TESSAR: Geometry-Aware Active Regression via Dynamic Voronoi Tessellation
Authors: Seong Jin Cho
Gwangsu Kim
Junghyun Lee
Hee Suk Yoon
Joshua Tian Jin Tee
Chang D. Yoo
Venue: ICLR 2026 Poster (2026)
Keywords: active learning
regression
Voronoi tessellation
least disagree metric
Primary area: other topics in machine learning (i.e., none of the above)
TL;DR: An active learning algorithm for regression that leverages Voronoi tessellation to guide efficient sample selection.

Abstract: Active learning improves training efficiency by selectively querying the most informative samples for labeling. While it naturally fits classification tasks–where informative samples tend to lie near the decision boundary–its application to regression is less straightforward, as information is distributed across the entire dataset. Distance-based sampling is commonly used to promote diversity but tends to overemphasize peripheral regions while neglecting dense, informative interior regions. To address this, we propose a Voronoi-based active learning framework that leverages geometric structure for sample selection. Central to our method is the Voronoi-based Least Disagree Metric (VLDM), which estimates a sample’s proximity to Voronoi faces by measuring how often its cell assignment changes under perturbations of the labeled sites. We further incorporate a distance-based term to capture the periphery and a Voronoi-derived density score to reflect data representativity. The resulting algorithm, *TESSAR* (TESsellation-based Sampling for Active Regression), unifies interior coverage, peripheral exploration, and representativity into a single acquisition score. Experiments on various benchmarks demonstrate that TESSAR consistently achieves competitive or superior performance compared to prior state-of-the-art baselines.

Published as a conference paper at ICLR 2026
TESSAR: GEOMETRY-AWARE ACTIVE REGRESSION VIA DYNAMIC VORONOI TESSELLATION
Seong Jin Cho Korea Institute of Oriental Medicine ipengek oim. re.kr
Gwangsu Kim
Jeonbuk National University s8801 20 jenuu.uua. .r
Junghyun Lee, Hee Suk Yoon, Joshua Tian Jin Tee, Chang D. Yoo" Korea Advanced Institute of Science and Technology (jh 1ee00,,00 hskyoon, joshuateet cd @o_yyoo]@aist..ac
ABSTRACT
Active learning improves training efficiency by selectively querying the most in- formative samples for labeling. While it naturally fits classification tasks-where informative samples tend to lie near the decision boundary-its application to re- gression is less straightforward. as information distributed across the entire dataset. Distance-bass sampling is commonly used to promote diversity but tends to overemphasize peripheral regions while neglecting dense, informative interior regions. To address this, we propose Voronoi-basee active learning framework that leverages geometric structure for sample selection. Central to our method is the Voronoi-based Least Disagree Metric (VLDM), which estimates sample's s proximity to Voronoi faces by measuring how often its cell assignment changes under perturbations of the labeled sites. We further incorporate distance- bassed term to capture the periphery and a Voronoi-derived density score to reflect data representativity. The resulting algorithm, TESSAR (TESSsellation-baaeed Sampling for Active Regression), unifies interior coverage, peripheral exploration, and rep- resentativity into single acquisition score. Experiments on various benchmarks demonstrate that TESSAR consistently achieves competitive or superior perfor- mance compared to prior state-of-the-at baselines.
INTRODUCTION
Active learning aims to improve model performance while reducing labeling costs by selectively querying the most informative data points (Cohn et al.) [996). This is particularly valuable in do- mains where labeling is expensive or time-consuming. Most active learning research has focused on classification tasks, where various strategies-such
uncertainty sampling (Lewis & Gale 1994 Balcan et al.) 2007). expected eтror reduction Yoo & Kweon 2019), expected model change (Frey- tag al. [0014), query-by-comee bom-mmmmtttteee (Beluch et al.] (2018). and Bayesian active learning (Pinsler et al.] have shown success. A common theme in uncertainty based methods is to select sam- ples where model predictions are most uncertain. For classification tasks, this often leads to the prioritization of samples near the decision boundary, where uncertainty is typically highest (Kremer ct al. 2014 Ducoffe & Precioso 2018 Cho et al.) 2024).
In regression, however, this coundary-centric notion does not apply all labeled samples contribute to the model globally rather than through local decisions. Consequently, the notions of uncertainty and informativeness must be redefined. Instead of focusing on boundary proximity, informative samples in regression are those that best improve generalization across the entire input space (Wul al. 2019 Cardenas al., 2023 Hübotter al. (024)). Such samples
typically diverse and representative of the data distribution. Thus, existing methods often address this by selecting sam- ples that are far from labeled points (Wu et 2019 Ash et al. 2220). This distance-based strategy encourages broad coverage and promotes diversity, but it often oversamples the periphery, while
"Corresponding author

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Published as a conference paper at ICLR 2026
Desance based sampling
Veroncl baced samplng
Combraticn both sampling
(a)
(b)
(c)
Figure 1: Examples of selected samples by distance-basse sampling (a), Voronoi face-based sam- pling (b), and their combination (c). The combination of both methods effectively captures both the internal and external structure of the data distribution.
overlooking dense and informative interior regions (illustrated in Figure lap. While some meth- ods introduce density- awarre corrections (Wu 2019 Holzmüller al. 2023 they still offer limited control over interior exploration.
To address this limitation, we consider Voronoi tessellation, which partitions the input space into cells around each labeled point (Voronoi 1908). In the context of Gaussian Process regression, Voronoi tessellation has been used to model discontinuous or heterogeneous geospatial data (Kim) al. 2005 Luo et al. 2021 Pope al. [021]. Beyond its use in modeling, we propose that Voronoi active classification (Seung et al.) Hanneke 2014 Cho et al., 2024) in regression. The key intuition is that samples near the boundaries between adjacent cells known as Voronoi Voronoifaces--a faces- lie in interior regions where the influence multiple labeled points intersects and competes. Such samples are valuable for enhanc- ing sampling diversity in interior regions, as illustrated in Figure [b] We further provide theoretical support that samples near Voronoi faces tend to exhibit high prediction variance, indicating greater model uncertainty and, thus, higher potential informativeness.
tessel atton serves as an effective surrogate for disagreement-
1992
To efficiently identify these samples, we propose the Voronoi-based Least Disagree Metric (VLDM), which quantifies how often sample's Voronoi cell assignment changes under perturbations of the labeled site, inspired by Cho et al. (2024). To ensure full spatial coverage, we combine VLDM with a distance-based sampling strategy, as illustrated in Figure 1c Finally, to complete the triad of effective active learning in regression-infeee informativeness, diversity, and representativity (Wu et al. 2019 we incorporate a density-based weight derived from Voronoi cell geometry (Holzmüller et al, 2023 Based on these insights, we introduce TESSAR (TESsellation-aasee Sampling for Active Regression), novel active learning algorithm for regression that combines VLDM, diversity, and representativity into a unified sampling strategy.
In detail, this paper makes the following key contributions:
We introduce the use of Voronoi tessellation for active learning in regression, specifically target informative samples from interior regions of the input space. We theoretically show that points near Voronoi faces-the the boundaries between Voronoi cells- high prediction variance, making them particularly valuable for improving model performance.
To efficiently identify samples near Voronoi faces, we propose the Voronoi-based Least Disagree Metric (VLDM), geometrie uncertainty measure that quantifies how often sample's Voronoi cell assignment changes under perturbations of the labeled site.
We develop TESsellation- Sampling for Active Regression (TESSAR), a practical active learning algorithm that combines VL.MM with strategies for promoting spatial diver- sity and representativity, balancing exploration of both interior and peripheral regions.
Extensive experiments across various benchmarks demonstrate that TESSAR achieves competitive or superior performance compared prior fate-of-the-an baselines.
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2 THE VORONOI-BASED LEAST DISAGREE METRIC (VLDM) FOR INFORMATIVE INTERIOR REGION SAMPLING
As discussed in Figure key limitation of previous distance- based sampling methods is their ten- dency to undersample interior regions where the influence of neighboring labeled samples competes. To effectively probe these ffttenneglected regions, we leverage Voronoi tessellations (illustrated in 2) A Voronoi tessellation partitions the input space into distinct cells, where each cell encom- passes all points closest particular labeled sample (the site). Points situated on the boundaries between these cells, known as Voronoi faces, are equidistant from two or more sites. Querying points near these faces allows model refinement precisely where the influence of multiple labeled samples converges, enhancing sampling diversity within these interior regions.
2.1 PRELIMINARIES AND NOTATION
Let X' and Y be the feature and label spaces, re- spectively, with X' y C I R. We consider multiple regression to learn a function f V. We assume that there exists unknown ground-truth function f. X + y that gov- ems the true relationship between inputs and outputs. During active learning we maintain labeled instances S (fi,.....js..
F
Fi2
Iabaled sumplle urleboled samples
V/
V/3
X, with noisy labels y/= fāx) mk. where T is a random variable satisfying E(nxl and M 1 Øg. A useful geometric perspective for analyzing and organizing the labeled data points in S through the concept of Voronoi tessellation. In this context, each point 3t in referred as site, and these sites collec- tively induce partition of the instance space X' into distinct regions as follows:
Vorondi face
V/3
Figure 2: Illustrative Voronoi tessellation. La- beled sites (dots) define cells. Points on faces (lines) are equidistant from multiple sites.
(1) Each convex region Vv8 is the Voronoi cell of site ã; and contains all points closer to that site than to any other. Whenever two distinct cells 1/ and V48 meet, their common boundary Fjx V n Va for each * called Voronoi face. Points on or near such faces are equidistant at least two sites, so no single labeled sample dominates their local geometry.
1x= : f E X': || - Ex 12 S | ã; l12 for all * k). k = SS).
2.2 INFORMATIVENESS OF VORONOI FACES: A THEORETICAL PERSPECTIVE
Geometrically, selecting samples near Voronoi faces naturally promotes diversity by focusing on regions between labeled sites. We argue that these regions also intrinsically informative from the perspective of model uncertainty.
Formally, suppose both the trained predictor î and the ground-truth function fa are L-Lipschitz, the observation noise 7/k is zero-mean, and "good" event holds with high probability such that (f(()) f- (*x)) <, for some c((S]) > 0. This statistical error typically decays as [S|-3 for some 9 O, depending the noise distribution and function class (ssbbkovv) 2009), and can be regarded as small.
For any unlabeled point x' E X' and labeled site H E S, the triangle inequality gives
1ī(x') f=(2)) < |f(=') i(xx)) | + 1((())) - fx(x)) + (f(+)) f=('))
- 2T| - uxl12 +
where the second line uses Lipschitzzess and the "good" event. Thus,
fx(') (2L||=/ ø +e) s F(x') < f((w') || tx 2l2 e). Under the "good" event, Popoviciu's inequality (Popoviciu 1935) then implies
Var[f(x')] < (2T. $ 2ll e)²
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As does not depend on X minimizing over k S shows that the predictive variance at æ' is controlled by the squared distance to the nearest labeled site.
Since predictive variance is governed by the distance labeled sites, it is natural to sample points that maximize this distance relative to multiple sites -namlly. those near Voronoi faces. Under Lipschitzness, each Voronoi cell can be viewed range, so points near faces are precisely those where this bounded variation is shared across sites. Such points are unstable: small perturbations of the labeled sites can shift the Voronoi partition and change the site to which they correspond. This instability parallels disagreement- classification, where informative samples lie near decision boundaries because small changes in the hypothesis flip their labels (Seung et al., 1992. [Hanekee 2014; [Coo et al.) [024). While regression lacks discrete boundaries, Voronoi faces play an analogous role, with samples near them forming natural candidates for informative queries.
region where labels differ only within bounded
active
2.3 VORONOI-BASED LEAST DISAGREE METRIC (VLDM)
Selecting samples near Voronoi faces offers better coverage of the interior regions the input space, but computing the Voronoi diagram is computationally prohibitive in high-dimensional settings. Specifically, constructing the diagram for S sites in 1d requires O (S' log S + sl4/21) time (Klee 1980 which is infeasible for high dimensions. To overcome this challenge, we introduce an efficent surrogate that estimates Voronoi face proximity without computing the diagram.
Let S E N denote the number of sites, and let X' be the instance space under consideration. Define (5) == (S c X |S] =} as the collection of all possible site configurations of size S. We fix feature mapping z x E X' + z E Rd e.g., the final-layer representation from neural network.
To define Voronoi cells in feature space, first assume fixed but arbitrary ordering within each S (3). This does not affect the geometry of Voronoi partitions and is used solely to make hs well-defined. We can then define the Voronoi hypothesis space = (hs S (5)), where we associate each S { with a hypothesis over X, hs X - [S], defined as
the sites
(ar) == arg min dd(a,, ax) - 1|2 - ==ul12]
kE[S]
We refer to d)(-.)) as the feature distance.
alignment. Since the label assigned by his corresponds to the index of the nearest site, the labels themselves are arbitrary up to permutation. For two Voronoi hypotheses his and lis,, we define the optimal permutation that attains the maximal overlap between the two Voronoi diagrams Ts,s' := arg eSym(S) Px-Dx (hs(X)
commutation-invariaan
o hss where Sym(S) is the set of permutations over [S]. This is analogous to the common practice in clustering evaluation, where accuracy is measured up to label permutations (Lu & Zhou 2016).
In practice, if S' is slight perturbation of S. then Ts.s' often corresponds maintaining the same label indices due to the geometric stability of Voronoi regions under small shifts (Reem) 2011). For instance, for S = ( and small perturbations {Ei ke(s)) we would have that S [ == के + Ex kets] i.e., the site labels do not change from S to S' and vice-versa. Thus, from hereon and forth, we will simply drop the dependency TS,"".
Voronoi-based Least Disagree Metric. Inspired by disagreement-basee active classifica- tion (Hanneke) 2014, Cho et al., (2024). we define the Voronoi-based Least Disagree Metric (VLDM) to quantify how easily the Voronoi cell to which a sample belongs changes under slight perturbations of the site configuration.
For each S
(3) and æo X' the VLDM is defined as follows:
{oths) hs) & PX~Dx hss (x))
inf I(hs, 20) 8.
I While instance-dependen errors are possihle, we disregard them here for simplicity.
Precisely speaking, small change of the sites yields a small change in the corresponding Voronoi cells with respect the Hausdorff distance (Reem 201T Theorem 5.1).
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Algorithm 1 Empirical Evaluation of VLDM
Input:
a: target sample
8(); site configurations
M: number of samples for approximation
(ov)==1> N: set of variance and number of perturbation
Lg =1
D2 = minagsto (2(2r, 2),, K = hgs (2)
(for TESSAR)
for 1 to do
for = 1 + (u J to N do
Construct ((x) with Zzr ~ (zz, I.)), Vz E S(U)
if hight (a:) + hgm (2:) then
L f- min ( Par (hgt)),go)) D min dx( T), KL²) hggt (a)) (for TESSAR)
return: La (for VLDM), (D kla), 1
Ja=o (for TESSAR)
where Dx is the marginal distribution over X' and Hhs.eo (hs- H h)(2)) A his (2no)) is the set of Voronoi hypotheses in Hy that disagree with lig on 2o Again, recall that as long as S' is obtained from a small perturbation of S, there no need explicitly compute TT,
2.4 EMPIRICAL EVALUATION OF VLDMM
We employ two approximation schemes to compute Eqn. 3 as in Cho et al. (2024). First, we replace Hhs,aa with a finite collection of N hypotheses, H Each las- Hy is generated by perturbing S using multiple Gaussian noise levels. Specifically, for each variance parameter of in the predefined set {oū)ı=1, we construct perturbed sites z ((z, T) to obtain S', For
each resulting perturbed configuration S', include the corresponding hypothesis hg in H whenever h (#o) * l2s)))). The use of multiple variances enables VLDM to capture how easily the Voronoi cell to which sample belongs changes across range of perturbation magnitudes. Second, we replace p with Monte-Carlo approximation with M samples:
Par hhs)
Σ [[hs:(X)) + hs(X))) X s.d. Dx, M
1
where [I[:] is the indicator function. Finally, we define the empirical VLDM as LN.M (hs, 2o) :=
inf, E PM (hss,,hs) Under certain regularity conditions, its asymptotic consistency is guar-
anteed (Cho et al. 2024 Theorem 1), which then implies that the ordering of empirically evaluated
VLDM values is preserved in probability (Cho et al. 2024 Corollary 1); see Figure 3 in Section for an empirical demonstration of this claim.
Algorithm [ summarizes the above discussions a pseudocode for empirically evaluating the VLDM of for given ((0), Note that other than the computed empirical VLDM Le, the algorithm J these are used for VLDM-based active learning
also outputs other values { {D()) <<())
to be described in Section 3
3 TESSAR: VORONOI TESSELLATIONN-E
ACTIVE REGRESSION
Acquisition Score. To enable balanced sampling across both the interior and periphery of the input space, we combine three geometry-based criteria: VLDM-base weight, distance score, and density-aware representativity term. Each component contributes to covering different spatial regions or properties of the input space. We first define VI.DM-based weight:
e Tma
(I.p T.g)+
Ne= =
where
7a
(5)
Enyepe Tay
Lg
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Algorithm 2 Active Learning with TESSAR
Input:
Co, Initial labeled and unlabeled samples
g: query size
T:: number of acquisition steps
for t = 0 to T
Train model using Lt
Set P C and ((0) fax, (a.,, E Le}
Get 1 (D _( j of and (8(m) Jn-o using Algorithm
Qo +
for j = to do
Compute Yo. Sn using Eqn. 5 and 7
Fnew = arg max ZEP Nie
Da [0]
* Sw
2, + 2j-1 U (Fnew
for E P do
Len: (D K(a), stu) 1o=0 UPDATEVLDM( Trew, Low, (Db ( ((m))
L441 < L. U ((0;,
we E C2). U41 < U4 \ Qr
subroutine UPDATEVLDM(z, &zew, Lu, (Dt)), kbr), (0n)
((0) + (t [deek
if dx, Tzen) < D then
D dz(x, ).ew), K(O) = 18
for 1 to V do
for + (v
[)[ to vl [N/V] do
Sample [((0)
A (i II
((w) g(1)
(ā(m))
if (ax, _((n))
< D then
D d,(w, ( K [8(m)
if [(') K(²) then
Lz min Lz, PMr (hgia), s(t))
return: Lm, (D()) k!"), ((
Here, Ly denotes the 4h smallest VLDM value in the pool data and (.) max This for- mulation gives exponentially higher weight to samples with smaller VLDMM values, encouraging selection near Voronoi faces and thus improving coverage of interior regions. To complement this, we use the sample's 's shortest feature distance to the sites, referred to as 'DIST":
D min (z, 2),
(6)
#ES
which captures how far the sample is from existing sites. This encourages exploration of under- represented peripheral regions. Together, VLDM and DIST provide coverage across the full input domain and jointly contribute both informativeness and diversity. However, they may overlook the underlying data distribution. To account for sample density, we incorporate representativity score inspired by cluster-based sampling (Holzmüiller et al. 2023), referred to as 'BIN':
Se
Σ (=')
D
(7)
This score is shared across all samples belonging to the same Voronoi cell and reflects the cell's local density based on intra-cell distances. It encourages sampling in more densely populated regions, aligning the query strategy with the overall data distribution. Finally, the three criteria are combined multiplicatively to score each candidate. This unified strategy ensures that selected samples are informative, spatially diverse, and representative of the underlying distribution.
TESSAR (TESsellation-base) Sampling for Active Regression). We now introduce TESSAR (Algorithm(2 2) a Voronoi tessellation- based active regression algorithm. At each step t, the model is trained L. extract features for the pool data, where the pool is the set of all unlabeled samples,

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Road
0.03
0.54
0.07
coplaate MLDH
0.05
1200
000
000
0.44
0.2
30
32 32
12P
10
10-
10'
201
(a)
(b)
(c)
Figure 3: Empirically evaluated VLDMs by A with respect the number of perturbations, N. on Protein (a), Road (b), and Stock (c) datasets. Observe that the evaluated VLDM monotonically decreases as N increases, and the rank order is well maintained.
P S Ui- The labeled inputs serve sites, (( = {ar; (a E Lx). For each x E P, the quantities Lay (D(") K(d)) =n are computed, and {S(m) N
1n=0 is obtained via Algorithm | The query set Qo is initialized as 0. For j = 1, ,...., U Yoe and Sn are evaluated for each æ E P using
Eqn. and Eqn. 7 The algorithm then selects Tnew E P maximizing Yiu * D Sa. which is
our acquisition score, and appends neow to 2y. Afterwards, L.g, {D(T) K=(a) ((()) n==0 are updated using subroutine UPDATE VLDM() described below. Finally, the algorithm queries the labels y, for all 2; E 2q. and proceeds until t = T - 1.
Naively, one would recompute the VLDM from scratch after every selection within a batch, as each newly selected sample alters the Voronoi structure, causing the Voronoi faces and hence the VLDM values. This would require N [P] q (IC) + (q + 1)/2) distance computations. To avoid this inefficiency, TESSAR employs dynamic update strategy to compute VLDM (subroutine UPDAT- EVLDM(). It first computes distances between all pool samples and the initial labeled site once, then incrementally updates only the distances involving newly selected samples. This reduces the total number of computations to N IP|- (|C) + 4), effectively shaving off a factor of q. Neverthe- less, runtime still scales with the perturbation budget N and pool size [P], which may require further optimization in large-scale settings (see Appendix [C.I). A simpler margin-based variant- where the margin is defined as the difference between the distances from sample its nearest and second- nearest Voronoi centers-avoids this dependence on N, but its performance is noticeably weaker than VLDM-based TESSAR (see Appendix C The subroutine UPDATEVLDMG implements this dy-
namic update: given a newly selected site nnew and Lag, (DL") k(()) s(n) 1, it computes the distances from &6 nnww (and its perturbations) the pool data, compares them with existing distances, updates {D(()) k<("), /n= and then updates the corresponding Le values. Morcover, a compari- son with static VLDM variant shows that removing these dynamic updates leads to substantially degraded performance, highlighting the necessity of the dynamic strategy (see Appendix C.3).
4 EXPERIMENTS
This section presents the empirical evaluation of VLDM and TESSAR. We compare its performance against various baseline algorithms on fourteen tabular datasets. We employ a 2-layer MLP with 512 hidden units. All results represent the average performance over 20 repetitions. Detailed descriptions of datasets and experimental settings are provided in Appendix A
4.1 CONSISTENCY OF VLDM
Figure 3 shows the empirically evaluated VLDMs with respect to N of the Protein, Road, and Stock datasets. We denote æ; as the 7th sample ordered by the final evaluated VLDM. The empirically evaluated VLDMS are monotonically decreasing while maintaining rank order as N increases.
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-2.175
-3.00
-2.10
BAICE
-3325
-3275
33000
V.BMWO ST-
+0.55
MLDM-- ZIN
-3325
DE51 3030y
D57 cdicl
D51 soicly
254
532
1894
2003
4245
256
512
1024 sarpples
2011
4336
256
512
1029
2048
0095
labeled sumples
(a)
(c)
Figure 4: The performance comparison based the combinations of VLDM (%a), DIST (Da), and BIN (Sx) on Protein (a), Road (b), and Stock (c) datasets. The combination of three criteria achieves the best performance.
4.2 EFFECT OF THE COMPONENTS IN TESSAR
We conduct a comprehensive performance comparison using various combinations of the three cri- teria. Figure 4 shows the mcan log of RMSE with respect to the number of labeled samples on the Protein, Road, and Stock datasets. Individually, VLDM and DIST yield limited performance gains, each covers only subset of the input space. However, combining them leads to significant performance improvement by jointly covering both the interior (via VLDM) and the periphery (via DIST), highlighting their complementary nature. Adding BIN this combination provides an ad- ditional improvement. The inclusion of BIN enhances the sampling strategy by aligning it with the underlying data distribution, particularly in dense regions. Based these results, we adopt a unified selection strategy that iteratively selects the sample that maximizes the product of the three scores.
4.3 COMPARING TESSAR TO BASELINE ALGORITHMS
We now compare the performance of the proposed TESSAR with various baselines.
Baseline algorithms Each baseline algorithm is denoted follows: 'Rand': random sampling, 'Coreset:: core-set selection (Sener & Savarese 2018), 'ProbCov': maximizing probability cover- age (Yehuda et al. 2022). 'BALD:" Bayesian active learning by disagreement (Houlsby al.. (011),
'BatchBALD'; mutual information between a joint of multiple data points and the model parame- ters (Kirsch al. 2019). 'BADGE': batch active learning by diverse gradient embeddings AAsh al.
(2020). 'BAIT: batch active learning via information metrics (Ash et al. 2021). 'ACS-FW'; active Bayesian coresets with Frank-Wolfe optimization (Pinsler al. 2019). and LLMDD: largest cluster
maximum distance (Holzmüller et al. 2023
Performance comparison across datasets The performance profile (Dolan More 2002) and penalty matrix (Ash et al. 2020) are utilized for comprehensive comparisons across all datasets.
The details of the performance profile and penalty matrix are described in Appendix B Figure 5a
shows the performance profile for regression of all algorithms with respect to 5. TESSAR consis- tently maintains the highest (6) across all considered values. Notably, RTTSSAR (0) 41%,
significantly exceeding the values of other algorithms. including LCMD (29%). Figure 5b) further supports TESSAR's superiority. In the first row, TESSAR outperforms all the other algorithms, including LCMD (1.0). Similarly, the first column shows that most algorithms fail to outperform TESSAR, with a maximum penalty of 0.3.
Performance comparison per dataset Table I presents the mean of performance differences (RMSE relative to Random) averaged over repetitions and steps. The negative values indicate better performance than Random. We observe that TESSAR consistently performs best or is comparable to other algorithms across all datasets.
5 RELATED WORKS
In active learning for regression, a variety of sampling strategies have been developed, each bal- ancing informativeness, diversity, and representativeness in different ways. Query by committee
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By BARCHBALD
TESSAR
Randi
Coresat
Prancav
BADGE
BAIT
ACS-PW
LCHO
TESSR
1:00
4.1
10.5
13.2
10
6.6
1.0
12
Dolan-More curve
Rand
0.1
0.0
3.2
0.0
8.8
4.0
0.0
1.
4.0
C.3
Coreass
0.0
6.2
0.0
6.0
11.6
39
17
15
5.8
0.0
10
0.8
ProbGov
0.0
0.0
3.1
0.0
9.4
4.5
0.0
1.
3.7
C.4
TESSAR: AUC== 86
BALD
0.0
1.3
0.0
14
0.0
0.0
9.
OC
0.0
0.0
Rg
0.6
Coreset: AUC=0 46
Rand: AUC==0:40
BetchBALD
0.1
5.7
1.3
5.6
10.5
0.0
0.6
9:
5.2
0.1
ProbCov: AUC-0.41
6
BALD; AUC-0013
BADGE
0.1
7.8
6.2
7.7
12.0
8.5
0.0
3.9
9.6
0.3
HatchBALLD AUC=0
RATT
0.3
18
0.2
AUC=0.55
AUC-0
0.0
3.0
1.0
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4.7
0.0
02
0.0
0.1
LCMD;
8.6
0.0
2
00000
0,005
0.010
0.015
0,020
0.025
0,030
6.1
5.0
4.2
10.3
5.8
1.
2.4
58
0.3
(a)
(b)
The performance comparison across datasets. (a) The performance profile results. The AUC value is expressed as a percentage. TESSAR consistently maintains the highest performance across all considered 6 values. (b) The penalty matrix results.
Figure 5:
The mean of the repetition-wise averaged performance (RMSE) differences, relative to Random, over the entire steps. The negative value indicates higher performance than Random. (bold+underlined: best performance, bold: second-best performance)
Table I:
TESSAR
Coreset
ProhCov
BALD
BatchBAL.D
BADGE
BATT
ACS-FW
LCMD
CT slices
-0.0679
-0.5004
-0.0040
0.0227
-0.0435
-0.0395
-0.0565
0.0028
-0.0679
Diamonds
-0.0110
-00094
0.0007
-0.0019
-0.0079
-0.0091
-0.0106
-0.0033
-0.0105
Friedman
-0.0030
-00033
0.0001
0.0031
-0.0026
-0.0011
-0.0049
-0.0017
-0.0026
KEGG undir
-0.1615
-0.4355
0.0088
0.0197
-0.0960
-0.1297
-0,1214
-0.0668
-0.1598
Methane
-0.0520
-0.0346
-0.0274
0.0251
-0.0185
-0.0432
-0.0355
-0.0265
-0.0510
MLR KNN
-0.1201
-0.0192
0.0031
0.0906
-0.0580
-0.0925
-0.0872
0.0006
-0,1182
Online video
-0.1183
-0.1000
-0.0001
-0.0655
-0.0943
-0.0991
-0.0946
-0.0718
-0.1130
Protein
-0.0082
0.01
-0.0003
0.0308
0.0207
-0.0075
0.0016
0.0065
-0.0054
Query
-0.0047
0.0004
-0.0001
0.0262
0.0121
-0.0023
-0.0029
0.0023
-0.0054
Road
0.0001
0.0176
0.0000
0.1337
0.0441
-0,0004
0.0109
0.0294
0.0036
SARCOS
-0.0215
-0.0880
-0,0004
0.0139
-0.0016
-0,0133
-0.0149
-0.0093
-0.0188
SGEMM
-0.0141
-0.0004
-0.0015
0.0817
0.0114
-0.0045
-0.0038
0.0129
-0.0121
Stock
-0.0051
0.0046
-0,0003
0.0100
0.0075
-0.0036
-0.0001
0.0003
-0.0028
WEC Sydncy
-0.0001
0.0163
0.0001
0.0229
0.0045
-0.0009
0.0004
0.0021
0.0010
(QBC) methods (Burbidge al. 2007 Fazakis et al. 2020) select samples with the highest pre- dictive disagreement among an ensemble of regressors. While they effectively capture uncertainty in well-specified models, they suffer in the presence of noise model misspecification and in- cur high computational cost due to repeated model training. Model change-based algorithms (Cai al. 2017 Park & Kim 2020) select samples that expected induce the greatest change in model parameters, often approximated via gradient information. These methods directly target model improvement but typically require ensemble estimation and suffer from high computational complexity, particularly in batch settings. Black box approaches (Kirsch) 2023) estimate predic- tive uncertainty using covariance kernels derived from ensemble predictions. They are compatible with non-differentiable models and achieve strong empirical performance, but rely on ensemble di- versity, which may degrade low-variance models such as random forests or boosted ensembles. Inverse distance-based methods (Bemporad) 2023) combine model uncertainty and spatial explo- ration using inverse-distame weighting. These methods avoid model retraining and generalize to both pool- and population baaialttooo--dddddddded settings, but their reliance on distance heuristics limits their effec- tiveness in fighh-imenssonal or discontinuous spaces. Greed sampling methods (Wu et al. 2019) select samples that maximize diversity in the input or output space. These methods model-aware

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and promote label spread and representativity, but require model updates after each selection, in-
creasing computational overhead. Distributiov/coverageebb based methods (Sener & Savarese [018]
Yehuda et al. 2022 Bac et al. 2024) formulate selection covering the unlabeled distribution in
a learned feature space. Both are label-agnostic and transfer to regression by measuring distances
in task-relevant embeddings. However, performance hinges the quality of the embedding/metric
and the choice of coverage radius, and the construction of the graph or mixed integer program (MIP)
can be costly for very large pools. Clustering- based methods (Wul 2019 Holzmüller et al. 2023)
select samples based on coverage and diversity in feature space. [w (2019) proposes a sequential epprsentative-diveen
(RD) framework using k-means clustering, optionally combined with uncer- tainty measures. Holzmüller et al. (2023) introduce LCMD, modular batch-mode method that leverages neural tangent kernels and clustering to balance core sampling principles. While effective, both methods may suffer from high runtime due to repeated clustering or kernel computations. TES- components, but fundamentally differs
SAR shares LCMD's use of diversity- and density-oriente in its VLDM term, which targets samples near Voronoi faces rather than cluster peripheries. This ge- ometric mechanism prevents selection of outer- bouud-byundary points- where no Voronoi faces form-au and instead reliably guides sampling toward informative interior regions.
More broadly, recent work in adjacent areas highlights a converging theme: efficiency gains come from exploiting structure decide where supervision, optimization, feedback should be ap- plied. For example, diffusion/generative modeling benefits from timestep- or stepwise-structure
optimization and preference signals (Hong et al. 2025 Tee al. 2025 Pham et al.) 2025), and pref- erence optimization can focus on confidence- or preference-critical regions of the signal (Yoon et al.,
2025a b). In multimodal pecision-makingg sample/feedback efficiency is increasingly achieved by leveraging large vision-language models for distillation or reward construction (Lee et al., 2025 Luu et al. [)) Finally, structure- awrre robustness has been explored in temporal/occ
or sequential domains (Eom et al., 2025 Gao et al., 20255 Kang et al. 2024 Yoon et al. (205cc), reinforcing the general idea that leveraging geometry/structure can systematically improve data ef- ficiency. These trends support our approach in active regression: using geometric structure induced by the Voronoi faces to identify interior regions where newly queried labels are most likely to yield
large gains.
6 CONCLUSION
This paper proposes TESSAR, a geometry active learning framework for regression based on Voronoi tessellation. At the core of TESSAR the Voronoi-based Least Disagree Metric (VLDMM,, which captures interior structure by identifying samples that lie near Voronoi faces. To ensure full spatial coverage, TESSAR combines VLDM with a distance-based score that promotes exploration of peripheral regions and a region-level representativity term that reflects local data density. This unified strategy enables the model to acquire informative samples from both the interior and pe- riphery while aligning with the overall data distribution. While classification-basee methods like LDM-S rely on label-defined decision boundaries and are inherently limited to supervised settings, TESSAR selects samples purely based on geometric relationships among input instances. Empir- ical evaluations across multiple regression benchmarks show that TESSAR consistently achieves competitive or superior performance.
We conclude by highlighting several promising directions for future work. Although dynamically updating the Voronoi structure in VLDM improves the efficiency of TESSAR, remains computa- tionally costly since each new sample perturbs the structure even within the same batch. Developing a more scalable variant of TESSAR, or even a new algorithmic principle inspired by our Voronoi- style intuition, is an important next step. Beyond active learning, one natural extension is to in- vestigate how Voronoi-based sample acquisition can guide pseudo-labeling or cluster selection in semi-supervised and unsupervised learning, where geometry rather than label information plays central role. Finally, while we implicitly assume homoskedasticity, it remains an intriguing open question whether similar Voronoi-style principles can be extended to heteroskedastic settings.
ACKNOWLEDGMENTS
We thank the anonymous reviewers for their helpful comments. This work was partly supported by the Institute of Information & communications Technology Planning & Evaluation (ITTP) grant
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Published as a conference paper at ICLR 2026
funded by the Ministry of Science and ICT (MSIT) (No. RS-2022-11220184, RS- RS-2019-11190075 and partly supported by Global Learning & Academic research institution for Master's P-D students, and Postdocs (LAMP) Program of the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (MOE) (No. RS-2024-004437144 This work was partly supported by grant number (No. KSN251 1 2201) from the Korea Institute of Oriental Medicine (KIOM), provided by the Commercialization Promotion Agency for R&D Outcomes (COMPA) grant funded by the MSIT (No. RS-2025-17632971) conducted at the KIOM (No. NSN2521040).
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APPENDIX
A EXPERIMENTAL SETTINGS
Table 2: Overview of used datasets.
Short Name
Citation
Source
Training size
Test size
# of features
CT slices
Graf al.
2011
UCI
42,800
10,700
379
Diamonds
OpenMI.
43,152
10,788
29
Friedman
(Friedman
1991
OpenML
32,615
8,153
KEGG under
Shannon et al.
2003
UCI
51,687
12,921
27
Methane
Slęzak et
2018
OpenML
200,000
300,000
MLR kNN
OpenML
89,403
22,350
132
Online vidco
Deneke al.
2014)
UCI
55,028
13,756
26
Protein
OpenMI.
36,584
9,146
9
Query
Anagnostopoulos et al.
2018
UCI
160,000
40,000
4
Road
(Kaul et al. 2013
UCI 200,000
234,874
2
SARCOS
Vijayakumar & Schaal
2000
GPML
35,588
8,896
21
SGEMM
Ballester-Ripol et al.
2019
UCI
193,280
48,320
Stock
OpenML
47,240
11,809
9
WBC Sydney
Neshat et al.
2018
UCI
$7,600
14,400
48
The datasets, deep network architecture, and experimental setup follow the framework proposed by Holzmüller et al. (2023). Table presents an overview of datasets used. We selected 14 tabular regression datasets from different sources. A fully connected neural network with two hidden lay- ers, each comprising 512 neurons (T. = 3, d1 = d2 512), is employed for all experiments. The neural tangent parameterization is used conjunction with the ReLU activation function. All biases are initialized to zero, and weights are independently sampled from N 1). Model training is per- formed using the Adam optimizer with default hyperparameters 31 = 0.9, 32 = 0.999. The initial learning rate is set to 0.375 and is decayed linearly to zero throughout training. A batch size of 256 and total of 256 training epochs are used. After each epoch, the RMSE is evaluated on a validation set of 1, 024 samples. For all datasets, the number of initial labeled samples is set to 256. At each active learning step, 256 samples are queried, and the process is repeated for 16 steps, resulting in final labeled set of 352 samples. In TESSAR, the number of perturbations N is set to 100, and is increased in the order of {0.0002, 0.0004, 0.0006, 0.0008, 0.001, 0.002, 0.004, 0.006, 0,008, 0.01), with every 10 perturbations. All experiments are conducted on NVIDIA TITAN Xp GPUs with 12GB of memory. We use PyTorch 3.7 with CUDA 10.0.
B PERFORMANCE PROFILE AND PENALTY MATRIX
B. PERFORMANCE PROFILE
Let err D.r.t denote the RMSE of alrogirhm A at step t E Tp, for dataset D and repetition r E [R], and define the performance gap A D.r,t. D (em D.rt). Here, Tp the number of steps for dataset D, and It is the total number of repetitions. Then, the performance profile is defined
Σn T(A D.rst <
RA = Top
Σ D
RTD
where n,, is the number of datasets. Intuitively, RA(5) is the fraction of cases where the performance gap between algorithm A and the best competitor is less than 8. Specifically, when 0, R, (0) is the fraction of cases in which algorithm A performs the best.
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B.2 PENALTY MATRIX
For each dataset, step, and each pair of algorithms (A,, A2), we collect R RMSE values ferr; ] and {eir) | respectively. We compute the t-score t v VRu/o where H Σr= (err) etr)) (err erry 12)2. In this framework, A, said to beat A, if 2.776, and vice versa if 2.776. When A, beats Aj. penalty of L/TD accumulated Pt,. and similarly for the reverse case. Summing the penalties across datasets yields the final penalty matrix.
and ō = V V E R
C ADDITIONAL RESULTS
C.I RUNTIME COMPARISON per DATASET
Table 3: The mean of runtime (sec) for each algorithm and each dataset.
TESSAR
Coreset
ProbCov
BALD
BatchBALD
BADGE
BAIT
ACS-FW
LCMD
slices
235.8
166.1
3,412.1
188.0
174.3
151.4
179.7
175.2
168.7
Diamonds
255.1
205.8
4,033.6
169.3
207.1
203.3
273.9
202.1
207.0
Friedman
287.7
202.7
4.398.7
169.9
207.4
201.3
264.1
200.0
270.6
KBGG undir
247.2
212.1
4,297.9
172.5
215.5
169.2
286.9
209.2
273.9
Methane
482.9
232.9
4,518.1
171.3
190.4
218.0
378.6
211.5
245.3
MLR KNN
367.3
213.4
4,424.7
167.7
216.5
198.3
306.5
197.7
288.3
Online video
254.7
214.9
4,375.2
170.3
216.8
169.5
295.9
209.6
279.7
Protcin
286.1
206.7
4.373.7
170.4
208.3
205.1
279.4
204.9
275.5
Query
423.0
237.4
4.396.2
175.8
231.8
196.1
344.0
204.0
264.2
Road
547.8
236.5
3.676.3
174.5
214.1
194.7
378.4
213.4
229.0
SARCOS
249.9
207.2
4,340.1
168.2
208.8
204.1
276.9
204.1
276.8
SGEMM
487.8
234.5
3,873.1
179.7
226.9
182.5
373.0
206.8
217.4
Stock
313.1
211.9
4.347.7
172.4
212.4
207.1
285.2
207.4
212.4
WFC Sydney
269.6
207.9
4.237.3
174.5
204.4
194.3
286.7
191.3
278.6
Table presents the mean runtime (in seconds) for each algorithm across datasets. For TESSAR, the runtime remains comparable to other strong- peronnpprforming algorithms such as BADGE, BAIT, and LCMD on smaller datasets. However, as the dataset size increases, TESSAR's runtime grows more noticeably. Nonetheless, the difference typically remains within few minutes and is negligible relative to the overall time required for labeling. This additional computational cost arises from TESSAR's deliberate design explore regions-particulan particularly interior areas that often underrep- resented by conventional sampling methods. Rather than a drawback, this represents a worthwhile trade-off, TESSAR consistently achieves superior performance in exchange for modest increases in computation. Our results further demonstrate that sampling from interior regions yields meaning- ful gains in regression tasks, underscoring the importance of this geometric perspective. We hope this finding motivates future research toward more computationally efficient algorithms that retain the benefits of interior-region aware sampling.
C.2 VLDM-BASEE BASED VS MARGIN- MARGIN-BASED TESSAR
To assess whether TESSAR's performance gains derive from the VLDM formulation or could be matched by simpler geometric uncertainty measures, we replaced VLDM with margin-based proxy. The margin is defined as the difference between the distances from a sample to its near- est and second-nearest Voronoi centers-an inexpensive approximation of local geometric ambiguity. We then ran TESSAR using this margin score in place of VLDM. Bsswws that margin-bases TESSAR incurs notable performance degradation across datasets, despite its lower computational cost. These results demonstrate that the improvements achieved by TESSAR cannot reproduced by simple geometric heuristic, thereby validating the necessity of VLDM's design.
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Figure 6: Comparison of VLDM-based and margin- based TESSAR Protein (a), Road (b), and Stock (c) datasets. The margin is defined as the difference between the distances from a sample to its nearest and second-nearest Voronoi centers. TESSAR using VLDM consistently outperforms its margin-basee variant.
C.3 EFFECT OF DYNAMIC VS. STATIC VORONOI UPDATES
To assess the impact of dynamic tessellation in TESSAR, included static VLDM and static TES- SAR baselines, in which Voronoi centers remain fixed after initial construction. This setting enables direct comparison between geomelry-aware sampling with and without adaptive updates. Figure 7 shows that static VLDM fails to meaningfully reduce error across datasets, indicating that a fixed Voronoi structure insufficient for guiding informative selection. Static TESSAR performs rea- sonably well due to its combined scoring components, but dynamic TESSAR consistently achieves lower error on all datasets, demonstrating that updating Voronoi partitions throughout the acquisition process provides clear performance benefit.
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Figure 7: Comparison of dynamic and static VLDM on Protein (a), Road (b), and Stock (c) datasets. While dynamic VLDM shows gradual improvement as more samples are labeled, static VLDM fails to improve across all datasets. Dynamic TESSAR also shows improved performance compared to its static counterpart, validating the importance of adaptive geometry-aware sampling strategies.
C.4 ROBUSTNESS TO HYPERPARAMETER
TESSAR, the primary hyperparameter is the number perturbations, denoted by N. This hyper- parameter controls the number of perturbed hypotheses sampled during the empirical evaluation of the VLDM, directly affecting both the estimation accuracy the metric and the overall computa- tional cost. Figure&ppreeettss presents the mean log RMSE with respect to N E {10, 50, 100, 500, 1000). and there is no significant performance difference. This suggests that TESSAR is robust to the choice of N.
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Figure& 8: The mean log RMSE with respect the number of perturbations Protein (a), Road (b), and Stock (c) datasets. There is no significant performance difference.
D THE USE LARGE LANGUAGE MODELS (LLMs)
We used LLM improve grammar and wording. The authors reviewed all edits and take full responsibility for the content.
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Reviews:
[{"review_id": "sdJp33m8qw", "reviewer": "Reviewer_brsN", "summary": "The paper discusses TESSAR - an active learning method for regression that picks new points to label by using geometrical structure. TESSAR builds a Voronoi diagram around the currently labeled points and seeks unlabeled samples that lie near the boundaries of the diagram, where the model is least certain. It then balances this with two complementary signals: a score that encodes the density of points or how representative they are, and a score the encodes diversity by measuring distances from labeled data. The result is a single scoring rule that aims to be informative, diverse, and representative. Across many tabular datasets, this approach matches or beats strong baselines, with a practical update trick to keep computation reasonable.", "questions": "Please address the relationship to the coverage-based literature discussed above, and clarify the method’s scalability to larger datasets.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "The paper presents a clear geometrical idea for the solution of a well motivated problem in active learning, which is integrated into a unified comprehensive strategy.\nAttention is given to computational complexity.", "weaknesses": "The technical sections are hard to follow, as several derivations are terse.\nThe experiments are limited to modest-size tabular datasets; given the inherent computational complexity of the method, more challenging datasets seem appropriate.\n\nThe authors appear unfamiliar with several active learning works that address a similar problem via coverage. Although those papers target classification at the low-budget regime, their focus - selecting spatially diverse and representative points from the underlying distribution - is closely related. Instead of employing a Voronoi diagram, the optimization is formulated in terms of set coverage; crucially, because the objective is submodular, the greedy solution enjoys efficient approximation guarantees. Published extensions in that line of work also incorporate uncertainty terms. It is therefore essential to compare against this coverage-based literature.\n\n1) Yehuda, Ofer, et al. \"Active learning through a covering lens.\" Advances in Neural Information Processing Systems 35 (2022): 22354-22367.\n2) Bae, Wonho, Junhyug Noh, and Danica J. Sutherland. \"Generalized coverage for more robust low-budget active learning.\" European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "IIwCu5n9xS", "reviewer": "Reviewer_5qY9", "summary": "This paper introduces TESSAR, an active learning framework for regression tasks that leverages Voronoi tessellation to improve sample selection. The core innovation is the Voronoi-based Least Disagree Metric (VLDM), which identifies informative samples near Voronoi faces in the input space, addressing the limitations of traditional distance-based methods that often overlook dense interior regions. VLDM is combined with a distance score for peripheral exploration and a density-based representativity term, resulting in a unified acquisition function. The authors provide theoretical motivation linking Voronoi faces to high predictive variance, along with an efficient approximation for VLDM computation. Empirical evaluations on 14 tabular regression datasets show that TESSAR matches or surpasses state-of-the-art baselines such as LCMD and BADGE in terms of RMSE, although its runtime increases with larger datasets, reducing efficiency, a limitation the authors explicitly address.", "questions": "Can we pre-evaluate how much TESSAR will outperform random sampling on a given dataset?\n\n Following LCMD’s analysis (Holzmüller et al., 2023), which showed that the ratio of initial RMSE to MAE on a small training set strongly predicts the benefit of LCMD-TP over random selection, a similar diagnostic could be developed for TESSAR. For example,\n a pre-evaluation metric could forecast TESSAR’s sample efficiency gains, helping practitioners decide when to deploy it. \n\t\t\nHow sensitive is TESSAR to the choice of feature extractor (e.g., vs. raw inputs or other  architectures)? The method relies on a feature mapping (e.g., neural network outputs), and varying this (e.g., with PCA) might affect Voronoi partitions and VLDM scores, warranting empirical sensitivity analysis.\n\nIn the theoretical analysis, the Lipschitz assumption is reasonable, but are there empirical cases where it fails, and how does TESSAR perform there?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The use of Voronoi tessellation as a geometric approximation for disagreement-based sampling in regression is a well-motivated idea. Unlike classification tasks with clear decision boundaries, regression lacks such structures, and this paper elegantly adapts the concept via VLDM. The theoretical analysis in Section 2.2, showing that points near Voronoi faces exhibit high variance under Lipschitz assumptions, provides solid grounding.\n\nTESSAR integrates informativeness, diversity, and representativity into a single score, with efficient dynamic updates (Algorithm 2) to avoid recomputing VLDM naively. The empirical consistency of VLDM (Figure 3) and ablation studies (Figure 4) clearly show the complementary benefits of the components in TESSAR.\n\nEvaluations on diverse datasets (e.g., Protein, Road, Stock) using performance profiles and penalty matrices (Figure 5, Table 1) highlight TESSAR's consistent superiority. It achieves the highest RA(0) of 41% in performance profiles, outperforming LCMD (29%). Runtime comparisons (Table 3) indicate it's competitive with baselines, with increases justified by better performance.\n\nThe paper is well-written, with clear pseudocode, evaluations and detailed appendices on datasets and metrics, and thoughtful discussion of limitations (e.g., computational cost in large pools, homoskedasticity assumption).", "weaknesses": "TESSAR's runtime scales with pool size and perturbations, making it slower on very large datasets (e.g., 547s on Road vs. ~150s for Coreset). The authors acknowledge this and suggest optimizations, but more scaling experiments (e.g., on million-scale data) could strengthen the case. Active Learning is designed for large data sets.\n\nThe related works section is comprehensive but could better highlight differences from clustering-based methods like LCMD.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yHtV95zWYq", "reviewer": "Reviewer_w4R2", "summary": "This paper proposes TESSAR, a geometry-aware active learning framework for regression. The key idea is to model uncertainty through VLDM, which measures the geometric instability of samples under small perturbations of labeled points. By combining VLDM with distance and density terms, the method dynamically selects informative samples in a model-agnostic manner.", "questions": "See weakness.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1. The paper proposes a novel geometric perspective, which is interesting. The use of Voronoi tessellation and the proposed VLDM provide an innovative and well-motivated formulation of uncertainty for regression tasks.\n2. The method achieves notable performance gains across various datasets and baselines.", "weaknesses": "1. The paper should include a static Voronoi or less frequent update baseline to show the effect of dynamic tessellation. Also what is the selection stragegy of Gaussian perturbation parameter? \n2. It would be helpful to include an ablation replacing VLDM with simpler geometric proxies such as nearest-neighbor distance or local label variance. This would clarify whether the performance gains truly stem from the proposed VLDM formulation or can be achieved by simpler uncertainty measures.\n2. Voronoi-based geometry can degrade in high-dimensional spaces due to distance concentration. Is the proposed approach still effective in high-dimensional regression tasks?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)