Jiang. \"CuCo: Graph Representation with Curriculum Contrastive Learning.\" In IJCAI, pp. 2300-2306. 2021.\n    - Wang, Jiyuan, Chunyu Lin, Lang Nie, Shujun Huang, Yao Zhao, Xing Pan, and Rui Ai. \"Weatherdepth: Curriculum contrastive learning for self-supervised depth estimation under adverse weather conditions.\" In 2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 4976-4982. IEEE, 2024.\n    -  This is essentially what the last sentence in italic before Equation (3) is about.\n  -  [**HL#1**] Please include citation and brief discussion of curriculum contrastive learning, i.e., in Section 2.\n  -  [**HL#2**] Please revisit the claims of novelty at the end of Section 1 and at the top of Section 3, as well as Section 5.\n- [**HL#3**] Hence, I would recommend to consider a title like: *Curriculum Contrastive Learning (with Adaptive Neighborhoods or Adaptive Sampling) for Brain Age Prediction on 3D Stiffness Maps*\n\n\nTechnical comments:\n================\n- [**T#1**] Please discuss data size\n  - A total of 311 subjects is very limited. This aspect of the study seems critical when comparing different ML approaches.\n  - This is also relevant in the choice of the ResNet model pre-trained on OpenBHB (5000 MRI scans from multiple sites).\n- [**T#2**] Since data non-uniformity was highlighted as a key challenge, it would help to discuss this more directly.\n  - I don't see where Figure 6 is referenced in the paper.\n  - Only Figure 3 was discussed, which seemed to suggest that non-uniformity mainly manifests due to the ages of participating subjects.\n- Contrastive losses\n  - Page-2, top: *by focusing on the fine distinctions between similar cases*\n    - Is this really what the adopted formulation does?\n    - [**T#3**] Please highlight the application of the loss within the embedding space.\n      - In reference to SimCLR, it is notable that a key finding was the benefit of an additional non-linear projection mapping before computing the distance.\n        - [**T#4**] It would help to consider this, e.g., as an ablation, or simply mention it for the benefit of follow up work.\n    - I wonder if what the authors mean is more properly explored in the study of Siamese approaches. I'm including this for the authors' reference:\n      - Chen, Xinlei, and Kaiming He. \"Exploring simple siamese representation learning.\" In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 15750-15758. 2021.\n    - In light of SimCLR and Siamese representations, it is notable that the proposed approach does not include augmentations.\n      - [**T#5**] It would help to consider data augmentation, e.g., as an ablation, or simply mention it for the benefit of follow up work.\n\nPresentation comments:\n================\n- Section 3\n  - [**P#1**] When defining the domain and range for the functions $f$ and $g$, there's no need to include $(\\cdot)$.\n    - [**P#2**] That said, $X$ was not explicitly defined. In addition, it would help to identify the embedding space with a symbol, e.g., $Z$.\n  - [**P#3**] It would have helped to include an equation for the standard contrastive loss, or perhaps reference Equation (2).\n  - [**P#4**] In Equation (1): please define the neighborhoods within the embedding space $Z$. That is, perhaps use symbols $z_i$ and $z_k$, or if necessary, $f_\\textrm{epoch}(x_i)$ and $f_\\textrm{epoch}(x_k)$.\n  - [**P#5**] Around Equation (1): please define the distance and make it clear that it is the same as the similarity $s_{i,k}$\n    - Note that $s_{i, k}$ was not formally defined around Equation (2).\n- P4 bottom: \"then explores the differences within those groups more deeply\"\n  - [**P#6**] Recommend a more technical description, e.g., the training objective evolves to focus exclusively on those groups.\n    - Note that an alternative sampling strategy may still include farther examples, perhaps at reduced rates, to help stabilize the training.\n    - [**P#7**] It would help to consider biasing the sampling rather than fully restricting to smaller neighborhoods, e.g., as an ablation, or to simply mention it for the benefit of follow up work.\n- P5, below Equation (3): *also improves the mode's ability on complex neuroimaging datasets*\n  - [**P#8**] Please clarify which ability is improved and provide evidence.\n- [**P#9**] I believe *repulsion samples/candidates* are more commonly referred to as *negative examples*.\n  - On P5 top: \"prompting the algorithm to minimize\" vs \"triggering the repulsion mechanism to increase\"\n    - It is the same algorithm. I recommend against highlighting repulsion too much as a distinct mechanism.\n- Figures\n  - [**P#10**] Figure 1: please clarify in the caption how the variable circle radii between $y_\\textrm{min}$ and $y_\\textrm{max}$ should be understood.\n  - [**P#11**] Where if Figure 2 referenced in the paper?\n  - [**P#12**] P6, bottom: where is Figure 4.1?\n\nNitpicking:\n========\n- Abstract\n  - laying the way -> paving the way\n- Section 3\n  - transforms brain images into a *representative* feature space -> into a feature/representation/embedding space?\n  - increasingly localized vicinities -> localized neighborhoods (as in the abstract)\n- Section 4\n  - In a closer look -> Upon careful examination?", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper introduces a novel supervised contrastive learning method in the context of brain imaging. All reviewers voted for accepting the paper.

The reviewers appreciated the novelty and strong empirical results in predicting the age based on brain imagining. The experiments were done on a convincingly broad set of datasets. Predicting the age based on brain stiffness maps was found novel and interesting.

The reviewers were not convinced about the impact of the proposed contrastive method beyond the scope of the work. I am leaning to agree with the reviewers. The method was not compared to other natural methods (e.g. purely supervised learning) nor tested on datasets from other domains. Hence, it is not straightforward whether the method will work in a broader context. Having said that, the proposed method is interesting and natural, hence it indeed might be of an interest to the contrastive learning community.

All in all, it is my pleasure to recommend accepting the paper. Please make sure to address comments made by reviewers. I would suggest adding a bit more clarity in writing, the method was not tested on enough different datasets to fully claim it is superior to other approaches. It would be fair to say it is a promising method.
Decision: Accept (poster)