Improving Detection of Rare Nodes in Hierarchical Multi-Label Learning
Authors: Isaac Xu
Martin Gillis
Ayushi Sharma
Benjamin Misiuk
Craig J. Brown
Thomas Trappenberg
Venue: Accepted by TMLR ()

Abstract: In hierarchical multi-label classification, a persistent challenge is enabling model predictions to reach deeper levels of the hierarchy for more detailed or fine-grained classifications. This difficulty partly arises from the natural rarity of certain classes (or hierarchical nodes) and the hierarchical constraint that ensures child nodes are almost always less frequent than their parents. To address this, we propose a weighted loss objective for neural networks that combines node-wise imbalance weighting with focal weighting components, the latter leveraging modern quantification of ensemble uncertainties. By emphasizing rare nodes rather than rare observations (data points), and focusing on uncertain nodes for each model output distribution during training, we observe improvements in recall by up to a factor of five on benchmark datasets, along with statistically significant gains in $F_{1}$ score. We also show our approach aids convolutional networks on challenging tasks, as in situations with suboptimal encoders or limited data.

Published in Transactions on Machine Learning Research (02/2026)
Improving Detection of Rare Nodes in Hierarchical Multi- Label Learning
Isaac Xui+ Faculty of Computer Science Dalhousie University
isuac.ou@dal.cm
Martin Gillist
portinggillisddan
Facully of Compuler Science Dalhousie Universily
Ayushi Sharma
ay84 @dol.cn
Faculty Computer Science
Dalhousie University
Benjamin Misiuk
Umisiuk-@mun.ccu
Department of Geography
Memorial University of Neufoundland
Craig J. Brown Deportment of Oceanography Dalhousie University
craig. brown @dal. ca
Thomas Trappenberg
H&Bcs.dal.c dal.cn
Faculty of Computer Science Dalhousie University
Reviewed OpenReview: https: oppenrvee.e....ieu.. net/ forum? ? id= hf=hffEEWWUE
Co-first authors.
Corresponding author.
Abstract
In hierarchical multi-label classification, a persistent challenge is enabling model predictions to reach deeper levels of the hierarchy for more detailed or fine-grained classifications. This difficulty partly arises from the natural rarity of certain classes (or hicrarchical nodes) and the hierarchical constraint that ensures child nodes are almost always less frequent than their parents. To address this, we propose a weighted loss objective for neural networks that combines node-wise imbalance weighting with focal weighting components, the latter leveraging modern quantification of ensemble uncertainties. By emphasizing rare nodes rather than rare observations (data points), and focusing on uncertain nodes for each model output distribution during training, we observe improvements in recall by up to factor of five on benchmark datasets, along with statistically significant gains in Fi score. We also show our approach aids convolutional networks on challenging lasks, as siluations with suboptimal encoders or limited data
Code available htte Lmmee___m_________ Imb__ocal, Wei__eeighh_____e Hd

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1 Introduction
In observing the natural world, contemplating the "relatedness" of objects can aid in understanding their properties. Hierarchies are therefore ubiquitous in the natural sciences. As machine learning techniques expand to these academic fields, there is growing interest in training hierarchical models capable of annotating
in ways useful to experts [Romero et al. 2022 Hunt & Steenstrup Pedersen 2023 Katija et al. 2022: Blondin itt al., 2024 Lowe et al. 2025 Battach et al. 2025). For this work, we describe broader higher- categories in the hierarchy as "ancestor" " or "parent" " nodes, while the lower-level detailed categories stemming from these are referred to as "descendant" or "child" nodes. More generally, hierarchies can be understood as directed acyclic graphs (DAGs), and can be tree-like (where nodes only possess singular parent) or otherwise (where they can be descended from multiple parents). Finally, there are almost always potential hierarchical associations inherent in data, even if not annotated in this manner.
Another property, the multi-label characteristic of the data, may also appear in datasets. Multi-label refers to the possibility of multiple classifications existing for a single observation. A contemporary challenge for machine learning is the need for big data and the lack of a singular large dataset in fields traditionally accustomed to working with small and unstandardized hand-annotated datasets (Kuznetsova et al. 2020 Lowe et al. 2025). As researchers work to amalgamate these potentially multi-label datasets, they may be forced to either exclude some of these datasets or, if additional processing separate the annotations is not available, accept the amalgamated dataset as also multi-label. Therefore, it scems reasonable that more multi-label datasets will emerge as the number of amalgamated datasets grows in various academic fields.
Combining hierarchical and multi-label properties transforms the data modelling process into a hierarchical multi-label (HML) learning task. Within HML rescarch, classification tasks may be further divided into full depth (HML-FD) and partial depth (HMI-PD). Full-depth refers to datasets where each observation is annotated to the maximum depth permitted by the hierarchy. Whereas, partial-depth permits annotations terminating at higher-level categories, prior to reaching the leaf nodes.
In HML data, class imbalance and rare nodes arise naturally from the hierarchical structure, leading to long-tailed distributions. Rare nodes often represent fine-grained distinctions crucial for research. For example, in seafloor classification, one of our areas of interest, detecting rare species or habitats, can indicate important environmental changes. This valuable information may then be used to guide government policies concerning maritime economies. Similarly, in medical domains, rare gene products identified through hicrarchical classification can help diagnose discase. Thus, handling imbalance and ensuring that rare nodes are meaningfully incorporated into HML models is essential for producing insights that are both scientifically relevant and actionable.
Addressing imbalance in the HML context, in order to attain deeper and more comprehensive prodictions, remains a relatively under-explored area and is a difficult problem even for modern methods with the majority of nodes in common benchmark datasets going unpredicted (Wehrmann
al. 2018 Giunchiglia & Lukasiewicz 2020 Percira et al.) 2018 2021). Existing works such as Percira et al. 22018 2021) apply resampling approach. This preference may be a result of the relationship between HML and pure multi-label problems, and the popularity of resampling methods in multi-label imbalance literature (Tarekegn et al. 2021 j.
Furthermore, any observation-base based approach risks overemphasizing common nodes due to the conjoined nature of annotations (Pereira et al. 2021]. This problem is exacerbated by the hierarchical nature, where it is typical for parent nodes to be common, while their child nodes are rare. By emphasizing the entire obscrvation, on the basis that it contains a rare component its annotation, additional emphasis on the already common components present. becomes nearly inevitable. Therefore, an observation-based approach is suboptimal in that it must also add to problem it is simultaneously attempting to solve. Instead, we propose looking at the problem through a node-based lens, where the emphasis on nodes is independent of the distribution of observations and depends on the node frequencies.
Finally, we look to further enhance this effect by utilizing the concept of model uncertainty in a manner inspired by focal loss [Lin et al., (020)). We propose to emphasize nodes characterized by increased uncertainty during training. To this end, we study and apply various ways of reliably quantifying uncertainty in modern literature (Kendall & Gal 2017 (Schweighofer et al. 2023 Gillis et al. 2025b
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Input x
Ground Truth
Baseline Prediction
Desired Prediction
B
D
B
D
B
D
Proposal
Imbalance
Get node-wiiee frequencies from data
Calculate node weights from frequencies
Use weights in training to emphasize nodes
Combine weights HML Loss
Focal
Estimate uncertainty from ensemble outputs
Focus training high-uncertainty nodes per sample
Build model ensemble
Figure 1: Overview of HML Rare Node Problem and Proposed Weighted Approach. The proposed approach towards detecting rare descendant nodes in HML problems consists of two branches. The imbalance branch focuses node-wise explorationweiggatnng system independent of sample frequency, while the focal branch employs modern measures of uncertainty in determining challenging nodes for the model ensemble.
Our main contributions are:
1. Imbalance weighting. Examination of the different ways imbalance weighting may be defined and implemented to improve hierarchical classification. Evidence is provided for which techniques are offective at fulfilling the objectives in the problem statement.
Focal weighting. The concept uncertainty, as defined in contemporary literature, is used to augment focal term, adapted for the HML context. Evidence is provided that incorporating this uncertainty term is beneficial for improving rare node detection.
An overview of the rare node detection problem and our proposed approach is available in Figure
2 Background
2.1
Learning with Hierarchical Constraint
One of the first requirements in modelling HML data is satisfying the hicrarchical constraint that is, the probability for the parent's presence in an observation must be greater than or equal the probability of any descendants. Within the literature, there exists number of ways address this matter (Wehrmann)
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al. 2018 Giunchiglia & Lukasiewicz 2020). For our work, apply Coherent Hierarchical Multi-Label Classificanl inssification Neural Network (C-HMCNN) (Giunchiglia & Lukasiewicz 2020). which remains a robust and competitive method, as a framework to demonstrate our experiments. The essence of the approach is in
translating the hicrarchical information into an adjacency matrix E RNN, where is the number of hierarchical nodes. Each element is defined as:
I Auj = {1
(1)
otherwise.
Where S; is the set of hierarchical descendants for node i, and by definition, node is a descendant of itself. Each row in the matrix A then acts as filter for an expanded model output, which turns off all the predictions that are outside of node i's direct descendant line. Finally, a max operation taken along the rows ensures that each prediction for a node is the max max(p(nodes), p(uodey)), thereby satisfying the hierarchical constraint. The loss, referred to Giunchiglia & Lukasiewicz (2020) as "max constraint loss" (LMc), involves applying this constraint mechanism in the fashion below, depicted with tensor notation for clarity, We define:
X R
data input, B batch size, F number of features;
YE BBXN
ground truth annotations;
0: RBPP + BBX
model parameters;
R E B
batchwise adjacency tensor for hierarchy (batched version of A); function enforcing the hicrarchical constraint, takes predicted probabili- Lies and R, returns constrained probabilities; and unreduced binary cross-entropy, takes predictions and targets, returns a loss for each node (reduction occurs prior to backpropagation).
fcM : B8N B DRRNNRBBB BxN
BCE: BxN, x BBN 4 BBN
YA fcm(((X),
(2)
Y fcm (YO()))
(3)
Y (1 (I-Y + YB
(4)
LMC BCE(Ý, Y)
(5)
One particularity in this process is the asymmetrical treatment of predictions for positive nodes (nodes that are labelled as present an observation) and predictions for negative nodes (nodes that are not present in an observation). If Y is interpreted as the predicted component for negative nodes, we see that it is filtered in [Equation 4 whereas the predicted component for positive nodes, Yn, filtered in Equation 3 This difference accounts for the possibility of model predictions for negatively annotated descendant nodes that happen to have positively annotated parents. In this case, it would be undesirable for the positive parent to have its prediction influenced by that of the negative child, which is why it is filtered prior to applying the constraint function in Equation 3) The recombined predicted probabilities (Equation 4) are then applied to calculate binary cross-entropy (BCE) loss (Equation 5). In Giunchiglia & Lukasiewicz (2020), an explicit example is presented for attempting HML directly with BCE. Without this constraint process, it is shown that gradients point in incorrect direction for model predictions which violate hierarchy. One last point to note is that Y is used only for training, For inference, YA from Equation 2 is used directly.
3 Methods
Our proposal better detect rare nodes HML observations involves augmenting the hicrarchical loss with two components: class imbalance weighting and a focal weighting, inspired by focal loss (Lin al. 2020
We define:
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E RN
vector of occurrence frequencies for each node within dataset;
W(Y,S) BBN
set of weights accounting for HML imbalance eeach node has its unique value, repeated across the batch;
Wo ER
minimum allowed weight (information gate) for imbalance weighting repeated value added to each element in the imbalance weights;
U(+(X)) E BBXN
of weights attained from ensemble of models (+) based uncertaintics, for cach sample and node;
Up E BxN
minimum allowed information for uncertainty gating - a repeated value added to each element in the uncertainty weights; scalar exponential factor to emphasize nodes with extreme uncertainties.
k E R
Liocal
Wo w(X,))
(U. (U++U((()))
LMc
(6)
imbalance weighting
focal weighting
3.1 Imbalance Weighting
As a starting point, we apply a conventional weighting method used in standard multi-class tasks:
Nobs
W/
(N Velasses... fs)=
(7)
Nelasses
where n, denotes the total occurrences of a node and its descendants Nobs is the number of data points, and Nelasses is the number of classes. There is some flexibility in defining Nelasses under a binary representation in HML: it could be defined either two, corresponding to the presence absence of node for given observation, or as the total number of nodes in the hierarchy. Empiriaally, we find that setting Nelasses equal to the number of hicrarchical nodes loads to improved model performance. However, both definitions systematically assign extremely small weights to common nodes while assigning large weights to rare nodes, which can impede effective learning. To mitigate this issue, we rescale the weights to enforce a zero lower bound and introduce a minimum weight parameter úo, ensuring that common nodes continue to contribute informative gradients during training:
W; Wmin
w; W + W;
(8)
Wmar min
Since presence and absence encode different information, node weights should depend on their positive negative annotations in each observation. In practice, observe that introducing imbalance weights for negative annotations does not improve performance across the formulations we evaluated. Accordingly, we define the node weights as follows:
if
(w:)
(9)
herwise.
Hence, in the abbreviated tensor notation in Equation the imbalance component contains the term W as a function of and f.
Throoughut, ny refers the aggregate for node and all its descendants.

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3.2
Focal Weighting
Focal loss was originally developed for dense object delection or image segientattio,, where annotations are often strongly imbalanced between items or pixels of interest and background. To address these conditions, Lin ct al. (2020) introduced loss term (1 - p(yl;; 0))* which determines the amount of weight given to an annotation based on the model's confidence - interpreted as p 0). Over time, it expected that the model's growing confidence would prompt the training process to ignore the common background and instead focus on the rarer annotations. The degree which extremes are emphasized or ignored modulated by the exponential parameter k. As in these tasks, HML tends to possess reliable but rare manual annotations for nodes deep within a label hierarchy, yielding problem we believe can benefit from focal-style weighting.
We define uncertainty as (1 (1-c), c), where c is confidence. Furthermore,, we note that p(y|2; 0) is not necessarily a reliable measure of model confidence (Hendrycks et al. 2019 Costa et al., 2024). Therefore, we introduce adjustments to the uncertainty term, motivated by developments in uncertainty quantification literature. In total, four plausible uncertainty quantitics are explored. To begin, we create an ensemble of models, θ to capture the distribution of models, p(0 X,, Y), for classification task with μ being the Bayesian Model Average (BMA) for this ensemble:
= ~ー O), o² = Varlp(y O)]]
(10)
Umax max(H, 1 p); and
(11)
Amax = 2 (Pmax - 0.5), ULBMA
-maax.
(12)
By taking the BMA, we apply a confidence and uncertainty metric which eliminates some of the individual noise stemming from independent models, thereby making the quantity more robust. An important point is the use of Amax rather than μ directly, as smaller predicted probabilities in binary representation do not just. indicate unconfident. predictions in classes, but also confident negative predictions. We refer to this measure as the binary Bayesian Model Average (bBMA), with its uncertainty counterpart being the first new focal term candidate.
Our second candidate is a signal-to-noise ratio (SNR) based metric, referred to as the Gated Margin Uncertainty (GMU) Giilis et al. 2025b), intended to capture variance across model predictions:
Mmax min (v, 1 1d);
(13)
SNR
Muax (max(()
and
(14)
Tmax + o maxi(2)
UGMU = 1 - (pmax(1-e -SNR))
(15)
In |qquaion 13 we use (2max(2), defined as the probability of the second largest predicted class, which the binary case also the minimum. The interpretation of the SNR that incorporates a notion of how much the models in θ agree with each other. Scaling this quantity by fmax then incorporates notion of "confidence" to the measure. This new gated confidence term is therefore large (close to one), given high certitude and agreement between the models, and is small (close to zero), given low certitude or little agreement between the models.
More generally, in the literature, uncertainty is typically decomposed into two forms: aleatoric (data) and epistemic (model) (Kendall & Gal 2017 Wimmer et al.] 2023 Schweighofer et al. 2023). Alcatoric refers the uncertainty inherent the data resulting from the collection method. Consequently, alcatoric uncertainty cannot be reduced with the collection of more data. Therefore, it should, in theory, be pointless to focus

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nodes with high alcatoric uncertainty. Instead, epistemic uncertainty - the uncertainty of the true model generating the data phenomenon - should be reducible with the acquisition of more representative data perhaps a review and focus on rare pieces of existing data.
In a recent work, Schweighofer et al.
2023 model uncertainty Uepistemie is defined (in our terms) as:
Uepistemic xx(xx) (x
(16)
This quantity can be interpreted as a matrix comparing the Kullback Leibler (KL) divergence for the probabilistic output of every model in θ with that of every other model in the set, with the expectation taken across the matrix dimensions:
Uepistemic
DEL (p(ulo (p 0));
(17)
N(N 8=10=1
with referring to the number of models in O or ensemble size.
In addition to this formulation of epistemic uncertainty, we experiment, with variant where the KT.- mcasure bounded by one, which can perhaps
divergence is switched for the Jensen-Shannon divergence, add interpretability and may perform better when scaling with other quantities in the loss.
As before, we define minimum weight in conjunction with the uncertainty term due to empirically observed benefits training, Icading to the focal component in the loss, as defined in Equation 6 Lastly, focal weighting is computed without gradients, as existing works suggest that training based on ensemble-derived quantities with gradients carries greater risk of ensemble collapse (Lee et al.) 2015
3.3 Metrics
Micro-averaged precision (AP) score is commonly used to evaluate HML classification performance. This metric is the rectangular approximation the area under the precision-recall curve (AUPRC). Its popularity is inherited from multi-label research, in which thresholding model outputs can be challenging (Bi Kwok 2011). While it can be informative, AP tends be overly optimistic, especially in sparsely annotated data. Furthermore, the AP score evaluates the dataset as whole and cannot provide insightful information the model's performance at node level. For practical purposes, we also value assessment of the model's predictions on data (not just probabilities), which cannot be easily attained without thresholding.
As a result of these motivations, we include the node-wise Fi, precision, recall, and binarized average precision score (Bin. AP) as part of the model evaluation. The F1, precision, and recall are calculated for each data point using the true positives, false positives, and false negatives tabulated for cach node. The Bin. AP score is simply the AP score evaluated on model predictions thresholded at 0.5, taking 2 0.5 a positive prediction for node, and < 0.5 negative prediction.
4 Related Works
Although our work focuses specifically on addressing HML imbalance, we consider it to be derivative of addressing multi-label imbalance more generally. Broadly speaking, approaches in this setting can be divided into four groups: resampling, classifier adaptation, ensemble approaches, and cost-sensitive algorithms Tarekegn et al. 2021) Resampling algorithms typically look to determine observations that contain either rare or common annotations and over- under-sample them, respectively (Charte et al. 2015a b). Classifier adaptation approaches consist of dedicated algorithms designed to train the model to learn the imbalance prior. These approaches are varied and include examples such as Chen et al. (2006). where multi-label problems are broken down into two-class subproblems and then recombined for inference. Zhang ct al. (2022) propose an ensemble approach, in which correlations between class annotations are exploited by converting multi-label binary datasets into trinary classification task, predicting the presence of one class in conjunction
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with another. The final output is then based upon the aggregation of the confidences from the binary and multi-class models. Finally, as an example of a cost-sensitive approach, Daniels & Metaxas (2017) employ Hellinger distance (Hellinger 1909), as an objective for random forests. Among these families of approaches, resampling remains the most popular (Tarekegn et al. 2021
Reflecting the more general multi-label trend, the most popular existing approaches to addressing HMT. imbalance appear to be resampling- based.. These have focused on either converting HML to a multi-label problem (Percira et al., 2018) or implementing resampling schemes such as hicrarchical random oversampling (HROS-PD) (Pereira et al., 2021). Pereira et al. (2018) convert HML to multi-label problem by treating each node within a hicrarchy as multi-label class. A multi-label resampling approach is then applicd. They compare popular multi-label imbalance methods such as LPROS/US /US (Charte et. al. 2015a), MLROS/US 2015b). multi-label SMOTE (Charte et al. 2015c and MLeNN [Luu et al. 2022 concluding
(Charte et al.
that LPROS held the strongest performance.
In Pereira al. 20011), , the leamn proposes an approach that determines the imbalance of the hierarchical nodes and then resamples them to acceptable threshold. In their work, it was discovered that the oversampling approach for rare nodes (HROS-PD) PDD outperforms the undersampling approach (HRUS-PD). However, the method is limited in two ways. First, it was designed to handle tree-like hicrarchies and therefore would not perform optimally for directed acyclic graph (DAG) hierarchies (as we would expect and demonstrate on our GO datasets). Furthermore, oversampling annotations conjoined with common nodes risks further oversampling already abundant nodes.
In our work, we include the HML to multi-label /LPPOS method and HROS-PD as benchmarks. Following the algorithm as described in (Percira et al. 2021), implement the approach from scratch and include it with our code. By disconnecting the weighting and confidence for each node from their observations, we also address the issues of working in both a tike-like or DAG-like hierarchical enviromment, as well as avoid overemphasizing already abundant nodes.
5 Experiments
The experiments section is divided into four parts: we first introduce the datascts, then analyze imbalance weighting on gene product data, followed by an evaluation of local weighting on the same datasels, and finally compare both methods on benthic imagery data, For gene product data, we use model ensembles to quantify uncertainty. For imagery data, we apply a shared encoder with an ensemble of output heads, a regularization strategy adapted for uncertainly estimation (Lee et al. 2015 Gillis et al. 2025a). Hyperparameters are provided in Appendix A
5.1 Datasets
We evaluate on 16 gene product datasets, evenly divided into two sets, with each set annotated under two distinct classification frameworks: Functional Catalogue (FUN) (Ruepp et al. 22044) and Gene Ontology ( [Ashburner et al. 2000). These two schemes were developed to catalogue gene products and proteins, and in the case of GO, the genes themselves as well. These datasets are popular benchmarks in HMI. works
Bi & Kwok 2011
Giunchiglia & Lukasicwicz
2020 Tarokegn et al. 2021 Percira et al. 2018 2021).
There are two key differences between FUN and GO. First, FUN contains hierarchical structures up to a depth of six (we count root node(s) as depth zero), with datasets typically containing 500 nodes, except for Eisen (FUN), which uses 462. GO contains over 4,000 nodes, with Eisen (GO) using 3,574 nodes. Nodes for GO are spread across 14 hierarchical levels. Furthermore, while FUN is tree-like, GO is a DAG.
We also make use of a subset of BenthicNet (Lowe et al. 2025), an image dataset cataloguing benthic habitats. The images we use are of Echinodermata, following the echinoderm branch of the Collaborative and Automated Tools for Analysis of Marine Imagery (CATAMI) biota hierarchical tree (Althaus et al. 2015 a classification scheme developed for the visual recognition of underwater biota and seafloor characteristics. The hereby dubbed "BenthicNet-E" contains 13 nodes, up to a depth of two, making it a comparatively
3 An introduction to GO is available httpp:://geneontoooogy/
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simpler structure than FUN GO. The Benthic.eetE dataset contains total of 5,077 training data points and 1,650 test data points, inherited from the original full Benthic.et partitions, which considered geospatial relations between observations (Lowe et al. 2025). The size and focus of BenthicNet--B is typical for a small locally sourced dataset in the occan sciences (Brown et al., 2012 Zhou et al. 2023). and is therefore similar in scope to popular problems the field.
5.2 Imbalance Weighting on Gene Product Data
Performances for the FUN category of datasets are presented in Table Since they show similar trends, results for the GO datasets are in Appendix C
These results suggest that the Bin. AP score, Pi, and especially recall scores benefit significantly from node-wise weighting, with recall improving by factor of five over the control, on certain datasets using dho 0.25. However, appears that in a few of these datasets, the gain in recall comes with possible trade-off in precision although the difference is often within two standard deviations (or). Additionally, in some cases, imbalance weighting may even improve precision (as seems to be the case for Derisi, Gasch-2, and SPO).
W9 = 1.00
1.0
W; =
Wo 0.50
0.8
0.8
Wa 0.25
We 0.00
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
10
15
10 Nodes (sorted by frequency)
15
Nodes (sorted by frequency)
(a) Precision
(b) Recall
Figure 2: Comparison of the Effects of Varying wo on Derisi (FUN). Plotted are node-wist precision and recall scores across the top-20 most frequent nodes in their respective datasets.
In Figure 2 note the behaviour of precision and recall the top-20 most frequent nodes in Derisi with varying wp- Firstly, observe that there appears to be trend of decreasing precision as we decrease Wp-- Gains in precision appear to be due to the detection of nodes which were previously being ignored at higher ūy values. Furthermore, we see that recall improves dramatically with almost all presented nodes, being perfectly recalled at. Wig = Nonetheless, we find that we lower th to this degree, too much precision is lost, resulting in a decrcase the overall F1 score. Empirically, we find wp 0.25 be a reasonable value boosting overall Fi. The impact of Wn is explored in greater resolution in Appendix H
This observed phenomenon is perhaps counterintuitive. It may seem surprising that smaller weights (< 1) positive instances for common nodes should improve recall and lower precision. Generally, we would expect that assigning a lower priority lo positive annotations for a node reduces the model's lendency to predict positively, except in the most certain cases, thereby decreasing recall and increasing precision. We reason that due the hicrarchical constraint, the model may learn classify these higher-level nodes indirectly through their descendant nodes. Subsequently, their recall increases at the cost of precision. The more we lower Wo the more encourage indirect node learning in this fashion.

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Table 1: HML Method Comparisons (FUN). Different strategies addressing HML imbalance are compared for the FUN datasets: no method used (Nonc), HROS-PD, and node weighting using th values of 0.25 and 0.50, Means that are significantly (> 20)) greater than all others for a dataset bolded.
Dataset (FUN)
Method
F1
Precision
Recall
Bin. AP
AP
CELLCYCLE
NONE
2.61 + 0.00
9.81 + 0.70
1.74 + 0.06
6.26 + 0.11
25.68 + 0.13
T.PROS
2.98 + 0.18
9.70
0.80
2.13
0.19
6.42 + 0.10
24.81 + 0.25
HROS-PD
2.70 - 0.25
9.57
0.90
1.88
+ 0.22
6.18 + 0.12
25.57 = 0.16
Ue = 0.25
4.85 + 0.11
9.13 + 0.36
4.59 - 0.11
10.21 + 0.08
25.45 + 0.10
Ue 0.50
3.54 +
9.34
0.36
2.68
0.07
8.20 +
25.69 +
DERISI
NONE
0.46 = 0.03
1.75 - 0.21
0.34 + 0.03
2.67 + 0.08
19.58 + 0.10
LPROS
0.50 0.02
1.96 0.16
0.02
2.66 1 0.08
19.18 1 0.10
HROS-PD
0.44 + 0.02
1.82 + 0.41
0.33 + 0.01
2.70 1 0.09
19.39 + 0.11
ūe = 0.25
1.82 0.05
+ 0.20
2.16 0.07
7.55 0.07
19.61 + 0.09
ie = 0.50
0.90 + 0.06
2.31 + 0.33
0.74 + 0.04
4.34 + 0.08
19.66 + 0.09
EISEN
NONE
4.82 + 0.25
14.03 + 0.62
3.29 + 0.20
9.36 + 0.14
30.70 = 0.07
LPROS
5.87 +
15.15
4.11
9.32 1
29.69 +
HROS-PD
4.58 + 0.25
13.81 1 0.62
3.09 1 0.27
8.43 1 0.15
30.19 + 0.07
ūp = 0.25
7.16 + 0.16
11.27 0.37
6.69 0.12
12.64 0.10
30.51 -
ūn = 0.50
5.92 + 0.21
12.79 + 0.54
4.55 + 0.15
10.91 + 0.17
30.73 + 0.07
EXPR
NONE
5.84 + 0.26
13.49 0.19
4.26 0.24
10.11 + 0.12
30.13 + 0.23
LPROS
7.16 + 0.26
14.84 + 0.73
5.40 + 0.22
9.90 + 0.17
28.45 + 0.13
HROS-PD
6.31 + 0.10
14.17 + 0.44
4.71 + 0.44
10.18 + 0.15
30.03 = 0.22
ūe = 0.25
8.50 + 0.30
11.92 + 0.35
8.10 = 0.42
12.50 - 0.12
30.30 =
ūp = 0.50
6.95 = 0.33
12.86 + 0.46
5.59 0.31
11.47 - 0.07
30.40 = 0.09
GASCH-1
NONE
4.98 0.52
12.56
1.67
3.64 0.37
8.27
28.44 +
LPROS
5.64 + 0.24
13.10 + 0.83
4.16 + 0.16
8.15 + 0.27
26.71 + 0.16
HROS-PD
5.63 0.16
13.36 0.48
0.10
8.27 0.17
28.28 1 0.13
iの = 0.25
7.42 1: 0.36
11.08 + 0.50
6.94 + 0.36
11.64 + 0.20
28.57 + 0.22
ii = 0.50
6.03 + 0.36
12.19
1.02
4.77 0.20
10.19 + 0.21
28.58 + 0.22
GASCH-2
NONE
2.61 -
8.72 0.61
1.80 + 0.08
5.47 + 0.13
25.83 -
LPROS
2.86 + 0.10
9.92 + 0.50
1.98 + 0.09
5.49 + 0.15
24.97 + 0.10
HROS-PD
2.58 +
8.55 0.22
1.79 1 0.06
5.38 1
25.54 1
To = 0.25
4.92 + 0.16
9.19 + 0.33
4.62 + 0.09
10.24 + 0.08
25.51 + 0.06
Up 0.50
3.47 + 0.12
9.21 0.59
2.63 0.11
7.66 +
25.76 + 0.06
SEQ
NONE
4.14 + 0.19
11.85 + 0.69
2.91 + 0.15
9.95 + 0.14
29.24 + 0.15
I.ROS
5.38 + 0.16
14.31 + 0.44
3.84
0.12
10.44 + 0.16
28.56 + 0.27
HROS-PD
4.78 -
13.29 + 0.36
3.43 + 0.18
10.29 + 0.11
29.40 = 0.26
Un = 0.25
6.60 + 0.12
10.57 + 0.61
6.29 - 0.20
12.13 - 0.15
28.91 = 0.20
To 0.50
5.29 - 0.11
11.83 + 0.63
4.18
0.15
11.12 +
29.17 7 = 0.16
SPO
NONE
0.61 + 0.04
3.03 - 0.17
0.43 + 0.02
3.39 + 0.11
21.54 + 0.07
LPROS
0.80 0.04
3.20
0.18
0.54
0.03
3.53 +
21.17 +
HROS-PD
0.60 + 0.04
3.09 0.19
0.42 1 0.02
3.37 1 0.10
21.38 1 0.06
ūe 0.25
1.94 0.04
0.05
0.02
7.82
0.05
21.21 1 0.09
to = 0.50
1.11 + 0.04
2.98 + 0.11
0.87 + 0.03
4.84 + 0.07
21.42
+ 0.08
In Appendix D. attempting to preserve precision, we implement a schoduler that dynamically transforms the weighted objective to unweighted over the course of training. Additionally, we explore the possibility of mixing the weighted and unweighted objectives through linear interpolation. We find that these approaches were mostly unsuccessful in retaining strong F; while preserving precision. However, in Appendix E we combine LPROS with weighted loss, and find significant improvements in preserving precision and thus inducing further boosts to the F score most gene product datasets.
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5.3 Focal Weighting Gene Product Data
We begin by observing the model performance dynamics we increase the number of models in our ensemble. For these experiments, a baseline, we use the imbalance weighted loss, with dh = 0.25 and all applications of focal weighting are used in tandem with this imbalance weighting, Additionally, predictions for ensembles are made by thresholding the mean of the outputs.
For F1, GMU and bBMA appear to perform well at augmenting recall (although all uncertainty candidate measures appear to outperform the baseline). Consequently, the higher recall and relatively unchanged precision boost F1, as can be seen in Figure 3a As one might expect, observe that the focal loss candidates perform better as the number of heads increases, suggesting that the ensemble becomes more reliable representation of the model distribution as the size grows. This observation is in contrast to the bascline without focal weighting, which remains relatively independent of ensemble size.
7.50
7.75
7.50
7.25
7.00
7.00
6.75
6.75
6.50
6.50
bBMA
6.25
GMU
6.25
Epistemic J5
6.00
Epistemic
6.00
Baseline
5.75
5
10
25
10
20
2'
Ensemble Size
Ensemble Size
(a) F
(b) Recall
Figure 3: Focal Weighting with Increasing Ensemble Size on Cellcycle (FUN). For both displayed measures, the bold central line indicates the mean of the uncertainty term used for focal weighting, while the blurred outline indicates a range of one a.
It is nonetheless surprising that epistemic uncertainty underperformed. This may be because, with sufficient training, aleatoric uncertainty typically dominates total uncertainty (Wimmer et al. 2023) leaving the smaller epistemic component with limited impact. Improved model calibration (Wimmer et al. 2023 Pavlovic 2025) could also yield more robust uncertainty astimates. Alternatively and in contrast to our initial hypothesis, models may benefit from attending to both epistemic and aleatoric uncertainly, especially if neural networks learn weightings more reflective of memorization than generalization.
Hereafter, implement static ensemble size of ten to evaluate different kinds of uncertainties for the full catalogue of gene product datasets. We confirm that the same trends we observe in | Figure 3 hold true for these other gene product datasets in both FUN and GO. Our results for Fi on FUN are presented in Table 2 A full set of metrics is presented in Appendix B
Notably, predictions show improvements over even the rongest performing approaches Table T
The degree
which improvements result from ensembling is represented via the bascline, which uses only imbalance weighting. There is strong evidence that both bBMA and GMU are practical candidates for focal weighting in improving Fi performance. A deeper look at how the minimum uncertainty gate and focal & impact performance is included in Appendix H.
In addition to gene-product data, and to provide a stronger claim for the generalizability of our proposed approach, additional experiments on "Enron" a text- based dataset, and "Diatoms" an image- based dataset for unicellular algac, are presonted in [Apendix G We find that in both, the same trends we observe gene-product datasets are present. Lastly, compute resource comparisons for the ensemble and a Monte Carlo dropout implementation of our focal weighting are available in Appendix F
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Table 2: Focal Weighting Fi Score Comparisons (FUN). Candidates for uncertainty in focal weighting are compared on the FUN datasets: only imbalance weighting (Bascline), bBMA, GMU, and Epistemic Uncertainty evaluated using JS and KL. Means significantly (> 20)) greater than baseline are bolded.
CELLCYCLE
GASCH-1
GASCH-2
DERISI
EISEN
EXPR
SEQ
SPO
Method
BASELINE
6,51 +
2.27 +
9.31 +
10.27 +
9.80 +
6.47 1
8.84 +
2,48 +
0.14
0.04
0.11
0.24
0.06
0.19
0.07
0.03
BBMA
7.39 +
2.54 +
9.79 +
10.53 +
10.24 +
7.23 +
8.67 +
2.91 +
0.16
0.03
0.23
0.35
0.30
0.08
0.12
0.06
GMU
7.31 +
2.54 +
9.78 +
10.53 +
10.35 +
7.20
8.65 +
3.03 +
0.20
0.03
0.22
0.30
0.35
0.07
0.13
0.02
EPISTEMIC JS
6.66 +
2.29 +
9.52
10.34 +
9.81
6.52 +
8.75 +
2.50
0.17
0.03
0.13
0.24
0.06
0.18
0:20
0.03
EPISTEMIC KL
6.81 +
2.28 +
9.39
10.58 +
9.82
6.35 +
8.62 +
2.48
0.16
0.02
0.12
0.28
0.07
0.11
0.24
0.04
5.4 Echinoderm Vision Modelling
For vision models, we experiment with a representative convolutional neural network ResNeet50 (He et al, 2016). We suspect that CNNs, specialized for visual and spatial data, are less affected by imbalance, at least for simpler lasks, where (ask-appropriale encoder is available, or there is abundant data capturing a phenomenon available for training. In other words, settings in which the classification task is easier for the model. Since the approach we introduce is intended for domains where rare node detection severe challenge, follows that the advantages provided would diminish were rare nodes not a serious problem.
No Weighting
60
bBMA Imb. Only
50
Epistemic
Epistemic KL
40
30
20
10
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
100
Training Factor
Training Factor
(a) F
(b) Difference in
Figure 4: Evaluation of F1 over Training Completion Echinoderms. The training factor acts
parameter shilting from 0.0 (randomly initialized encoder) to 1.0 (fully trained ImageNet encoder). In Figure 4a. the weighting methods and an unweighted bascline are compared to cach other. In Figure 4bj the difference between GMU and the unweighted baseline shown, illustrating the dynamical advantage of the weighting method as the encoder becomes better trained.
Figure 4a shows how F, for echinoderm classification changes as we linearly interpolate between untrained and pre-trained encoders using a 'training factor." " As training factor increases and noise diminishes, so too do the benefits of imbalance and focal weighting. As with gene product datasots, bBMA and GMU focal-basod methods combined with imbalance weighting yield the largest gains when the encoder is noisy. Anppeeddix provide deeper look at the individual node performance for the dataset at the extremes with untrained
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and fully-trained encoder. We find that even in the case where the encoder is fully trained, the effects of our method are still present in the rarer nodes. However, the improvements are less dramatic, and these positive effects are approximately cancelled out by small degradations elsewhere in the hierarchy when averaged.
Another way to challenge the model by limiting the available data for training. We discuss this restricted data experiment in Appendix J. To summarize this experiment, training data restricted range of 1% to 30% of the total available. We find that the relative Pi performances show significant advantages early with fewer training examples, and it diminishes to around zero when more data becomes available in support of our hypothesis.
6 Conclusion
Our goal was to enable consistent detection of rare nodes deeper in a hierarchy, which are often ignored during model inference due to naturally arising sources of imbalance in datasets - a persistent problem HML modelling. We attempted to achieve this objective through the implementation of node-wise weighting. We observe significant benefits to the recall of rare nodes in gene product datasets, with increases of up to five times that of existing methods, with models demonstrating the capability of predicting hierarchical nodes which were previously ignored. We also find that focal weighting with a sufficient ensemble size tends to improve recall, especially when focal loss incorporates the bBMA or the GMU as the uncertainty term. In general, the benefits of this approach appear most pronounced for challenging HML tasks.
7 Acknowledgements
We thank the Digital Research Alliance of Canada (DRAC) for access to computational resources that supported this research as part of the Resources for Research Groups (RRG) program. Additionally, this research was supported with funding provided by the Occan Frontier Institute (OFT) as part of the Benthic Ecosystem Mapping and Engagement (BEcoME) project, through an award from the Canada First Research Excellence Fund.
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A Hyperparameters
A.1 Gene Product Modelling
Our hyperparameters for all methods applied to the gene product datasets are identical to those retricved from Giunchiglia Lukasiewicz (2020), to ensure lair comparisons belween the approaches. For all our experiments on gene product datasets, we use batch size of four and the number of layers equal three. In other words, have one input layer mapping from input size to hidden size, one hidden layer mapping from hidden size to the same hidden size, and finally one output layer mapping from hidden size to output size. Additionally, the layers use dropout of 0.7, and ReL.U (Agarap 2018 as non-linear activation.
For focal weighting experiments, we use a Up = 0.25 (matching our applied imbalance minimum gate wo); and a set == - an empirically derived value in preliminary testing.
Table 3: Hyperparameters for experiments ran on FUN and GO datasets. Input, Output, and Hidden refer to dimensional size.
Output (FUN)
Output (GO)
Hidden (FUN)
Hidden (GO)
LR (FUN)
LR (GO)
Epochs (FUN/GO)
Dataset
Input
Cellcycle
77
499
4122
500
1000
le-4
1e-4
106 / 62
Derisi
499
4116
500
500
le-4
1e-4
67
Eisen
79
461
3570
500
500
le-4
le-4
110
123
Expr
499
4128
1250
4000
1e-4
1e-4
20
Gasch1
173
499
4122
1000
500
le
le
42 122
Gasch2
52
499
4128
500
500
le-4
le-4
123 177
Seq
529
499
4130
2000
9000
le-4
le-4
13 45
Spo
86
499
4116
250
500
le-4
le-4
115
103
A.2 Echinoderm Modelling
The most drastic difference for models echinoderm data. is the use of frozen shared vision encoder. The employed batch size was 128. Given the common encoder, we opt for multi-layer perceptron classifier component of the same design, consisting of three layers for our ensembles. Dimensional mapping occurs from the embedding dimension of the vision architectures used to the hidden dimension (equal to the embedding dimension), and then to a dimensional size of 13, reflecting the number of nodes the echinoderm hicrarchy. Additionally, we use a learning rate of x 10-3 and a weight decay of x 10-1, training for epochs.
For our training factor analysis, we apply À and randomly initialized one and an ImageNet pre-trained onc. As gradually increase the training factor, we run trials using each of the compared methods in accordance with the described settings.
mixing between the weights of two encoders: a
B Focal Weighted FUN Results
In Table 4 we present the full results for our experiments with focal weighting on the FUN datasets. We see that while gains recall and Fj are almost always present for bBMA and "GMU" basod uncertainty terms, there are no statistically significant trends for any of the other measures. Notably, we see that even in where Fi was not significant, as in "Expr" and "Seq" datasets, the means were still greater. Based on these observations, we believe that including focal term is strategy that generates benefits but produces little to no observable downside when appropriate parameters are selected.
C Experiments on GO Hierarchy
In Table 5 and Table we present our results for the GO datascts. The overall trend performance matches those presented for the FUN hierarchy. However, we note the significant drop in HROS-PD performance. This decrease may be expected as the method not designed for DAG hierarchies (Pereira al. 2021).
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Published in Transactions on Machine Learning Research (02/2026)
Table 4: Focal Weighting Comparisons (FUN). Different uncertainties for implementing focal weighting are compared for the FUN datasets: only imbalance weighting (Baseline), bBMA, GMU, and Epistemic Uncertainty evaluated using JS and KL. Means which are significantly (> 20)) greater than the baseline are bolded.
Dataset (FUN)
Method
F
Precision
Recall
Bin.
AP
AP
CELLCYCLE
BASELINE
6,51 + 0.11
9.83 = 0.31
6,56 + 0.10
10.53 t 0.11
25.32 = 0.03
BBMA
7.39
0.16
9.47 = 0.30
7.65
0.15
10.46
0.07
24.79
0.06
GMU
7.31
1 0.20
9.36 = 0.36
7.57
+ 0.19
10.44
+ 0.10
24.81
1 0.07
EPISTEMIC JS
0.17
9.83 = 0.28
0.13
10.58 0.11
25.43 = 0.04
EPISTEMIC KL
6.81 + 0.16
10.35 + 0.38
6.77 + 0.15
10.62 + 0.05
25.60 = 0.02
DERISI
BASELINE
2.27 + 0.04
3.35 = 0.28
2.61 0.02
7.66 1 1.u.
19.19 + 0.05
BBMA
2.54 +
3.53 0.04
2.87 + 0.01
7.70 0.03
19.19 0.05
GMU
2.54 + 0.03
3.52 + 0.07
2.88 + 0.02
7.70 + 0.03
19.20 + 0.05
EPISTEMIC JS
2.29 0.03
3.51 = 0.21
2.63 0.02
7.68 0.04
19.20 0.05
EPISTEMIC KL
2.28 = 0.02
3.52 = 0.18
2.61 + 0.02
7.70 + 0.03
19.19 = 0.07
EISEN
BASELINE
9.31 - 0.11
12.87 - 0.26
8.85 0.10
12.57
0.10
30.22 0.07
BBMA
9.79 + 0.23
12.42 - 0.36
9.62 - 0.18
12.11 + 0.13
29.60 = 0.07
GMU
9.78 1 0.22
12.50 + 0.33
9.59 + 0.17
12.16
0.13
29.65 + 0.07
EPISTEMIC JS
9.52
13.32 +
8.98
12.59 + 0.08
30.34
EPISTEMIC KL
9.39 + 0.12
13.18 + 0.34
8.89 + 0.10
12.58
0.06
30.54 = 0.06
EXPR
BASELINE
10.27
0.21
11.89 - 0.17
0.30
12.21 0.09
29. 29.68 0.07
BBMA
10.53 = 0.35
11.36 - 0.21
11.53 + 0.47
11.91 + 0.13
29.02 = 0.11
GMU
10.53
0.30
11.31 1 0.23
11.54 1 0.39
11.89 0.08
29.03 0.11
EPISTEMIC JS
10.34 1 0.24
11.82 1 0.23
10.79 1 0.29
12.25 1 0.13
29.76 1 0.08
EPISTEMIC KL
10.58 - 0.28
11.96 + 0.28
11.09 + 0.33
12.26 0.14
29.89 0.12
GASCH-1
BASELINE
9.80 0.06
12.73 +
9.67
11.41 0.05
27.94
BBMA
10.24 + 0.30
12.08 + 0.51
10.71 + 0.18
10.92 + 0.10
27.11 + 0.12
GMU
10.35 + 0.35
12.23 +
10.79 0.26
10.94
27.12 0.12
EPISTENIC JS
9.81 + 0.06
12.58 + 0.21
9.72 + 0.04
11.35 + 0.03
27.96 = 0.11
EPISTEMIC KL
0.07
12.60 + 0.09
9.70 0.04
11.34 0.02
28.02 0.10
GASCH-2
BASELINE
6.47
0.19
9.70 0.46
6.42 0.16
10.56 0.06
25.54 0.02
BBMA
7.23 + 0.08
9.60 = 0.27
7.43 - 0.11
10.46 0.05
25.30 0.04
GMU
7.20 + 0.07
9.59 = 0.17
7.37 - 0.13
10.45 + 0.06
25.32 - 0.03
EPISTENIC JS
6.52 + 0.18
9.78 = 0.39
6.46 0.16
10.60 1 0.04
25.62 = 0.02
EPISTEMIC KL
6.35
9.71 0.45
6.32
10.61 0.09
25.76 =
SEQ
BASELINE
8.84 + 0.07
13.11 + 0.28
8.31 + 0.07
12.41 + 0.11
29.46 = 0.10
BBMA
8.67 0.12
11.70 - 0.21
8.56 0.14
12.02 0.09
29.23 0.08
GMU
8.65 1 0.13
11.61 1 0.36
8.54 1. 0.12
12.03 1 0.13
29.25 1 0.10
EPISTEMIC JS
0.20
12.69 1 0.41
0.17
12.39 0.10
29.59 0.09
EPISTEMIC KL
8.62 + 0.24
12.22 + 0.49
8.34 + 0.22
12.33 + 0.12
29.78
SPO
BASELINE
2.48 + 0.03
3.87 = 0.31
2.79
0.02
8.21 1 0.06
21.18 + 0.02
RBMA
2.91 +
3.78 0.20
3.20 +
8.19 0.04
21.16
GMU
3.03 + 0.02
4.08 + 0.06
3.27 + 0.03
8.22 + 0.03
21.19 + 0.02
EPISTEMIC JS
2.50
0.03
3.86 = 0.19
0.03
8.21
0.06
21.24 0.03
EPISTEMIC KL
2.48 + 0.01
3.51 = 0.20
2.77 + 0.04
8.20 + 0.06
21.35 = 0.01
Combining Imbalance Weighted Learning Objectives
Given our obscrvations, we are motivated to ask if it is possible to mitigate the decrease in precision by sctting wn to a scheduler. We hypothesized that, as a model learns lo recall certain nodes given the weighted learning objective, we switch to an unweighted learning objective later on in training, once it has already learned recall certain nodes, precision decline may be mitigated. In testing, we explored both an epoch-basod schoduler where we progressively approach an unweighted learning objective in the later epochs, and a batch-based scheduler where approach the unweighted objective every epoch. We find that batch-based
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Published in Transactions on Machine Learning Research (02/2026)
Table 5: HML Method Comparisons (GO). Different strategies in addressing HML imbalance are compared for the FUN datasets: no method used (Nonc), HROS-PD, and node weighting using th values of 0.25 and 0.50, Means which are significantly (> 20r) greater than all others for a dataset and measure are bolded.
Dataset (GO)
Method
Fi
Precision
Recall
Bin.
AP
AP
CELLCYCLE
NONE
1.16 + 0.07
3.23 + 0.19
0.86 + 0.05
16.31 0.16
41.34 + 0.10
LPROS
1.38 + 0.05
4.05
0.13
1.01 + 0.04
16.45 0.41
40.70
+ 0.14
HROS-PD
0.59 + 0.06
2.26
1 0.31
0.43
+ 0.04
11.37
0.60
40.29
1 0.11
Wp 0.25
1.94
0.07
3.22
1 0.26
1.86
0.05
19.84 + 0.09
40.93 1 0.08
0.50
1.47 + 0.04
3.29 + 0.14
1.23 + 0.04
19.49
0.14
41.24 + 0.12
DERISI
NONE
0.34 + 0.01
0.69 + 0.12
0.30 + 0.01
12.88 = 0.36
37.01 + 0.06
LPROS
0.33 +
0.63 +
0.28 +
12.77 0.78
37.02 +
HROS-PD
0.19 + 0.02
0.55 + 0.05
0.15 + 0.02
8.79 + 0.39
36.38 + 0.04
Wo
0.77 0.05
0.97 = 0.22
0.95 0.01
17.38 = 0.08
36.86
Up = 0.50
0.53 + 0.02
0.78 + 0.13
0.57 + 0.02
17.22 0.08
36.95 = 0.06
EISEN
NONE
1.90 + 0.18
4.50 + 0.32
1.45 - 0.15
19.57 = 0.61
45.34 + 0.15
LPROS
2.15 + 0.10
4.90 + 0.34
1.62 - 0.07
19.25 0.10
44.70 + 0.15
HROS-PD
1.41 + 0.09
4.17 + 0.19
1.02 + 0.07
16.19 = 0.51
44.66 + 0.16
0,25
3.17 0.07
4.78 +
3.04 +
22.47 +
44.75 + 0.14
Üp = 0.50
2.40 + 0.22
4.40 + 0.36
2.04 + 0.18
22.38 = 0.16
45.14 + 0.14
EXPR
NONE
3.80 0.17
7.41 + 0.37
2.98 + 0.20
16.93 0.25
38.13 0.25
LPROS
3.75 + 0.05
7.31 + 0.21
2.93 + 0.07
16.48 0.25
37.47 + 0.30
HROS-PD
2.35 1 0.14
5.94 1 0.63
1.69 1 0.11
15.15
0.70
38.89 1 0.31
Wо = 0.25
4.61 1 0.10
6.87 1 0.15
4.13 1 0.13
19.37 + 0.28
40.41 1 0.43
Úo = 0.50
4.31 + 0.09
7.42 + 0.20
3.56 + 0.12
18.11 = 0.23
39.21 + 0.18
GASCH-1
NONE
1.52 1
3.08 +
1.19 +
17.79
43.61 +
LPROS
1.97 + 0.07
4.01 + 0.17
1.56 + 0.05
18.04 = 0.44
43.27 + 0.06
HROS-PD
0.86 +
2.38 +
0.63 +
12.96 0.51
42.48 +
Wo = 0.25
2.66 + 0.08
3.98 + 0.25
2.61 + 0.05
21.48 = 0.09
43.40 - 0.11
To 0.50
2.06 0.06
3.53 - 0.20
1.80 + 0.04
21.21 0.14
43.57
0.11
GASCH-2
NONE
1.19 + 0.02
3.52 - 0.10
0.86 = 0.02
16.43 0.49
41.56 + 0.10
LPROS
1.30 + 0.04
3.80 0.03
0.95 + 0.04
16.54 = 0.45
41.45 + 0.12
HROS-PD
0.49 + 0.03
1.57 - 0.10
0.36 + 0.02
11.10 0.57
40.34 + 0.10
Üp = 0.25
1.84 + 0.09
3.21 + 0.26
1.84 + 0.08
20.03 = 0.12
41.13 1 0.06
0.50
1.42 +
3.42 +
1.20 +
19.82
41.40 +
SEQ
NONE
3.94 + 0.25
8,96 + 0.10
2.91 + 0.19
17.77 0.38
38,60 + 0.28
LPROS
4.07 + 0.14
9.34 +
3.01 + 0.10
16.74 0.59
37.30
HROS-PD
2.46 1: 0.21
6.84 1 0.37
1.72 1 0.17
15.17 = 0.81
39.63 1: 0.33
wo 0.25
4.46 1 0.33
7.93 1 0.66
3.65 1 0.26
19.69 1 0.27
39.90 1 0.32
0.50
4.29 + 0.21
8.63 + 0.23
3.31 + 0.19
18.95 0.37
39.22 + 0.44
SPO
NONE
0.68 1 0.10
1.85 + 0.33
0.54 1 0.07
13.65 = 0.56
38.19 1 0.05
LPROS
0.78 +
2.25 +
0.59 +
13.51
0.27
37.94 +
HROS-PD
0.31 + 0.05
0.94 + 0.37
0.25 + 0.03
9.15 + 0.32
36.98 + 0.11
Wo 0.25
1.26
0.02
2.29
+ 0.21
1.29 0.01
18.12 = 0.04
37.88 0.07
To = 0.50
1.01 + 0.02
2.49 + 0.11
0.89 + 0.02
17.95 0.20
38,09 + 0.05
schedulers perform significantly stronger. While this result isn't surprising from life-long learning multi-task learning perspective (Robins! 1995 Silver et al. 2013), it seems to suggest that the loss landscapes for an HML imbalanced weighted objective and an unweighted objective do not easily transition from one to the other and are likely conflicting.
In total, we explore four approaches combining our learning objectives: lincar, exponential, alternating, and mixed loss. Of the four, alternating and mixed loss explore an alternative hypothesis, that the order which the weighted and unweighted tasks occur does not matter. Alternating refers to switching between the
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Published in Transactions on Machine Learning Research (02/2026)
Table 6: Focal Weighting Comparisons (GO). Different uncertainties for implementing focal weighting are compared for the FUN datasets: only imbalance weighting (Baseline), bBMA, GMU, and Epistemic Uncertainty evaluated using JS and KL. Means which are significantly (> 20)) greater than the baseline are bolded.
Dataset (GO)
Method
Fi
Precision
Recall
Bin.
AP
AP
CELLCYCLE
BASELINE
3.50 + 0.01
5.26
+ 0.20
3.24 t 0.03
19.71 + 0.06
40.39 + 0.01
BBMA
3.77
0.0G
5.03
0.11
3.67
0.06
18.92
0.10
39.59 +
GMU
3.79 + 0.05
5.04
+ 0.07
3.69 + 0.04
18.89
+ 0.10
39.56 1 0.04
EPISTEMIC JS
3.51
0.03
5.25
0.07
3.26 + 0.03
19.67
0.04
40.34 1 0.04
EPISTEMIC KL
3.53 + 0.04
5.17 + 0.19
3.30 + 0.03
19.64 + 0.09
40.31 + 0.07
DERISI
BASELINE
1.28 + 0.04
1.93 1 0.12
1.37 + 0.04
17.26 0.01
36.58 + 0.02
BBMA
1.40
0.02
1.97
0.10
1.51 0.03
17.03
0.04
36.38 +
GMU
1.40 + 0.02
1.96 + 0.10
1.51 + 0.01
17.00 + 0.03
36.38 + 0.01
EPISTEMIC JS
1.27
0.02
0.08
1.37 = 0.03
17.24 0.03
36.56 + 0.02
EPISTEMIC KL
1.28 + 0.01
1.90 + 0.15
1.37 + 0.03
17.25 + 0.05
36.54 + 0.01
EISEN
BASELINE
5.16
0.11
7.20 + 0.24
4.93 - 0.08
22.37 0.06
45.05 + 0.04
BBMA
5.54 + 0.12
6.93 + 0.22
5.59 = 0.15
21.62 + 0.11
44.41 + 0.09
GMU
5.56 + 0.13
6.98 1 0.17
5.60 - 0.17
21.62 0.08
44.41 + 0.08
EPISTENIC JS
5.19 + 0.12
7.10
5.01 +
22.34 0.09
45.07 +
EPISTEMIC KL
5.18 + 0.11
7.09 + 0.17
5.00 + 0.14
22.34 0.06
45.09 + 0.07
EXPR
BASELINE
5.28
0.12
8.67
0.25
4.50 + 0.09
16.34 0.09
36.13 + 0.06
BBMA
5.20 + 0.10
8.29 + 0.14
4.54 + 0.09
16.42 + 0.12
35.78 + 0.08
GMU
5.26
0.07
8.28 0.11
4.57 + 0.09
16.51 0.12
35.84 1 0.07
EFISTEMIC JS
5.24 1: 0.08
8.37 1 0.15
4.47 + 0.05
16.51 1 0.13
35.95 1 0.01
EPISTEMIC KL
5.48 - 0.11
8.64 + 0.22
4.77 = 0.07
16.95 + 0.13
36.27 + 0.00
GASCH-1
BASELINE
4.23 +
5.62
4.32 +
21.12
43.93 +
BBMA
4.92 0.12
5.90 + 0.20
5.33 + 0.09
20.28 + 0.10
43.16 + 0.06
GMU
4.94 0.11
5.92 0.21
5.33
0.12
20.26 0.07
43.13 +
EPISTEMIC JS
4.30 + 0.06
5.63 + 0.09
4.43 + 0.07
21.09 + 0.05
43,92 + 0.03
EPISTEMIC KL
4.29
0.03
5.75 0.08
4.39 0.03
21.17 0.07
43.98 = 0.05
GASCH-2
BASELINE
3.40 = 0.04
5.24 + 0.07
3.37 = 0.04
20.23 0.06
41.73 + 0.02
BBMA
3.71 + 0.05
5.11 + 0.14
3.74 = 0.05
19.76 0.07
41.49 + 0.04
GMU
3.75 + 0.09
5.23 + 0.12
3.77 = 0.08
19.81 + 0.08
41.47 + 0.02
EPISTENIC JS
3.39 + 0.09
5.14 + 0.13
3.38 + 0.08
20.20 0.08
41.71 + 0.02
ÉPISTEMIC KL
3.35 +
5.07 + 0.14
3.31 +
20.23 0.04
41.70 +
SEQ
BASELINE
7.52 + 0.08
14.03 + 0.25
6.04 + 9.06
17.77 - 0.08
39.39 + 0.01
BBMA
7.31
0.14
13.55
0.33
5.88 + 0.11
17.30 0.10
38.95 +
GMU
7.43 4: 0.10
13.80 1: 0.33
5.98 1 0.07
17.28 1 0.13
38.91 1: 0.08
EPISTEMIC JS
7.50
0.13
14.08
0.09
6.01 1 0.12
17.83 0.18
39.19 1 0.13
EPISTEMIC KL
7.73 + 0.12
14.10 + 0.31
6.24 +
18.11 + 0.05
39.41 + 0.10
SPO
BASELINE
2.01 + 0.06
3.36 1 0.06
1.91 1 0.05
17.91 0.03
37.57 1 0.03
aBMA
2.28 +
3.47
2.21
0.05
17.58
0.05
37.49 +
GMU
2.34 + 0.05
3.54 + 0.07
2.26 + 0.04
17.62 + 0.07
37.49 + 0.02
EPISTEMIC JS
2.03
0.07
3.32
0.08
1.93 + 0.06
17.89
0.05
37.57 + 0.04
EPISTEMIC KL
2.04 + 0.08
3.41 + 0.15
1.92 + 0.06
17.96 + 0.08
37.64 + 0.02
weighted and unweighted objectives every batch, and mixed loss imposes À and 1 relationship between the two objectives.
For our linear scheduler, we evenly space out w update steps to the number of training steps (Nsteps) in 1-4;
cach epoch. Our exponential schoduler divides exponential steps as Aw; = (Natep--1>+ Exponential updates are then performed as 0 W + AwØ, where we introduce the second subscript index in an epoch, while the exponential term. For our experiments, we = 3. Note that this k is unique to the scheduler and should not be confused with the & applied in focal weighting.
describe the batch
20

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Published in Transactions on Machine Learning Research (02/2026)
Nana
Hiedd 19:25
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CELLOICE (60)
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(a) Schedulers
(b) A-Mixed Loss
Figure 5: Combining Weighted and Unweighted Objectives. a Scheduler effect on Fi score across all FUN and GO datasets, and b mixed loss objective, with varying À effect.
Overall, despite the variety of methods to combine learning objectives, none surpassed results from working solely with the weighted loss. our results are presented in Figure 5
E Combining Imbalance Weighting with LPROS
Table 7: Combined LPROS and Imbalance Weighting Fi Performance. Results which exceed 2 o in comparison to the previously best (Prev. Best) performing method for their corresponding dataset are bolded. Previous best values are attained from Table and Table
LPROS Imb. Weighting
Prev. Best
Dataset
FUN
GO
FUN
GO
CELLCYCLE
5.22 +: 0.16
2.33 +: 0.18
4.85 0.11
1.94 + 0.07
DERISI
2.01 + 0.08
0.94 + 0.05
1.82 = 0.05
0.77
- 0.05
EISEN
8.28 + 0.29
3.52 + 0.12
7.16 = 0.16
3.17
- 0.07
EXPR
9.29 1
4.40 + 0.11
8.50 1 0.30
4.61 +. 0.10
GASCHI
8.05 1 0.16
3.09 1 0.04
7.42 1 0.36
2.66 1 0.08
GASCH2
5.39 +
2.09 +
4.92 0.16
1.84 +
SEQ
7.57
+ 0.35
4.60
+ 0.14
6.60 + 0.12
4.46 + 0.33
SPO
2.24 + 0.03
1.35
0.08
1.94
0.04
1.26 +
Rather than attempting to merge losses to enhance precision in imbalance weighted learning as in Appendix D could seek to integrate resampling methods instead. Tn Table 1 and (Table 5) we observe that LPROS often attains the highest precision in comparison to other approaches. Furthermore, LPROS may be applied in conjunction with DAG-like hierarchies, as in the case of our GO datasets, in contrast to HROS-PD. We are therefore motivated ask if this performance could be combined constructively with the effects of imbalance weighting.
Firstly, examining the individual node performances across datasets revealed that LPROS impacts the nodes in multi-faceted manner. While some nodes traded recall for improved precision, others saw precision gains. Additionally, the LPROS-trained model began predicting previously unpredicted nodes, but also ceased predictions for some previously predicted nodes. These results suggest that LPROS behaves differently from imbalance weighting, and their combination may derive synergistic benefits. For the purposes of this work, and given finite computational budgets, we calculate node weights after resampling. We reason that this ordering safer option provide beneficial results, given the unknown effects of their combination. Our results presented in Table
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As observed, the combined approach exceeds the previous best method (imbalance weighting with uh 0.25) across almost all gene product datasets. Although we had expected a jump in Fi score due to increased precision, which was indeed observed, surprisingly, the recall too was boosted as a result of this combination. However, we caution that the combined method did not perform strongly on our echinoderm dataset. is difficult to ascertain why this unexpected difference performance occurred, as there may be myriad of issues pertaining computer vision, such as hyperparameter specifications for differing architectures, or suggeentaiion-relateed influences, and so on. Further investigation would be required.
F
Dropout and Ensemble Computational Performance
To examine the viability of computationally faster alternatives to full ensembles classifier ensembles, test dropout-based approach for our focal weighting scheme, using GMU. We present findings in Table
Overall, switching from ensemble to dropout results in a reduction in training time of 68. 1 reduction in memory usage of 66.4 + 13.2%, and reduction in Fi score of 6.06 + 5.48%. Interestingly, we observe an increase F1 performance for the SEQ dataset. Generally, however, switching to F1 appears to drop the performance to slightly higher than the results from (Table 4 for the imbalance-only weighting.
Dropout was implemented by passing the data through the model a number of times equal to the nunber of models present in the ensemble during training. Our training hyperparameters are unchanged from Appendix A] No dropout is used during testing and inference, including for the reported results, dropout was used purely as means to mimic the hypothetical distribution of plausible models to capture uncertainty during training.
Table Comparisons of Ensemble and Dropout on FUN Datasots. Dropout performance is presented in the top row for each dataset, while ensemble performance is presented in the bottom row.
Dataset (FUN) Inference (s/epoch)
it/s
Mem. Usage (MB)
Fi
CELLCYCLE
1.99 + 0.07
434.0 + 14.4
47.2
6.65
5.55 = 0.06
155.0 + 1.7
121.4
7.46
DERISI
L.97 =
432.2 15.9
46.4
2.23
5.50 + 0.07
154.5 + 2.0
119.6
2.47
EISEN
1,20 0.06
471.3 20.4
38.6
9.35
3.54 = 0.04
159.6 +: 1.6
110.3
9.90
EXPR
2.07 = 0.10
418.8 = 19.2
101.9
10.03
7.91 + 0.08
109.3 1.07
503.7
10.58
GASCH-1
2.01 + 0.09
430.1 + 16.7
68.5
10.02
6.61 0.06
130.5 + 1.2
300.9
10.20
GASCH-2
1.95 + 0.07
442.9 + 14.5
46.2
6.57
5.52 = 0.09
156.4 + 2.6
118.7
7.21
SEQ
2.37 +
375.3 13.8
152.2
9.19
11.13 + 0.10
80.0 + 0.7
1015.9
8.69
SPO
L.94 0.07
438.5 16.1
42.2
2.53
5.32 + 0.05
159.6 + 1.6
71.0
2.88
These tests were conducted on a workstation with an 19-13900KF CPU, Nvidia RTX 4090 GPU, and 32 GB of RAM.
G Additional Datasets
We expand upon the data modes explored using FUN and GO gene product data. To this end, we apply our experiments additional datascts: "Enron" Klimt Yang (004) and "Diatom" (Dimitrovski al., 2011h. Enron is language dataset, consisting of emails, each of input size 1000, with 56 nodes, while Diatom
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encompasses unicellular micro-algae processed image data, each of imput size 371 with 398 nodes (Wehrmann) et al. 2018).
Our results are provided in Table 9 We observe that the benefits of imbalance and focal loss appear to definitive in Enron, while the benefits appear more muted Diatom, with imbalance weighting alone performing slightly worse than the no weighting baseline, in terms of mean performance alone.
Table 9: Focal Weighting Comparisons (Others). Different uncertainties for implementing focal weighting are compared for the additional datasets: "No Weighting" (no imbalance or focal weighting applied), "Imb. Only" (imbalance weighting appliod only), bBMA, GMU, and Epistemic Uncertainty were evaluated using JS and KT. Means which significantly (> 2x) greater than the "No Weighting" and "Imb. Only" baselines are bolded.
Dataset (FUN)
Method
Fi
Precision
Recall
Bin.
AP
AP
ENRON
No WEIGHTING
12.65 + 0.11
18.23 = 0.91
11.30 + 0.09
47.80 + 0.17
75.77
+ 0.05
IMB. ONLY
14.64 1 0.09
18.53 + 1.24
14.37 + 0.04
50.60
1 0.13
75.86
1 0.04
BBMA
15.39 1 0.06
+ 20.07
14.87
0.07
+ 50.69
75.90
1
GMU
15.40 + 0.08
20.21 = 0.21
14.85 + 0.05
50.71 + 0.23
75.88
+ 0.06
EPISTEMIC JS
14.68 0.11
18.78
1.61
14.41 +
50.61 + 0.18
75.88 +
EPISTESIC KL
14.84 + 0.13
18.92 = 1.12
14.56 + 0.09
50.82 + 0.24
75.88 1 0.05
DIATOM
No WRIGHTING
57.47 + 0.36
64.82
0.32
55.12 + 0.40
57.53 + 0.26
79.43 + 0.04
İMB. ONLY
57.17 + 0.39
63.66 = 0.49
55.39 +
56.69 + 0.28
79.01 +
BBMA
57.55 + 0.26
63.99 - 0.31
55.83 - 0.23
57.39 + 0.31
79.24 + 0.02
GMU
57.65 + 0.21
64.05 = 0.30
55.9
0.15
57.34 + 0.22
79.26
+ 0.02
EPISTEMIC JS
57.12 1 0.16
63.54 1 0.20
55.38 1 0.20
56.89 1 0.20
79.09
1 0.02
EPISTEMIC KL
57.12 1 0.16
63.35 +
55.57 +
56.59 1
1 79.05
H Exploring Robustness of wp up and focal k
When designing the information gates, wh and (not to be confused with its tensor form Uo), we aimed to introduce parameters which did not require meticulous fine-tuning for cach dataset, as such a requirement would diminish its value. For the main experiments, a value of 0.25 was used for both gates. To investigate the effect of these gates at greater resolution, we conduct an experiment on the Expr (FUN) dataset, testing variety of values ranging from 0 to 1.5. Additionally, we test the focal exponent k from a range of 0 to 3.5.
As can be seen in Figure 6a observe that as wp increases, the precision increases logarithmically, while recall decays exponentially, both with hetcroscedassicitty This behaviour is likely why we are able to significantly increase recall with relatively small costs to precision. We also find that the optimal F, in this case is in the values lower than wi = 0.2, which is smaller than our general setting in this work. Nonetheless, this is a parameter that should be chosen for the particular problem of interest.. precision is a factor that cannot be compromised, higher values of around 0.5 to 0.8 appear reasonable, and may still deliver strong recall demonstrate in earlier results. However, if detecting rare cases is especially important, smaller values that more generally improve Fi may be desirable. In contrast, the uo and k have dampened effect. We note that uh decreases recall for values larger than 0.1 to 0.2, while gradually incrcasing precision. Additionally, a larger k lends to decrease precision and increase recall. The former likely acts similarly to Wo, in that it is a similar minimum gating term, and perhaps because the latter emphasizes extremes, larger values benefit. recall.
Effects on BenthicNet-E Nodes
In this section, we examine the effects of the combined weighted loss more closely on BenthicNet-E. We present findings in Figure 7
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20.0
17.5
15.0
12.5
10.0
7.5
5.0
0.
0.8
1.0 1.2
0.5
1.0
155
3.0
(a) t0g
(b)
(c) k
Figure 6: Exploring Weighted and Focal Hyperparameters" Effect on Performance, Plotted is representative example of the effect of wp, Uo and l on model Fi, precision, and recall performance using the Expr (FUN) dataset. The results for uo, and & were attained with w set to 0.25.
Echinoderms 1,-100%
Feather 77999377%
Ophiuroids f 53.38%
Sea Cucumbers 5,.7%35%
Sea Stars
Seai Urchins 168.4979%
322.2.19
151.65
60 60.95/63..8 IBS
42, 60166 20118..25.
(56.5
84.76 80.55
54.94 (4,. 89
48.5 188.84149.88 49.69
72.10/88.02
77.44
64..8.0
Unstaliked Crinoids
Basket Stars
Brittle/ Snake Stors
Benthic 1.14478%
Pelagic Swimming fog -0.06%
Imreularr Urchins
Regular Urchins f 73.41%
6-1.89%
f 10.38%
714,6666%
[52 24
81.61 84.38
88.49/86.79
49.14/48.41
90.19/51
86.31
Figure 7: Node-level Examination for BenthicNet-E Performance. Displayed is the BenthicNet-Ei hicrarchy. The Fj scores attained are shown below each node. The top row in the score boxes refers to the untrained encoder extreme, while the lower row shows the fully trained case. The left of the score boxes shows the unweighted performance, while the right shows the performance for a combined imbalance and focal weighted objective.
Despite its apparently limited impact in the case of a fully trained encoder, we observe the more subtle effects present. Notably, the weighted approach appears to increase performance for deeper nodes, with a slight cost to nodes higher the hierarchy - as we might expect. these deeper nodes tend to have greater weightings, due to imbalance and their difficulty learn.
In the untrained case, the improvement is drastic, we observe not only performance gains in the deeper nodes, but also for the higher-level nodes, with multiple previously undetected nodes now becoming detectable.
In general, we posit that the method does not fail in these cases for trained or untrained encoders. Rather, we interpret this observation as evidence that it remains active in its intended purpose of improving detection and performance on rare nodes. The difference between the two cases is that, the model is learned to a degree that it largely already recognizes the rare nodes present in dataset, then there is little more gain on these rare nodes. Therefore, there may exist disruptions on the common nodes as we reshuffle the weightings to prioritize learning the rare nodes.
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Epoch
2.0
Epoch 2
Epoch
1.5
1.0
0.5
0.0
2
-0.5
0
0.05
0.10
0.15
0.20
0.25
0.30
0.05
0.10
0.15
0.20
0.25
0.30
Fraction of Training Data Used
Fraction of Training Data Used
(a) ResNet-18
(b) ResNet-50
Figure 8: Weighted vs. Unweighted Fi Advantage by Training Fraction. The y-axis advantage factor is proportional to the percent increase in F1 due to weighting: 2.0 means 200% higher, 1.0 is 100% higher, 0.0 is equal. Trendlines are displayed for training on available data for 1, 2, and 5 epochs.
J Data Ablation Study for BenthicNet-E
An alternative way of controlling the difficulty a classification task by limiting the amount available data for model during training. By reducing the training data, we expect our approach in combining imbalance and uncertainty weightings to greatly benefit the model in its downstream task when available data and training are low. As we increase available data, expect the advantage from our methods to diminish as available data saturates the model to the phenomenon and rare node detection becomes less of challenge.
In this ablation study, our training parameters are largely the same as our main experiments. However, batch size has been altered to min(d. (d, 128), where d is the dataset length. Additionally, the encoder and classifiers are prepared from scratch with weights trainable. We compare the advantage in F1 score between the full set of weightings applied and the unweighted baseline. The uncertainty method applied is GMU. Advantage is calculated as Adv. F"-F" where FY the F1 score with weighting, and F1 is the F1 score without. FT
weighting. Figure 8 displays our results.
Notably, our results provide additional evidence for the hypothesis regarding where our method provides the greatest advantages. It is also worth noting that the larger ResNet-50 backbone develops greater instability for these low data domains, in comparison to the ResNet-18 architecture. This effect may be the result of overfitting. If that is the case, the emphasis on rare nodes may help combat overfitting, as can be seen by the dramatic improvements in F relative to the bascline in these settings.
25


Reviews:
[{"review_id": "j6jK7qOgga", "reviewer": "Reviewer_f5e4", "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": "**Contributions**\n\nThe paper proposes a composite loss formulation that integrates node-wise imbalance weighting and uncertainty-based focal weighting to improve detection of rare nodes in hierarchical multi-label learning. The authors make two main claims: (a) the proposed loss improves detection of rare nodes across HML datasets, and (b) it also benefits vision CNNs when the encoder is not specialized for the downstream task.\n\n\n**Strengths**\n  - Novel methodological idea: Authors propose weighting rare nodes directly instead of resampling observations, which differs from prior HML imbalance methods.\n  - Core claim (improving detection of rare nodes) is well supported. \n\n**Weaknesses**\n  - _The problem is not motivated._ The paper never clearly argues why rare node detection is practically important, nor why existing approaches are inadequate.\n  - _Method and background lack rigor._ Notation requires the reader to infer missing definitions (e.g., domains, tensor shapes).\n  - _Hard to follow._ The prose often reads like a stream-of-consciousness log of what was tried rather than a structured, self-contained presentation of the contributions.\n  - _Second claim is not well supported_ (see below). \n  - _No discussion of limitations._", "claims_and_evidence_yn": "No", "claims_explanation": "The second claim—that the joint loss benefits vision CNNs when encoders are not fully adapted to the task—is not convincingly supported by the experiments. The vision evaluation uses only a single, small dataset, and the “weak encoder” condition is created by literally linearly mixing random and pretrained weights, which seems like an artificial degradation that does not correspond to any realistic training process.", "audience_yn": "No", "audience_explanation": "The paper does not convincingly motivate why rare-node detection in HML matters in practice, nor does it show that existing approaches fail in applications. Without a concrete use case or previously demonstrated practical relevance, it is unclear to me why the TMLR audience should be interested in the findings.", "requested_changes": "1. [necessary] _Motivate the problem._ The introduction only mentions that class imbalance in HML is an under-explored area. Is there a real use case where rare node detection in HML affects downstream tasks? Is there evidence that current methods are inadequate?\n2. [necessary] _Clarify notation and problem statement._\n    - The variables in Sections 2–3 lack basic definitions such as their domains (possible values) and shapes (scalar/vector/matrix, with dimensions).\n    - Define the data and explicitly state the prediction problem.\n3. [necessary] _Provide evidence (empirical/analytical or citation) for the following claims_:\n   - \"Observation-wise imbalance weighting risks over-emphasizing common components of an annotation […] therefore we conduct weighting on a node-wise basis.\" \n   - \"Regardless of formulations for negative weightings, we were unable to achieve strong performance.\"\n4. [necessary] _Expand CNN vision experiments to validate second main claim_\n    - either include realistic partially specialized encoders (e.g. fine-tuning a pretrained model with only the last block unfrozen) OR report basic sanity metrics across different training factors.\n    - add more CNN backbones (smaller and/or larger ResNet).\n    - test at least one more hierarchical vision datasets or clearly state that conclusions may not generalize beyond BenthicNet-E.\n5. [necessary] _Discuss limitations and computational complexity._ \n    - What are the limitations of the method? Does the loss increase training cost (especially the focal weighting component)?\n    - How do the limitations and complexity compare to resampling approaches?", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "wTs0x3TNtC", "reviewer": "Reviewer_i5Ky", "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 presents a novel training objective for rare-node detection in hierarchical multi-label classification (HML). It extends the hierarchy-consistent loss (C-HMCNN) by introducing two multiplicative gates:\n\n1.\tNode-wise imbalance weighting — using a learnable floor term ($\\tilde{w}_0$) to reweight rare nodes.\n2.\tUncertainty-driven focal weighting — derived from ensemble-based uncertainty (bBMA, GMU, epistemic), controlled by an exponent k.\n\nThe combined objective encourages confident predictions for uncertain rare nodes while maintaining hierarchical consistency. Experiments on gene-function (FUN/GO) and benthic imagery datasets show improved recall and F1 for rare nodes compared to hierarchy-aware baselines (HROS-PD, LPROS, etc.).\n\nStrength:\n\n1. Well-motivated rare-node focus: The problem of hierarchical imbalance is important yet underexplored, and the modular weighting design directly addresses this.\n2. Conceptual clarity: The two-gate formulation ($\\tilde{W}(Y,f)$ and $U(\\Theta(X))^k$) makes the method interpretable and easily extensible.\n3. Strong recall improvements: Particularly in the FUN dataset, the method achieves up to $5×$ recall improvement over the base hierarchy-consistent loss.\n4. Comprehensive uncertainty treatment: Evaluates multiple ensemble-based uncertainty types (bBMA, GMU, epistemic) and shows consistent recall/F1 gains with larger ensemble sizes.\n5. Reproducibility: Equations, algorithms, and ablation analyses are clearly presented; easy to implement atop existing HML models.\n\nWeakness:\n\n1. Limited generalization – Most results are on gene-product datasets; on the benthic imagery dataset, gains shrink or vanish when strong pretrained encoders are used (§5.4). This limits generality across visual hierarchies.\n2. Ensemble dependency – The uncertainty term requires ensembles of size 10, which raises computational cost during both training and inference. The paper lacks compute/performance trade-off analysis.\n3. Precision–recall trade-off – While recall improves, precision often drops in several setups. The authors do not quantify the severity or propose mitigations (e.g., dynamic reweighting schedules).\n4. Incomplete sensitivity analysis – The impact of hyperparameters ($\\tilde{w}_0, k, U_0$) and differences between ensemble types (bBMA vs. GMU vs. epistemic) are only partially explored.\n5. Comparative positioning – The discussion of why node-wise reweighting outperforms observation-wise schemes (e.g., HROS-PD) remains superficial.\n6. Scalability – No experiments on large DAGs or text/image hierarchies beyond small-scale datasets; unclear how the method behaves under noise or multi-parent nodes.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Claims about recall improvement and uncertainty-driven adaptation are supported by consistent quantitative evidence.", "audience_yn": "Yes", "audience_explanation": "The paper targets readers in hierarchical learning, uncertainty modeling, and imbalanced classification, aligning with the TMLR audience.", "requested_changes": "Please go through the Weakness section to find the detail suggestions and changes. In brief, the suggested changes are as follows:\n\n1. Compute overhead: What are the relative training/inference costs for ensemble size $10$ vs. single models? Can MC-Dropout or snapshot ensembles offer similar uncertainty signals?\n2. Failure regimes: Under what imbalance ratios or hierarchy depths does the precision degrade? Can a dynamic $\\tilde{w}_0$ scheduling alleviate this?\n3. Ablation depth: Please provide sensitivity plots for $\\tilde{w}_0$, $k$, and $U_0$ across both datasets to show robustness.\n4. Broader benchmarks: Can you validate the method on larger-scale HML benchmarks (e.g., iNaturalist, OpenImages-Hierarchy) to confirm the claimed generality?\n5. Calibration and thresholding: Have you evaluated calibration metrics (ECE, Brier) to ensure that improved recall is not simply due to lower thresholds on ensemble-averaged outputs?", "broader_impact_concerns": "Nil", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "z15zUSGsOj", "reviewer": "Reviewer_d5mR", "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 addresses the Rare Node Problem in Hierarchical Multi-Label Classification (HMLC), where models fail to achieve satisfactory Recall for deep, low-frequency categories. The core contribution is a novel weighted loss objective, L_focal, which multiplies a Node-Wise Imbalance Weight (W) by an Ensemble-based Focal Weight (U) applied to the baseline LMC loss.\n\nKey Strengths:\n\nConceptual Synergy: The principle of combining statistical rarity and model confusion (epistemic uncertainty) into a single multiplicative penalty is a novel and powerful mechanism for gradient prioritization.\n\nExceptional Empirical Gain: The reported up to five-fold increase in Recall and statistically significant F1 score gains on genomic benchmarks provide strong empirical validation that the core thesis is correct.\n\nKey Weaknesses:\n\nComputational Infeasibility: The reliance on an explicit model ensemble for U creates a massive cost and memory barrier.\n\nGeneralization Fragility: The method's failure to perform strongly on the vision dataset (BenthicNet-E) suggests a lack of robustness across data modalities.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The claims are supported by convincing empirical evidence derived from rigorous ablation studies on established benchmark datasets (e.g., Gene Ontology). The reported gains in both Recall (up to 5×) and statistically significant F1 score improvements validate that the proposed L_focal objective successfully directs model capacity toward the detection of rare nodes. Furthermore, the systematic testing against baseline methods (LMC and resampling methods like LPROS) clearly establishes the superiority of the combined weighting approach. The LMC component ensures structural coherence (the hierarchy constraint) is maintained, which is a key technical requirement.", "audience_yn": "Yes", "audience_explanation": "The findings are of high interest to the TMLR audience because they solve a major, practical, and long-standing failure mode in HMLC. HMLC is a critical component in domains such as bioinformatics (Gene Ontology classification), large-scale document organization, and taxonomy construction. The ability to achieve reliable deep-level classification directly impacts scientific discovery and knowledge organization. The paper provides a novel principle that can initiate further research into low-cost, uncertainty-aware loss functions.", "requested_changes": "1. Address Computational Infeasibility (Ensemble Cost)\n\nThe current reliance on an explicit model ensemble for computing $U$ introduces substantial computational overhead, undermining the method’s practical feasibility. The authors must:\n\nExplore and quantify the performance of at least one low-cost proxy for model uncertainty (e.g., Monte Carlo Dropout, Evidential Deep Learning) to demonstrate a pathway toward a single-model, scalable solution.\n\nInclude a transparent cost–benefit analysis (e.g., a table comparing F1 score vs. inference latency / memory overhead) to clearly quantify the computational trade-off introduced by the ensemble.\n\n2. Address Generalization Fragility (Vision Data Failure)\n\nThe method’s failure on the BenthicNet-E vision dataset requires a deeper, mechanism-focused explanation rather than surface-level reporting. Specifically:\n\nDiscuss the interaction between the highly weighted semantic loss, CNN gradient dynamics, and augmentation strategies.\n\nIdentify the failure modes responsible for the degradation in visual domains.\n\nSuggest explicit boundary conditions under which the proposed method is expected to perform reliably (e.g., tasks involving semantic or discrete hierarchies).\n\n3. Address Optimization Stability ($\\tilde{w}_0$ Sensitivity)\n\nThe hyperparameter $\\tilde{w}_0$ currently serves as a manual control over the precision–recall trade-off, which raises concerns about optimization stability. The authors must:\n\nProvide a rigorous discussion of $\\tilde{w}_0$ as a sensitivity factor and its impact on convergence.\n\nExplore methods to dynamically learn or adapt $\\tilde{w}_0$ during training, or\n\nPresent empirical evidence that the objective function remains stable across a broad, practically relevant range of $\\tilde{w}_0$ values.\n\nStrengthening Revisions (Recommended)\n1. Wider Domain Testing\n\nEvaluate the proposed method on an additional, distinct data modality (e.g., text classification hierarchy) to provide stronger evidence of generalizability beyond the current genomic datasets.\n\n2. Detailed Ablation Analysis\n\nInclude a supplementary ablation study focusing on the performance of common (frequent) nodes to confirm that the significant recall gains observed on rare nodes do not cause catastrophic underfitting or reduced predictive quality on other parts of the hierarchy.\n\n3. Reproducibility Documentation\n\nExplicitly state recommended initialization or starting ranges for key hyperparameters ($U_0$, $k$, $\\tilde{w}_0$) to lower the barrier for independent reproduction and reliability validation.\n\nSummary Justification\n\nThese revisions are critical to ensure the proposed approach is computationally feasible, theoretically robust, and empirically generalizable across domains. The current formulation demonstrates promising results but lacks practical viability and clarity on optimization stability. Addressing the above points would significantly strengthen both the methodological soundness and the real-world impact of this work.", "broader_impact_concerns": "No significant broader impact concerns are present beyond the standard risks associated with machine learning (e.g., bias propagation), which is mitigated by the objective nature of the genomic and taxonomic data used. No additional statement is required.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)