Topological Inductive Bias fosters Multiple Instance Learning in Data-Scarce Scenarios
Authors: Salome Kazeminia
Carsten Marr
Bastian Rieck
Venue: Accepted by TMLR ()

Abstract: Multiple instance learning (MIL) is a framework for weakly supervised classification, where labels are assigned to sets of instances, i.e., bags, rather than to individual data points. This paradigm has proven effective in tasks where fine-grained annotations are unavailable or costly to obtain. However, the effectiveness of MIL drops sharply when training data are scarce, such as for rare disease classification. To address this challenge, we propose incorporating topological inductive biases into the data representation space within the MIL framework. This bias introduces a topology-preserving constraint that encourages the instance encoder to maintain the topological structure of the instance distribution within each bag when mapping them to MIL latent space. As a result, our Topology Guided MIL (TG-MIL) method enhances the performance and generalizability of MIL classifiers across different aggregation functions, especially under scarce-data regimes. Our evaluations show average performance improvements of 15.3% for synthetic MIL datasets, 2.8% for MIL benchmarks, and 5.5% for rare anemia classification compared to current state-of-the-art MIL models, where only 17–120 samples per class are available. We make our code publicly available at https://github.com/SalomeKaze/TGMIL.

Published in Transactions on Machine Learning Research (02/2026)
Topological Inductive Bias fosters Multiple Instance Learning in Data-Scarce Scenarios
Salome Kazeminia
Helmholtz Munich
Technical University of Munich
Carsten Marr
Helmholtz Munich
Ludwig- Mozimilian- Universityy Hospital University of Munich
DKTK, German Cancer Consortium
Munich Center for Machine Learning
Bastian Ricck
bostian sesttan.oosscnaacherrunii...
Helmholtz Munich
University of Fribourg
Reviewed on OpenReview: https: // openreview. net/ net/forum? forum? id= 1h2y92jjCe
Abstract
Multiple instance learning (MIL) is framework for weakly supervised classification, where labels are assigned to sets of instances, i.c., bags, rather than to individual data points. This paradigm has proven effective in lasks where fine-grained anmotations are unavailable or costly to obtain. However, the effectiveness of MIL drops sharply when training data are scarce, such as for rare disease classification. To address this challenge, we propose incorporating topological inductive biases into the data representation space within the constraint, that encourages the
MIL, framework. This bias introduces a topology-preserving instance encoder to maintain the topological structure of the instance distribution within each bag when mapping them to MIL latent space. As result, our Topology Guided MIL (TG-MIL) method enhances the performance and generalizability of MIL classifiers across different aggregation functions, especially under scarce-data regimes. Our evaluations show average performance improvements 15.3% for synthetic MIL datasets, 2.8% for MIL benchmarks, and 5.5% for rare anemia classification compared to current state-of -tate-of-the-art the-art MIT. models, where only 17-120 samples per class available. We make code publicly available at htttps://github. com wtt.///aaaaaaa///TTTTTTIII
1 Introduction
Multiple Instance Learning (MTT.) is a variant weakly supervised learning that operates without annotations for individual data points. MIL, cach 'bag,' which represents group instances, is assigned a single label (Babeuko) 2008 Lu al. 2020). A bag is labeled positive if it contains least one positive instance; otherwise, it is labeled negative. For example, in blood sample-based based disease classification, each sample be viewed as a bag of individual cells. The sample is labeled positive if it contains any atypical cells and negative otherwise.
Proper instance representation is critical for ensuring model reliability in clinical decision decision-making, However, data scarcity, a common issue in the diagnosis of rare discascs, hinders MIL modols' ability to learn such representations. In such cases, the need for MILebased training approaches that operate in the scarce-data regime is paramount.

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Bag
Instances
Latent axd
Bag latent
Aggregator
Bag label
Instance encoder
1x
Classifier
Lekuss
x (2
Zr (2, R2 2g.
Sbu
Prediction
Distance calculation
Distance calculation
Persistent diagram
A A : "a",a"......
A (aa,
Persistent homology calculation
π
Liopo
π Xoa
Figure 1: Topologically Guided Multiple Instance Learning (TG-MIL.): We calculate the distance matrix A of imput instances 2; inside each bag Xe,.- Subsequently, we apply persistent homology based the Vietoris- Rips complex by treating each bag's instances as point cloud. We employ the same process for the latent feature vectors Z of each bag. Generating shape descriptors (persistence diagrams T) for both the latent space and the image space representations of the bag, we calculate a topological loss (Trop)) and combine with the standard MIL loss (Lelass).
A potential solution to leverage additional structure from data via inductive biases, strategy that has shown promise in other machine learning domains (Goyal & Bengio 2022). We treat each bag point cloud in high-dimensional data space, consistent with Deep Sets and Pointnet (Zaheer et al. 2017 ct al. 2017) and define an inductive bias based on the bag's topological features. These features should be preserved after embedding bag instances into the model's latent space, ensuring that the data's essential topological properties are maintained. Being able to capture fundamental topological principles data at multiple scales, topological algorithms recently arose as source of such inductive biases, permitting the integration into deep learning models (Hensel et. al., 2021). The primary appeal of such algorithms lies in their robustness to noise and perturbations, resulting in stable multi-scale representations. Also, these algorithms improve generalizability and predictive performance when pronounced topological signal is present in the data (Horn et al. 2022 Waibel et al. (2022), even in the presence of singular structures, which preclude the use of standard techniques (von Rohrscheidt. & Rieck 2023).
We introduce Topologically Guided Mulliple Inslance Learning (TG-MIL), data-centered solution to address the challenges of training MIL with scarce data in an end-to-end manner. By leveraging multi-scale shape descriptors on the level of MIL bags, we develop a scheme that preserves crucial topological information in the latent space of our model (see Figure [ for schematic overview). We demonstrate that maintaining even only the connectivity-baser topological bias (captured via (l) persistent. homology) inherent in bag's data distribution improves the performance of MIL classifiers. This topological bias, reflecting each bag's natural structure and relationships, carries critical information for accurate classification. Preserving this intrinsic structure allows MIL classifiers to learn and generalize more effectively, improving performance accuracy, robustness, and adaptability across different training data. The main contributions our work are:
We develop TG-MIL, the first (opological method to improve the generalizability of MIL data-scarce scenarios.
Our method can be integrated with any MIL aggregation strategy, improving performance under data scarcity in an end-to-end training setting.
TG-MIL outperforms the state-of state-of-the-art the-art on MIL benchmarks and rare anemia classification.
2 Background
MIL Architectures. MIL architectures typically comprise three key components: an instance encoder, an aggregation function, and a classifier (Figure D.. Given a collection of M bags b,,..., bM; each bag bm contains a set of instances, represented as X,,.. = .., with n denoting the number of instances in the
Despite their name, these algorithms also capture geometrical aspects data, but we will refrain from writing geometrical- topologieal algorithms for brevity.
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bag. An instance encoder fo with parameters 9 transfers each instance into latent space, yielding feature vectors 24 := fo(r;). The aggregation function then creates global representation of the bag St.,. from these embedded instances, from which the classifier head predicts the bag's overall label.
Geometry & Topology. Our work based on advances in topological machine learning (Hensel et al, 2021), a nascent field that aims to leverage the geometry and topology of data to elicit improved repre- sentations. We employ persistent homology, technique for calculating multi-scale topological information from data [Edelsbrunner & Harer 2009). Persistent homology treats data point cloud and aims to define this cloud using simple geometric elements (simplices) that describe the overall geometry of the data, such as connected components, loops, higher-dimensional voids, and geometric properties like curvature or convexity (Bubeník et al.) 2020 Turkes et al., 2022). This information is collected in a set of persistence
diagrams, which serve as multi-scale topological descriptors. These descriptors are calculated by approximating the data with a simplicial complex-a generalized graph-typical typically based on distance functions like the Euclidean distance (Figure I. Recent work proved that persistent homology can be integrated with deep learning models, leading to new class of hybrid models that are capable of capturing topological aspects of data. Such models have shown exceptional performance regularization terms in different applications CChen ct al.
2019
Vandacle et al. 2022
Waibel et al. 2022).
3 Related Work
Recent advances in MIL can be categorized into two main methods and use cases: i) Methods using transfer learning for feature extraction and only focusing on training aggregation mechanisms (Shao et al. 2021
Zhang et al.] 2022; Liu et al.] 20233 Tang et al. 2023 Fourkioti et. al. 2024 Castro-Macias et al.] 2024 p. These approaches are designed for histopathology applications and have not been evaluated on basic MIL problem settings. Bags typically consist of thousands of spatially correlated patch instances extracted from a single whole-slide image. Due to architect ural and computational constraints, instance representations are kept fixed using frozen pre-trained encoders, and end-to-end training is not supported. In contrast, our work focuses on improving instance representation learning in end-to-end MIL settings with spatially independent instances and limited training data. Adapting the above methods would require removing certain components (e-g.; positional embeddings in TransMIL. (Shao et al. 202T)), reducing the complexity of the aggregation model, and considering proper learnable instance encoder. These changes would substantially alter the original architectures and make a fair comparison non-trivial. Therefore, we exclude these approaches from aggregation comparisons, while noting that our proposed framework is, in principle, compatible with such aggregation mechanisms. ii) End-to-end approaches that optimize both bag aggregation and instance representation during training. Tise et al.] (2018) introduced the Attention-based MIL (APMIL), which learns instance-level attention weights, and the Gated Attention MIT. (GAPMIT.) variant, which incorporates a gating mechanism modulate those weights. Recently, APMILwD and GAPMILwD (Zhu et al., 2025) extended the classical attention-based frameworks by introducing instanco-level dropout, which regularizes attention learning and significantly improves generalization, achieving state-of-the-art results classic MII benchmarks. However, the attention-basee pooling mechanism (see Appendix, equations 13 and may still lack reliability, as it does not uniformly enhance representation across all instances, while, in medical diagnosis and drug discovery, accurate identification of individual components (e.g., cells in microscopic blood sample images or chemical compounds) is crucial for making accurate predictions at the sample level. Other end-to-end methods have focused on designing alternative aggregation mechanisms to better capture complex instance relationships and improve MIL classification. BDRMIL (Huang et al. 2022 modeled pairwise relations between instances within bag, capturing inter-instance dependencies. DistNet (Oner et al.) 2023 proposed distribution-awars formulation that represents cach bag via statistical properties of its instance embeddings, enabling aggregation through learned distributional representations rather than attention scores RGMIL (Du et al. 2023) further enhanced instance-level representation through a regressor- guided aggregator that aligns instance- and bag-level predictions, improving the signal flow through the encoder. Although this approach refines instanco-level representation and enhances overall MIL performance, it struggles accurately capture nuanced variations in the data when training data is scarce.
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In medical applications, like classifying rare anemia disorders, key factors such the severity of cell deformation and the ratio of deformed cells in a blood sample are paramount. Thus, it is essential that instance-level representations capture the distribution of cell classes while maintaining an interpretable bias toward deformation severity, thereby ensuring both the reliability and interpretability of the MIL model's predictions. State-of-the-art approach (Kazeminia et al. 2022) in this domain refines aggregation techniques, i.c., anomaly-aware pooling, to encourage the encoder to push healthy cells toward a normal distribution. However, optimal performance of this method still relies on a large amount of training data, thus limiting its potential to achieve higher accuracy in data-scarce environments.
To overcome the challenges posed by data scarcity, we introduce topological inductive bias that incentivizes models to preserve topological information in latent representations. Our method thus falls into the second category of end-to-end techniques and emphasizes the crucial role of data representations in MIL.
4 Methods
We consider each bag point cloud in high-dimensional space whose topological features should be adequately captured by the model. Each instance influences the bag's "shape," with positive instances notably altering its shape in comparison to the distribution of negative samples. We thus need descriptor that captures the characteristics of a point cloud while remaining stable to perturbations and invariant under transformations irrelevant to determining the overall shape, such as translations and rotations. Persistent homology provides a suitable descriptor, as [Sheehy (2014) demonstrates that critical topological-geomeetee features captured by persistent homology are approximately preserved even under projections or emboddings of the data, making it highly robust.
The calculation of persistent homology requires choice of distance metric. While our framework remains agnostic to the specific choice of distance metric, we have chosen to use the per-pixel Euclidean distance for its ease of calculation and empirical evidence from Moor et al. (2020a), which demonstrates the adequacy of Euclidean distances in capturing topological features. We calculate the Vietoris Vietoris-Rips simplicial complex (X )) at each distance e, which yields all subsets of X such that the pairwise distance between instances 2, and 2, is less than or equal to e.
#3 (X ) {ar E X, + Ty : ||:0; - 22y12 S {
Formally, this leads to a filtration of simplicial complexes {Roo (X ) R.y (Xom (xm))..... Re.. (Xem }}, with an ordered sequence of distance thresholds 0- = 60 < <... < em (Figure 1p Persistent homology tracks the evolution of topological features (e.g., connected components ( (OD), loops (ID), voids (2D), etc) across different distances. Consistent with previous work (Moor et al. 2020b), we restrict most of our experiments to OD topological features, as incorporating highher-dimensional topological features substantially increases computational cost. Given the distance matrix A, we consider the sorted distance values as the e set at each space. For each e E e, if topological feature is born or destroyed, e; is recorded as a persistent edge, and the pair of data points whose interaction causes this event is recorded as the persistence pair NT.
For example, let us consider (D topological features for two connected components of points, (a1, 23) and (24.*6, 25, Jo Let E2 be the distance between I and ze, representing the smallest distance that connects these two components. Thus, 62 is the persistent edge, and (I1, is the corresponding persistent pair. The collection of persistent edges and pairs for all e called the topological signature of the point cloud. Thus, the topological signature of bag bm in input space contains Nmm and x Xem. Similarly, A and nt To represent the topological signature of the bag in the latent space.
Our objective is to incorporate the topological signature of the input space inductive bias into the model. We define a loss term to penalize the encoder fo for any inconsistency in the bag's topological signature during projection from inpul to latent space. To this end, we utilize the topological loss proposed by [Moor et al. (2020b), which enables backpropagation through topological descriptors. This loss penalizes differences of topological signature of the latent space with the input space using an -norm. Specifically, first, the persistent edges in the two input and latent spaces, using the input persistence pairs, are compared using Txxmm -mmm Then, the persistent edges in the two spaces using the latent. persistence pairs are compared
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L 2om +m We account for both losses to enforce consistency between the two mappings (data latent and latent data), while remaining invariant to the ordering of instances within each bag. The final topological loss is defined as
Liopo = Lxn 7om Zoo XXom
(2)
where
Lixom 7m = 2
Xem [ NoN - A Tmo [ X bm
11
(3)
and
1 1| || [ A Num
π 7mm 11
L +X
(4)
2
The topological loss is defined in terms of pairwise distances between instances within bag. It makes any permulation of instances to change only their ordering and leaves the set of pairwise distances unchanged. Under the assumption that pairwise distances unique, their relative ordering is also preserved. Consequently, the induced topological loss is invariant to arbitrary permutations of instances.
Our framework is flexible and can integrate any aggregation function to represent the whole bag Sbar Similar to standard MIL models, we train the MIL classification head using cross-entropy loss. Our formulation also yields a variant of a multi-classifier head approach, such as the auxiliary loss proposed by Kazeminna et al. (2022). The final loss of our topologically guided MIL (TG-MIL) framework, Liotal is the weighted sum of the MIL classification loss Lelass and topological term Iatpa:
Liotal
Lecnss + Xitopo:
(5)
where À is a hyperparameter to adjust the influence of the topological loss.
Complexity and Parameters. The computational complexity involved in calculating certain topological features is comparable to the rate of the inverse Ackermann function (Cormen et al. 2022), which increases significantly slower compared to the rate of increasing n. The computational complexity of the topological signature calculation of bag containing instances is dominated by the calculation of pairwise distances, i.e., O(n²), considering that only OD topological features are used. The topological signature calculation does not introduce any additional learnable parameters, thereby keeping the model's 's parameter size unchanged. It introduces only one topological loss and one hyperparameter, denoted by X.
The primary limitation of our approach is that the calculation of topological features does not exhibit favorable scaling parameters in case that higher-order topological features are required. While our implementation supports topological features of arbitrary dimension, their calculation scales progressively worse; connected components, i.c., OD features, can still be efficiently calculated (sce previous paragraph), but higher-order features may prove limiling. We plan on investigating miligation strategies in future work, using, e.g., approximate filtrations (Sheehy 2013) or distributed computations Waagner et al. 2021
Limitations.
Instance Learnability. Each bag B = (a1,.... Φn) contains instances with latent instance labels y E (0.1} for binary classification task. The bag label is generated by a monotone aggregation rule
You olyi....,
such the standard OR assumption in MIL. Changing any instance label from negative to positive cannot change positive bag label to a negative onc. This assumption holds for the aggregation functions used in this work. As our proposed method does not introduce any new aggregation function, we omit further demonstrations for the aggregations considered. We focus on the distinction between instance-level and bagelevel operations, where fo represents the bag-level operation, which jointly encompasscs the aggregation function and the predictor.
You go (1Jo(s;))
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TG-MIL
MIL
TG-MIL
MIL
Negative bag instances Positive bag instances
Negative bag Positive bag
Latent dimension
Latent dimension 2
Latent dimension
Latent dimension
Latent dimension (b) 2D representation of bags.
Latent dimension 1
(a) 2D representation of instances.
Figure 2: TG-MIL achieves more distinguished representation of negative and positive bags. For toy dataset, instances are sampled from a hypersphere when projecting them to the 2D latent space (a), leading to more distinguished latent representation of bags (b).
Following Jang & Kwon 2024], we define the bag-level risk as
Rbag = EE Trelass (Y, Y)]
(8)
and the instanco-level risk as
Rinst (h) = (Lattsss((((((()))))))))))
(9)
where h(.) is an explicit instance predictor. Considering Rinst (h) as the true instance risk, there exists an empirical instance risk (h) trained on the finite training set of size m
Risss (h)
Lidass (h(())))
(10)
In general Rinst (h) + Rimst() (h) due finite training data and model capacity. The larger this gap becomes, the poorer the instance learnability is. In our framework, the topological loss acts exclusively on the instance encoder fo and therefore directly influences only the instance-level risk Rmst- It does not modify the aggregation function or the bag-level predictor Je, and hence cannot directly reduce the bag-level risk Rhag- Instead, the topological inductive bias restricts the hypothesis space of the instance encoder, improving the learnability and robustness of instance-level representations. Such improvements at the instance level can indirectly benefit bag-level inference through the shared encoder, while preserving the standard MIL aggregation assumptions. Thus, our proposed approach satisfies the necessary conditions for instance learnability without introducing additional instance-level supervision altering the bag-level decision rule.
Toy datasct. To demonstrate the importance of preserving the topology of bags in MIL, we utilize toy dataset. In this dataset, negative instances are sampled randomly from 100D space, while positive instances are sampled from the surface of a 100D sphere-an an established geometric object. To satisfy the positive bag definition of MIL, the sphere overlaps with the space of random negative instances. We consider a simple 2-layer encoder projecting instances from the 100D space a visualizable representation (see Figure 2 We apply our framework utilizing regressor-guided aggregation (Du et al. 2023] as the baseline MIL model (see Appendix Table 5). Figure illustrates the resulting instance and bag representations, contrasting the scenarios with and without topological guidance. TG-MIL preserves the topology of posilive instances, resembling a circle, as the expected 2D projection of hypersphere, As result, the aggregated bag's latent is more distinct, leading to a higher classification accuracy (MIL and TG-MIL yield 0.55 + 0.05 and 0.80 0.22 accuracy, respectively, averaged over 5 runs).
2
5 Experiments
We evaluate TG-MIL's performance across different datasets. Synthetic MIL datasets provide a controlled environment for investigating TG-MIL's performance across varying amounts of training data. MIL bench-

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marks offer insight into its general effectiveness across heterogeneous data modalities while facilitating fair comparison with state-of-the-art methodologies. Furthermore, our evaluation contains real-world application, i.e, the classification of rare anemia, that presents additional challenges inherent to the MIL problem domain, such as the contribution of severity and the ratio of positive instances within the bag class.
5.1 Synthetic Datasets
To evaluate the robustness the TG-MIL framework across varied MIL data properties, including the number of training bags, instance image complexity, and bag sizes, we draw on the methods outlined by [sse et al. (2018). We create two series of synthetic datasets: the first comprises bags of MNIST images as instances, and the second comprises bags of Fashion MNIST (Xiao et al. 2017) images more challenging scenario with complex visual data. In constructing the MIL synthetic datasets, a bag is labeled positive if it contains at least one instance of the digit "9" in MNIST or the "Dress" class in Fashion MNIST; otherwise, it is labeled negative. We construct distinct training datasets containing 10, 14, 20, 50, 100, and 200 bags to evaluate the influence of the quantity of training data. Additionally, we explore different instance counts per bag, sampling from Gaussian distributions with means and standard deviations of (10, 2), (50, 10), and (100, 20), respectively. Positive bags are defined as those containing at least one positive instance, accounting for up to 20% of the instances within the bag.
Models. We use deep instance encoder architecture introduced by llse et al. 2018 (see Appendix Table 6). It consists of two convolutional layers with kernel size 5, stride 1, and ReLU activation. These layers generate 20 and 500 feature maps, respectively, followed by a fully-connected layer. The attention network comprises two linear layers, resulting in a final output dimension of 128 followed by 1. The topological signature of input instances is calculated in image space and latent space, using pixel-wise Euclidean distances between instance images and latent feature vectors (Figure
Results. We evaluate the effectiveness of topological guidance utilizing three aggregation functions in MIL: max pooling, average pooling, and attention-based pooling (Ilse al.) 2018), which serves as the baseline for numerous studies in the field, in addition to the regressor-guided pooling technique (Du et al. 2023). We analyze the average F1-score and its standard deviation for different numbers of training bags (Figure 3) and bag sizes (Figure in the appendix) over five runs. Without topological guidance, models trained with few training bags perform poorly, akin to random guessing, while adding topological guidance provides a reasonable complexity for the encoder to resolve overfitting (Figure in the Appendix shows learning curves of MIL and TG-MII, for MNIST synthetic data) and improves the MIL model performance across both datascts. Notably, topological guidance narrows the performance gap between basic aggregations of max pooling and average pooling compared to advanced attention and regressor-guideel pooling techniques.
We conduct a statistical analysis using the Wilcoxon rank-sum test (Haynes et al. 2013) to assess the significance of the improvements resulting from topological guidance (Table Given the 24 tests for each dataset, we applied the Bonferroni correction (Weisstein) 2004) to account for multiple comparisons, reducing the significance level from 0.05 to approximately ("24 R3) 0.002. Topological guidance significantly enhances classification in out of 48 cases, particularly when using average pooling (TTble 1
5.2 MIL Benchmarks
Dataset. We assess the performance of TG-MIL using five benchmark MIL datasets commonly employed in evaluating end-to-end MIL methods in the literature. These include three image- based datasets (FOX, TIGER, and ELEPHANT) described in Dietterich et al. (1997), each comprising 200 bags. In these datascts, only tabular features of instances are available. Although these classic benchmarks are relatively small and of limited quality, we include them to ensure a fair and consistent comparison with previous MIL. approaches.
We evaluate our method on the MUSK1 and MUSK2 datascts (Andrews et al. 2002). which contain data from 92 and 102 molecules, respectively. In these datasets, each molocule is represented as a bag of instances, where each instance corresponds to different. molecular conformation. The number of instances per bag
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Max pooling
Average pooling
Attention pooling
Regressor guided pooling
1.0
11-score
0.8
Pashion MNIST MNIST
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
MIL
0.2
TG-MIL
0.0
14
20
20 Number of training bags
50 100
100
Figure 3: TG-MIL outperforms MIL across different pooling strategics (max, average, attention, and regressor guided) on both MNIST and MNshionMNIST datasets. For each number of training bags, the plots show the mean and standard deviation of F Fi-scores over runs for different bag sizes containing 10, 50, and 100 instances (15 runs in total), highlighting consistent gains especially for smaller training scts.
Table 1: The Wilcoxon rank-sum test shows the significance of topological guidance cnhancement over MIL models. Results are reported as p-valtes for each amount training data and aggregation technique. P-values less than 0.002 indicate significant enhancement after multiple testing correction(*)
Number of training bags
Pooling
10
14
20
50
100
200
MNIST
Max
6.6 x 10
7.7 x 10-1
3.7 x 10-3
1.4 x 10
3.8 x 10-2
4.8 x 10
Average
1.3 X 10
7.5 x 10
3.1 x 10 10-6+
3.1 X 10
3.7 X 10
1.7 x 10
Attention
7,9 x 10
2.3 x 10
8.0 x 10-1
3.8 x 10
6.0 X 10
6.5 x 10
Regressor
7.1 x 10
7.8 x 10
6.6 10-3
x.1 10
5.1 X 10
3.9 x 10
Fashion
Max
1,1 x 10-1
1.5 x 10 10-3*
5.8 x 10-3
1.3 x 10
1.1 10-2
9.7 x 10-2
Average
1,2 x 10
2.8 x 10
9.7 x 10-5+
2.9 x 10
1.1 10
5.6 x 10-1
Attention
3.8 x 10
5.1 X 10-3
1.1 X 10
6 x 10
2.3 X 10
4.3 x 10
Regressor
9.3 X 10
6,2 x 10
2.8 10
3,5 X 10
2.9 X 10
4.1 X 10
ranges from to 1044, providing a comprehensive assessment of our model's adaptability and robustness across different scales of data representation.
Models. We an encoder architecture from the literature to clarify and ensure a fair comparison with existing MIL. methods. This architecture includes 2 linear layers with ReLUU activations, projecting the input features into 512-dimensional space for both layers (see Appendix Table 7 For the aggregation function, we opt for agressor-guides pooling (Du et al. 2023). Among all prior methods listed in Table we specifically select RGMIL. for reimplementation, as it provides a simpler MIL framework without additional instance-dissciimnation modules introduced in more recent models such as DistNet (Oner et al. 2023 and OPMILD//APMILL
(Zhu et al.) 2025). In this way, the only modification to the network architecture of RGMIL in our setup (TG-RGMIL) is to integrate the topological signature calculator into the instances' input and latent spaces.
Rosults. The original RGMIL model used 231 features for FOX, TIGER, and ELEPHANT datasets and 167 features for MUSK1 and MUSK2 datasets, including last feature representing the repeated label of the bag for each instance. However, in our re-implementation, we follow the standard benchmark settings of 230 and 166 features for the respective datascts to align with previous works and provide comprehensive comparison (see Table When using this instance feature vector, we observe decline in the performance of reimplemented RGMIL baseline, which aligns with the standard benchmark configuration. We run both
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MUSKI
MUSK2
FOX
TIGER
ELEPHANT
100
Accuracy
70
RGMIL (FF
(Q-
60
.001
.005
.01
.05
.001 .005
.11 .05
.001 .005
.01
.05
.1
.001
.005
.01
.05
.1
.001
.005
.01
.05 .1
Figure 4: TG-RGMIL accuracy as function of the topological loss coefficient À on benchmark datasets. Mean and standard deviation (σ) are computed over five runs.
the RGMIL and TG-RGMIL models 5 times using 10-fold cross-validation and report the average optimal performance. We select the coefficient À heuristically by searching over range of values compatible with the relative scales of the classification loss Tolass and the topological loss Tropos illustrated in Figure (and Appendix Table
TG-RGMIL consistently outperforms the non-topological approach in all datasets Incorporating higher- dimensional topological features generally improves performance across most cases (MUSK1, FOX, ELE- PHANT datascts). For MUSK2 and TIGER, TG-MIL, considering higher-order fcatures, remains compotitive with TG-MIL using only OD topological features, while still outperforming stale-of-the-ar methods (Ta- ble 2 In these two datasets, the underlying instances' topology is likely dominated by connectivity; thus, highher-imensional topological features do not provide additional class-discriminative cues.
More analysis of these experiments reveals a tendency for the RGMIL model to overfit, which is mitigated by including topological guidance (see Appendix Figure 10 This phenomenon is characterized by the MIL
classifier performing best during the initial training epochs.
5.3 Anemia Classification
The diagnosis of anemia relies on the presence a minority of red blood cells a patient's blood sample that shows morphological deformations associated with the disease. Anemia disorders lead to various aberrant shapes, such as sickle-shaped (SCD), crumpled or perforated (thalassemia), star-shaped (Xero), or spherical (HS) cells. These deformations manifest with varying degrees of severity and in different proportions, while it is also possible for other cell types unrelated to anemia. conditions to coexist.
Datasct. Our dataset consists of 521 microscopy images of blood samples obtained from patients who underwent various treatments at different times. Each sample comprises 4 to 12 images, each containing 12 to 45 cells. The data is distributed among five classes: (i) SCD with 13 patients and 170 samples, (ii) Thalassemia with 3 patients and 25 samples, (iii) Xero with 9 patients and 56 samples, (iv) HS with 13 patients and 89, well as (v) healthy control group consisting of 33 individuals and 181 samples. Similar to previous works, we implement patient-centric approach by dividing the dataset into three equivalent folds. This division allocates two folds for training and reserves one for testing. This dataset is generated using a pre-trained segmentation method to crop single-cell images (instances) from the whole sample (bag). Cropped images are vero-padded be the same size, and their encoded extracted features (4 x 256) in the segmentation model are used as the input of the MIL instance encoder (see Appendix Table D) We posit that features extracted by the segmentation model, regardless of cell lype, may lack crucial shape information and may even alter the bag's topology. Then capture the topological reference signature of each bag directly from the image instances, and preserve it in the 500D latent space.
Models. For fair comparison, we apply topological guidance the previous MIL architecture used for this application, where the instance encoder contains convolutional layers followed by ReLu and Tanh activation functions and 2 linear layers obtain latent representation of instances in 500D space.
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Table 2: Topological guidance improves the classification accuracy (%) SOTA approaches in MIL benchmarks.
Among previous methods, we specifically reimplemented RGMIL for our analysis. Other results (gray) are collected from papers proposed by [Ise al. (2018) (APMIL and GAPMIL), Yan et al. (2018) (DPMIL), Tu ct al. (2019) (GNNMIL), Li et al. (2021) h (DSMIL), Huang et al. (2022) (BDRMIL), Oner et al. (0033)
NDist.Net), Zhu et al. (2025) (APMILwD w and GAPMILwD), and Du et al. 2023 (RGMIL). The last three
rows correspond to topologically guided RGMIL using increasing levels of topological features: OD (connected
components) only, OD and 1D (loops), and OD, 1D, and 2D (voids).
Method
MUSKI
MUSK2
FOX
TIGER
ELEPHANT
APMIL (2018)
89.2+4.0
85.8+4.88
41.5
83.912.2
86.8+2.2
GAPMIL (2018)
90.0+5.0
86.314.2
60.3#2.9
84.5=1.8
85.7+2.7
DPMIL (2018)
90.7++3.6
92.6:14.3
65.5:15.2
89.7:12.88
89.4
GNNMIL (2019)
91.7+4..8
89.2+1.11
67.9=0077
87.6+1.
90.3+10
DSMIL (2021)
93.242.3
93.0+2.0
72.9#1.8
86.9
92.5
BDRMIL. (2022)
92.6+7.9
90.5++9.2
62.9+11.0
86.9+6.6
90.8+5.4
DistNet (2023)
92.3#7.1
93.246.77
68.0=7.55
86.4#5.4
90.0#7.7
APMILwD (2025)
96.4
95.41+1.9
78.9
91.7#3.6
93.4::466
GAPMILwD (2025)
96.7
95.8:12.1
7..8+116
91.9
92.7#3333
RGMIL (2023)
94.0=
92.0+10.6
71.4=10.7
84.248.8
91.5+4.2
TG-RGMIL [0]D
94.6+7..8
97.0+4.2
74.7+-..4
96.1+4..0
94.1+5.44
TG-RGMIL [0,1]D
96.6+4.8
96.7+4.44
78.5=5.0
95.3+4.11
94.2#5.11
TG-RGMIL [0,1,2]D
98.2+3.4
96.243.4
79.2-5.1
95.7+4.2
96.3
Results. We employ five standard evaluation metrics: Accuracy, F1-Score, Area Under the Receiver Operating Characteristic Curve (AUROC), Precision, and Recall. Recall reported to assess sensitivity to missed positive cases. All metrics are macro- weighted due to dataset imbalance. Table 3 shows that topological guidance improves the performance of MIT models using all aggregation functions and results in higher average performance, often resulting in reduced variance. Topologically guided MIL with average pooling surpasses other aggregation schemes. This aligus with our findings from experiments on synthetic datasets, where we observe that topological guidance particularly narrows the gap in performance between MILs employing different aggregation functions. The inherent ambiguity in the anemia dataset for MIL suggests that enhancing instance projection in latent space via average pooling more effective than attention pooling, as it better captures the ratio of positive instances. Without topological guidance, scarce training data impede the instance encoder from generating meaningful, generalizable latent representations. However, integrating topological inductive bias into the latent space mitigates these challenges, significantly improving MIL. performance. x = 0.005 provides the best overall performance across pooling strategies. Notably, the performance is relatively stable across 2 orders of magnitude of X (see Figure 5 and Appendix Table 10
Instance-level analysis. Figure 0 shows anomaly scores with and without topological guidance. Without topological guidance, the anomaly detector assigns inconsistent scores to visually similar instances, indi- cating instability in instance representation learning rather than instanco-level diagnostic reliability. This inconsistency is mitigated by topological guidance, highlighting challenge in uniformly evaluating similar data points and demonstrating its effectiveness in improving representation consistency and interpretability. Further illustrating this point, we visualize the distance matrix of instances within a bag in the input space and compare them with their corresponding matrices in the latent space, both with and without topological guidance. Figure shows that MIL with topological guidance better preserves the relative distances between bag instances in the latent space projection. In contrast, MIL without topological guidance selects limited number of instances and pushes them far away from the majority in the latent space. This behavior suggests
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Average
Anomaly-aware
Attention
Max
Accuracy
80
MIL (u:l))
TG-MIL ((vt)))
0005
.008 .01
.05
.0005 .001
.005 .0005
.001
.005 .05
.0005
.001
.005
.01
.05
h.
À.
Figure 5: Effect of the topological loss weight À on TG-MIT, performance for the anemia classification task. Accuracy is reported for four pooling strategies across five À values. μ and a indicate the average and standard deviation of accuracy across 3 runs.
Table 3: Topological guidance improves classification performance (%) for all pooling strategics in Anemia classification. We apply it to different MIL methods with various pooling techniques containing Average, Anomaly-aware (Kazeminia et al. 2022), Attention (Sadafi et al. 2020), and Max pooling. Numbers depict average classification performance and standard deviation from 3 cross-validation runs. Best performance is indicated by bold text. We compare classification performance without (X) and with (V) topological guidance, with the superior result underlined.
Pooling
Average
Anomaly-aware
Attention
Max
Lropo
X
X
Accuracy
72.317.0
81.312.5
77.9
81.1=2.2
73.7
77.8
64.3
71.415.6
F1-Score
70.5+7.4
80.313.1
76.7+4.0
79.2=2.6
72.4+3.8
74.7#1.6
63.0#5.0
68.8
AUROC
89.912.7
93.714.4
89.114.3
93.1-4.0
91.613.0
91.912.5
84.812.8
89.713.1
Recall
59.7+7.8
65.1+5.0
63.243.2
6..9-0.7
59.3+6.4
60.4+:.3
52.8+8.6
53.8+4.77
Precision
61.817.1
79.1+12.0
67.4+4.5
69.6=0.6
64.9149
73.2
52.919.6
63.4
that, without topological guidance, only a few instances dominate the bag representation, explaining the observed instability instance-level scores.
TG-MIL Anomaly
MIL Anomaly
High
Anomaly score
Low
Figure 6: Topological guidance enhances the model's ability to identify disease-relevant (sickle) cells more effectively. TG-MIL. results in more uniform anomaly scores for deformed cells, in contrast to the varied scores resulting from MIL Anomaly.
In addressing potential inquiries about our choice topological guidance over a distance- iettance-peseeration-beer basod loss, is worth noting the distinct. advantages of our approach. Topological loss is particularly robust to noise
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Instance
High
Instance
Low
Image
TG-MIL Latent
Anomaly MIL Latent
Figure 7: Hcatmaps of distances between instance images (left), TG-MIL latent vectors (middle), and anomaly-awan aware MIL latent vectors (right) for the same bag. Topological guidance preserves the topological characteristics of the image space, making the latent space more closely resemble the original high-dimensional space.
and effective in high-dimensional spaces, and exhibits scale invariance, enabling preservation of relative distance patterns among instances within bag. These properties allow the model maintain meaningful instance relationships in the latent space, thereby supporting more stable bag-level predictions and qualitative interpretability, rather than instanco-level diagnostic conclusions.
5.4
Unit Test
We evaluate TG-MIL using the unit test introduced by Raff & Holt (023), which serves functional check to verily that MII. model does not exploit invalid shortcuts when predicting bag-level labels.
Concept. The unit test follows the classical singlo-concept MIL formulation of Dictterich al. (1997] in which bag labels are determined by the presence of single positive concept. The concept class is unilary, consisting of a positive concept and a null concept 0. A bag is labeled positive if and only if at least one instance corresponding to is present. Each bag contains instances sampled from simple Gaussian distributions. Most instances are negative instances, drawn from a background distribution (O,,, Ia), which corresponds to the null concept and carries no label information. Positive bags additionally include a small number of informative instances drawn from one of two non-co-occurring distributions, (O, 3la) or (1, both mapped to the same positive concept C₁ As no single positive pattern is shared across all positive bags, correct prediction requires aggregating evidence across instances rather than detecting fixed prototype. The unit test further introduces a bait distribution (o-10, 0.1 which is trivially separable from all other instances. During training, & poison instance from the bait distribution appears exclusively in negative bags, creating an invalid but easier-to-leany decision rule based on the absence of the bait instance. This rule violates the MIL assumption that bag labels depend on the presence of positive concepts. Models that learn this MIL-violating shorteut achieve high training performance but generalize incorrectly at test time, where the label correlation is reversed. Following the authors' criterion, model is considered to fail the unit. test if it achieves training AUC 0.5 but test AUC 0.5, indicating learning anti-correlated, invalid decision rule rather than the intended existential MIL rulc.
Results. Table reports the unit-test results of TG-MIL under different pooling operators.
TG-MIL with average pooling achieves strong generalization, with test balanced accuracy of 0.90 and an AUC of 0.90, indicating reliable recovery of the intended existential MIL decision rule. Both altention-based and parressor-guider pooling pass the unit test according to the authors' criterion, achieving test AUCs 0.91 and 0.90, respectively. However, their test balanced accuracies (0.74 and 0.47) are substantially lower than average pooling, indicating less stable decision behavior under the test distribution and greater sensitivity spurious correlations. Max pooling fails the unit test, yielding test-balanced AUC of 0.50, corresponding
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Table 4: Unit-test results of TG-MIL with different pooling operators.
Pooling Method
Train AUC
Test Acc.
Test AUC
Average Pooling
0.99
0.90
0.90
Max Pooling
0.98
0,50
0.50
Attention Pooling
1.00
0.74
0.91
Megressor-guidees Pooling
0.99
0.47
0.90
to random--uessing behavior. While topological inductive bias improves max pooling compared to a MIL baseline (increasing test AUC from 0.00 0.50), this remains insufficient to pass the test.
5.5 Practical Computational Cost
We empirically evaluate the computational overhead introduced by the topological signature calculation using two complementary timing metrics: (i) the average training time per iteration, which reflects the end-to-end cost of one optimization step, including forward propagation, loss computation, and backpropagation, and (ii) the wall-clock forward time, defined as the real elapsed time during a single forward pass. The baseline MIL model requires 0.021 seconds per iteration, whereas TG-MIL requires 0.077 seconds per iteration, 3.7x
increase in end-to-end training time per itcration. For a bag of size n 200, the wall-clock forward time increases from 0.15 seconds for MIL to 0.35 seconds for TG-MIL, a 2.33 fold increase and a A/(20 = 0.20 seconds. For a bag of size n = 100, the corresponding increase is from 0.12 seconds to 0.18 seconds (1.53 fold change, (t(0)) = 0.059 seconds). When the bag size doubles from 100 to 200, the additional forward-time overhead increases by a factor of approximately 3.5, which close to the factor of 4 predicted by the quadratic complexity analysis. Since TG-MIL roduees additional learnable parameters, these observations support. the quadratic dominant term identified in the thcorctical analysis.
CO2 Emission Related to Experiments. All experiments were conducted for 228 hours on institute's infrastructure with 0.432 kgCOzeq/ /kWh /Whh carbon efficiency and A100 PCIc 40/80GB hardware (TDP 250W), resulting in 24.62 kgC02eq total emissions with no direct offset. Calculations utilized the MachinelLearning
Impact calculator Lacoste et al. 2019
6 Conclusion
We introduce TG-MIL, a novel approach that leverages the topological properties of imput bags as an inductive bias for their latent reprosentation in MIL. This is achieved by employing a topological loss term within the MIL objective function. Our method ensures that the intrinsic geometrrie-lppoloicaa characteristics of bags in the input space are consistently preserved in their latent projections. Testing our approach across different datasets, show that preserving data topology in latent MIL models leads to substantial improvements in predictive and generalization performance, especially when dealing with scarce training data. While the datasets used in our experiments involve non-trivial MII. problems, the individual instances (images) exhibit relatively simple visual structures, e.g., centered, grayscale, background-free. In such settings, pixel-level differences provide an effective reference for defining topology in the latent space. However, in more visually complex domains, where instances are more complex, e.g., with greater diversity of textures, colors, or higher background noise, pixcl-basod topology may become less reliable, as can transfer irrelevant visual noisc into the latent representation. The robustness of TG-MIL on benchmark datasets, where the original images were unavailable and only pre-extracted image features were used inputs, further suggests that defining topology over higher-level feature representations is viable alternative. This observation does not imply a direct comparison with image-based inputs but rather highlights the potential of feature-level topology as a more general inductive bias for visually complex image instances.
As for future rescarch directions, we plan to explore alternative methods for describing image gcometry and topology, with particular focus on cubical complexes that can directly operate on images. Additionally, we aim to investigate the geometrical and topological properties of bag spaces, leveraging recent advances in
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metric geometry, including the Gromov Hansdorff distance, which has previously been utilized to characterize shapes in related studies (Chazal et al. 2009
Broader Clinical Impact Statement
Notably, the current clinical setting, Al tools based on our method should used strictly as decision- support systems for clinicians, rather than as standalone diagnostic oracles, due to the weakly supervised nature of MIL, potential misclassifications, data distribution shifts, and clinical liability considerations.
Acknowledgments
We gratefully acknowledge Anna Bogdanova, Asya Makhro, and Ario Sadafi for providing the biomedical dataset used in this research. The anemia dataset is not publicly available. Access may be granted upon reasonable request to the data owners (Sadafi al. 2020
The Helmholtz Association supports the present contribution under the joint research school "Munich School for Data Science- MUDS". C.M. has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 866411). B.R. was partially supported by the Bavarian state government with funds from the Hightech Agenda Bayern.
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A Appendix
A.1 Toy experiment
Table specifies more details of the MIL architecture we developed to classify toy dalaset.
Component
Configuration
Input channels
100
Instance encoder
Linear + 64), ReLU, Linear(64 2), ReLU
Latent dimension
Pooling
Regressor guided pooling
Classifier head
Linear (100 - 2)
Loss
BCEWithLogitsLoos and Ltopo
Optimizer
Adam (Ir: 0.0005)
A
0.005
Table Architecture of the MIL model for the toy experiment.
A.2 Synthetic data experiments
For syuthetic data we employed same architecture for both MIL-MNIST and MIL-PashionMNISST datasets. We explored different aggregation functions containing max pooling,
max 2
(11)
ESm
average pooling,
Ct..
Ziml
(12)
and allention pooling with parameters W and
Som
a;
(13)
where
eXp(WT (anh((2?))
04 E.
i= exp(WTT tanh(V2?)))
(14)
The RGMIL (Du et al. 2023) model uses regressor guided pooling technique. In this model, the regressor (with parameters and B) calculates the binary probability value of instance latent representation 24 as
(pt == TT 24 + B,
(15)
where p and P show the probability of instance to belong to the positive or negative class. Then it gets the difference between these two achieved probabilities,
Pi P.
Pi
(16)
normalizes the result
wi Pi Esp.]
(17)
/ar(p:)
and applies softmax on
exp(wi)
a; Σ exp(w;j
(18)
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poeling
Averge pooling
pooling
Ascrage pooling
200
10
20
Attenioon poolins
Regressor Guided pooline
Aftectinn pooling
Regressor Guided pooling
Flagore
MNNIS sumbera Inining bage
MNIST Inining bag.
FashimMNIST munber taiinin bugs
FashinMNIST bage
(a) MIL MINST
(b) MIL MNIST
Figure 8: TG-MIL outperforms MIL models irrespective the aggregation function when subjected to a limited amount of training bags. For each number of training bags, the average and standard deviation for the Fl-score of the model's performance in 5 runs for each bag size of 10, 50, and 100 (in total 15 runs) is shown.
where, a₂ specifies the pooling weight of 2, Then the latent of bag is
Sb
exp(a.2,).
(19)
Table shows the settings of TG-MIL architecture architecture used for synthetic dataset classification.
Parameter
Max Pooling
Average Pooling
Attention Pooling
RGP Pooling
Pooling
Max
Average
Attention
Regressor guided
In dimension
28 x 28
Input channel
Instance encoder
(1near(1-20)), ReLU, Linear 1innear2005500 20-+50), ReLU, Linear(50+5000, ReLU
Latent dimension
500
Attention latent dimension
128
Linear layer
500 x 2
Loss
BCEWithLogitsLoss and Liopo
Optimizer
Adam (LR: 0.005)
Adam (LR: 0.0005)
Batch size
Max epochs
100
Table 6: General architecture and configurations of TG-MIL Model for synthetic datasets over different
pooling strategies. The value À is not reported here as it differs between datasets, training budgets, and bag sizes. Please find its relevant value in the source code.
Figure g distinctly illustrates how topological guidance addresses data scarcity issue in MIL considering different scenarios, containing different amount of training data and bag sizes.
Figure g display the learning curves of training RGMIL alongside TG-RGMIL on synthetic dataset. For RGMIL, the loss corresponds to the bag-level cross-entropy loss, while for TG-RGMIL, it is the total loss, defined as the sum of the cross-cntropy (CE) and topological losses. Since the topological loss operates at a larger scale, the lotal loss magnilude for TG-RGMIL is higher, particularly during the early stages of training. Despite the different loss scales, TG-RGMIL consistently converges to a lower final total loss, indicating that the cross-cntropy component also converges to a lower value compared RGMIL, making the two approaches comparable convergence. The introduction of topological giudance addresses overfitting in RGMIL and results in significant improvement in its classification performance.
18

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Published in Transactions on Machine Learning Research (02/2026)
Number bags: 10
Number of begs: 14
Number of bags: 20
Number of bags: 50
Number of bags: 100
0.31
RGMIL L,855
0.85
0.64
0.9
0.58
Trussing
3.41
0.74
0.73
9.68
0.9
9.30
0.62
0.63
0.60
0.00
9.00
TG-RGMIL Loss
6.40
6.00
4,80
1.20
1.00
Validmioo
4.50
4.50
3.60
01900
0.75
3.20
3.00
0.60
1.60
1.50
1.20
0.30
0.25
2.45
1.25
0.83
1.10
Tevining Validation
1.00
CE
1.50
0.75
0.45
0.45
0.75
0.25
0.15
0.00
0100
0.00
01:00
0.00
1425
1330
1040
300
Troining
Topology Loss
Validation
835
795-
630
460-
475-
570
630
470
130-
51.-
0.00
0100
12
20
12
10
25
Epochs
Figure 9: Topological guidance enhances the RGMIL model generalizability for scarce training data. Each column displays the learning curves of models trained with 10 bags, each containing approximately 10 instances on average.
A.3 Benchmark experiments
Table shows the settings of TG-MIL architecture architecture used for benchmark experiments.
Components
Elephant, Fox, Tiger
Musk1, Musk
Input channels
230
166
Instance encoder
Linear(231, 512), ReLU, Linear(512, 512), ReLU
Latent Dimension
512
Pooling
Regressor guided pooling
Classifier head
Linear (512 + 2)
Loss
BCEWithLogits and TopoRegLosss
Optimizer
Adam (Ir: 0.00005, Betas: [0.9, 0.999]
Max Epochs
40
X
0.05
Table 7: Architecture of the MIL Model for Benchmarks
Table shows the sensitivity of TG-RGMIL to À coefficient for benchmark datasets.
Figure 10 shows how topological guidance helps with overfitting of the RGMIL model tends on benchmark
datasets.
19

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Published in Transactions on Machine Learning Research (02/2026)
Table 8: TG-RGMIL accuracy (%) across different values of (mean + std) for Benchmark datasets.
Dataset
A = 0.001
À = 0.005
A 0.01
X = 0.05
== 0.1
MUSKI
6.8
95.6 + 5.8
91.2 + 4.4
94.6 + 7.8
92.8 6.1
MUSK2
96.4 9.6
3.9
97.0
99.6 1.8
FOX
73.6 5.6
72.5 10.8
74.7
76.4 + 6.6
TIGER
90.1 4.7
88.8 - 4.0
90.3
96. + 4.0
94.8 5.0
ELEPHANT
96.1 +: 3.8
90.2 + 7.5
95.7 + 2.7
94.1 + 5.4
92.5 + 3.4
MUSKI
MUSK2
FOX
TIGER
ELEPHANT
140
RGMIL Loss
110
100
1.25
1.05
0.82
55
0.63
0.53
0.41
//
0.31
0.26
0.70
0.00
25
17
25
35
17
24
53
17
75
35
9
12
24
860
720
4.27
10.05
4.90
TG VG-RGMILLL Loss
Traiz
692
575
3.47
8.04
Validation
W
345
290
1.71
4.02
1.96
170
145
0.85
2.01
17
25
33
17
25
35
17
25
33
17
25
35
17
25
35
Epochs
Figure 10: Topological guidance enhances RGMIL model generalizability for Benchmarks. Each column shows learning curves achieved by MIL benchmark dataset.
A.4 Anemia experiments
For anemia classification followed the architecture of the state of the art in this application (Kazeiinia et al. 2022) (Table D)- This method introduced anomaly score to be considered in addition to attention values to estimate the importance of each instance. To this end the distribution of negative instances is estimated from negative bags by fitting a gaussian mixture model on their latent representation. The anomaly score of each instance latent 2; calculated as
di = V (zi - -)).
(20)
where 4 and Σ are mean and covariance of the fitted GMM on negative distribution. Then the pooling weight of the instance is calculated as linear combination of allention score a, and anomaly score d, With this the bag latent is
Shm > (W W W.,..).n
(21)
The other consideration of this approach is the formulation of Lossclass with dual classifier head Sadaai et al. 2020) that comprises bag classifier head and an instance classifier head. The bag classifier head is trained using a cross-entropy loss function Lbag, calculated as the difference between the predicted bag label and the corresponding ground truth label for the bag. The instance classifier head trained using a cross-entropy loss function Listance that utilizes the noisy labels of instances as the repeated labels of the bag for instances. The final MIL. classification loss calculated as
Lagaase = (1 - L + + IIInttancce
(22)
where y is a coefficient that decreases as with epoch number increasing.
20

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Published in Transactions on Machine Learning Research (02/2026)
Parameter
Max Pooling
Average Pooling
Aux Attention
Anomaly Detection
Image dimentions
64 x 64
Image channels
Feaburus chanuels
256
Instance encoder
Conv2D(256-3300 -301), ReLU, (301 550),
(301-5000) ReLU, (000006550-6)))) Tanh, Lincar (650 (650->500)
Latent dimension
500
Instance classifier head
Linear (500 500), Linear(500 (500 + 5)
Pooling
Max
Average
Attention
Anomaly
Atiention layer
Lincar (500-1120) -128), Tanh, Lincar(12 (128 +1)
Bag classifier head
Lincar
2)
Loss
bag CrossEttropyLss and TopoRegLoss
CrossEntropyLos (bag and instance) and TopoRogLoss
Optimization
Adam (I==0.0005
Learning rate
0.0005
Max epochs
300
Early stopping
patienne: 50
Image input channels
0.005
Table 9: Configuration of MIL model for anemia classification with different pooling strategics
Table 10: TG-MIL accuracy (%) across different values of (mean std) over different aggregations for anemia dataset.
Pooling Method
À = 0.0005
À 0.001
= 0.005
== 0.01
== 0.05
Average
77.3 + 4.5
81.3 3.7
4.1
68.6 + 18.2
Max
65.1 5.2
2.8
5.6
64.8 66.5
Attention
75.9 + 2.0
7..2
77.8 1.6
7..2
69.2 8.0
Anomaly-aware
78.0 - 5.0
4.11
81.1 2.2
8.
77.4
21


Reviews:
[{"review_id": "Z32NZAPB0y", "reviewer": "Reviewer_wSEY", "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": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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 introduce Topologically Guided Multiple Instance Learning (TGMIL), a novel method to incorporate topological inductive biases into deep MIL models. Specifically, the authors utilize a topology-preserving constraint to ensure that the topology of the instances within a bag are maintained when mapped from the input space to the MIL latent space. The proposed framework is evaluated across synthetic datasets, standard MIL benchmarks, and a real-world clinical application involving rare anemia classification.\n\n**Strengths.**\n- Clarity and presentation. The paper is well written and is easy to follow. \n- Novelty. This work represents the first attempt to incorporate topological data analysis (TDA) into the MIL paradigm. \n- Flexibility. A major advantage of TGMIL is its modularity; the topological loss can be integrated into any existing deep MIL architecture.\n- Convincing experimental section. Although the methods considered for comparison are limited (see next section), the experimental results look convincing: the proposed methodology improves performance, specially when training data is limited. \n\n**Weaknesses / Suggestions.**\n- Accessibility of TDA concepts. The paper assumes substantial prior knowledge of Topological Data Analysis (TDA), which may limit accessibility for a broader audience. Although the authors reference the loss formulation introduced in prior work, the presentation would be strengthened by including a concise algorithmic description or an explanatory paragraph detailing the step-by-step computation of persistence diagrams.\n- Meaning of 0-dimensional topological features. Due to efficiency constraints, the topological loss is restricted to 0-dimensional topological features. For someone who is not well-versed in TDA, it is not clear what information these features capture. It would be helpful if the authors could clarify this point. \n- Omission of modern MIL architectures. Recent MIL methods are completely ignored. It is well-known that accounting for (local or global) interactions between instances can lead to significant performance gains in MIL. This has been done through Transformers [1], Graph Neural Networks (GNNs) [2], or the combination of both [3,4]. Since the proposed methodology explicitly incorporates information about interactions among instances within a bag, a discussion of these related approaches (and their relationship to the proposed method) would be highly relevant.\n- Extension of the experimental section. In the experimental section, performance is evaluated only by applying TGMIL on top of relatively simple aggregation mechanisms. As noted above, the proposed framework could naturally be combined with more expressive aggregation models. In particular, it would be interesting to see how TGMIL influences the learned representation space of a Transformer-based MIL model. Note that the current results suggest that TGMIL consistently improves performance across various aggregation mechanisms, and thus it is expected that this result will carry over to more powerful architectures. If considering these architectures for comparison does not make sense, it would be useful to explain why. \n\n**Other comments.**\n- In the anemia classification task, instance-level analysis is done qualitatively (Figure 4). Can this be evaluated quantitatively? If instance-level labels are available, classification performance metrics could be computed using the model’s anomaly score. \n- Figures 7 and 8 in the Appendix aim to illustrate how TGMIL mitigates overfitting through learning curves. However, the loss scale differs across rows. It is also unclear which loss is being reported. If the curves correspond solely to the cross-entropy loss, I don’t see an obvious justification for using different scales. As presented, these plots are not comparable. \n\n**References.**\n\n[1] Shao, Zhuchen, et al. \"Transmil: Transformer based correlated multiple instance learning for whole slide image classification.\" Advances in neural information processing systems 34 (2021): 2136-2147.\n\n[2] Tu, Ming, et al. \"Multiple instance learning with graph neural networks.\" arXiv preprint arXiv:1906.04881 (2019).\n\n[3] Castro-Macías, Francisco M., et al. \"Sm: enhanced localization in Multiple Instance Learning for medical imaging classification.\" Advances in Neural Information Processing Systems 37 (2024): 77494-77524.\n\n[4] Fourkioti, Olga, et al. \"CAMIL: Context-aware multiple instance learning for cancer detection and subtyping in whole slide images.\" arXiv preprint arXiv:2305.05314 (2023).", "claims_and_evidence_yn": "No", "claims_explanation": "The authors claim that “TG-MIL outperforms the state-of-the-art on MIL benchmarks and rare anemia classification”. As explained before, the comparison against several SOTA baselines is missing. If the comparison does not make sense, then the authors should explain why.", "audience_yn": "Yes", "audience_explanation": "This is the first work exploring the use of topological information in MIL. It is applied to an important medical-imaging problem. It shows promising results and this could potentially advance the research frontier in MIL.", "requested_changes": "I believe that this is a good paper that should be considered for acceptance in TMLR. I suggest that the authors take into accounts the recommendations listed in the “Weaknesses / Suggestions” and “Other comments” sections before.", "broader_impact_concerns": "I don't identify any major ethical concern.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "PSL4LG3yZE", "reviewer": "Reviewer_KdtF", "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": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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 method to improve MIL frameworks in data-scarce regimes. The authors introduce a topological loss term on both the input bag (image space) and the latent bag embedding. The loss forces the latent space topology (leveraging VR Filtration) to preserve the persistent pairings found in the input space. They evaluate this on synthetic MNIST/FashionMNIST bags, standard MIL benchmarks (MUSK, Fox, etc.), and a rare anemia dataset, claiming improvements in low-data settings.", "claims_and_evidence_yn": "No", "claims_explanation": "Addressing data scarcity in MIL is a valid and important problem, particularly for medical applications like rare disease classification, where labeled bags are expensive. The method leveraging VR Filtration to describe the topology, which is also different from related graph-based methods, requires using a dataset prior to describing the topological relations. The authors included a section on CO2 emissions, which is good.\n\nHowever, the submission fails to meet the TMLR criterion for claims supported by clear and convincing evidence. There is a substantial disconnect between the paper's broad theoretical claims regarding \"topological inductive bias\" and the limited empirical evidence provided by the actual implementation:\n\n- The authors repeatedly claim to leverage \"geometrical-topological\" information, explicitly citing features like \"loops (1D), higher-dimensional voids (2D)\"  to motivate their method. However, in the implementation details (Section 4, Complexity), they admit they \"only capture 0-dimensional topological features\" (connected components) to maintain computational efficiency. If I understand correctly, (0-dimensional) persistence is mathematically equivalent to analyzing the edge lengths of a single-linkage clustering. It essentially acts as a pairwise distance regularizer that enforces connectivity.\n\n- The authors frame the treatment of an MIL bag as a \"point cloud\" as a core contribution and insight. This ignores foundational literature in Geometric Deep Learning (e.g., PointNet, Deep Sets) which established the equivalence between processing point clouds and permutation-invariant sets years ago. Presenting a standard problem definition as a novel insight weakens the credibility of the submission's contributions.\n\n- Fig. 2 is also a little bit vague. Why not use ABMIL as the baseline?", "audience_yn": "Yes", "audience_explanation": "Yes, there is an audience for this paper because data scarcity is a massive, real-world headache, especially in medical fields like rare disease diagnosis. Even though the math has holes, the core idea, using the \"shape\" or structure of data to help models learn from just a few examples, is an intuitive and promising direction. Researchers struggling with expensive or limited datasets will want to see if this \"structural\" approach can help them, regardless of the theoretical flaws.", "requested_changes": "- Again, as I mentioned earlier, if I understand correctly for the 0-dimension implementation. The authors need to rephrase the claim. i, e. The paper repeatedly claims to leverage \"geometrical-topological\" information, explicitly mentioning \"loops\" and \"higher-dimensional voids\" in the Introduction. However, Section 4 admits the method is restricted to 0-dimensional features ($H_0$) due to complexity constraints.\n\n- Rewrite the analysis of Figure 2 to remove the claim that the \"circle\" shape is a direct result of the topological loss.\n\n- Cite Foundational Geometric Deep Learning Literature The paper frames \"treating a bag as a point cloud\" as a novel perspective, e.g,. Deep Sets.", "broader_impact_concerns": "No major ethical concerns that would require rejecting the paper, but there is a missing discussion on medical safety.\n\nSince the paper focuses on diagnosing diseases (like anemia) using very small datasets, there is a risk that the model might not be reliable enough for real-world patient care. When AI is trained on very few examples (\"data-scarce scenarios\"), it is easy for the model to be biased or fail when it sees a patient who is slightly different from the small training group.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "BYcerTfQfx", "reviewer": "Reviewer_YjLR", "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": "", "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 focuses on Multiple Instance Learning with limited training data. To this end, the authors propose Topologically Guided Multiple Instance Learning (TG-MIL), a framework that introduces a topological inductive bias into the MIL training process. Specifically, the authors assume that the topological features of the bag should be preserved after embedding bag instances into the model’s latent space, ensuring that the essential topological properties of the data are maintained. Such inductive bias is introduced via a topological loss term $L_{topo}$ that penalizes discrepancies between the topological structures of the input space and the latent embedding space.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Synthetic Datasets, five benchmark MIL datasets, and a dataset for anemia classification are included for evaluation. The experimental results generally prove the effectiveness of the proposed TG-MIL. \n\nHowever, some experimental details are not clearly described. For example, regarding the benchmark experiments, it is not entirely clear whether TG-MIL and RGMIL utilized identical network structures particularly the pooling layers, at least based on the main text alone.", "audience_yn": "Yes", "audience_explanation": "Multiple Instance Learning (MIL) is a classic and widely adopted paradigm for weakly supervised learning. Even in the era of large models, MIL remains highly relevant, particularly in biomedical research. This paper introduces an interesting perspective, suggesting that preserving the topological structure of bags can enhance performance, especially in data-scarce scenarios. Therefore, I think the MIL-related theoretical insights presented in this paper will be of interest to a portion of the TMLR’s audience.", "requested_changes": "1. The experimental section should describe the experimental setup in greater detail, particularly within the main text. For instance, it is currently unclear whether TG-MIL maintained the same network architecture as RGMIL during the benchmark experiments. If the architectures differed, ablation studies on the benchmark datasets are missing and should be added.\n\n2. It is recommended to include a hyperparameter sensitivity analysis, specifically examining the impact of the topological loss weight on model performance.\n\n3. The notation in the Methods section requires more detailed explanation, particularly regarding symbols representing dimensions and quantities.\n\n4. The computational cost of the topological loss is currently limited to theoretical analysis and lacks experimental support. I suggest adding empirical evidence in the revised version.\n\n5. The authors introduce a real-world MIL application regarding anemia classification. To foster subsequent research in this field, I encourage the release of this dataset, provided that ethical and privacy constraints allow.", "broader_impact_concerns": "No", "additional_comments": "Major revision", "extra_scores": {}, "extra_text": {}}, {"review_id": "lxoyY5ioIT", "reviewer": "Reviewer_B9LH", "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": "", "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 **Topology Guided Multiple Instance Learning (TG-MIL)**, a novel framework that incorporates a **topology-preserving inductive bias** into the MIL latent space. This constraint acts as a powerful regularizer, ensuring the intrinsic structural distribution of instances within a bag is maintained when mapped to the latent space. The primary contribution is providing an effective solution for MIL's sharp performance drop in **data-scarce scenarios** (e.g., rare disease classification), showing consistent and substantial empirical improvements.\n\n#### Key Strengths:\n\n1.  **Novelty:** Innovative integration of **Topological Data Analysis (TDA)** as a structural inductive bias for generalization.\n2.  **Practical Relevance:** Directly addresses the critical challenge of data scarcity in high-stakes applications.\n3.  **Strong Performance:** Reports significant performance gains (up to 15.3% on synthetic and 5.5% on rare disease data) under limited training data conditions.\n\n#### Key Weaknesses:\n\n1.  **Methodological Opacity:** Lacks clear mathematical formulation and definition of the specific TDA metrics used for the topological loss ($L_{\\text{topo}}$).\n2.  **Fundamental Property Concern:** **Critically, the paper omits theoretical proof and empirical unit testing** to verify the method maintains the essential MIL property of **instance permutation invariance**.\n3.  **Unquantified Cost:** Computational overhead from TDA calculation is not adequately measured or discussed.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The claims are convincingly supported by the evidence, particularly regarding efficacy in **data-scarce regimes**.\n\n1.  **Targeted Validation:** Results (Figures 6, 7) consistently show that TG-MIL significantly outperforms baselines when trained with a **limited number of bags**. This empirically validates the method's core goal of addressing data scarcity.\n2.  **Generalizability Confirmed:** The topological constraint acts as an effective regularizer, helping models like RGMIL **mitigate overfitting** on small benchmark datasets (Figure 8), thereby supporting the claim of enhanced generalizability.\n3.  **Practical Proof:** Success on the rare anemia dataset provides strong real-world evidence of the method's utility in high-stakes, data-limited applications.", "audience_yn": "No", "audience_explanation": "The findings are of high interest to several segments of the TMLR audience due to the novel methodology and significant practical impact:\n\n1.  **MIL Researchers:** The paper introduces a novel, principled regularization technique, offering a new structural **inductive bias** for the MIL latent space.\n2.  **Topological Machine Learning (TML) Community:** It provides a strong, practical example of how **Topological Data Analysis (TDA)** techniques can be effectively integrated as a loss term to solve complex machine learning problems. \n3.  **Applied AI/Medical Practitioners:** The demonstrated ability to achieve superior results in high-stakes, **data-limited fields** (like rare disease classification) is highly valuable to application-focused readers.", "requested_changes": "It is a good paper. However, these changes are fundamental to the algorithmic correctness and rigorous presentation required for an MIL submission. **The novelty of integrating a topological constraint (TDA) introduces a necessary burden of proof to ensure foundational MIL properties are preserved.**\n\n1.  **Rigorous Verification of Instance Permutation Invariance:**\n    * **The authors must explicitly address the uncertainty regarding whether the introduction of $L_{\\text{topo}}$ alters the inherent permutation invariance of the standard MIL aggregation mechanism.**\n    * **Theoretical Proof:** Provide a formal mathematical argument in the main text demonstrating that the total loss function ($L_{\\text{total}} = L_{\\text{MIL}} + \\lambda L_{\\text{topo}}$) is invariant to any arbitrary permutation of instances within a bag.\n    * **Empirical Unit Test:** Include an explicit algorithmic unit test, as recommended by [2]. This test must empirically show that randomly permuting instances within a fixed test bag does not change the model's predicted bag label and confidence score. This is non-negotiable for a valid MIL algorithm.\n\n2.  **Detailed Methodological Formulation:**\n    * Provide the **exact mathematical formulation** of the topology-preserving constraint/loss function $L_{\\text{topo}}$. This must clearly specify:\n        * Which **Topological Data Analysis (TDA) features** are computed (e.g., Persistence Diagrams, Betti numbers).\n        * The **distance metric** used to compare the topology between the original and latent spaces (e.g., Wasserstein or Bottleneck distance).\n\n3.  **Contextualization with Instance Learnability:**\n    * Include a discussion section that **cites and integrates the findings of [1]**. Authors should try to explain how the topological inductive bias specifically enhances the **learnability and robustness of instance-level representations**, thereby indirectly aiding instance-level inference derived from the bag labels.\n\n---\n\n**References:**\n\n[1] Are Multiple Instance Learning Algorithms Learnable for Instances? NeurIPS, 2022.\n\n[2] Raff E., & Holt J. Reproducibility in Multiple Instance Learning: A Case for Algorithmic Unit Tests. NeurIPS, 2023.", "broader_impact_concerns": "1.  **Safety and Error Modes (False Negatives):** In rare disease diagnosis, a **False Negative** (missing a diagnosis) can have catastrophic consequences for the patient. The authors must discuss the model's **robustness** and potential **failure modes** regarding high-risk outcomes. Specifically, they should comment on how their method controls or impacts the False Negative rate compared to baselines, even when data is scarce.\n2.  **Dataset Bias and Generalizability:** The method is tested on specific rare anemia datasets. Any inherent bias in the data source (e.g., patient demographics, imaging equipment/protocols from a specific clinic, or geographical location) could mean the learned topological bias is not truly generalizable. The authors should acknowledge these potential **domain shifts** and discuss how the model's performance might degrade when deployed to external hospitals or patient populations.\n3.  **Misinterpretation of Instance Predictions:** The method seeks to improve instance representations. This encourages the use of the model for **interpretable localization** (identifying which instance is \"pathological\"). If the instance-level predictions are used for diagnosis, the authors must caution against over-reliance, as MIL is inherently a weak supervision framework. The Broader Impact Statement should advocate for the model to be used as a **decision support tool** for clinicians, not as a standalone diagnostic oracle.", "additional_comments": "None", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)