ST-HHOL: Spatio-Temporal Hierarchical Hypergraph Online Learning for Crime Prediction
Authors: Keqing Du
Yufan Kang
Xinyu Yang
Wei Shao
Venue: ICLR 2026 Poster (2026)
Keywords: Crime prediction
Spatio-temporal graph neural networks
Spatio-temporal data mining
Primary area: learning on time series and dynamical systems
TL;DR: We propose ST-HHOL, an online spatio-temporal crime prediction framework that leverages hierarchical hypergraphs to uncover dual-specific patterns and tackle concept drift in non-stationary crime data.

Abstract: Crime prediction is a critical yet challenging task in urban spatio-temporal forecasting. 
Sparse crime records alone are insufficient to capture latent high-order patterns shaped by heterogeneous contextual factors with spatial and criminal specificity, while high non-stationarity renders conventional offline models ineffective against concept drift. 
To tackle these challenges, we propose a Spatio-Temporal Hierarchical Hypergraph Online Learning framework named ST-HHOL. First, we propose a hierarchical hypergraph convolution network that integrates crime data with heterogeneous contextual factors to uncover dual-specific crime patterns and their co-occurrence relations. Second, we introduce an iterative online learning strategy to address concept drift by employing frequent fine-tuning for short-term dynamics and periodic retraining for long-term shifts. 
Moreover, we adopt a Partially-Frozen LLM that leverages pre-trained sequence priors while adapting its attention mechanisms to crime-specific dependencies, enhancing spatio-temporal reasoning under sparse supervision.
Extensive experiments on three real-world datasets demonstrate that ST-HHOL consistently outperforms state-of-the-art methods in terms of accuracy and robustness, while also providing enhanced interpretability.  Code is available at https://github.com/777Rebecca/ST-HHOL.

Published as a conference paper at ICLR 2026
ST-HHOL: SPATIO- HIERARCHICAL HYPERGRAPH ONLINE LEARNING FOR CRIME PREDICTION
Keqing Du', Yufan Kang", Xinyu Yang"; Wei 3.4
Xi'an Jiaotong University, M University, DDat661, CSIRO, *University of New South Wales dukeqi dukeqinggst.ai wtg.st..uu.. xjtu. aettu.eduu. enu tina. www.kkannmmsss.e.... edu, yxyphdemai xjtu. eduuueedu.c. en, wei. (data6l csiro. au, unsw. au)
ABSTRACT
Crime prediction is a critical yet challenging task in urhan spatio-temporal forecast- ing. Sparse crime records alone insufficient to capture latent high-order patterns shaped by heterogencous contextual factors with spatial and criminal specificity, while high non-stationarity renders conventional offline models ineffective against concept drift. To tackle these challenges, we propose a Spatio-Temporal Hierarchi- cal Hypergraph Online Learning framework named ST-HHOL. First, we propose a hierarchical hypergraph convolution network that integrates crime data with heterogeneous contextual factors to uncover dual-specific crime patterns and their co-occurrence relations. Second, we introduce iterative online learning strategy to address concept drift by employing frequent finettning for short-term dynamics and periodic retraining for long-term shifts. Moreover, adopt Partially-Free Frozeen LLM that leverages pre-trained sequence priors while adapting its attention mecha- nisms crime-specific dependencies, enhancing spatio-temporal reasoning under sparse supervision. Extensive experiments on four real-world datasets demonstrate that ST-HHOL consistently outperforms state-of-the-ar methods in terms of ac- curacy and robustness, while also providing enhanced interpretability. Code is available https::: //github. con/ 77 (e777eeeecca/S11
INTRODUCTION
Crime prediction is critical task in urban spatio-temporal forecasting, with significant implications for public safety and social stability. Recent advances in deep neural networks have significantly promoted the development of this field, leveraging attention mechanisms (Xia et al., 2021, Rayhan &
Hashem 2023) to model dynamic crime correlations, and graph neural networks (GNNs) (Zheng et al.
2020 Wu et al. 2020a Zhou et al. 2024) to capture temporal evolution and spatial heterogeneity.
However, sparse crime data alone cannot reveal the multifaceted crime patterns with spatial and criminal specificity. Potential risk depends the joint influence of spatio-temporal factors, such as environment, mobility, and weather, whose type and strength vary across regions and crime categories. For example, as shown in Figure [a), assaults often rise around bars during late hours, whereas thefts are more prevalent near subway stations during daytime. Prior studies that incorporate auxiliary data typically model it as homogeneous graphs, pairwise graphs, or rely on simple feature fusion (Huang et al. 2018 Zhou et al. 2024 Zhu et al. (2022). which cannot capture the high-order, dual-specific interactions of coexisting factors in shaping crime occurrence. Consequently. these methods fail to account for the latent heterogeneity of crime patterns and lead to biased predictions.
Moreover, crime data exhibits pronounced non- stationarity, challenging conventional offline models that struggle to adapt to concept drift (Tsymbal 2004). As illustrated in Figure [ crime counts in different areas fluctuate sharply over a few days, particularly in regions outlined by the white border. Seasonal and environmental factors further intensify these dynamics, leading to distributional shifts
where Pirain X * (Y( Although recent approaches (Xia et al. 2023 Zheng et al. 2022
"Corresponiigg author.

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Published as a conference paper at ICLR 2026
Yang al. 2022 attempt to extract invariant terms, they often assume complete data availability and static inter- variable relationships, limiting their adaptability to emerging dynamics.
Noww
2024-06-01
2024:06-02
2024-08-03
2024-06-04
Asssuft
Subety
Shation
Theft
@
(b)
Figure I: (a) Example of the heterogeneity of latent crime patterns: assaults near nightlife at midnight, thefts near subways in daytime. (b) Spatial distribution of "Criminal Damage" in Chicago (June 1-5, 2024), with the thite-bordered region indicating non- stationarityy.
To tackle these challenges, we propose ST-HHOL, novel Spatio-Temporaa Hierarchical Hypergraph Online Learning framework for crime prediction. To uncover latent crime patterns, we propose hicrarchical hypergraph convolution network (HHGCN), a novel idea that first builds heterogeneous hypergraphs to model latent crime patterns by integrating crime data with specific contextual factors, and then constructs homogeneous hypergraphs to model crime co-occurrence relations. HHGCN jointly captures the dual-specific crime patterns and their interaction, yielding richer and more interpretable representations. To handle concept drift in non-stationary crime data, ST-HHOL adopts an iterative online learning strategy that separates short-term fluctuations from long-term gradual shifts in streaming data. It leverages frequent fine-tuning to adapt to rapid temporal dynamics, while periodic retraining addresses long-ten spatial shifts. Moreover, to address the limited supervision of sparse crime records, we incorporate a Partially-Froon
L.M (PF-LLM) as a spatio-temporal dependency learner. PF-LLM leverages the pre-trained sequence modeling priors of GPT-2, while selectively adapting its attention mechanism to capture crime-specific dependencies.
Our main contributions are summarized as follows:
We propose ST-HHOL, an online apatio-temports crime prediction framework that jointly captures high-order, dual- spel-fpe crime patterns and adapts to concept drift.
We develop iterative online learning strategy that combines frequent fine-tuning for short-term fluctuations with periodic retraining for long-term concept drifts.
We design a hierarchical hypergraph convolution network that integrates contextual factors to uncover latent crime patterns with spatial and criminal specificity, and their co-occurrence relations.
We conduct extensive experiments on four real-worke urban crime datasets, showing that ST-HHOL. consistently surpasses oate-off-hhear baselines in both accuracy and robustness, while offering improved interpretability.
RELATED WORK
Crime Prediction. Beyond conventional statistical and machine learning approaches (Catlett et al.
2018
Kumar et al. 2020), GNN-based models-such as STGCN (Yu et al. 2018). DCRNN (Li
al.
2017), AGCRN (Bai al. 2020), MTGNN (Wu et al. 2020b), and GMAN Zheng al.
2020
exhibit considerable promise for capturing intricate spatial and temporal dependencies. To
further enhance predictive performance, some studies have integrated auxiliary data sources, including
points of interest (POI), 311 service requests (Yang et al.) 2018 Wang et al.) 2016 Huang et al.
2018), and mobility data (e.g., taxi and bike inflow and outflow) (Zhao et al. 2022
al. 2020a),
either fusing them with crime records or constructing multi-graph structures enrich representations.
Nevertheless, crime records are sparse and have skewed distribution, compounded by pronounced heterogeneity across crime types. To tackle these challenges, prior works introduce a tensor decom- position framework (Zhao & Tang 2017a) to capture inter-regional and inter-type dependencies, or employ transfer learning (Zhao & Tang 2017b) to adapt knowledge from data-rich data-scarce areas. Furthermore, fine- ane-grained spatial partitioning further amplifies the imbalance and risk of over- fitting. ST-Trans (Wu et al. 2020a) addresses this by jointly modeling spatial, temporal, and semantic
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model to jointly address Published as a conference paper at ICLR 2026
dependencies with adversarial training to enhance rare-event prediction. Similarly, NAHC Liang cet al. 2022) combines multi-graph convolution with attention mechanisms to improve hour-level forecasting accuracy.
Recognizing that spatial correlations in crime data often exhibit high-order dependencies, recent efforts have turned to hypergraph-basse methods. ST-SHN (Xia al. 202T demonstrates the utility of hypergraphs in capturing such cross-regional interactions, extending spatial correlations beyond conventional N-hop neighborhoods. ST-HSL (Li et al. 2022b) incorporates self-supervised framework, aligning global hypergraph-based features with local CNN-based ones to strengthen model robustness. Building on this, HCL (Liang et al. 2024) proposes
temporal contrastive strategy to identify co-occurrence patterns. Most recently, ST-MoGE, (Wu et al,, 2024) adopts a Mexture-of-Graph-Eiiie spatial and semantic heterogeneity in crime.
augmentation and a negative-free
Despite these advances, most prior work remains offline and cannot adapt to pronounced non- stationarity concept drift. Existing hypergraph-based crime models also build homogeneous or flat bierarchical hypergraphs directly from sparse crime records, overlooking high-order interactions between heterogeneous contextual factors and crime semantics-resullee unstable patterns under sparsity. In contrast, our approach (1) models heterogeneous latent crime patterns by assigning factor-specific hyperedges to each region-cree -crine anchor and capturing their dynamic coupling, and (2) introduces hierarchical temporal adaptation to address multi-scale concept drift two abilities absent in prior hypergraph-basse methods.
in mixed semantics and
PRELIMINARIES
In this section, first introduce the relevant definitions and formulate the research problem. The raw crime records provide timestamps, location coordinates, crime types, and additional descriptions. We organize them into processed crime data X Nx where N, and denote the number of regions, time slots, and main crime types, respectively. Each entry x represents the occurrence of crime type e in region n during time slot 1. Since crime data are often sparse and in skewed distribution, zero observations do not indicate zero risk, we further incorporate auxiliary urban sata-such as 311 service requests, weather conditions, and POI density-denoted as R XXXXXM where M is the number of auxiliary variables. The main notations and definitions are also provided in Appendix A
Problem Statement. Given the historical crime data X E NXTXC and the multi- source auxiliary data S E Nx the crime prediction task aims to learn a mapping function F(.): ( TXXXXC NCC that forecasts crime occurrences TT+1 NxC during the next time slot:
X I: S S.:T)
F(-)
T+1
(1)
Heterogeneous and Homogeneous Hypergraph. hypergraph is defined as - EV,E, To, Te). where V and & denote the sets of vertices and hyperedges, and To and Te represent their respective types. If |T.| | + |Te| > 2, the hypergraph is considered heterogeneous; otherwise, it is homogeneous. Unlike traditional pairwise graphs, where each edge connects exactly two vertices, a hyperedge can simultaneously connect multiple vertices, enabling the modeling of higher-order relations. Details of hypergraph convolution are provided in Appendix
METHODOLOGY
As shown in Figure ST-HHOL follows an online learning paradigm to tackle crime pattern specificity and concept drift. It consists of two components: (1) hierarchical hypergraph convolution network (HHGCN) that captures crime patterns with spatial and criminal specificity, as well as their co-occurrence relations, and (2) spatio-temporal dependency learner that captures temporal dynamics and spatial correlations to forecast. To handle non-stationary streaming data, ST-HHOL adopts iterative online learning strategy after warming up, where partial fine-tuning adapts to short-term fluctuations and periodic retraining addresses long-term distributional shifts. The detailed design of the pipeline and its components will be introduced in the following parts.
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Unco every halt mont:
erary months
Warm up
Fine- tune
Re-ii
Crime polterr
Time incormation
Crime recoed
External factors
Crime recond
Esterna factors
Crime recoed
Esternll
Input Layer
Encoder
Encnder
Encnder
Encnder
Encodee
Encodee
Layer Norm
Crime pottems Hyporgraph
Crime pothoms Hyporgmph
Crime paltems Hypestesph
X
Co-ocrureuue Hy Rypergraph
Co-occumeuue Hypertaph
Co-occummoo Hypergroph
Spatio Tempoml Learer
Spotio Tempona Leamer
Spetio- Temperal Leatnee
Layur Nomm
Predictor
Predictor
Predictor
Feed Forward
weight
Lusd weight
+ Addition
Forwart
Prozen
Training
C
Positional Encoding
Figure The framework ST-HHOL.
4.1 HIERARCHICAL HYPERGRAPH CONVOLUTION NETWORK
To capture the spatial and criminal specificity of crime patterns, we propose a hierarchical hypergraph convolution network to more accurately perceive the potential risks crimes. It first constructs heterogeneous hypergraphs 9 that fuse multi-source contextual signals such as POIs, 311 service requests, weather, with crime records to reveal the heterogeneous latent patterns that cannot be extracted from sparse counts. We then build homogeneous hypergraphs Go model the dynamic co-occurrence among latent crime patterns, as illustrated in Figure
Heterogeneous Hypergraph Construction. Given C' crime types and M multi-source fac- tors, we obtain the initial embeddings X E RNXC' and St RNX for all regions at time t. We construct the heterogeneous hyper- graph Oj Et), where the vertex set con- sists of all crime and contextual nodes: V; Each crime embedding "he serves primary node, and together with its contextual nodes {st. ja mm=1 forms a heterogeneous hyperedge. The latent crime pattern representations computed
Crime data
O
Contestual factors
Crime pattern
Crime patter hyperedge
Hierarchical Hypergaph
Co-occumence hypensdge
{xt,, (un,en==,.=11 U (sh 1eh.m-=1..m
Figure 3: The hierarchical hypergraph consists of heterogencous hypergraphs capturing crime pat- terns and homogeneous hypergraphs modeling co- occurrence relationships.
X = (x
where X E IR NCC denotes the latent crime patterns at time t. O' E Rl a learnable incidence matrix mapping vertices to hyperedges, and H. = N x C' is the number of heterogeneous hyperedges. The operator denotes feature concatenation, a(.) is the sigmoid activation function, and f()) is nonlinear transformation implemented by three-layer MLP with LeakyReL.U activation. For any vertex of Vr, its contribution crime pattern the X is defined as:
( 1, Phmoo 0,
of x/
o/f
of 1M otherwise,
where pl.n. (0, 1) quantifies the association strength between contextual factor of and latent crime pattern 3t ",,-
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Homogeneous Hypergraph Modeling. To capture high-order spatial co-oceurrence relationships, we further construct the homogeneous hypergraph G over the latent crime patterns. The hypergraph convolutional network aggregates the co-occurrigg patterns
E' = ( ( (D')) ( (a
where + is the homogeneous incidence matrix, and D and D'g denote the degree matrices of hyperedges and vertices, respectively. For model simplification, we approximate the matrix (D&))= - x (D'))= with a learnable parameter matrix @ E (RH))((N)), where H, is hyperpa- rameter denoting the number of homogeneous hyperedges.
4.2 SPAPIO-TEMPORAL DEPENDENCY LEARNER
To enhance
reasoning non- -tatsoationary and heterogeneous crime patterns, we adopt a Partially-Frroo -rroze- Large Language Model (PF-LLM) (Liu et al. (2025a) built on GPT-2 (Radford et al.) 2019). The key intuition that transformer self-attention is modality- forward networks (FFNs) encode generalizable sequence priors and few-shot reasoning capabilities learned from large-scale text corpora. These priors remain useful even when crime data are sparse and noisy. PF-LLM freezes the FFNs to preserve these transferable reasoning abilities, while fine-tuning the attention and normalization layers adapt them crime-specifie, spatio-temporal structures and their non-stationary dynamics.
and the pretrained feed-
For tokenization, we treat each region as token and transform crime patterns E E NxTxC into sequence E (Ei..... Ex ). where E, E RTxx encodes the C' type of crime patterns region n over T time steps. To preserve temporal semanties, we extract day-of-week (ld) and month-of-year (fm) indicators from each timestamp and encode them using one-hot vectors followed by sinusoidal positional encoding sin(-). The resulting temporal embedding Er combines multiple periodic components E and E
E sin(ta),
ET sin(tm),
ET
E ET.
(5)
To align the input dimension with the hidden space of GPT-2, we apply a set of non-linear transfor- mation layers-one for each crime type and additional one for temporal features-to project the raw inputs into the model's latent space. We also incorporate Pre-Layer Normalization (Pre-LN) scheme (Huang et al. 2023 Liu et al. 2025b) to stabilize training and accelerate convergence. The resulting representations are then fed into the partially frozen GPT-2 architecture as follows:
H' Concat (Ei), (fi,), ..r......o(EBB (C(E), (Er)),
H ' (H)( + H', H FFN((NN(H))) + H
where fi...., fcr fC+1 are non-linear functions that project C' crime types and one temporal feature into the model's latent space. {Ei..... Ec} E xCxN** XT represent the tokens distinguished by crime types. Concat(-) denotes the concatenation operation. H denotes the initial input embedding, H' is the input to the I-th layer, H' is the intermediate representation produced by the unfrozen Layer Normalization (LN) and Multi-Head Attention (MHA) components, and H is the output by applying the unfrozen LN and the frozen FFN. The MHA, LN, FFN operation is formally defined as:
MHA(H') = Concat(head,,.. head,,
) W
LN(H') =
H'
P σ
B
(H'W9) W
head, = softmax
H' H'WV FFN(H') = ReLU(W H' W,) + b
Vdl
where 7 and B are learnable scaling and translation parameters, j and o represent the mean and standard deviation, respectively. @ denotes the Hadamard product. W W W and W denote the projection mappings for the output, query, key, and value, respectively. head, represents the i-th attention head, d, represents the dimension of each attention head. W, and W, are the weights of the linear transformations, and b,, ba are bias terms.
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4.3 ONLINE LEARNING STRATEGY
Conventional offline models often implicitly assume a stationary data distribution. However, crime patterns inherently susceptible concept drift, which be formally characterized as:
プイ> O, ( X) P+++ X)) 2 6,
(8)
where P.(Y) X) denotes the conditional distribution of crime events time t. DKL denotes the Kullback-Leibler divergence, and ő is a predefined divergence threshold.
To address the non-stationary nature of crime dynamics, we propose an iterative online learning strat- egy for ST-HHOL that explicitly disentangles spatially invariant and temporally variant components. While crime co-occurrences exhibit volatility over time, as shown in Figure [T]). the heterogeneous components driving crime patterns and their strengths remain relatively stable across space. We parameterize short-term fluctuations and long-term gradual shifts {O,; Oa(()) C O, where:
e Parameters encoding spatial invariance and long-term gradual shifts. These parameters are associated with the first-stage hypergraph Gf, which constructs crime patterns from multi-source inputs S' and crime records X'. Given their dependence on relatively stationary spatial attributes, such as sociocconomic indicators and POIs, + evolves slowly over time and can be modeled
de, dt
R O,
++ = O + E 6. ((0
1.
Oa((): Parameters capturing short-term temporal fluctuations. These parameters associ- ated with the second-stage hypergraph Gü. which captures rapidly evolving co-occurrence structures among crime patterns E'. Unlike e a reacts abrupt regional fluctuations, characterized by || || > 0. Such shocks trigger enforcement adjustment L Lद + ( and consequently reshape regional interactions D Di + g( L,+1), where and g denote the response and coupling mechanisms, respectively. Consequently, the dynamic parameters evolve more rapidly and can be modeled as:
O +/.
(10)
Thus, after initial warm-up. ST-HHOL adopts iterative two-phase update scheme. This design balances short-term responsiveness with long-term stability and improves robustness under non- stationary crime dynamics:
Every t steps, the spatially invariant parameters O, are frozen and only the temporally dynamic parameters @a(t), along with the spatio-temporal dependency learner OFF-LLM, are updated. This phase enables rapid adaptation to recent fluctuations by solving:
Fine-tuning Phase:
mingxe, C C(Y+1,, ( (.)):
Retraining Phase: Every T steps (T r), O unfrozen and jointly updated with Oa(t). This phase captures long-term gradual shifts and evolving co-occurrence structures by optimizing: ming L cy (())
4.4 MODEL PREDICTION AND OPTIMIZATION
Under different online learning modes, ST-HHOL maintains unified prediction and loss computation framework. The output H'+1 from the final layer of the spatio-temporal dependency learner is passed through crime-specific regression heads to generate future forecasts:
Concat [RConv, (H(+*), RCony (H{+)))
(11)
where g++l e NCC denotes the predicted crime records for the next time slot.
So far, the loss function of ST-HHOL consists of prediction loss and hypergraph regularization loss:
y y + 41 1 +2 10
(12)
r+1 where Y the ground-trutt value at time slot + 1, ! and e ++1 are the incident matrix elements of the crime patterns within heterogeneous hypergraph Gi+1 and the co-occurrence relation- ships within homogeneous hypergraph Gh at t respectively. \ and X are two hyperparameters balancing the loss terms.

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Published as a conference paper at ICLR 2026
5 EXPERIMENTS
In this section, we evaluate our proposed ST-HHOL framework on four real-world urban crime datasets. Extensive experiments are designed to address the following research questions:
RQI: How does ST-HHOL perform on crime quantity and occurrence prediction?
RQ2: How does each module within ST-HHOL enhance the overall model performance?
RQ3: How do varying retraining and fine-tune soneetnnngg frequencies affect the performance?
RQ4: What impact do different hyperparameter settings have on ST-HHOL?
RQ5: Does the hierarchical hypergraph constructed in ST-HHOL enhance model interpretability?
Table I: Summary of the four urban crime datasets.
Datasets
Region Num
Time Span
Time Interval
Crime Data
CHI
77
January 1, 2023
December 31, 2024
day
Theft, Battery, Assault, Damage Larceny, Assault, Mischief, Robbery Theft, Assault, Vehicle, Mischiel Assault, B&E, Robbery. Theft
NYC 123
January 1, 2022-
December 31, 2024
1 day
PHI
6
January 1, 2023-
December 31, 2024
1 day
TOR
158
January 1. 2023-
December 31, 2024
day
Datasets & Baselines. We conduct experiments four urban crime datasets from Chicago (CHI), New York City (NYC), Philadelphia (PHI), and Toronto (TOR) with multi-source contextual data, including 311 service requests, weather, and POI distributions. For comparison, we include broad range of baselines; statistical methods (SVM (1998), ARIMA (2015)), spatio-temporal forecasting models (DCRNN (2017). STGCN (2018), AGCRN (2020). MTGNN (2020b), GMAN (2020).
MoSSL (2024)) crime prediction models (DeepCrime (2018), ST-HSL (2022)), ST-SHN (021)), and online learning models (DLF (024). FSNet (2023). OneNet (2023). More details about the datasets and baselines are provided in Appendix D We evaluate offline baselines under two settings
(Pre-trained and Re-trained), while online baselines under their inherent Online setting:
Pre-trained: models are trained once on the full dataset under the conventional offline setting.
Re-trained: offline models are adapted into an online variant, which is periodically retrained every
two months using streaming data after initial warm-up.
online models incrementally update according to their native online learning strategies using streaming data.
Online:
Implementation Details. All models are implemented in PyTorch 2.0 and trained on an NVIDIA RTX 3090 GPU. We use the Adam optimizer with a batch size of 32, an initial learning rate of le -3 and a decay factor of 1 -4, The number of hyperedges in go is set to 64. PF-LLM utilizes GPT-2 (Small), comprising 2 layers, 12 attention heads, and hidden size of 768. X and X2 are both set to 0.1. The dataset is chronologically split into warm-up and online training phase in a 25:75 ratio. Following (Liang et al., 22224] Wu et al. 2024), we set the temporal input length to 7 and the forecasting horizon to I. More settings and eva evaluation metrics are provided in Appendix D.3 D.4
Table 2: Overall performance of crime quantity prediction over CHI, NYC, PHI, and TOR datasets. The results are 5-run error comparison, the bold font means the best result.
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131
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103
233
1240
235
174
13:
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Published as a conference paper at ICLR 2026
5.1 COMPARISON TO STATE-OF-THES METHODS (RQ1)
Table and Table summarize ST-HHOL's performance on crime quantity and occurrence prediction. ST-HHOL consistently outperforms all baselines across all datasets, with complete results and visualizations provided in Appendix E.. and E.3 For quantity prediction, ST-HHOL reduces average MAE and MAPE by 5.37% and 9.21% on CHI. 3.52% and 8.83% on NYC, 2.97% and 5.85% on PHI, and notably 6.45% and 11.32% on TOR dataset, demonstrating its effectiveness across diverse urban environments. Notably, converting the offline model to an online learning paradigm further improves performance on non-stationary crime data.
In occurrence prediction, ST-HHOL. achieves gains of 0.94% (Micro-F1), 1.09% (Macro-Fl), and 1.69% (TZR) on NYC; 0.70% (Micro-FI), 0.70% (Macro-FI), and 3.08% (TZR) on CHI. The consistent superiority in True Zero Rate (TZR) across all datasets particularly confirms ST-HHOL's robustness in handling data sparsity and skewed distributions, effectively identifying true zero- occurrence scenarios that are prevalent in crime prediction tasks.
In addition, we evaluate robustness, scalability, complexity, and execution efficiency, with detailed results reported in Appendix E.2 E.4
Table 3: Comparison of crime occurrence prediction over NYC and CHI datasets.
Dalaset
Metric
SVM
ARIMA
DCRNN
STGCN
DeepCrime
GMAN
STNN
OneNet
DI.F
STTHOL
Micro-FI
0.478
0.452
0.562
0.569
0.575
0.553
0.635
0.602
0.638
0.644
NYC
Macro-F1
0.493
0.468
0.570
0.573
0.580
0.556
0.636
0.606
0.640
0.647
TZR
0.482
0.475
0.564
0.558
0,589
0.588
0.647
0.615
0.652
0.663
Micro-FI
0.608
0.565
0.648
0.678
0.063
0.679
0.710
0.661
0.692
CHI
Macm-Fi Fl
0.606
0,574
0.649
0.679
0.669
0.681
0.712
0.664
0.693
0.717
TZR f
0.603
0.579
0.637
0.675
0.676
0.669
0.714
0.673
0.688
0.736
5.2
ABLATION STUDY (RQ2)
To comprehensively assess the contribution of each component in ST-HHOL, compare
0,692
0.60
0.80 0,789
0.68
0.64
0.76
0.759
0, 0.742
several variant models as follows: (1) w/o g"; removes the multi-source input and the het- erogeneous hypergraph in HHGCN; (2) w/o 9o: discards the homogeneous hypergraph in HHGCN; (3) w/o Er: inputs only crime patterns into the spatio-temporal dependency learner, excluding temporal information; (4) w/o PF-LLM: removes the PF-LLM compo- nent and replaces it with standard Trans- former. (5) w/o OL: removes the online learn- ing strategy and reverts to the standard offline setting. The ablation study results over four datasets shown in Figure
0.6L7
0.60
wio G
wio E
wb PF-LLA
web OL
STHHOL
wio E
wo LLM
w/o OL STIHHO
wo
wio
wib
3.625
3.6
5.430
0.813
3,422
0.80
0.769
0.787
3.0
2,037
0.76
0,55
0.72
wio G
wo E, w/ PF LLMLL
wo el
STHHOL
wia
wib Gr
E, wi PF LLM
wio OL
STHHOL
Figure 4: Ablation experiment results.
Each component contributes to the overall performance ST-HHOL. G and Go enhance accuracy by capturing crime-specific and co- occurrence dependencies, respectively. The partially frozen strategy leads to a more efficient transfer of few-shot reasoning ability than standard Transformer trained from scratch. Moreover, the incor- porated online learning mechanism enables the model to adapt concept drift in evolving crime patterns continuously.
Pustram
Full Tuning
PFA
P1-1th (STHHOL)
We also compare several PF-LLM variants: (1) Frozen Pretrained Transformer (FPT); (2) models without pretraining (No Pretrain); (3) fully tuned models with no frozen layers (Full Tuning): (4) freez- ing only attention modules (PF-A); and (5) freezing only FFN layers (PF-FFN). As shown in Figure 5 FPT exhibits limited adaptabil- ity. whereas Full Tuning reduces errors but incurs higher variance (RMSE), indicating overfitting on sparse data. By contrast, PF-FFN achieves better trade-off between retaining pretrained knowledge and adapting to the target domain.
Figure 5: Comparison results for different variants of PF. LLM.
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5.3
TIME ADJUSTMENT ANALYSIS (RQ3) & HYPERPARAMETER EEPERRARAMETER STUDY (RQ4)
MAE MAPE (scaled)
Once Month
Once Two Months
Once Three Months
Once per Four Months
1.18
0.76
1.16
RMSE
1.14
MAE
RMSE
MAPE
MAE
RMSE
MAPE
MAE
RMSE
MAPE
MAE
RMSE
MAPE
Updane: 0.25 mo
Update: mo
Update: 0.75
Figure 6: The time adjustment study on the frequency the fine-tuning and retraining. For intuitive comparison, we scale MAPE to the same vertical axis as MAE.
To assess the impact of retraining and fine-tuning frequency in online learning, we evaluate ST-HHOL under retraining intervals of {1, 2, 3, 4} months and fine-tuning intervals of {0.25, 0.5, 0.75} months (the latter used only with 3-month retraining interval). To justify these choices, we first conduct an FFT-based decomposition of the crime series. The analysis reveals pronounced periodic components two scales: (1) short-term cycles within 1-3 weeks, reflecting fast behavioral fluctuations, and (2) long-term cycles spanning 1-4 months, corresponding slower structural changes. Such multiscale periodicity aligns with the known nature concept drift in spatio-temporal crime data. Consequently, the retraining intervals T {1, 21,2,3 3, 4] months are designed to capture longer-term drift, while the fine-tuning intervals т E {0.25, 0.5, 0.75] months short-temn dynamics.
are chosen to align with
Experiments on the CHI dataset (Figure 6 report average results across all crime types. Notably, biweekly fine-tuning (0.5 months) consistently outperforms weekly updates (0.25 months), indicating that crime dynamics evolve over a roughly two-week horizon, while overly frequent updates may induce catastrophic forgetting. A two-month retraining interval offers the best trade-off' between adaptability and stability. Although 0. 75-5mmoth fine-tuning slightly improves RMSE and MAPE under the 3-month retraining setting, it does not reduce MAE, limiting its utility. Overall, combining two-month retraining with biweekly tine-tuming proves to be the most effective strategy.
MAE /MAPE (scaled)
Batch
Hyperedge
Dimension
Layers
1.20
0.80
RMSE Value Value
1.15
0.75
1.10
0.70
1.05
8
64
16
128
MAE
RMSE
MAPE
Figure 7: The impact study of different hyperparameter settings over the CHI dataset. Average MAE, RMSE, and MAPE (scaled to align with MAE axis) are reported across all crime types.
We conduct sensitivity study to evaluate the impact of key hyperparameters ST-HHOL using the CHI dataset, as shown in Figure Specifically: (1) Batch Size: Among (4, 8, 16, 32, 64), batch size of 32 yields the lowest prediction error. (2) Hyperedge Number: Varying the number of hyperedges (H,) in G among {8. 16, 32, 64, 128). Setting to 64 yields the best performance, while increasing to 128 introduces redundancy and increases eттоr. (3) Hidden Dimensio on: We explore hidden dimensions of features among {8, 16. 32, 64, 128). Setting to 16 offers the best performance, while overly high dimensions may amplify prediction errors, such MAF. (4) PF Layers: We evaluate the number of partially frozen layers in the PF-LLM from to Setting to offers the optimal trade-off across metrics, while unfreezing more than two layers leads to overfitting under sparse and long-tailed crime data, disrupting pretrained inductive biases.
5.4 CASE STUDY (RQ5)
We visualize the crime co-occurrence relationships captured by the homogeneous hypergraph and the heterogeneous influences of multi-source data constructed by the heterogeneous hypergraph in Figures and respectively. Key insights include: (1) ST-HHOL captures complex crime co- occurrence patterns. Hyperedge es links frefrruuency regions, 1s and ez7 cover mid-frequency

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Overall Battery Crime
e_8
e_16
e.37
e_51
1.00
Normalized Intensity
Crime Count
0.75
0.50
0.25
0.00
Figure 8: The visualization of the homogeneous hyperedge of crime co-occurrence relations, taking Battery on May 30, 2024 in Chicago as an example.
Assault Nune)
Assault IDecemberi
Theft (une)
Theft (December)
Loop
0.96
0.83
0.93
0.80
Near South
0.63
0.45
0.61
0.46
Austin
0.29
Dunning
0.04
0.31
-0.44
0.22
Albany
Hum
Hum
Figure 9: The visualization of the impact multi-source factors on crime patterns across types and regions, captured by heterogeneous hyperedges. (CDOT: traffic order, DOB: building violations, Rest: restaurants, Rail: railway stations, Une: unemployment rate, Tem: temperature, Hum: humidity)
areas, and 6şI clusters high-frequency regions. (2) ST-HHOL reflects cross-region and cross-crime type heterogeneity. Crimes in the Loop are shaped restaurant and station densities, while in low-income areas like Austin, the unemployment rate is the dominant factor. (3) ST-HHO effectively adapts the temporal evolution. Compared to December, elevated temperatures in June significantly intensify Theft and Assault in commercial zones such as Loop and Near South.
6 CONCLUSION AND LIMITATIONS
In this paper, we propose ST-HHOL, an online spatio-temporal learning framework that models crime dynamics with hierarchical hypergraph and adapts non-stationary environments. Leveraging PF-LLM further enhances its ability to learn from sparse and evolving dependencies. Experiments on multiple urban crime datasets show that ST-HHOL achieves superior accuracy, robustness, and interpretability, while offering insights into the dynamics of crime occurrence.
We identify two main directions for future work. First, although ST-HHOL performs well four diverse urban datasets, its generalizability warrants evaluation across a broader range of cities with heterogeneous urban structures and socioeconomic conditions as more high-quality streaming data become available. Second, this study focuses structured spatio-temporal features; integrating multimodal signals, such as textual reports, video, or social media streams, could uncover richer latent factors and improve the modeling of complex crime dynamics.
7 ETHICS STATEMENT
The goal of ST-HHOL is to analyze long-term and latent data, rather than support real-time operational decisions or individual- levell risk assessment. The framework operates exclusively region-level aggregated crime statistics and does not incorporate individuals, demographic attributes, law enforcement resources. Consequently, its outputs char- acterize relative temporal and spatial trends across regions and crime types, instead of actionable signals for targeted intervention, which structurally limits risks biased profiling or over-policing
crime patterns in streaming
We evaluate ST-HHOL across regions with heterogeneous socioeconomic characteristics and observe consistent predictive behavior, indicating that the learned representations are driven primarily by spatio-temporal structure rather than latent demographic bias. Under these constraints, ST-HHOL intended as an analytical tool for understanding urban crime dynamics, not for prescriptive or punitive decision-making.
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ACKNOWLEDGMENT
This research was conducted by the ARC Centre Excellence for Automated Decision-Man Making and Society (ADM+S, CE200100005), and funded fully by the Australian Government through the Australian Research Council.
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Supplementary Material
ST-HHOL: Peatio-Tempora Hierarchical Hypergraph Online Learning for Crime Prediction
TABLE OF CONTENTS
A Notations..
Extended Related Work.
C More Details of Hypergraph
Experimental Details..
15
D.1
Datasets Details...
D.2
Baseline Details..
D.3
Evaluation Metries Details.
D.4
Experimental Settings..
E
More Experimental Results
E.1
Complete Comparison Results
18
E.2
Robustness Analysis..
20
E.3
Scalability Analysis
20
E.4
Efficiency Analysis...
20
E.5
Visualization of Prediction Results.
F
The Use of Large Language Models (LLMs).
A
NOTATIONS
Key notations used in the paper and their definitions summarized in Table Main notations and their definitions.
Table 4:
Notation
Definition
X
the crime data at time t, X E RNC the auxiliary data at time S' NMM the number of regions
S
N
C
the number of crime types the number of auxiliary data the crime patterns at time t, E' R NxC the heterogencous hypergraph of HHGCN the homogeneous hypergraph of HHGCN the incident matrix of G at time & the incident matrix of g at time t the number hyperedges 9 and G
M
E'
ge
go
Oc
Ho. H.
B EXTENDED RELATED WORK
Online Learning. Online learning has emerged as an effective paradigm for handling concept drift in streaming data [Tsymbal 2004), enabling models to adapt to evolving data distributions through continual updates. This capability makes it particularly suitable for real-time applications such as recommendation systems (Song et al. 2014 Zhou et al. 2019) and network security detection (Yu) et al. 2021). Recent efforts have focused on developing adaptive update strategies that trade off knowledge retention and model plasticity, especially in long-term forecasting tasks. For example, Ddg-da (Li et al., (202a),, FSNet (Pham et al. (202)), and LSTD (Cai et al.) (2025) explore different mechanisms to maintain stable performance over time. OneNet (Wen al. 2023) proposes
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dynamic ensemble strategy that adjusts the weights of dual-stream models based the distribution of streaming data, rather than relying on a single model.
In the context of urban spatio-tempores data, concept drift often manifests gradually. DOST (Wang ct al. 2025) addresses this by employing an twake-hibernad learning strategy to adapt to non- stationary patterns. Similarly, DLF (Wang et al. 2024) decomposes time series into seasonal components and latent trends, using iterative updates to track evolving dynamics. However, crime data present additional challenges due their inherently abrupt fluctuations- that offline models trained solely on historical data struggle to capture. To address these challenges, we propose an online learning framework, ST-HHOL, specifically designed for crime prediction. ST-HHOL iteratively fine-tunes to capture short-term fluctuations, while periodically retraining to adapt to long-term gradual shifts in crime patterns. The detailed description of the ST-HHOL. presented in Section
surges or drops
C MORE DETAILS OF HYPERGRAPH
A hypergraph (Sun et al. 202 lb can be defined as = (V,E, TeJ. Here, is the set of vertices and & the set of hyperedges. Ty and Te denote the sets of vertex types and hyperedge types, respectively. If [Tel + iTel 2, the hypergraph is heterogeneous. Otherwise, the hypergraph is homogeneous. Compared to pairwise graph, in which each edge connects two vertices, a hyperedge in hypergraph can connect more than two vertices. For any hyperedge E it can be denoted e {U): Uj....., ] C V. A positive diagonal matrix W R [ denotes the hyperedge weights. The relationship between vertices and hyperedges can be represented by an incidence matrix H I [e] with entries defined as:
[1, if E H (0. otherwise.
(13)
Let D. E M and D. E RlEI denote the diagonal matrices containing the vertex degrees and hyperedge degrees, respectively, where (D,)a = Eeer We Hi,e and (De)is = -vev Hnj-
The hypergraph convolution operator can be defined as θ o (D. HWD, D., +) and the hypergraph Laplacian can be denoted as I
D MORE DETAILS OF DATASETS AND BASELINES
D.1 DATASETS DETAILS
We conduct experiments four real-world urban crime datasets from Chicago (CHI New York City [. Philadelphia (PHI and Toronto (TOR 4 as summarized in Table 5 Each dataset includes four major crime types, with corresponding timestamps and spatial locations. The CHI and PHI datasets contain records for 77 boroughs in Chicago and 6 boroughs in Philadelphia, respectively, spanning from January 1, 2023 December 31, 2024. The NYC dataset covers 123 police districts from January 1, 2022 to December 31, 2023, while the TOR dataset includes 158 neighborhoods with daily crime records from January 1, 2023 to December 31, 2024. addition, we collect diverse multi-source contextual data, including dynamic 311 service requests, weather conditions, static POI distributions, and socio-cconomic indicators. Detailed categories and variables are provided in Table
D.2 BASELINES DETAILS
We select 14 representative baselines spanning traditional models and state-of- state-of-the-ars the-art deep learning approaches. The baseline descriptions are organized as follows:
Chicago data portal is available at: htt.tppp///ttaaattcccllaapppp
"NYC open data available /
"Philadelphia open data is available at: hts http:pp//ooommetapphh1yy.oo
Toronto Police Service Open Data: hta.thhtta http:s///bbaaatccroooppll.......
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Table Summary of the four urban crime datasets.
Datasels
Region Num
Time Span
Time Interval
Crime Data
CHI
77
January 1, 2023
December 31, 2024
day day day day
Theft, Battery, Assault, Damage Larceny. Assault, Mischief, Robbery Theft, Assault, Vehicle, Mischief Assault, B&E. Robbery. Theft
123
January 1, 2023
December 31, 2024
January 1, 2023
December 31, 2024
TOR
158
January 1. 2023
December 31, 2024
Table 6: The description of variables contained in multi-source data.
Datasets
311 Service Types
POI
Weather
Others
Streets and Samitation
CHI
CDOT
Department of Transportation
Restaurant&Café
Temperature
DOB Buildings
School& University
Income Unemplayment rate
Humidity
Ieleaal Parking
Plagrronng
Windspeed
NYC
Noise - Residential
Hospital
Blocked Driveway
Railway station
Abandoned Vehicle
Shopping
PHI
Illegal Dumping
Bank, Police
Graftiti Removal
Entertainment
Property & Favironment
TOR
Noise Roads & Traflic
SVM (Mattera & Haykin 1998): Learns maximum-margin hyperplanes in kernel-induced feature spaces for time series regression.
ARIMA (Box et al.
2013): Combines autoregressive integration with moving average components
to handle non stationary temporal patterns.
DCRNN (Li et al.
2017): Models spatial diffusion processes via bidirectional random walks, architecture for temporal modeling.
coupled with sequence-to-sequeee
Establishes spatio-temporal correlations through stacked graph convolu- tions and temporal gated convolutions, eliminating recurrent units.
STGCN Yu al.
2018):
AGCRN Bai et al.
2020): Automatically infers node-wise dependencies with adaptive graph
generation while learning personalized patterns through node-specific parameters.
MTGNN (Wu et al.
2020b): Designs mix-hop graph diffusion layers with dilated temporal
convolutions capture multi-range spatio-temporal dependencies.
GMAN (Zheng al.
2020): Integrates spatial attention and temporal attention in stacked trans-
former blocks for cross cooss-space-tiee dependency modeling.
2024): Constructs multi-granularity self-supervision tasks to enhance repre- sentation learning for temporal, spatial, and feature variations.
MoSSL (Deng et al.
DeepCrime (Huang al. 2018 : Unifies crime embedding learning with hierarchical attention dimensions.
mechanisms over spatio-temporal-categrrr
ST-HSL (Li et al. 2022b): Addresses label scarcity through hypergraph structure learning and contrastive self-supervision on region representations.
ST-SHN (Xia et al. 202I): Models crime category dependencies via multi-channel hypergraph
routing in sequential prediction framework.
2024): Decouples trend-seasonal patterns through frequency domain analysis with momentum-updautt dual experts.
DLFF (Wagg et al.
2023): Balances fast adaptation and memory retention via parameter-efficient adapter modules and Hopfield network-based associative memory.
FSNet (Pham et al.
2023): Dynamically fuses temporal and cross-variable dependency models through meta-leamed architecture controller.
OneNet (Wen et al.
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D.3 EVALUATION METRICS DETAILS
Crime quantity prediction. To assess the performance of crime quantity prediction, we employ the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) as the evaluation metrics. MAE measures the average magnitude of errors in predictions, providing an intuitive sense of the overall prediction accuracy. RMSE penalizes larger errors more heavily, thus highlighting the model's sensitivity to significant deviations. MAPE expresses prediction errors as percentage, providing scale-independent evaluation that is particularly useful for comparing performance across different regions or periods.
1 N
MAE(U. 0)
Vn Unl
(14)
RMSE(Y. =
(i/ - 0nn2
(15)
n=1
MAPE(y.0)
1
yn
In
(16)
N
where y represents the actual value, represents the prediction. N denotes the total number of regions.
Crime occurrence prediction. For crime-occurrenc, prediction (binary: 1 crime occurs, 0 no crime), we define the confusion counts over all N samples as:
N TP
1s = 1A = 1}.
FP = 1B = - In =1},
==1
==1
NN
N
FN
Σ
1in 1 0}, TN= Σ
1 = 0 9n 0),
(17)
==1
where yn {0, 1) is the ground-truth label and 9. {0,1) is the predicted label.
Precision, recall and Fl for the positive class (crime occurrence) are as follows:
TP
TP
2- Preciision Recalll
Precision) FP
Recall
Fl Precision; + Recalll
FN
(18)
Precision, recall, and F1 for the negative class (no crime) can be computed follows:
TN
TN
2 Precisiong Recallo Precisiong Recallo
Precisiono
Recall
Flo
TN FN'
TN + FP
(19)
In total, Macro-F1 and Micro-F1 can be defined as:
Macro-F1 F1, Flo
E7E (0.1) TP.
TP +NN
Micro-F1 2E. + E. PP. + PN,
(20)
D.4 EXPERIMENTAL SETTINGS
All experiments are conducted server equipped with NVIDIA RTX 3090 GPU using PyTorch 2.0. We implement ST-HHOL and all baseline models in a unified framework to ensure fair com- parisons. We use the Adam optimizer with initial learning rate of 1 10-3 decay factor of i x 10-4 applied periodically, and a batch size of 32. Model training is conducted for a maximum of 100 epochs with early stopping strategy triggered if validation performance does not improve for
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10 consecutive epochs. The dataset is chronologically split into warm-up and online training phase in a 25:75 ratio. The warm-up phase is further divided into training and validation subsets in 7:3 ratio. Following prior studies (Li et al. 2022b; Liang al. 2024 Wu et al. 2024). we set the temporal input length to 7 and the forecasting horizon to 1. Kach deep learning model is trained and evaluated across five independent runs, and the final performance is reported as the mean of the evaluation metrics. For ST-HHOL, the loss function includes two balancing coefficients a and Ag. both set 0.1. The core component of the spatio-temporal dependency learner PF-LLM, is instantiated with GPT-2 small architecture with two layers, a hidden size of 768, and 12 attention heads. The internal hidden dimension of ST-HHOL is set to 16, and the number of hyperedges in the homogeneous hypergraph 9 is set to 64.
E MORE EXPERIMENTAL RESULTS
E. COMPLETE COMPARISON RESULTS
For fair comparison, except for the online models DLF, FSNet, and OneNet, we transform all offline baseline models into an online version. Specifically, these models are periodically retrained using new streaming data after the initial warm-up phase. Tables 7 8 and 10] ST-HHOL with variety of baselines across several crime types and datasets. ST ST-HHOL consistently outperforms all baselines across different datasets and metrics. For quantity prediction, it reduces average MAE and MAPE by 5.37% and 9.21% CHI, 3.52% and 8.83% on NYC, 2.97% and 5.85% on PHI, and 4. 12% and 7.94% on TOR, demonstrating its effectiveness and generalizability.
Moreover, summarize the key findings follows: (1) ST-HHOL consistently outperforms all baselines across crime types, metrics, and datasets. This superior performance is attributed to its hierarchical hypergraph design, which effectively models spatial and criminal specificity, thereby enhancing robustness and generalization. (2) ST-HHOL achieves significantly lower MAPE than the second- best models, demonstrating stronger capability to accurately detect non-zero crime occurrences. This indicates that ST-HHOL is more effective at uncovering latent crime patterns and generating precise predictions.
(3) The online learning strategy tailored in ST-HHOL effectively addresses concept drift, outperforming methods like FSNet, OneNet, and DLF, whose update mechanisms are not optimized for the dynamic and heterogeneous nature of crime data. Moreover, FSNet and OneNet, originally designed for long-term sequences, struggle to adapt to highly varied crime types, limiting their effectiveness in evolving scenarios. (4) Existing spatio- temporal models, such DCRNN and STGCN, can capture temporal dependencies but often underperform when facing crime pattern heterogeneity and skewed distribution. For instance, while they achieve competitive performance on Assault in NYC, they struggle on several high-frequency crimes like Theft and Battery in CHI. In summary, ST-HHOL not only delivers superior predictive performance but also demonstrates enhanced stability across diverse crime categories and spatial distributions.
Table 7: Overall performance of crime prediction on CHI dataset. The results are 5-run error comparison, the bold/ / underlined font means the best / the second-best result.
Method
MAE
Theit RMSSE
MAPE
MAE
Rartery RMSE
MAPE
MAE
Assaui RMSE
MAPE
MAE
Damage RMSE
MAPE
SVM
1.54
1.75
0.51
0.94
1.89
0.56
0.60
0.98
0.51
0.69
0.94
0.52
ARIMA
1.52
1.76
0.52
0.99
1.72
0.61
0.91
0.96
DCRNN
291 2m.
3.94 aam
201
3.17 ss.6
20m0
200
0.98 2s1
2010
21:1
1.75 4mm
0.46 21:
STGCN
2,82 20.0
3.66 1m7
0.58
2009
2.03 2014
2.74 22:
0.61 230
0.50 200
1.45
2015
0.45
2M:4
2010
2.19 2am
0.57 c00
AGORN
0.99 gm11
1:53 ==m
0.50 2017
0.88 2917
1:31 2m
0.51 2m0
0.54 2pm
0.88
0.66
2m
0.65 2m
0.99 2017
0.57
MIGNN
1,45 2m
2.34 2e.a
0.58
TD6 2m
1.56
0.00
0.36 201
1.04
0.70
0.90 2::1
1.11 2m3
0.71
GMAN
L.6
2.12
0.92
1.44
0.53
0.74
1.45
1.31
0.65
McSSL
Lcan
18x
1.33 41:3
0.85 -011
10:0
0.92 1MU
DeepCrime
1.27 2014
1,66 1825
0.57 Ja0
0.94 Joss
1.34 1027
0.59 1307
0.68 ruee
0.91 .o.5
0.51 1611
0.69 1022
1.01 JXIS
0.65 .A30
ST-SHN
1,07 20:8
1.63 2817
0.67
20t5
0.90
2011
1.35 2x31
0.78 a30
0.69 330
0,90 2001
0.52 2MM
0.68 st14
1.03 2113
0.67 2015
ST-HSI.
1.13 2r9
1.68
0.50
0.94
1.31
0.52
066
0.99
0,42
0.72
1.03
0.47
2.89 1011
2011
1.87 2015
2.10 1AH
FSNet
2.24 2018
3.17 1834
0.60 2011
1.99 2005
2.38 2019
0.53 2308
0.99 2x12
1.12 2006
0.45 260
0.96 10:
1.30 2m1
0.63 2015
OneNet
2.53 gr
3.25 1313
0.58 2017
1.53 2014
2.04 mm
0.54 2m11
1.06 2011
1:24 g111
0147 2mm
1.00 2017
1.48 2m13
0.64 2m
ST-HHOL
(Ouns)
0.95
1.52
0.43
0.87
1.26 2mi
0.46
0.51
0..84
0.27
1158
0.90 2310
0.40
'The source code of GPT-2 is available at: https::/huugg htwphhhuggggggggccccooc httpaaaccco/ppaaaaaaaaaaa -ommmnniccoooooooooo
2
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Table 8: Overall performance of crime prediction on NYC dataset. The results are 5-run error comparison, the bold/ / underlined font means the best / the second-best result.
Model
MAE
Larceny RMSE
MAPE
MAE
RMSE
MAPE
MAE
Mischief RMSE
MAPE
MAE
Robbery RMSE
MAPE
SVM
1.81
2.55
0.61
0.79
1.29
0.53
0.50
0.97
0.68
0.80
1.13
0.69
ARIMA
2.58
1.21
0.76
1.16
DCRNN
1.42am0
2.67
044
g.8
1.60ga
g.50
0.33
0.76-au
0.20
0.62a
1.6g
0.20gam
STGON
1.4
2.44
mm30
0.66
1.76g3
0.46
0.35
0.17aem
0.70amm
1.14gm
0.20gam
AGCRN
1.26.115
2.19
0.74
1.06:3.e
0.52
1.16.as
0.31
MIGNN
1.44
2.26
0.57
1,54
a.60
0.85
1.06-aae
0.72
0.86
1.8
0.70aam
GMAN
1.5621m
2.64gr m
0184
1.63gmm
g.71
1.04gm
1 1,87
0.75gem
1
1.77gme
0.87
MoSSL
0.98
1.8
1.06:am
0.56xea1
0.54
1.6
3.21
DeepCrime
1.36230
2.642m:
0.59
2.82
1.18
2.45
0.64
0.88
0.20
0.68am1
1.302mm
0,40z
ST-SHN
1.32
2.16
0.51 a1
0.75
1.10
0.35
0.84 0.49
0.27
0.57
L.1::uus
0,36 1su
ST-HSL
1.25
2.35
045-am
0.77
432
0.44.0m
0.65
0.95-am
0.44
0.79
0.47
DLF
148:30
3,23ica
0.38
194
0.33
0.06xcay
1.44-am
0.40:e21
0.30
FSNet
1,3430
3,02
0.51
0.96
1.9
2.44
0.87
1 86
0.462em
1.12
1 160gme
0.32gan
OneNet
1.23a1
2.99
0.52-am
6.82
1.1
0.47
0.73
1.50.an
0.46.aa
1.09
1.24:0m
0.35 jau
ST-HHOI.
(Ours)
0.97
1.84g
0.35
0.66
1.05
2.29
0.34gmm
0.73
0.15
0.50
1.04
0.18aam
Table 9: Overall performance of crime prediction on PHI dataset. The results are 5-run error comparison, the bold/ underlined font means the best / the second-best result.
Model
Theit RANNE
Assanlt RMSE
Vehicle RMSF
Mischief RWSE
MAF
MAPE
MAE
MAPE
MAR
MAPE
MAR
MAPE:
SVM
6.82
4.76
3.49
3.65
ARIMA
3.68
6.89
0.41
3.89
4.87
0.42
2.62
3.78
0.49
3.34
3.72
0.58
DCRNN
5.86
7
0,57=mm
2.6
0.43
3.09
3.89g2
0.47gen
3.43gm7
4.52gt
0.S0gam
STOCN
7.47am3
3.60
4.17,3
3.50.223
2.78
3.62:244
AGCRN
3.13
6.62
0.39 -u0
3.18
4.0
0.39
2.68
3.46-a1
2.70
3.53
0.49
MTGNN
m.08gin
6.1
0.49
3.48
4.37
2.45
2.59
4.53g
0.48gsit
2.93
3.67210
0.48
GMAN
6:15amm
4.05.13
a.42
3.69.124
3.36:
4.52:1
MoSSL
4.13
5.27
0.28 am
3.02 oou5
1.7
0.35 mz
2.62 tes
3,51 aue
0.65 iem
2.43 100
3.36
0.55 rax
DeepCrime
4.01
5.14
0.31
3.24
4.24:131
0.40.oo
2.75
3.52.a3
0.50.em7
2.53
3,24:04
0.57.am
ST SHIN
5.62
7.34
0.33-ax
4.79
4,86,33
a.4
2.80
3.57-am
0.52
2,88
3.73.ou2
0.47
ST-HSI.
3.96
5.31
0.25_mm
3.16
4,25
a.38
2.62grmn
3,65-1
0.49
2.49
3.26
0,49.
DLF
6.80a1
1.78
0.4b-am
1.88am
4.92g
0.42
3,36.1
0.42..
2.65
3.98a0
0.49.am
FSNet
5.30gmm
6.19gm
0.40_mm
1.80gm
4.64.3
2.89g
3,43
0.37
2.54
3.9720s
0.48ga
OccNet
4.88
5.47
0.48.av
3.54.04
4.57
0.45
2.88
3.42.ax
0.40.e:s
3.04.1a
4.15
0.87.a1s
ST-HHOL
(Our)
3.83:1
4.97
0.22
3.04
4.05
0.34
2,54
3.35
0,36.1.
2.34
3.22.00
0.47
Table 10: Overall performance of crime prediction on TOR dataset. The results are 5-run error comparison, the bold/ / underlined font means the best / the second-best result.
Method
MAE
Assault RMSE
MAPE
MAE
B&E RMSE
MAPE
MAE
Rabbery RMSE
MAPE
MAA
Theit RMSE
MAPE
SVM
1.62
2.04
0.83
1.15
1.77
ARIMA
0.71
1.18
0.50
1.56
2.02
0.55
0.89
1.15
0.68
1.52
1.73
0.53
DCRNN
0.74 20M
1.12 1m1
0.44 2003
1.50 2039
2,50 1x:
0.45 1308
0.63 aae
1.14 2005
0.20 11:7
2.13 sc1e
3.07 2n14
0.47 2o05
STGCN
0.83
1.26
0.49
1.43
2,41
0.43
0.71
1.15
0.21
2.04
2:96
0.50
AGORN
0.62
1.72
1.12
2m15
0.95 2::1
1.32 spu
2114
201
2.30 25:m
#012
1.28 mm1
2012
GMAN
0.98 14:34
1.37 4us
0.52 2015
1.30 2087
2.20 44.1
0.55 45m6
[.3] 4ue
L.77 -025
0.29 16:0
1.30 +4.00
2:21 4012
0.59 -0z3
McSSI
0.74 2r
0.93 23m
0.41
2001
1.02 g00z
1.71 2mm
0.40 2mm
0.54 20m
1.06 2m14
(1.21
2mm
1.0% 2mm
1.70 gm
[1:45 2017
DeepCrime
0.70 2m.h
1.16
0.41
1.33
2.09
0.49
0.68
1.32
0.40
1.27
2.14
0.56
ST-SHN
0.72
1.13
0.35
1.82
0.57
1.12
1.90
STHSLL
0.64 1C18
1.02 186
J0L1
2.93 1E81
1.88 -025
1081
1.99 1Ms
DLF
1.05 2:
1.76 4am
0.33 1010
1.04 2005
5.01 24:1
0.49 20m
1.02 241
2.03 gm
0.30 28.3
1.26 25.
3.11 2m11
0.50 2014
FSNet
0.78 sc:3
1.63 442a
0.39
1.38 20.5
2.73
64:34
0.47
1.12 4ue
1.60
0.32
1,46 s01
3.04 443s
0.54
OneNet
0.94
1.91
1.46
2.92
1.24
0.35
1.52
2.75
0.52
ST-HHOL
(Qurs)
0.58 2r
0.89 sare
0.96 gm0
1.68 2r-31
gmm
1.02 2017
0.18 2m:1
0.98 gma1
1.70 gm1
0.40 gm:
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E.2 ROBUSTNESS ANALYSIS
To further assess the robustness of ST-HHOL under data sparsity, we analyze its performance in regions with low crime frequencies. Based on the frequency distribution of different crime types across areas in the test set, we categorize regions into two uowffrquencyy intervals: [0,0.25) and (0.25,0.5). As illustrated in Figure I0, we visualize the MAE of ST-HHOL and several strong baseline models within these intervals, using the CHI dataset as case study.
Theft
Battery
Assault
Damage
1.00
0.75
0.50
0.25
0.00
(0,0.25)
(0.25.0.5)
[0,0.25)
(0.25.0.5)
(0,0.25)
[0.25,0.5)
[0,0.25]
(0.25.0.5)
ST-HSL
ST-SHN
DeepCrime
GMAN
ST-HHOL
Figure 10: The robustness study of low-frequency crime areas for different crime types.
The results reveal that ST-HHOL maintains superior predictive performance even in sparsely pop- ulated urban zones. Despite the inherent challenges posed by imbalanced spatial distributions, ST-HHOL mitigates these limitations by incorporating ubiquitous multi-source data to enrich the sparse crime records. Instead of relying solely observed data, it uncovers latent crime patterns with spatial and criminal specificity that serve as more informative and generalized crime representations, enabling more reliable predictions in now-frequency regions.
E.3 SCALABILITY ANALYSIS
To assess the scalability of ST-HHOL, further evaluate it the NYC Tax dataset against several representative spatio-tempordl forecasting methods. As shown in Table II ST-HHOL achieves competitive results across different variable types and evaluation metries. Although originally designed for online crime prediction, the underlying motivation of ST-HHOL lies in modeling multivariate spatio-temporal streams with spatial and variable specificity as well as concept drift, which makes it broadly applicable beyond the crime domain.
Table 11: Performance comparison over the NYC Taxi dataset for both pick-up up and drop-off prediction. The best and second-best results are highlighted in bold and underline, respectively.
Method
Pick-up RMSE
Drop-oli RMSE
MAE
MAPE
MAE
MAPE
DCRNN
5.40
9.71
0.35
5.19
9.63
0.37
STGCN
5.71
10.22
0.36
5.38
9.60
0.39
AGCRN
5.79
10.11
0.40
5.45
9.56
0.40
GMAN
5.43
9.47
0.34
5.09
8.95
0.35
ASTONN
5,90
10.71
0.40
6.28
12.00
0.49
ST-IIIIOL (Ours)
5,38
9.56
0.35
5,06
9.54
0.36
E.4 EFFICIENCY ANALYSIS
To compare the computational cost between ST-HHOL and state-of-the-art crime prediction methods, present their model complexity and execution efficiency, demonstrated in Table [2] It can be observed that ST-HHOL achieves highly competitive training and inference speeds. Although ST-HHOL comprises 47.39M parameters, approximately 98% of them originate from the spatio- temporal dependency learner (PF-LLM) based on GPT-2. The additional components, such as the hierarchical hypergraph structure, impose minimal computational overhead. Moreover, since parameters of certain modules-sune as the feedforward layers of GPT-2 and the crime-patten hypergraph fine-tuned during training are frozen, the actual computational resource consumption of ST-HHOL remains relatively modest.
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Table 12: Complexity and execution efficiency analysis of models over CHI dataset.
Method
ST-HSE
SE-SHN
DORNN
STGCN
GMAN
McSSI
DL.F
NI-HHOL (rwns)
-0"
-0"
-PP-LTT
3 Parameters (M)
0.378
0.012
0.377
0.422
0.210
1836
0.092
47.391
0.23
0.14
46.50
Memory (MB)
114.98
76.98
290,78
253.57
185.95
272.08
248.52
24.13
Training cost (epoch)
0.144
99.62s
1.06s
0.065
0.384
0.47s
0.27%
0.44s
0.045
0.035
0.360
Test cost (epoch))
0.03s
14,47s
0,14s
0.14s
0.06s
0.11s
0.04%
0.0%%
0.007
0.005
0.078
Avergee
Avenge RMSE
1.23
1.22
2.47
2.53
1.54
1.18
2.77
1.13
E.5 VISUALIZATION OF PREDICTION RESULTS
To intuitively illustrate the discrepancy between ST-HHOL's predictions and the ground truth, we visualize several representative examples in Figure II These heatmaps span multiple time periods and crime categories. As observed, the high consistency between the prediction results and actual spatial distributions of different crime occurrences underscores ST-HHOL's outstanding predictive performance.
Overall, ST-HHOL effectively models both regional differences and category-specific variations in crime intensity. It accurately distinguishes high-frequency crime regions and estimates threshold effects with notable granularity. Moreover, its online learning mechanism continually updates model parameters in response to streaming data, allowing the model to remain responsive to short-term fluctuations and long-term gradual shifts in crime distributions. As result, ST-HHOL maintains stable forecasting quality over extended time horizons. These results collectively demonstrate the model's 's robustness and practical utility in real-world, temporally evolving environments.
F THE USE OF LARGE LANGUAGE MODELS (LLMS)
LLMs were used solely as general- general-purpose purpose assistive tool for language polishing and improving the clarity and readability of the manuscript. The authors independently developed all scientific ideas, experiments, analyses, and results. The LLM did not contribute to any research ideation, methodology design, interpretation of results.
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Published as a conference paper at ICLR 2026
Assiuit, CHI, May, 2024
Damage, CHi, May. 2024
Ground Tuth
Pradiction
Ground Truth
Prediction
Ize
Crine Count
Theft, CH), 2024
Thatt, CHI, 2024
Ground
Prediction
Ground
Pred
4c0
Fhe Crimio Court
208
100
100
Damage, CHi,, Septembeer,
Thef, CHi, October,
Prodiction
300
ize
ce
50
Damage, CHI, Octobar. 2024
Assoult, CHE, November, 2024
Ground Tuth
Prediction
Ground truth
Prediction
300
to
Cilnn Count
Po
Battery.
Battery,
Crima Court
Figure 11: The visualization of prediction results and ground truth.
22


Reviews:
[{"review_id": "r7tTc7rgPf", "reviewer": "Reviewer_dQeU", "summary": "This paper proposes a ST-HHOL for crime prediction to tackle the insufficiency of variety, high-order dependency, and non-stationality in sparse crime records. ST-HHOL includes (i) hypergraph modeling for integrating crime data with heterogeneous contextual factors and their co-occurrence relations, (ii) an iterative online learning for addressing concept drift by employing frequent fine-tuning for short-term dynamics and periodic retraining for long-term shifts, and (iii) a partially-frozen LLM for enhancing spatio-temporal reasoning under sparse supervision. The authors conducted extensive experiments on three real-world datasets and demonstrated that ST-HHOL consistently outperforms state-of-the-art methods in terms of accuracy and robustness, while also providing enhanced interpretability. In summary, this paper proposes an well-motivated designs for crime prediction to address the problems, conducts extensive experiments, and provides reasonable readability. However, this study would be further improved: (i) more theoretical justification on, for example, regret analysis of online learning and criteria for determining timings of fine-tuning and retraining; (ii) scalability and computational complexity of ST-HHOL; (iii) evaluation of concept drift (what types of concept drifts and how ST-HHOL adapt to them); (iv) empirical demonstration of ST-HHOL on datasets outside U.S.", "questions": "Please answer the points described in the Weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- Well-motivated design: To address the challenges in crime prediction, this paper unifies three components: hypergraph modeling, online learning, and pretrained sequence prediction. \n- Extensive experiments: The authors conducted extensive experiments on many cities, ablation study, hyperparameter study, and visualization. \n- Readability: The paper is overall easy to follow", "weaknesses": "- Theoretical background: Most of the proposed algorithm are based on intuitive and empirical insights. In other words, the theoretical background is relatively weak. For example, regret analysis on online learning (Shalev-Shwartz 2012) and criteria for determining $\\tau$ (fine-tuning) and $T$ (retraining) are missing. \n- Scalability: Hypergraph construction and periodic retraining may become expensive for large-scale city meshes. The computational complexity of ST-HHOL and its empirical results for larger datasets should be discussed. \n- Evaluation under Concept Drift: The experimental results do not provide what concept drift types are in the datasets (e.g., sudden, gradual, reccuring) (Gama et al. 2014) and how ST-HHOL adapt to such drifts. \n- Variety of Datasets: This paper conducts experiments on US cities datasets only, and the numbers of regions are up to order 100. \n\n[Shalev-Shwartz 2012] Shai Shalev-Shwartz: Online learning and online convex optimization. Foundations and Trends® in Machine Learning, 4(2), pp.107-194, 2012. \n\n[Gama 2014] Joao Gama, Indre Zliobaite, Albert Bifet, Mykola Pechenizkiy, and Abdelhamid Bouchachia: A survey on concept drift adaptation. ACM Computing Surveys, 64(4), pp.1-37, 2014.", "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": "7f47yL5znt", "reviewer": "Reviewer_pemE", "summary": "This paper addresses urban crime prediction by tackling two key challenges: (1) sparse crime records that fail to capture latent high-order patterns shaped by heterogeneous contextual factors, and (2) high non-stationarity that renders conventional offline models ineffective against concept drift. The authors propose ST-HHOL, a Spatio-Temporal Hierarchical Hypergraph Online Learning framework that integrates a hierarchical hypergraph convolution network with a Partially-Frozen LLM (PF-LLM) and an iterative online learning strategy. Experimental results on three real-world datasets demonstrate that ST-HHOL consistently outperforms state-of-the-art methods across various metrics while providing enhanced interpretability.", "questions": "1. Given that hierarchical hypergraph approaches have been extensively studied in recent years, what specific architectural innovations or theoretical contributions distinguish your hierarchical hypergraph design from existing methods beyond the particular application to crime prediction?\n\n2. Could you provide an ablation study that completely removes the PF-LLM component and replaces it with traditional sequence modeling approaches (e.g., LSTM, GRU, or Transformer without pre-training)? This would help quantify the actual contribution of the LLM component.\n\n3. Have you considered experimenting with more recent and powerful language models? Would a comparison with prompt-based approaches using stronger LLMs (e.g., through in-context learning) provide insights into whether the fine-tuning approach is truly necessary, or if the computational cost could be better justified?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "1. **Well-motivated problem formulation**: The paper is well-motivated to solve the sparse data problem and the concept drift challenge in crime prediction. Particularly noteworthy is the authors' approach to addressing concept drift through an innovative online learning mechanism that explicitly disentangles spatially invariant and temporally variant components. This separation allows the model to freeze spatial parameters (Θs) associated with crime patterns while adapting temporal parameters (Θd(t)) for co-occurrence relationships, providing a principled solution to handle both short-term fluctuations and long-term distributional shifts.\n\n2. **Novel online learning mechanism**: The paper proposes a sophisticated iterative two-phase update scheme that combines frequent fine-tuning (every τ steps) for rapid adaptation to recent fluctuations with periodic retraining (every T steps) for capturing long-term gradual shifts. This mechanism effectively addresses the non-stationary nature of crime dynamics by balancing short-term responsiveness and long-term stability, which is a significant contribution to the online learning literature in spatio-temporal forecasting.\n\n3. **Effective LLM integration strategy**: Experiments demonstrate that the Partially-Frozen LLM (PF-FFN) approach is effective in leveraging pre-trained sequence modeling priors while adapting to crime-specific dependencies. The ablation study shows that this approach achieves a better trade-off between retaining pretrained knowledge and adapting to the target domain compared to fully frozen or fully tuned alternatives.\n\n4. **Comprehensive experimental evaluation**: The experimental evaluation is thorough and well-designed, featuring 14 diverse baselines spanning traditional methods (SVM, ARIMA), spatio-temporal forecasting models (DCRNN, STGCN, AGCRN, MTGNN, GMAN), crime-specific models (DeepCrime, ST-HSL, ST-SHN), and online learning models (DLF, FSNet, OneNet). Beyond performance comparison, the authors conduct extensive analyses including robustness studies, scalability analysis on NYC Taxi data, efficiency analysis, hyperparameter sensitivity studies, and interpretability case studies with visualizations.", "weaknesses": "1. **Limited novelty in hierarchical hypergraph design**: Though having some differences in motivation, hierarchical hypergraph neural networks and various GNN or hyperGNN designs have been fairly explored in previous works one to two years ago. The key innovation and contribution of this hierarchical hypergraph construction (heterogeneous G^e for crime patterns and homogeneous G^o for co-occurrence) is not very prominent considering the existing literature on hypergraph-based spatial-temporal modeling.\n\n2. **Incomplete ablation study for LLM component**: The paper lacks a complete ablation experiment that entirely removes the PF-LLM component. While the authors compare different LLM variants (FPT, No Pretrain, Full Tuning, PF-A, PF-FFN), there is no comparison with a baseline that replaces the LLM with traditional neural networks (e.g., RNN, CNN, or MLP). This makes it difficult to assess the true necessity and contribution of the LLM component to the overall performance.\n\n3. **Limited LLM baseline consideration**: The paper uses GPT-2, which has relatively low foundational performance compared to existing near-human-level language models. This raises questions about the necessity of fine-tuning such a weak model. It would be valuable to explore whether more powerful large models could achieve better results through prompt-based in-context learning rather than parameter fine-tuning, especially given the potential computational overhead of the current approach.", "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": "LlLDIOkTau", "reviewer": "Reviewer_GDKr", "summary": "The authors have proposed a spatio-temporal online learning model for crime prediction. It is a mix of hierarchical hypergraphs to model context-crime interactions with a partially frozen GPT-2 module for temporal reasoning and make use of a staged online training strategy to adapt to concept drift. The method is evaluated on three public city-crime datasets and shows improvements over baselines.", "questions": "- What are the modeling insight that separates this from prior hypergraph-based crime methods beyond stacking modules?\n- Why is GPT-2 the right backbone rather than a standard temporal transformer or Time-LLM? Is the gain coming from pretraining or just extra capacity?\n- How is fairness monitored? Crime data is biased; what prevents feedback loops?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The authors have addressed a real-world spatio-temporal problem with clear motivations in the paper.\n- The proposed work combines hypergraphs and online updates in a sensible pipeline.\n- Good experimental effort across multiple cities and metrics.\n- The ablations and sensitivity studies are good to see.\n- Interpretability figures are a plus in understanding and analyzing the work.", "weaknesses": "- The novelty in this paper is a little incremental. Hypergraph + online updates + partial LLM freezing feels like an engineering solution proposed by combing current methods.\n- The claims around “hierarchical hypergraph” are mostly architectural rearrangements or engineering solution, not a fundamentally very new formulation.\n- The “partial GPT-2 freezing” choice appears heuristic and could be swapped for many LLM-augmented temporal modules without changing the story.\n- The concept-drift handling is also not theoretically grounded.\n- There is no clear insight into why this model generalizes better, beyond “more components.”\n- The ethical context is thin, considering the sensitivity of predictive policing. Have more discussions on that end.", "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": "wMfMESA4Uf", "reviewer": "Reviewer_9AaK", "summary": "This paper proposes ST-HHOL, a spatial-temporal hierarchical hypergraph online learning framework for urban crime prediction. The framework captures dual specificity of crime patterns through hierarchical hypergraph convolutional networks, enhances spatial-temporal reasoning via partially frozen LLMs, and employs an iterative online learning strategy to address non-stationarity and concept drift, achieving state-of-the-art performance on three real-world datasets.", "questions": "1. Could you provide a more clear and detailed explanation of how the data sparsity problem is resolved in your framework? Specifically, which components of ST-HHOL directly contribute to mitigating sparsity, and what mechanisms enable this?\n\n2. While I understand the \"online learning\" scenario that the paper aims to address, I am uncertain whether the definition and usage of \"online learning\" in this context strictly aligns with the formal definition in machine learning literature. Could you clarify your interpretation and justify its appropriateness for this application?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1. The introduction section accurately identifies multiple challenges in crime prediction, such as data sparsity and distribution drift. The proposed solutions to address these challenges are novel and well-motivated.\n\n2. The \"online learning\" scenario presented in this work is more suitable for real-world applications, which enhances the practical value of the proposed framework.\n\n3. The experimental evaluation is comprehensive, including multiple state-of-the-art baselines and validation of the model across multiple dimensions.", "weaknesses": "1. The proposed method exhibits considerable complexity in its design, which may lead to an excessive number of parameters. This could potentially affect the model's scalability and computational efficiency.\n\n2. The description of how the data sparsity problem is addressed lacks clarity and detail.", "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": "1LsYH980lK", "reviewer": "Reviewer_3QXX", "summary": "In this paper, the authors designed a online learning model for crime prediction, and it has a good performance in three datasets.", "questions": "See weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. A very clear introduction about the methodology. \n2. It is innovative to include online learning in this problem.\n3. Numerical results show that this model is competitive. \n4. The case study is illustrative and useful.", "weaknesses": "1. Generally, there are many zeros in crime data; how do this model address this problem?\n2. True zero rate is an important metric; however, it is overlooked in this paper.\n3. Importance of e multi-source auxiliary data is not comprehensively discussed. Additionally, ablation study of the other two datasets should also be included since the importance of online learning should be shown.", "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)