Statistical Detection of Positional Bias in LLM-Based Recommender Systems: Methodologies and Empirical Evidence
Authors: Carlos Peláez-González, Francisco Herrera, Andrés Herrera-Poyatos
Organizations: Department of Computer Science and Artificial Intelligence, Andalusian Institute of Data Science and Computational Intelligence (DaSCI), University of Granada, Spain. · Department of Algebra, University of Granada, Spain.
Large Language Models (LLMs) are increasingly used as recommendation generators in conversational recommender systems (RS) via retrieval-augmented generation (RAG). This flexible design introduces new sources of structural bias. This paper studies positional bias in top-1 and single-turn LLM-based RS: systematic dependence of the recommended item on the order in which candidates are presented in the prompt. We propose two complementary detection methodologies: (i) POB-ICM, based on contingency matrix analysis and Chi-square independence testing, and (ii) POB-UNBP, a sample-efficient approach derived from a uniformity null model under permutation-based evaluation, enabling stochastic decoding with formal statistical guarantees. Using a controlled RAG testbed for product recommendation, built on a real product catalog, a fixed prompt template and 2000 template-generated user queries with 20 permutations each (40,000 instances), both methodologies reject the null hypothesis of positional independence and uniformity in all evaluated state-of-the-art models. We introduce three complementary metrics -- permutation sensitivity, positional bias, and strong positional bias -- to quantify this effect, the latter targeting cases where the position displaces the recommendation towards clearly less relevant items rather than only choosing among comparably relevant ones. A robustness analysis across candidate-set size and decoding temperature shows that the bias is structural and model-dependent, not an artifact of deterministic decoding or candidate-set size. These results establish positional bias as a measurable, reproducible property of prompt-mediated recommendation pipelines in the evaluated setting and motivate routine auditing and governance controls (e.g., order randomization, standardized prompting) for deployed LLM-based RS. Source code is publicly released.
Figures & tables
Figure 1: LLM-based RS architecture used in this paper.
Figure 2
Figure 2: Several user queries examples included in our dataset. These are generated from templates, where the underlined words indicate a placeholder.
Figure 3: Titles of the selected products for the query "Find me an eco-friendly protein snack". These are sorted by the cosine similarity to the query using BAAI embedding model.
Model name
Error rate
Refusal rate
Top-5
Top-10
Top-15
Top-20
Top-5
Top-10
Top-15
Top-20
DeepSeek R1 32B
0.35%
0.39%
0.24%
0.26%
4.03%
3.89%
3.82%
4.06%
DeepSeek R1 7B
0.81%
1.58%
1.99%
2.46%
7.39%
5.38%
5.14%
4.36%
DeepSeek R1 8B
0.37%
0.40%
0.21%
0.23%
0.01%
0.01%
0.00%
0.00%
LLaMA 3.1 8B
0.60%
1.99%
3.23%
4.01%
0.01%
0.01%
0.01%
0.01%
LLaMA 4 Scout
0.21%
0.48%
2.05%
3.20%
0.17%
0.06%
0.08%
0.05%
Table 1: Recommendation parsing error rate and refusal rate for each candidate-set size, each computed over the 40,000 samples of the corresponding query-permutation dataset.
Model name
p -value (POB-ICM)
p -value (POB-UNBP)
L
Permutation sensitivity (PS)
Positional bias (PB)
Strong Positional Bias (sPB)
DeepSeek R1 32B
<0.0005
7.456e-07
0.97%
21.857
2.563, CI: (2.0, 3.2)
3.1
DeepSeek R1 7B
<0.0005
6.197e-60
4.15%
33.983
5.612, CI: (5.1, 6.3)
9.8
DeepSeek R1 8B
<0.0005
5.875e-05
0.79%
29.758
2.391, CI: (1.8, 3.0)
6.7
LLaMA 3.1 8B
<0.0005
4.457e-26
3.01%
30.395
4.187, CI: (3.6, 4.8)
6.7
LLaMA 4 Scout
<0.0005
1.188e-04
0.87%
22.393
2.886, CI: (2.4, 3.4)
3.2
GPT OSS 120B
<0.0005
8.879e-30
3.14%
15.487
4.368, CI: (3.8, 5.0)
1.0
Table 2: Results from the proposed bias quantification metrics and proposed statistical methodologies for top- 5 setting. POB-ICM p -values are Monte Carlo estimates from B=2000 permutations, so their smallest attainable value is 1/(B+1)=0.0005 . L value is the lower bound of TV(p(⋅),Uk) according to the POB-UNBP test. Confidence intervals of sPB reported at Appendix E .
Figure 4: Contingency matrix from subsection 4.3 , shown as a heatmap. The plot was generated using LLaMA 3.1 8B as recommender. Each column shows the empirical distribution of recommendations conditioned on a permutation, with permutations sorted lexicographically. Red lines indicate when the first, second, third, fourth, and fifth product are shuffled to the first position, respectively. Consistency was ensured by shuffling products according to the permutation sample, generating the recommendation, and then unshuffling the recommendation positions.
Figure 5: Bias analysis given the Equation 3 for different recommender LLMs. For each model, a column of its associated heatmap represents the mean of the (non-normalized) counts of selected products by the model when these were moved to the position represented by said column. In the absence of positional bias, all columns would be identical.
Top-5
Top-10
Top-15
Top-20
Model name
p -value
L
p -value
L
p -value
L
p -value
L
DeepSeek R1 32B
7.456e-07
0.97%
5.130e-17
2.83%
2.202e-47
4.29%
2.098e-48
6.78%
DeepSeek R1 7B
6.197e-60
4.15%
9.362e-55
5.79%
5.966e-79
9.51%
4.449e-70
9.89%
DeepSeek R1 8B
5.875e-05
0.79%
1.150e-11
1.96%
2.253e-46
4.30%
2.111e-71
7.24%
LLaMA 3.1 8B
4.457e-26
3.01%
4.928e-17
3.13%
3.379e-16
4.08%
1.465e-26
3.77%
LLaMA 4 Scout
1.188e-04
0.87%
1.438e-60
8.30%
8.023e-208
21.43%
1.341e-249
30.19%
Table 3: POB-UNBP statistical test p -value and the computed lower bound L for different top- K values and a fixed temperature t=0 . Bold values represent statistically detectable positional bias according to the threshold of 0.05 .
t=0.0
t=0.2
t=0.4
t=0.6
Model name
p -value
L
p -value
L
p -value
L
p -value
L
DeepSeek R1 32B
7.456e-07
0.97%
2.001e-09
1.14%
6.392e-06
0.79%
6.290e-07
1.12%
DeepSeek R1 7B
6.197e-60
4.15%
1.924e-64
4.29%
7.115e-58
4.24%
2.998e-66
4.40%
DeepSeek R1 8B
5.875e-05
0.79%
8.181e-06
0.90%
9.225e-08
1.21%
1.701e-16
1.65%
LLaMA 3.1 8B
4.457e-26
3.01%
2.049e-28
2.67%
4.884e-21
2.27%
1.925e-17
1.97%
LLaMA 4 Scout
1.188e-04
0.87%
1.476e-05
0.97%
5.367e-05
0.97%
6.510e-05
1.00%
Table 4: POB-UNBP statistical test p -value and the lower bound L for different decoding t temperatures and a fixed K=5 . Bold values represent statistically detectable positional bias according to the threshold of 0.05 .
Figure 6: Representation of probability distribution p(i) defined in Equation 1 for different k values. Red-dashed lines represent uniform baseline 1/k .
Model name
Temperature
p(1)
p(2)
p(3)
p(4)
p(5)
DeepSeek R1 32B
0.0
0.1874
0.1869
0.2060
0.2083
0.2114
0.2
0.1869
0.1868
0.2046
0.2080
0.2137
0.4
0.1873
0.1879
0.2055
0.2097
0.2097
0.6
0.1872
0.1852
0.2053
0.2103
0.2119
DeepSeek R1 7B
0.0
0.1738
0.2514
0.2004
0.2043
0.1701
0.2
0.1686
0.2535
0.2012
0.2039
0.1729
Table 5: Probability distributions p(i) defined in Equation 1 for different temperature values and top-5 setting. Uniform baseline is 0.2 .
Figure 7: Selection counts of each candidate item, by original (pre-shuffling) position, for twenty random queries of the exhaustive configuration, using LLaMA 3.1 8B. Each panel shows, for one query, how many of the 120 permutations recommended each item.
Model name
PS
PB
sPB
5
10
15
20
5
10
15
20
5
10
15
20
DeepSeek R1 32B
21.9
29.4
34.1
37.2
2.6
5.0
7.1
9.4
3.1
6.9
10.7
13.7
DeepSeek R1 7B
34.0
45.1
52.7
58.1
5.6
8.9
13.5
13.0
9.8
20.1
26.6
33.2
DeepSeek R1 8B
29.8
38.6
43.2
46.4
2.4
4.5
7.1
10.1
6.7
14.8
19.4
20.6
LLaMA 3.1 8B
30.4
41.9
46.9
49.6
4.2
5.3
6.8
7.0
6.7
15.7
20.7
24.1
LLaMA 4 Scout
22.4
38.3
51.5
61.6
2.9
10.5
24.3
33.8
3.2
12.9
24.5
36.6
Table 6: Permutation sensitivity (PS), positional bias (PB), and strong positional bias (sPB), all expressed as percentages, across k∈{5,10,15,20} . Confidence intervals of sPB metric reported in Appendix E .
Model name
PS
PB
sPB
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
DeepSeek R1 32B
21.9
22.7
22.9
23.4
2.6
2.6
2.5
2.8
3.1
3.3
3.4
3.5
DeepSeek R1 7B
34.0
34.6
35.3
35.9
5.6
5.9
5.9
6.0
9.8
10.0
10.4
10.4
DeepSeek R1 8B
29.8
30.9
31.5
32.6
2.4
2.1
2.7
2.8
6.7
6.9
8.7
9.9
LLaMA 3.1 8B
30.4
31.4
32.3
33.0
4.2
4.0
3.6
3.0
6.7
7.1
9.3
9.4
LLaMA 4 Scout
22.4
22.6
22.6
22.9
2.9
3.1
3.1
3.0
3.2
3.2
3.2
3.3
Table 7: Permutation sensitivity (PS), positional bias (PB), and strong positional bias (sPB), all expressed as percentages, for top- 5 across decoding temperatures t∈{0.0,0.2,0.4,0.6} . Confidence intervals of sPB metric reported in Appendix E .
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 16
Model name
sPB
L
IoU of R(X)
p -value
(i)
(ii)
(iii)
(ii)
(iii)
(i), (ii)
(i), (iii)
DeepSeek R1 32B
2.9 (2.8, 3.1)
3.1 (2.9, 3.2)
3.4 (3.3, 3.6)
1.0
1.1
78.9
79.8
2.2e-08
DeepSeek R1 7B
9.1 (8.8, 9.4)
9.8 (9.5, 10.1)
10.2 (9.9, 10.5)
4.2
4.4
70.2
70.6
7.4e-09
DeepSeek R1 8B
6.6 (6.3, 6.8)
6.7 (6.5, 6.9)
7.5 (7.3, 7.8)
0.8
1.6
73.6
73.4
4.3e-11
LLaMA 3.1 8B
6.9 (6.7, 7.2)
6.7 (6.4, 6.9)
7.5 (7.3, 7.7)
3.0
2.0
74.3
74.5
1.6e-08
LLaMA 4 Scout
2.3 (2.1, 2.5)
3.2 (3.0, 3.4)
3.3 (3.1, 3.5)
0.9
1.0
76.4
76.6
5.1e-19
Appendix
Table 10: Strong positional bias (sPB), POB-UNBP lower bound L of TV(p(⋅),Uk) for the configurations with permutations, and mean intersection over union (IoU) of the relevance sets with configuration (i), for top- 5 under configurations (i) stochastic decoding, (ii) random permutation and (iii) both. sPB and IoU are percentages and L is in percentage points, with 95% confidence intervals for sPB. The last column reports the Holm-adjusted p -value comparing the sPB of configurations (iii) and (i); bold values are significant at the 0.05 level.
Model name
sPB
L
IoU of R(X)
p -value
(i)
(ii)
(iii)
(ii)
(iii)
(i), (ii)
(i), (iii)
DeepSeek R1 32B
2.6 (2.4, 2.8)
3.1 (2.9, 3.2)
3.5 (3.3, 3.6)
1.0
2.6
78.6
78.9
3.0e-18
DeepSeek R1 7B
9.5 (9.2, 9.8)
9.8 (9.5, 10.1)
10.4 (10.1, 10.7)
4.2
3.9
71.0
71.3
2.4e-07
DeepSeek R1 8B
6.0 (5.8, 6.3)
6.7 (6.5, 6.9)
7.2 (6.9, 7.4)
0.8
3.7
72.4
72.4
1.3e-14
LLaMA 3.1 8B
6.0 (5.7, 6.2)
6.7 (6.4, 6.9)
7.3 (7.0, 7.5)
3.0
0.3
73.9
74.0
7.8e-21
LLaMA 4 Scout
2.7 (2.5, 2.9)
3.2 (3.0, 3.4)
3.2 (3.1, 3.4)
0.9
0.9
79.2
80.6
2.4e-07
Appendix
Table 11: Strong positional bias (sPB), POB-UNBP lower bound L of TV(p(⋅),Uk) for the configurations with permutations, and mean intersection over union (IoU) of the relevance sets with configuration (i), for top- 5 under configurations (i) random labels, (ii) random permutation and (iii) both. sPB and IoU are percentages and L is in percentage points, with 95% confidence intervals for sPB. The last column reports the Holm-adjusted p -value comparing the sPB of configurations (iii) and (i); bold values are significant at the 0.05 level.
Model name
Top- k
k=5
k=10
k=15
k=20
PS
DeepSeek R1 32B
21.9 (21.0, 22.7)
29.4 (28.5, 30.4)
34.1 (33.1, 35.2)
37.2 (36.2, 38.3)
DeepSeek R1 7B
34.0 (33.1, 34.9)
45.1 (44.2, 45.9)
52.7 (51.8, 53.6)
58.1 (57.3, 59.0)
DeepSeek R1 8B
29.8 (28.8, 30.7)
38.6 (37.7, 39.5)
43.2 (42.3, 44.2)
46.4 (45.5, 47.4)
LLaMA 3.1 8B
30.4 (29.5, 31.3)
41.9 (41.0, 42.8)
46.9 (46.0, 47.8)
49.6 (48.6, 50.5)
Appendix
Table 12: Permutation sensitivity (PS) and strong positional bias (sPB) across candidate-set sizes k at temperature t=0 , with 95% confidence intervals obtained by percentile bootstrap at the query level. Values are percentages.
Model name
Top- k
k=5
k=10
k=15
k=20
Min.
Max.
Min.
Max.
Min.
Max.
Min.
Max.
DeepSeek R1 32B
86.8
87.4
80.6
80.8
76.7
77.1
74.0
74.7
DeepSeek R1 7B
78.4
78.8
67.3
68.3
60.6
61.1
55.0
55.7
DeepSeek R1 8B
80.8
81.6
72.9
73.5
68.8
69.5
65.9
66.9
LLaMA 3.1 8B
81.7
82.1
71.4
71.9
66.4
67.0
63.4
64.1
Appendix
Table 13: Minimum and maximum of the threshold τ of sPB across the five folds, for candidate-set sizes k at temperature t=0 . Values are percentages.
Model name
Temperature t
t=0.0
t=0.2
t=0.4
t=0.6
PS
DeepSeek R1 32B
21.9 (21.0, 22.7)
22.7 (21.8, 23.6)
22.9 (22.0, 23.8)
23.4 (22.5, 24.3)
DeepSeek R1 7B
34.0 (33.1, 34.9)
34.6 (33.8, 35.5)
35.3 (34.4, 36.2)
35.9 (35.0, 36.8)
DeepSeek R1 8B
29.8 (28.8, 30.7)
30.9 (30.0, 31.8)
31.5 (30.5, 32.3)
32.6 (31.7, 33.4)
LLaMA 3.1 8B
30.4 (29.5, 31.3)
31.4 (30.5, 32.3)
32.3 (31.4, 33.1)
33.0 (32.0, 33.8)
Appendix
Table 14: Permutation sensitivity (PS) and strong positional bias (sPB) across decoding temperatures t at top- 5 , with 95% confidence intervals obtained by percentile bootstrap at the query level. Values are percentages.
Model name
Temperature t
t=0.0
t=0.2
t=0.4
t=0.6
Min.
Max.
Min.
Max.
Min.
Max.
Min.
Max.
DeepSeek R1 32B
86.8
87.4
86.1
86.2
85.6
86.0
85.1
85.3
DeepSeek R1 7B
78.4
78.8
77.9
78.2
77.7
78.6
76.9
77.6
DeepSeek R1 8B
80.8
81.6
80.1
80.8
79.7
80.1
78.5
79.1
LLaMA 3.1 8B
81.7
82.1
80.2
80.9
79.4
79.7
79.0
79.6
Appendix
Table 15: Minimum and maximum of the threshold τ of sPB across the five folds, for decoding temperatures t at top- 5 . Values are percentages.
k=5
k=10
k=15
k=20
Model name
Δ sPB/SD (95% CI)
Rel.
Δ sPB/SD (95% CI)
Rel.
Δ sPB/SD (95% CI)
Rel.
Δ sPB/SD (95% CI)
Rel.
DeepSeek R1 32B
-0.08 (-0.25, 0.09)
-2.6%
-0.41 (-0.66, -0.16)
-5.8%
-0.58 (-0.89, -0.27)
-5.4%
-0.66 (-1.05, -0.26)
-4.8%
DeepSeek R1 7B
-0.26 (-0.58, 0.05)
-2.7%
-0.60 (-0.96, -0.23)
-3.0%
-1.09 (-1.49, -0.68)
-4.1%
-0.95 (-1.33, -0.56)
-2.9%
DeepSeek R1 8B
-0.30 (-0.54, -0.05)
-4.4%
-0.84 (-1.19, -0.49)
-5.7%
-0.59 (-0.98, -0.20)
-3.0%
-0.94 (-1.32, -0.55)
-4.5%
LLaMA 3.1 8B
-0.22 (-0.47, 0.03)
-3.3%
-0.81 (-1.17, -0.46)
-5.2%
-0.90 (-1.29, -0.50)
-4.3%
-0.60 (-1.02, -0.17)
-2.5%
LLaMA 4 Scout
-0.30 (-0.48, -0.12)
-9.3%
-0.85 (-1.22, -0.48)
-6.1%
-0.89 (-1.27, -0.51)
-3.7%
-1.08 (-1.44, -0.72)
-3.0%
Appendix
Table 16: Change of sPB, in percentage points, per standard deviation of retrieval score dispersion (95% CI), and relative to the sPB of each model (Rel.), across candidate-set sizes at t=0 . Bold: significant at the 0.05 level after Holm correction.
t=0.0
t=0.2
t=0.4
t=0.6
Model name
Δ sPB/SD (95% CI)
Rel.
Δ sPB/SD (95% CI)
Rel.
Δ sPB/SD (95% CI)
Rel.
Δ sPB/SD (95% CI)
Rel.
DeepSeek R1 32B
-0.08 (-0.25, 0.09)
-2.6%
-0.07 (-0.25, 0.11)
-2.2%
-0.19 (-0.37, -0.02)
-5.7%
-0.05 (-0.23, 0.13)
-1.5%
DeepSeek R1 7B
-0.26 (-0.58, 0.05)
-2.7%
-0.66 (-0.96, -0.36)
-6.6%
-0.74 (-1.04, -0.43)
-7.1%
-0.38 (-0.68, -0.07)
-3.6%
DeepSeek R1 8B
-0.30 (-0.54, -0.05)
-4.4%
-0.16 (-0.40, 0.09)
-2.2%
-0.42 (-0.72, -0.13)
-4.4%
-0.51 (-0.81, -0.20)
-5.1%
LLaMA 3.1 8B
-0.22 (-0.47, 0.03)
-3.3%
-0.33 (-0.58, -0.08)
-4.7%
-0.55 (-0.85, -0.26)
-5.9%
-0.17 (-0.46, 0.12)
-1.8%
LLaMA 4 Scout
-0.30 (-0.48, -0.12)
-9.3%
-0.17 (-0.34, 0.00)
-5.3%
-0.34 (-0.51, -0.17)
-10.4%
-0.29 (-0.46, -0.12)
-8.7%
Appendix
Table 17: As Table 16 , across decoding temperatures at k=5 .
Model name
Metric
Top-5
Top-10
Top-15
Top-20
All
CC
All
CC
All
CC
All
CC
DeepSeek R1 32B
L
0.970%
0.563%
2.827%
2.291%
4.291%
4.114%
6.775%
6.618%
p -value
7.456e-7
0.002
5.130e-17
7.082e-17
2.202e-47
2.072e-38
2.098e-48
2.859e-40
DeepSeek R1 7B
L
4.151%
5.279%
5.786%
7.430%
9.506%
9.432%
9.894%
9.969%
p -value
6.197e-60
2.169e-64
9.362e-55
1.299e-45
5.966e-79
2.045e-47
4.449e-70
2.075e-33
DeepSeek R1 8B
L
0.788%
0.785%
1.959%
2.093%
4.303%
4.387%
7.238%
7.256%
Appendix
Table 18: Sensitivity of POB-UNBP to the discarded generations. For each model, the first row reports the lower bound L of the total variation distance to the uniform distribution and the second row the p -value of the POB-UNBP test, computed on all queries (All) and on the complete-case queries (CC), for which no generation was discarded.
Large language models (LLMs) used as listwise rerankers in recommendation systems suffer from position bias when serializing candidate sets into prompts. We show this order sensitivity creates an exploitable attack surface: an attacker can promote a label-0 target into the top-k solely by reordering candidates, without changing item content, labels, or model parameters. We introduce promo@k to quantify this vulnerability, measuring the fraction of label-0 targets that can be elevated into top-k rankings via permutation. Evaluating across three domains (MovieLens, Amazon Books, and Amazon Fashion), promo@5 reaches up to 0.57 at an attack budget of R = 50 orderings. Furthermore, ordinary permutation stability predicts vulnerability without running the attack. While a bidirectional T5 encoder scorer reduces exposure, permutation-consistency regularization and architectural invariance effectively mitigate it. Pointwise scoring avoids the bias issue but degrades ranking quality. These results demonstrate that input candidate order in listwise LLM reranking is a security-relevant attack vector. Code and data are available at https://github.com/geoz-lab/position_bias_attack.
Large language models (LLMs) are increasingly used for recommendation reranking, but their listwise predictions can depend on the order in which candidates are presented. This creates a mismatch between the set-based nature of recommendation and the sequence-based computation of decoder-only LLMs, where permuting an otherwise identical candidate set can change item scores and final rankings. Such order sensitivity makes LLM-based rerankers difficult to rely on, since rankings may reflect prompt serialization rather than user preference. We propose InvariRank, a permutation-invariant listwise reranking framework that addresses this dependence at the architectural level. InvariRank blocks cross-candidate attention with a structured attention mask and negates position-induced scoring changes through shared positional framing under Rotary Positional Embeddings (RoPE). Combined with a listwise learning-to-rank objective, the model scores all candidates in a single forward pass, avoiding permutation-based invariance training objectives that require multiple permutations of a candidate set. Experiments on recommendation benchmarks show that InvariRank maintains competitive ranking effectiveness while producing stable rankings across candidate permutations. The results suggest that architectural invariance is a practical route to reliable and efficient LLM-based recommendation reranking. The source code is at https://github.com/ejbito/InvariRank.
Current Large Language Models (LLMs) are gradually exploited in practically valuable agentic workflows such as Deep Research, E-commerce recommendation, and job recruitment. In these applications, LLMs need to select some optimal solutions from massive candidates, which we term as LLM-as-a-Recommender paradigm. However, the reliability of using LLM agents for recommendations is underexplored. In this work, we introduce a BiasRecommendation Benchmark (BiasRecBench) to highlight the critical vulnerability of such agents to biases in high-value real-world tasks. The benchmark includes three practical domains: paper review, e-commerce, and job recruitment. We construct a Bias Synthesis Pipeline with Calibrated Quality Margins that 1) synthesizes evaluation data by controlling the quality gap between optimal and sub-optimal options to provide a calibrated testbed to elicit the vulnerability to biases; 2) injects contextual biases that are logical and suitable for option contexts. Extensive experiments on both SOTA (Gemini-{2.5,3}-pro, GPT-4o, DeepSeek-R1) and small-scale LLMs reveal that agents frequently succumb to injected biases despite having sufficient reasoning capabilities to identify the ground truth. These findings expose a significant reliability bottleneck in current agentic workflows, calling for specialized alignment strategies for LLM-as-a-Recommender. The complete code and evaluation datasets will be made publicly available shortly.
Zichen Tang, Zirui Zhang, Qian Wang +3
The Hong Kong University of Science and Technology · National University of Singapore · The Hong Kong University of Science and Technology (Guangzhou)