ProtoTS: Learning Hierarchical Prototypes for Explainable Time Series Forecasting
Authors: Ziheng Peng
Shijie Ren
Xinyue Gu
Linxiao Yang
Xiting Wang
Liang Sun
Venue: ICLR 2026 Poster (2026)
Keywords: Time series forecasting; Interpretability
Primary area: learning on time series and dynamical systems

Abstract: While deep learning has achieved impressive performance in time series forecasting, it becomes increasingly crucial to understand its decision-making process for building trust in high-stakes scenarios. Existing interpretable models often provide only local and partial explanations, lacking the capability to reveal how heterogeneous and interacting input variables jointly shape the overall temporal patterns in the forecast curve. We propose ProtoTS, a novel interpretable forecasting framework that achieves both high accuracy and transparent decision-making through modeling prototypical temporal patterns. ProtoTS computes instance-prototype similarity based on a denoised representation that preserves abundant heterogeneous information. The prototypes are organized hierarchically to capture global temporal patterns with coarse prototypes while capturing finer-grained local variations with detailed prototypes, enabling expert steering and multi-level interpretability. Experiments on multiple realistic benchmarks, including a newly released LOF dataset, show that ProtoTS not only exceeds existing methods in forecast accuracy but also delivers expert-steerable interpretations for better model understanding and decision support. The source code is available at https://github.com/SKURA502/ProtoTS.

Published as a conference paper at ICLR 2026
PROTOTS: LEARNING HIERARCHICAL PROTOTYPES FOR EXPLAINABLE TIME SERIES FORECASTING
Ziheng Peng -2,3- Shijie Ren 12,3+ Xinyue Gu
Linxiao Yang?. 2.3 Xiting Wang 1t
Liang Sun 2.3f
!Gaoling School of Artificial Intelligence, Renmin University of China Beijing 2DAMO Academy, Alibaba Group *Hupan Laboratory
Sachengppeng shj_ren, xitinggn xitingwang ) ruc- wew.rruuuuu......e. on [guxinyue, gxy, linxiao. ylx, liang. sun @al 1 baba aeaba-innc..e com
ABSTRACT
While deep learning has achieved impressive performance in time series fore- casting, it becomes increasingly crucial to understand its decision-makinn pro- cess for building trust in high-stakes scenarios. Existing interpretable models often provide only local and partial explanations, lacking the capability re- veal how heterogencous and interacting input variables jointly shape the over- all temporal patterns in the forecast curve. We propose ProtoTS, a novel inter- pretable forecasting framework that achieves both high accuracy and transparent decision-making through modeling prototypical temporal patterns. ProtoTS com- putes instance-prototype similarity based a denoised representation that pre- serves abundant heterogeneous information. The prototypes are organized hierar- chically to capture global temporal patterns with coarse prototypes while captur- ing finer- aner-grained local variations with detailed prototypes, enabling expert steering and multi-level interpretability. Experiments cluding a newly released LOF dataset, show that Proto'TSS not only exceeds exist- ing methods in forecast accuracy but also delivers expert-steerable interpretations for better model understanding and decision support. The source code is available htttps://iithun com///XUR4022//rtto/
multiple realistic benchmarks, in-
INTRODUCTION
Time series forecasting has been widely applied in high-stakes scenarios such as load forecast- ing (Jiang et all 2024 Yang all 2023), energy management (Deb all 207; Weron. 2074), weather prediction (Angryk et all, 2020: Karevan & Suykens, 2020). all of which involve consid- erable financial impacts. In these applications, while achieving high forecast accuracy is crucial, understanding why and how the model makes specific predictions is equally important. It aids in preventing substantial financial losses and building the trust necessary (Rojat et all (OZT).
A range of explainable time series forecasting methods have been developed to simultaneously en- sure interpretability and good predictive performance (Oreshkin ct 2019; Lim ef all 202T; Zhad atl 2024: Lin et all 2024). However, their overall interpretability and potential for further perfor- mance improvement are limited, since they mainly provide local, partial explanations for both the output and input sides:
C1: For the output side, existing methods (Lim et all 202I: Zhao et all, 2024) mainly explain the prediction at individual time steps, lacking the ability to help users quickly interpret the rea- sons behind the overall trend in the forecast curve. For example, they fail explain why three peaks occur in the predicted electricity load curve at the noon, afternoon, and night, respectively, and why the three peaks gradually descend (Figure aa))).. Understanding such overall temporal
"Equal contribution. Work done during internship at DAMO Academy. Corresponding author.
Work partly done Beijing Key Laboratory of Research on Large Models and Intelligent Governance and Engineering Research Center of Next-Generation Intelligent Search and Recommendation, MOF.

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Published as a conference paper at ICLR 2026
Predict window
Summer load
Rest day
Spring Festival al
Electric load
(n1)
High sccand attermonn peek
Humnnn woek
Noon evening due factory stop
00:00
12:00
24:00
Global Reitiiv variables
Relative varialess Holiday Weekend
Output
Calendor
Relutive variabler, Lunar calendar Holiday
Temperatuue
Endogenous
book-back window
variobles:
Prototype-1
Prototype-2
Prototype-K
variables:
Instance
Instancee
vartables
Prototype similarit
Prototype similarity
Holkly
Summmee load
2024.7.20
Spring Festival
2025.1.25
waribdes
Locul: :
Restday day
Predict
M
Rest day drop
Predict
Tempenaure
Hunidity
variabees)
2024.9.25
Input
2024.10.4
3
K
00:00
24:00
2 3
24:00
(a)
(b)
Figure 1: (a) An example of time series forecasting with numerous heterogeneous variables, where exogenous variables (e.g., temperature, holiday) influence the evolution of endogenous variables (e.g., electric load). (b) Illustration of prototypical explanation method: a set of learned prototypes provides user-friendly global overview of typical temporal patterns. For each instance, model computes its similarity to all prototypes to form prediction, enabling detailed local interpretation.
patterns is of great importance in real-world scenarios. For example, power system experts need to ensure demand peaks are identified correctly, so that they can make dispatch decisions (Taanos al. 2013), such as whether additional electricity should be purchased from external sources. Failing to provide such analyses limits interpretability and prevents experts from steering the model to improve its accuracy.
C2: For the input side, existing explanations are often limited to certain types of variables, such as focusing solely on endogenous variables (Lin ctall 2024).. However, as shown in Figure Ma), there many different types of input variables, and understanding how their interactions impact the temporal patterns is critical. For example, the typical temporal pattern of extreme summer conditions can only be observed when both temperature and seasonal variables are sidered together.
To address these challenges, we propose Prototypical Time Series Forecasting framework (ProtoTS) that effectively models the overall temporal patterns (C1) and enables prototypes to cap- ture the interactions among inputs (C2).
As shown in Figure Ibb), each of our prototypes corresponds to a typical temporal pattern. For example, the curve of the Spring Festival prototype indicates that there are peaks in the morning and evening during the Spring Festival period. This pattern occurs at specific combinations of covariates (i.e., when the inputs indicate both holiday and the first month of the lunar calendar), enabling it to explain both the formation of the overall temporal pattern and how it is influenced by the combination of multiple input features (C2). These few prototypes provide a global explanation by summarizing typical patterns across the entire dataset, thereby supporting expert intervention (e.g.. refining the temporal pattern of the prototype, Sec. - At the same time, the model improves accuracy by effectively modeling the local interactions of covariates.
To construct an effective end-to-end framework, we introduce the following technical innovations:
Hierarchical prototype learning strategy (C1). Traditional prototypes are typically limited to explaining individual classification results, while we extend the prototypes so that they model a temporal pattern, which consists of a sequence of regression results. Learning such sequen- tial temporal pattern is hard to balance predictive performance with interpretability. Using too few prototypes leads to poor forecasting accuracy, while employing too many can compromise interpretability by producing overly similar patterns. To address this, we design a hierarchical prototype learning strategy, where a small set of coarse prototypes ensures global interpretability, and prototypes are progressively refined into lower levels to capture local details and improve ac- curacy. This design allows experts to intervene by specifying which prototypes should be further split, enabling efficient and user-friendl model adjustments.
'The name "Spring Festival" is now manually summarized based on relevant covariates and temporal pat- terns, though it also he generated using large language models.
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Multi-channel prototype similarity computing (C2). To enable effective modeling of the inter- actions among imput variables of different types and their impact on the output curve patterns, we compute the prototype-instaney similarity by incorporating a multt-channel embedding and bottle- neck fusion mechanism, which improves both the interpretability and the accuracy of the model.
Our framework achieves state-of- tatte-o--hheannd -tttheeertttttt performance with good interpretability and steerability. In particular, ProtoTTS reduces MSE by 48.3% and MAE by 20.9% compared to the state-of-the-arr model on the LOF dataset. Moreover, its accuracy decreases much more slowly when the amount of training data is reduced, compared to the baselines. A case study demonstrates that our expla- nations enable an easy-to to-understand overall and detailed understanding, Expert edits based on the explanations reduced MSE by 0.009 and further improved explainability.
2 RELATED WORK
Time Series Forecasting with Exogenous Variables Time series forecasting with exogenous variables has been extensively explored in both classical and modern approaches. Traditional statis- tical models such as ARIMAX (Williams. 2001) and SARIMAX (Vagropoulos et all, 2016) extend the ARIMA framework to incorporate correlations between exogenous and endogenous variables. Seeking richer dynamics, Transformer families like TFT (Lum all (02l and TimeXer (Wang alall 2022), introduce attention mechanisms to tackle this task. Parallel work in MLPs pursues ef- ficiency and long-horizon stability: NBEATSx (Oreshkin all 2019) appends a dedicated stack for auxiliary factors on top of a residual basis expansion, TiDE (Das etal 2023) factorizes temporal and feature projections with two dense encoders to harness knownfuture variables, and TSMixer (Ekam- baram all 2023; Chen all 2023) alternates mixing layers to effectively model their interactions. Outside deep learning, generic tabular learners such XGBoost (Chen & Guestrin, 2016). Light- GBM (Ke ci all 2) and GAM (Yang et all 2022), perform well when exogenous variables are informative and strongly correlated with the target. Our method, ProtoTS, achieves strong perfor- mance on this task while offering interpretability and steerability for domain experts, effectively handling large amounts of heterogeneous variables while filtering out irrelevant information.
Time Series Interpretability Time series interpretability can be divided into post-hoc and ante- hoc approaches. Post-hoc interpretability focuses on unveiling the reasoning of pre-existing black- box models eG all, 2025). Generic explanation techniques such as SHAP (Lundberg & Lee, 2017), LIME (Ribeuro all 2016), IG (Sundararajan et all 201Z) can be directly applied time- series models. Crabbé & Van Der Schaar (20221) learns sparse perturbation masks over the time- feature dimensions, struggling to quantify each inputs effect on a regression forecast. Consequently, regression tasks tend to favour ante-hoc models whose interpretability is built in by design. Follow- ing the attribution-centri view of posthoc explanations, TFT (Lim etall, (02I) provides explorable attention over input time steps, and DiPE-Linear (Zhao el all 20244) parameterizes filters in both temporal and spectral domains to visualise the regions of interest. N-BEATS (Oreshkin et all 2019)
uses residual blocks for generic, trend, and seasonal components, and Olivares all (2(22) extends the scheme to exogenous variables. These works are limited to local explanations and fail to provide global view that experts need for a shared understanding. CycleNet (Lin et all 2024) identifies common periodic patterns in time-series data but only focuses on endogenous variables. In con- trast, ProtoTS holds a global of prototypical patterns and explains each forecast by matching to them, offering both global overview and local interpretation. Its hierarchical structure supports expert steering multiple levels, ensuring faithful overall understanding.
Prototypical Time Series Model Previous works have already shown the value of prototypes in time series models. These methods typically fall into two categories. 1) prototypes decoded as inter- mediate representations (Shen. 2023: Li all 2023at Um et all. 2023a) or model parameters (Chen stall 2024).. For example, II al (2023a) uses prototypes to map time-series embeddings into tex- tual embeddings for large language models. Such designs enrich the models architecture but leave the prototypes detached from the output. 2) prototypes directly mapped to output variables (Queen' etall 2023: Li atl 2024; Ming et all 2MD: Ohermair et all, 2023), serving typical examples of the outputs. While the latter offers stronger interpretability, existing approaches decode prototype into only single output variable (e.g., a class prediction). In contrast, method is, to the best of our knowledge, the first to decode a prototype into a sequence of output variables (c.g., a 96-step forecasting curve), enabling holistic interpretation of temporal dynamics.
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Multi-channel prototype similarity computation
Similarities
Repeat
Root prototpe- Roctprotohpe
proteepe
Endogenouus veriables
Endogenous
Battleneck channel
Similarity
82
Input
Discrete variables
crcocling
Discrete
Feeture
boot Sonth
fusion
Terpoood
bottleneck
computing
0.32
8
0
0565
0.03
Exagenous
encodingchenrrel
0.02
0
05
variables
Continuous varibles
Xton
enooding channel
Condinuous
0.2 0.1
71 72
0.3
Y3
0.3
74
75
76
Prototype
Root
Root
Root
embedding
prototype-1
prototype-2
protatype-3
Ju.
Prediction
Y4=0.3 74 M
Prototype
Root
Root
Root
11=0.2 8
temporal pattern
prototype-1
prototype-2
prototype-3
Y==0.1
Y3
Othersc0.1
T
M
M
Hierarchical prototype learning
The overall framework of ProtoTS, which comprises two main modules: the multi-channel prototype similarity computation module and the hierarchical prototype learning module.
Figure 2:
METHOD
3.1 FORMULATION AND FRAMEWORK
Problem Formulation We consider the task of time series forecasting with exogenous variables, as shown in Figure Ia),, since abundant heterogeneous exogenous variables provide rich information to boost endogenous predictability. Formally, let the historical endogenous variables (e.g.. electric load) as YI.f. = {y,, (yI.y2... y2............ yr. E R4x1 and the associated exogenous variables (e.g., temper- ature and holiday) XI.L (2,, x R. where L is the look-back window size and C' is the number of exogenous variables. In many practical scenarios (Wessel, 2020; Lam all, 2023), future exogenous variables X (XL+1,--.. XL+#1 For example, in the LOF dataset, we obtain forecasted weather variables (e.g.. temperature) from commercial weather services, and calendar variables (e.g., holiday flags) are accessible in advance. In our setting, we explicitly incorporate future exogenous variables, as these substantially improve forecasting performance. The goal is predict the future curve of the endogenous variable for the next H time steps, denoted as L++1-++ = {yL+1..... EL+HE } E g(xl The forecasting model F takes the input variables to predict the future endogenous variables Y:
E RR. #xC are also available.
LLTELHH = F YILL, X1LL. XL+IL+H).
(1)
Framework Overview The ProtoTS framework illustrated in Figure Z It contains two mod- ules. The multi-channel prototype similarity computation module effectively models the interac- tions between input variables and their impact on prototypes. The hierarchical prototype learning module structures prototypes hierarchically, with coarse-grained root prototypes capturing global patterns and fine-grained child prototypes modeling local variations, ensuring good explainability. steerability, and accuracy. The two modules will be explained in detail in Sections B
and K
3.2 MULTI-CHANNEL PROTOTYPE SIMILARITY COMPUTATION
This module ensures effective modeling of interactions between input variables and their relations with prototypes by using three steps: the multi-channel embedding step effectively embeds hetero- geneous variables in separate channels, the bottleneck channel fusion step then models complex interactions between variables without causing overfitting and outputs the final input embedding, and the prototype similarity computing step finally estimates the relations between each input and the prototypes by computing the similarities between their embeddings.
Multi- Channel Embedding In ProtoTS, we adopt multi-channel embedding where endoge- nous and exogenous variables are processed separately to achieve optimal encoding for each type. Specifically, endogenous variables are directly encoded through an endogenous encoding channel,
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implemented non-line non-linear projection y using a multi-layer perceptron with activation functions, a widely used design (Das et all, 2023). For exogenous variables, we follow standard practice in tabular learning (Wang & Sun, 2022). We categorize them into discrete variables (e.g., is holiday, day of week) and continuous variables (e.g., temperature, humidity), and apply tailored embedding methods best capture the properties of each variable. Concretely, exogenous variables X, time t are decomposed into x E NC and x!t E RR Cais and Coon refer to the number of dis- crete and continuous variables. Discrete variable x are processed through discrete encoding channel using dedicated embedding tables E, E R [2/d, where 92 is the vocabulary and d is the embedding dimension. Continuous variables x are projected into the embedding space through continuous encoding channel, applying variable-specific non-linear projections 1/j. This multi- channel embedding allows the model better preserve the information contained in heterogeneous variables Munz- Körner & Weiskopi (2024).
To effectively fuse all variables information at time step and obtain a full representation, we aggregate the embeddings of all variables through addition, which integrates information across heterogeneous variables without additional parameters (Arora et all 2017):
Bottleneck Channel Fusion
(lv)) +
E
(x
Σ
bh (x))))
t [1 L]
(Look-back Window)
Z,
(2)
Σ E
(xi,))
t 1E|L+1:
(Forecast Window)
During the forecast window, where yr is the target to be predicted, only exogenous variables are used to construct Z, The embedding ZI:L-H (Zi.... Z,,.. encodes rich amount of information from endogenous and exogenous variables. However, such rich embedding may also introduce noise, as irrelevant information from heterogeneous inputs can be mixed into the representations. To mitigate this, ProtoTS introduces a bottleneck layer to filter out irrelevant information while retaining the most predictive components. Concretely, we project the high-dimensional embeddings into dower-dimensionn
= , E R(L+H)xd now
latent space through a bottleneck projection, R. + IR dhwale + Rd, where dboute < d. The compressed representation is then mapped back to the original space, retaining the most relevant information while filtering out noise (Wang all, (02I)). We apply the bottleneck layer within an MI.P M-MMeer architecture (lölstikhin et all 20221), inserting it into both MLPreature and MLP Lime- Fusion performed sequentially, first along the feature dimension and then along the temporal dimension, T denotes the transpose of the vector:
(3) The bottleneck fusion layer is stackable, where denotes the layer index. After stacking, we obtain ZIZ. E Hdd in the original embedding dimension. To enable prototype matching in a uni- fied one-dimensional vector space, we perform linear aggregation along the temporal dimensions:
Z Z MLP time (MLPieature (Z (Zi:++))))
Ż Z W, 2 Rd
(4)
where W E (L++H))x1 projects the sequence length from T. + H to 1.
Prototype Similarity Computing To provide user-friendly global explanation while handling complex information at a local level for detailed interpretation and accurate forecasting, ProtoTS integrates prototypical explanation directly into its prediction mechanism via a learnable set of pro- totypes II (Zhang et all (024B). Each prototype in II is represented as an embedding μa E IRd and its corresponding temporal pattern p R which are both learnale parameters. Here, fr is used to compute the similarity between the query representation Z and the prototypes, by applying a softmax over their distances d(2. 14). The distance can be chosen flexibly, such as Euclidean dis- tance, cosine similarity. We adopt Euclidean distance, under which the prototypes are equivalent to a Gaussian mixture model in the embedding with an identity covariance matrix (Allen et all 2019). Meanwhile, temporal pattern p is used to form the final prediction. Specifically, type temporal pattern p over a predefined period of length T. and during forecasting, the prototype pattern is aligned with the forecast window H based its phase and length (Lin et all 2024).
fix each proto-
3.3 HIBRARCHICAL PROTOTYPE LEARNING
The key challenge in designing the prototype set II lies in balancing predictive performance with interpretability. Using too few prototypes may lead poor forecasting accuracy, while employing
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too many can compromise interpretability by introducing overly similar patterns that are hard to distinguish and reason about. To address this trade-off, ProtoTS adopts a hierarchical prototype learning strategy that organizes the prototype set in tree structure, effectively combining modeling capacity with multi-level interpretability.
Root Level Learning At the root level, ProtoTS aims capture the overall pattern using only small set of prototypes, thus ensuring interpretability by allowing users to efficiently form a global understanding. These root prototypes typically correspond coarse-grained temporal patterns that consistently recur over long horizons (e.g,, seasonal trends, holiday effects; see Figure BY Layer-- The similarity of root prototype e is computed based on Pe. followed by a softmax operation:
exp( (d Mc))
f(2 P2) = E exp(-d p.))
(5)
The final prediction is then generated as weighted combination of the temporal patterns from all root prototypes:
N Y Σ (() Ps-
(6)
At the first stage, the model is trained using the root prototypes until convergence. This root-level learning allows the model to establish globally interpretable set of representative temporal patterns, providing users with an intuitive understanding of the models decision logic at high level.
Splitting Strategy Once the model converges, each root prototype is further split into M child prototypes introduce fine-grained variations. For root prototype i, its M child prototypes denoted as {(Ms. Pt,)) 1M The similarity between Ž and its child prototypes is computed within this local group, ensuring all child prototypes remain associated with their root:
exp( - (2, pi,k)
f(Z)Ma,)) Σ/ exp( - d( Z, pi,))
Based on this hierarchical matching, the final prediction is formed as weighted combination of all child prototypes, modulated by both leoe- and child-level similarities. The complete forecasting output is given by:
N
M
Σ
f( p
Σ ==1
f(2(mu.)) Paj-
(8)
Algorithm Prototype Splitting Rule
Input:
Training dataset D, leaf prototypes Heat {leaf lection ratio a.
leaf }. top-k activation count, se-
Initialize: Loss[[] < 0, Count[[] <- 0 for all leaf prototypes leaf, For each training instance (ar, y) in D:
Compute prediction ÿ and instance loss L = MAE(y, 9) Compute similarity scores { 1 over all leaf prototypes. Let 7 be indices of top-k similar prototypes based on 81.
For each E T:
Loss[[] <- Loss[[] + L. Count[[] + Count([) [1 +
Normalized loss:
Loss [
if Count([] > 0,
NormLoss[[]
Count(]
otherwise.
Select leaf prototypes with top a% values in NormLoss([].
While the above describes a two-level hierarchy, the structure is general: any leaf prototype can be incrementally split to form multi-level tree. However, not all prototypes need splitting, and some

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Published as a conference paper at ICLR 2026
splits may yield overly similar temporal patterns. Therefore, propose splitting rule for deter- mining which leaf prototypes should be further refined. The rule is designed to identify prototypes whose current temporal patterns are insufficiently representative of their associated instances and thus require additional fine-grained refinement. The pseudocode is provided in Algorithm MI
This hierarchical design enables experts first obtain a global understanding through high-level root prototypes (e.g., distinguishing between seasonal or holiday-related patterns), and then refine their insights by examining lower-level child prototypes that capture more localized variations (e.g., differentiating between long holidays and short holidays). Moreover, the hierarchy empowers expert interaction. Experts can steer the model by selectively splitting specific prototypes. introducing new root-level prototypes, or directly editing the temporal pattern to integrate domain knowledge.
Loss Function In addition to the standard LI forecasting loss, we incorporate an entropy-based regularization on the prototype weights f(Z μ4), with controlling the strength, encourage few main prototypes to cover most predictions. We note that an L2 loss can also be used.
== I LILL+H Y
((
(9)
EXPERIMENTS
We conduct extensive experiments to thoroughly evaluate the effectiveness of ProtoTS. The main results show that ProtoTT consistently delivers strong performance on time series forecasting with exogenous variables. ProtoTS also achieves high accuracy the multivariate time series forecast- ing, as shown in Appendix G. We further analyze the effectiveness of model components and the quantitative evaluation confirms that ProtoTS provides the most understandable and usable expla- nation. Finally, a case study illustrating our ability to provide global explanations and fine-grained understanding, while supporting expert editing enhance both performance and interpretability.
4.1 OVERALL PERFORMANCE
Load Forecasting dataset (LOF) is synthetic electric load dataset, including 22 sup- porting covariates and covering four regions. We also evaluated on the Electricity Price Forecasting (EPF) dataset (Lago et all 2021), which covers hourly electric prices from five Nordic markets. The specific details of the datasets can be found in the Appendix B.I.
Datasets
Baselines To provide wideranging comparison, benchmark eight models in total: five state- of-the-art deep-learning methods (TimeXer (Wang et all, 2022),, i'Transfomerr (Liu et all 2023), TiDE (Das R0223), TFT (Lim et all ((2AA),, NBEATSx (Olivares all 2023) together with three strong machine-learning baselines (XGBoost (Chen & Guesstri, 2016), LightGBM (Ke ei 2007). pyGAM (Serven & Brummuti, 2018). All deep-learning models support exogenous variables as inputs, and we further extend TimeXer and ITransformer to incorporate future covariates. The machine learning models generate forecasts recursively with exogenous inputs.
The MAE on the LOF dataset is shown in Table M. ProtoTS achieves state-of-the-ar per- formance across four datasets, reducing MSE by 48.3% and MAE by 20.9% over the best baseline. Interpretable models like N-BEATSx are sensitive to outliers, resulting in high MSE. Transformer- based models fail to capture heterogeneous exogenous information due to single-channel encoding. Although TiDE incorporates exogenous variables in both encoder and decoder, its performance is hindered by irrelevant noise. Machine learning models perform well on stable datasets but struggle with complex scenarios. In contrast, ProtoTS effectively captures diverse information and filters noise, achieving superior performance. Visual comparison can be found in Appendix E.
Results
We also evaluate ProtoTS the EPF dataset. Unlike LOF, this task involves fewer covariates but exhibits higher volatility, posing challenges for accurate forecasting. As shown in Table R ProtoTS achieves the best performance across all five markets, reducing MSE by 8% and MAE by 8% compared to the best-perforning baseline. We further conduct a sensitivity analysis under random seeds, Appendix C.3, Full implementation details can be found in the Appendix B.2.

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Table 1: MAE results the L.FF dataset with 22 supporting covariates. The look-back window and forecast window are set to 384 and 96 for all methods. A means the relative improvement of ProtoTS over other baselines. Full MSE results can be found in Appendix C.I.
Model
PSotoTS
TimeXer
iTans.
TIBE
TFT
NBEATSx
XGBoost
LightGBM
PyGAM
0.198
0.272
0.279
0.253
0.342
0.388
0.405
0.366
0.388
YC
0.055
0.079
0,080
0.057
0.116
0.572
0.084
0.082
0.117
L.F
EA
0.059
0.096
0.097
0.061
0.108
0,589
0.092
0.085
0.108
PC 0.112
0.182
0.139
0.164
0.285
0.704
0.230
0.222
0,269
Avg
0.106
0.157
0.149
0.134
0.213
0,563
0.203
0.189
0.221
32%
29%
21%
50%
81%
48%
44%
52%
Table 2: MAE results EPF dataset equipped with 6 supporting covariates. The look-back window and forecast window are set to 168 and 24 for all methods. means the relative improvement of
ProtoTS over other baselines. Full MSE results can be found in Appendix ew
Model
ProtoTS
TimeXer
iTrans
TiDE
TFT
NBEATSx
XGBoost
LighIGBM
PyGAM
NP
0.213
0.240
0.264
0.318
0.277
0.266
0.488
0.431
0.480
PJM
0.152
0.173
0.171
0.226
0.226
0.182
0.292
0.256
0.351
EPF
BE
0.226
0,241
0.266
0,323
0.277
0.324
0.451
0.392
0.607
FR
0,183
0,192
0.213
0,281
0.242
0.340
0.374
0,361
0,570
DE
0.318
0.343
0.335
0.474
0.489
0.408
0.539
0.506
0.551
Avg
0.218
0.238
0.250
0.324
0.302
0.304
0.429
0.389
0.512
8%
13%
33%
28%
28%
49%
44%
57%
4.2 ABLATION STUDY AND SENSITIVITY ANALYSIS
Ablation Study We conduct an ablation study to assess the contribution of the three key compo- nents in ProtoTS: multi-channel embedding, bottleneck layer and hierarchical structure. To assess the modeling of heterogeneous variables, we perform ablations by simplifying the embedding single channel, removing the bottleneck layer, and flattening the hierarchical prototype structure. The ablation results in Table B demonstrate the importance of each key component ProtoTS. While removing any component degrades performance, the full model with all three achieves the best results, confirming the effectiveness of the overall design.
Table 3: Ablation Results. Evaluating the performance after removing one of the following compo- nents: bottleneck layer, multi-channel embedding, and hierarchical structure.
Models
PC
YC
EA
AVG
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
w/o bottleneck
0.044
0.160
0.013
0.089
0.129
0.248
0.010
0.073
0.049
0.143
multi-channel
0.034
0.130
0.006
0.058
0.108
0.216
0.007
0.062
0.039
0.117
hierachy
0.026
0.117
0.006
0.060
0.089
0.202
0.007
0.061
0.032
0.110
ProtoTS 0.025
0.112
0.006
0.055
0.085
0.198
0.007
0.059
0.031
0.106
Number of Root Prototypes We evaluate how the number of root prototypes affects model perfor- mance, as shown in Figure (la). The results clearly show that prototypes number is correlated with forecasting accuracy. Increasing the number of prototypes leads to lower MAF, as more prototypes enable the model capture richer variety of temporal patterns for better representation. However, once the number of root prototypes reaches threshold, the performance no longer improves. This indicates that the prototypes have already covered all typical patterns in the dataset.
Proportion of Train Data To evaluate the impact of limited training data on model performance, we gradually increase the size of the PC dataset from 50% to 100%. As the available data de- creased, existing baselines such TimeXer, iTransformer, and TiDE show clear drops in MSE. In contrast, ProtoTS maintains stable results with only minor performance loss, which improves high data efficiency (Ii et all 2023N.. The comparison results are illustrated in Figure ((b).
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0.117
ProtoTS
ITransformer
0.117
Timxer
TIDE
MAE
0.115
0.114
0.09
0.113
0.113
0.111
0.111
0.111
0.07
0.202
MSC
0.06
0.202
0.201
RE
0.05
0.201
MAE
0.04
0.200
0,199
0.199
0.199
0.199
0.02
12
15
18
50%
62.5%
75%
87.5%
100%
(a)
(b)
Figure 3: Sensitivity analysis: (a) Effect of increasing root prototype numbers from {6, 9, 12, 15, 18). (b) Data efficiency as the training data proportion increases from 50% to 100%.
4.3 QUANTITATIVE EVALUATION INTERPRETABILITY
In this section, we conduct quantitative evalua- tion of interpretability. We aim to answer the two questions: 1) How understandable and accurate are the prototypes in explaining the predictions? 2) How usable the explanation systems provided by different interpretable models (ProtoTS, TFT. NBEATSx)? Specifically, we provide 24 users with different explanations as well as the corresponding predictions, where the three models are pre- sented randomly to avoid bias. Users were asked conerete questions about the input variables, such as "Given this prediction and explanations, which season does the predicted day most likely belong to?". To evaluate interpretability, we define User Precision (UPrec) as the proportion of correctly answered variable-related questions, reflecting whether users can accurately infer the values of rele- vant input features from the explanations ee 2025).. To further assess usability, we adopt the System Usability Scale (SUS) (Brooke all (1996), widely used questionnaire that measures users perceived ease of use and overall satisfaction with a system. The quantitative results are reported in Table !L with additional details in Appendix D
Table 4: Quantitative Evaluation.
Model
UPrec
SUS Score 1
ProtoTS
77 + 3.6%
73.36
TFT NBEATSx
64 = 3.4%
29.74
62 + 2.8%
38.66
4.4 CASE STUDY OF INTERPRETABILITE AND STEERABILITY
Figure H iillustrates how ProtoTS discovers meaningful and interpretable hierarchical prototypes that help better understand electricity load forecasting and facilitate expert edits that improves model performance. We use the RE case in LOF. The load is shaped by multiple external factors, including seasonal, temperature and weekday/holiday. ProtoTS is initialized with 6 root prototypes, each fur- ther refined into 2 child prototypes. This hierarchy captures both coarse and fine temporal patterns. Time series predictions are weighted combinations of these prototypes (Figure I()). The activation weights link each prototype's contribution to predictions and are also the key to interpretation.
Obtaining overall understanding of temporal patterns. The root prototypes provide coarse tem- poral patterns of high-level concepts (Figure g(b), layer-l); workdays, non-workdays, holidays, winter, mild temperature, and summer. For example, the summer pattern (blue) exhibits high day- time peaks due to air-conditioning dominance. Autumn and winter data are dominated by distinct seasonal load profiles in red and orange. The brown prototype with a dual-peak pattern active during holidays. This contrasts with the green weekday pattern with single afternoon peak. The dual peaks suggest that industrial activity is paused, and the load driven by residential behavior.
Fine- sinengrained analysis of detailed temporal patterns. The child prototypes provide fine-grained refinements these general patterns (Figure Bb),, layer-2). For example, the root holiday prototype is split into two children: one capturing the pattern of the major holiday, Spring Festival (Chinese New Year), and the other representing the rest of the normal holidays. The Spring Festival prototype shows more pronounced evening peak and flattened noon peak.

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Published as a conference paper at ICLR 2026
Monday
Sunday
(x)
Adtvatinn Campotton
Mid-Aunum Festival Day
Year
Spring Festival
2024.7
2025.2
Deviline
Holidaay Pasteern
Winnter Paltern
Mild Pateen
Sammmer Putters High lane macriin
Mars ooee Busicy
Cold meciinn! Moaltopppo
Epicilly nooulee Workityy
Bax Bay
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Morh
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Sprtay Drastvall Pattern
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MILL Patterat Lame
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Figure 4: Case study of interpretability and steerability: (a) Activation patterns of prototypes, which each colored bar shows the degree of activation of its corresponding prototype each day. This vi- sualization shows seasonal, weekly, and holiday-related prototype activations. (b) The learned pro- totype hierarchy that illustrates typical temporal patterns and their correlations with covariates for interpretable load forecasting. After the expert splits the first prototype at layer-2, the mean MSE across five random seeds decreases from 0.099 to 0.090 for Spring Festival related predictions.
Steering the model to improve accuracy. Editing the model for improvements becomes feasible thanks the clearly interpretable temporal patterns learned in protoTS (Figure Eb,), layer-3). Based on domain knowledge that the Spring Festival itself contains distinct sub-patterns of pre- and mid-holiday behaviors, we manually split the Spring Festival prototype into two prototypes, which learns basc pattern and special pattern. The base pattern stays consistently active through the whole Spring Festival period. The special pattern starts from the Lunar Jan. 1s, strengthening progressively day by day, reflecting deepening holiday atmosphere: reduced daytime electrical usage, and stronger evening peaks as people stay home. This edit reduced the MSE during Spring Festival by 0.009, showing how expert adjustments can enhance both accuracy and explainability.
CONCLUSION
In this work, we proposed ProtoTS, a novel forecasting framework that achieves both high accuracy and multi-level interpretability through hierarchical prototypes. It learns low-noise representations from heterogeneous variables and matches them with prototypes to generate predictions and expla- nations, while the hierarchy enables coarse-to-fine pattern learning and expert-steerability. Extensive experiments and case studies on realistic datasets show state-of- tate--of-the-ar performance and transparent support, enabling experts to refine model behavior and bridging accuracy with interpretability.
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ACKNOWLEDGEMENTS
This work was partly supported by the National Natural Science Foundation of China (NSFC) (NO. 62476279, NO. U2436209), Major Innovation & Planning Interdisciplinarry Platform for the Double- First Class Initiative, Renmin University of China, the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China No. X4.24XNK This work was partially supported by fund for building world-class universities (disciplines) of Renmin Uni- versity of China and Public Computing Cloud, Renmin University of China. This work was partially supported by DAMO Academy (Hupan Laboratory) through DAMO Academy (Hupan Laboratory) Innovative Research Program.
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A USE OF LLMS
We used large language models (LLMs) only to aid or polish writing. Specifically, LLMs were employed to: (I) check grammar and spelling: (2) assist with professional academic English phras- ing without hurting the original meaning; and (3) perform light-length reduction to meet formatting constraints. LLMS were not used to generate ideas, methods, experiments, figures, or results. LLMs were not used to find related works or to retrieve references. All suggestions were reviewed and verified by the authors, who take full responsibility for the final text.
B IMPLEMENTATION DETAILS
B. DATASET DESCRIPTIONS
LOF dataset The LOF dataset is an synthetic electric load forecasting dataset. is designed to predict future electricity demand at the provincial and city levels, enable electricity generators, distributors, and suppliers to plan effectively ahead and promote energy conservation among the users eN 2020. Due to the influence of human industrial and commercial activities, electric- ity demand exhibits a clear daily cycle, maintaining a relatively stable and predictable pattern under normal conditions. The difficulty of load forecasting mainly arises from special instances that strongly correlated with a large amount of exogenous information, such as time-related attributes and comprehensive weather data. Consequently, accurate electricity load forecasting requires models to not only effectively handle these variables but also provide insights into how they affect prediction results. Hence, electricity load forecasting is a typical task of time series forecasting with exogenous variables, characterized by high demand for interoperability. The LOF dataset ranges across three years, with sampling interval of 15 minutes. The LOF dataset includes 22 exogenous variables, consisting of 14 discrete time-related variables and 8 continuous weather variables. The specific details of these exogenous variables are presented Table III
EPF dataset The EPF dataset is an electricity price forecasting datasets (Lago et al. 2021). col- leets from five distinct day-ahead electricity markets in Northern Europe, covering a six year period with sampling interval of hour. The five datasets are described as follows: (1) NP corresponds to the Nord Pool market, providing hourly electricity prices, grid load data, and wind power fore- casts from 2013-01-01 market, including zonal electricity prices for the Commonwealth Edison (COMED) zone, along with system-wide load and COMED-specific load forecasts, covering the period from 2013-01-01 to 2018-10-24. (3) BE represents the Belgian electricity market, offering hourly price data, load forecasts for Belgium, and generation forecasts for France, collected from 201 1-01-09 2016-10- 31. (4) FR pertains to the French electricity market, comprising hourly price records, load forecasts, and generation forecasts over the timeframe from 2012 2012-01-09 2017-10-31. (5) DE covers the German electricity market, documenting hourly electricity prices, zonal load forecasts for the TSO Amprion area, as well as wind and solar generation forecasts, with data available from 2012-01-09 to 2017-10-31.
2018-10-24, (2) PJM refers to the Pennsylvania-New Jersey-Maryland
B.2 IMPLEMENTATION DETAILS
All experiments are implemented using PyTorch (Paszic (01 and executed on a single NVIDIA V100 GPU with 32GB of memory. For model optimization, we employ the Adam (Kingma, 2014) optimizer with an initial learning rate of and use our Loss as the objective function. The training set for a maximum of 30 epochs, with early stopping applied to prevent overfitting. In our proposed model, the number of bottleneck fusion blocks selected from the set 2, 2, 3). while the dimension of the series representations, denoted as model dimensions, is chosen from (32, 64, 128, 256, 512), the number of initial prototypes is searched from [6, 8, 12), the deepest level is chosen from (1, 2, 3), the number of each prototype can split is selected from the set 12, 3). All baseline models used for comparison are re-implemented based on the TimeXer Repository benchmark. All baseline use REVIN (Kim et all, 202T) in training and test process.
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C FULL RESULTS
C.I FULL RESULTS OF LOF DATASET
Full results of the LOF dataset can be found in Table E, including both MSE and MAE metrics. ProtoTS achieves state-of-the-art performance across all four datasets, reducing MSE by 48.3% and MAE by 20.9%. TimeXer, iTransformer, and TiDE show the most competitive results, with TiDE performing the best among them. Machine learning methods achieve decent performance with very short training time.
Table 5: Full results of LOF dataset the time series forecasting with exogenous variables task, equipped with 22 supporting covariates. The look- -bac window and forecast window are set to 384 and 96 for all baselines. A means the relative improvement of ProtoTS over other baselines.
Model
RE
YC
EA
PC
AVG
A
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSB
MAE
ProtoTS
0.085
0.198
0.006
0.055
0.007
0.059
0.025
0.112
0.031
0.106
TimeXer
0.167
0.272
0.011
0.079
0.015
0.096
0.073
0.182
0.067
0.157
53%
32%
iTransoormer
0.169
0.279
0.013
0.080
0.018
0.097
0.043
0.139
0.061
0.149
49%
29%
TiDE
0.158
0.253
0.007
0.057
0.008
0.061
0.066
0.164
0.060
0.134
48%
21%
TFT
0.228
0.342
0.025
0.1
0.021
0.108
0.154
0.285
0,107
0.213
71%
50%
NBEATSx
0.815
0.388
1.553
0.572
2.185
0.589
2.467
0.704
1.755
0.563
98%
81%
XGBoost
0,300
0.405
0.014
0.084
0.017
0.092
0.101
0.230
0.108
0.203
71%
48%
LightGBM
0.253
0.366
0.012
0.082
0.014
0.085
0.094
0.222
0.093
0.189
67%
44%
PyGAM
0.263
0.388
0.022
0.117
0.019
0.108
0.126
0.269
0.108
0.221
71%
52%
C.2 FULL RESULTS OF EPF DATASET
Full results of the EPF dataset can be found in Table including both MSE and MAE metrics. ProtoTS achieves state-of-the-ar performance across all five datasets, reducing MSE by 8% and MAE by 8%. Similarly. TimeXer, iTransformer, and TiDE show competitive results, with TimeXer performing the best in this case. Machine learning methods perform poorly on EPF, where the number of covariates is limited.
Table 6: Full results of EPF dataset on the time series forecasting with exogenous variables task, equipped with supporting covariates. The look-back window and forecast window are 168 and 24 for all baselines. A means the relative improvement of ProtoTS over other baseline.
Model
NP
PIM
BE
FR
DE
AVG
Metrie
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAB
MSE
MAE
MSE
MAE
ProtoTS
0.168
0.213
0,064
0.152
0,353
0.226
0,351
0.183
0,271
0.318
0.241
0,218
TimeXer
0.194
0,240
0.078
0.173
0.365
0.241
0.355
0.192
0.319
0.343
0.262
0.238
8%
8%
Transformer
0.208
0.264
0.076
0.171
0.375
0.266
0.386
0.213
0.282
0.335
0.265
0.250
9%
13%
TiDE
0.306
0.318
0.121
0.226
0.495
0.323
0.492
0.281
0.533
0.474
0.389
0.324
38%
33%
TFT
0,259
0,277
0.138
0.226
0.412
0.277
0.452
0.242
0.709
0.489
0.394
0.302
39%
28%
NBEATSx
0,222
0,266
0.079
0.182
0.507
0.324
1.920
0.340
0.430
0.408
0.632
0.304
62%
28%
XGBoost
1.002
0.488
0.276
0.292
0.817
0.451
0.622
0.374
0.618
0.539
0.669
0.429
64 %
49%
LightGBM
0.678
0.431
0:234
0.256
0.598
0.392
0.603
0.361
0.549
0.506
0.532
0.389
55 %
44%
PyGAM
0.599
0.480
0.281
0.351
1.028
0.607
1.116
0.570
0.671
0.551
0.739
0.512
67 %6
57%
C.3 SESSTIIVE ANALYSIS
To investigate the consistency of the model's performance across different randomized scenarios, selected five random seeds and reported the mean and standard deviation of the model's perfor-
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mance. The experiments in Table R and Table E show that the model maintains stable performance without statistically significant variations in most cases.
Table 7: Sensitive Analysis on LOF dataset. We report our performance in mean+ std format.
Model
ProteTS
TimeXer
iTransformer
TiDE
Meuic
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
PC
0.025 amn
0.113200012
0.0754:: no0ss
0. 0.186200088
0.043:2.006
0.161
0.06622..001
0.164
YC
0.006
0.055 0001
0.0124amm6
0.080
0.014
0.083
0.007
0.057
RE
0.093 no074
0.206 oome
0.179
0.291
0. 0.169
0.275
0.158
0.253
EA
0.007
0.059
0.015#a0012
0.092#00070
0.01 0.008
a.097
0.008
0.061 #0,002
AVG
0.033 e 0,0022
0. 108 00011
0.070 0.00355
0. 1626 0.0033
0.061 a 0.0005
0.154 0.054
0.060# 0.0001
0.134 0.0022
Table 8: Sensitive Analysis on EPF dataset. We report our performance in mean std format.
Model
ProtoTS
TimeXer
Trransfommer
TiDE
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
NP
0.169 00219
0.21 0001s
0.194
0.2382nma2
0.212200009
0,269
0.31620081
0.326:00058
PJM
0.067 u00r3
0.153 90020
0.078 omm
0.17
0.081 a uxp0p
0.171 20007
O. 0.11000005
0.222an003
BE
0,364 0.0033
0.227
0,0020
0,362 00040
00001
0.381=00000
0. 0.266=00022
0, 0.480
0.3 0.3100000000
FR
0.354 0.0077
0.183 0,0057
0,007
=00017
00000
0.215
0. 000007
0.272=40007
DE
0.277 = 0.0097
0.321 0,0000
0.300=
0.338=00066
0.294
0.340
0. 0.545 s0000n
0.48 10005
AVG
0.246
0.219
0.258 0.0044
0.236
0.271 0.00172
0.252
0.385 00127
0.323
D USER STUDY DETAILS
We conducted the user study using a questionnaire format, the specific layout of which is shown in Figure & The questionnaire consists of two parts: Variable-related Questionnaire and System Us- ability Scale (SUS) Questionnaire. The first part is Variable-related Questionnaire, aims to evaluate the accuracy and comprehensibility of explanations provided by different explainable models. Par- ticipants are asked to perform causal inference on variablessuch as holidays, seasons, Chinese New Year, and other related variableshased on the models predictions and its generated explanations. This section has unique, objective correct answers, and we measure the readability of the explanations by calculating the accuracy of participants responses. The second part is System Usability Scale (SUS) Questionnaire, designed to assess the usability of the explanation systems offering different levels of explainability. Participants are asked to subjectively rate the system based on their experience completing the first part (lu 2024). The SUS yields a single number representing composite measure of the overall usability of the system under study. Note that scores for individual items are not meaningful on their own. To calculate the SUS score, first sum the score contributions from each item. Each items contribution ranges from 0 to 4. For items 1, 5, 7, and 9, the contribution is the scale position minus 1. For items 2, 4. 6, 8, and 10, the contribution is 5 minus the scale position. Multiply the total sum of these contributions by 2.5 to obtain the overall SUS score, which ranges from 0 to 100.
E VISUAL COMPARISON
To intuitively illustrate the differences between ProtoTSS and existing methods in predictions, we vi- sualize the prediction results. The models chosen for comparison are iTransformer and Timexer, and the visualization is presented in Figure R For the prediction on August 2nd ProtoTS successfully captures the evening peak, whereas the other two models perform poorly. For the predictions on Oc- tober 9th and December 1hth although all three models capture the overall shape reasonably well, ProtoTS preserves significantly more fine- mme-grained details. Regarding the prediction for February 1st, PS more accurately forecasts noon peak of the day.
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ProtoTS
TimeXer
iTrans
TiDE
msfiter
40.8
19.5
12.5
11.1
Table 9: Training time per iteration (ms).
F DISCUSSION
Although ProtoTS achieves high forecasting accuracy while providing multi-level, expert-steerable interpretability, it also has some potential limitations:
Limited adaptability to non-periodic patterns: ProtoTS relies on prototypical representations to capture typical temporal patterns. While this works well for seasonal or periodic data, its effectiveness diminishes when dealing with highly irregular, nonrepetitive time series. In such cases, more prototypes are needed cover diverse patterns, increasing model complexity and reducing interpretability.
Dependence on domain expertise for refinement: The interpretability of ProtoTS benefits from expert-guided prototype editing. However, this process requires sufficient domain knowledge and manual effort. domains where expert resources are hard to access or knowledge is difficult to formalize, the usability and effectiveness of this feature may be limited (Zhang al] ((ZZE).
Computational cost: ProtoTS introduces additional computational overhead compared to transformer-based MLP-based baselines (e.g., iTrans and TiDE). Under the same hardware and training configuration (optimizer, learning rate, sequence length, and batch size), ProtoTS shows higher per-iteration training time due multi-channel embedding design and hierarchi- cal prototype modules, both of which require extra forward computations.
G MULTIVARIATE TIME SERIES FORECASTING
In this section, we evaluate the performance of ProtoTS on standard multivariate time series fore- casting tasks.
Datasets We conduct comprehensive experiments on six benchmark datasets to evaluate the mul- tivariate forecasting capability ProtoTS, These datasets cover a variety of domains:
ETThl and ETTH2 (Zhou et all, 2021):: Hourly electricity load data from two different nodes in
power grid. They capture seasonal patterns and variable interactions across multiple features, serving standard benchmarks for long-term forecasting.
ETTml and ETTm2 (Zhou et all 202T)): Minute-level electricity load datasets focusing on finer temporal granularity. They emphasize short-term dynamics and present challenges in modeling high-frequency fluctuations.
Weather (Zhon all (001):: A multivariate weather dataset containing temperature, humidity, wind speed, and other meteorological variables collected from multiple stations. Exchange (Laretal) 2018): A financial time series dataset with daily exchange rates of eight foreign currencies.
For all datasets, we follow standard experimental protocols, using 96 look-back window and fore- casting multiple future steps (96, 192, 336, 720} to evaluate both short-term accuracy and long- horizon stability.
Baseline We compare ProtoTS against a broad set of baselines. including: Transformer bbased models (TimeXer (Wang all, 2024), iTransformer (Liu et all 2203)), PatchTST (Nie all 2022),
TimesNet (Wn et all, 2022). Crossformer (Zhang & Yan. 2023), Stationary (Lm et all 20221)
Autoformer (Wu all 2021) MI.P-based architectures (TiDE (Das et all 2022)), DLinear (Zeng
2023) RLinear et (0) SCINet cLl 2022))).
The results in Table indicate that ProtoTS achieves leading performance across most multivariate forecasting tasks. On structured datasets like ETThl and ETTh2, ProtoTS consistently outperforms all baselines at both short and long horizons, confirming its strength in modeling global temporal patterns. For high-frequency datasets such ETTml and ETTm2, ProtoTS shows clear improvements in short-term forecasts, but its advantage narrows at longer horizons (e.g.. 720 steps), where methods like PTtchTST and NemesNet achieve comparable results. On the Weather dataset,
Results
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Published as a conference paper at ICLR 2026
ProtoTS maintains strong performance, though models like Crossformer remain competitive. For the challenging Exchange dataset, ProtoTS delivers robust forecasts but faces slight performance gaps against simpler models like DLinear at certain horizons. Overall, ProtoTS shows stable and strong performance across different tasks.
We are evaluating the interpretability of existing interpretable time-series models. Purpose of the questionnaire: To assess how readable and understandable different forms of model explanations are to humans.
Each question the questionnaire includes model's explanation and four corresponding questions. The model's explanation consists of:
The model's load forecast for specific day, and An interprelability analysis explaining how the model arrived that prediction. The primary format of each question Given the model's prediction and its explamation. infer what charactcristics the model's input data might have exhibited.
After completing all questions, please fill out System Usability Scale (SUS) Questionnaire.
System Usability Scale Questionnaire
Variable-related Questionnaire
Sirongly
Strongly agree
1. Based on the model's prediction and interpretation, which season is the input data most likely from?
think that would use system frequently
disagree
2. I found the system unnecessarily complex
A: Spring or Autumn
B: Summer
I thought the system casy to
C: Winter
2. the input data from a weekend?
4. think that I would need the support of technical person lo be able to use this system
A:
B: No
found the yarious functions in system were well integrated
3. Is the input data from the Spring Festival (Chinese New Year)?
6. I thought there way loo much inconsistency in this system
A: Yes
B: No
7. I would imagine that most people would learn use this system very quickly
4. Is the input data from public holiday?
I found the system very cumbersome to use
A: Yes
9. I felt very confident using the system
B: No
needed to learn things hefore could get going with this system
Figure 5: User Study Questionnaire. Bottom: An overview of the questionnaire's purpose, question formats, and response instructions. Left: The Variable-related Questionnaire, where users are asked to infer input variables based on the provided explanations. Each question has single correct answer, used evaluate the accuracy of the system's explanations. Right: The System Usability Scale (SUS) Questionnaire, which captures users' subjective assessments to measure the usability of the current system.
19

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Look-back window
Predict window
Itranstormer ProtoTS Timexer
Camm
Time Steps
Look-back window
Predict window
3.0
Ground Truth
maansforme
Timexer
2.0
1.5
0.5
24.20.5
24.10.6
24.10.7
24.10.8
24.20.9
Time Steps
Look-back window
Predict window
Ground Truth itransforiner
Timexer
24.12.6 0:00
24.12.7
24.12.8 0:00
24.12.9 0:00
24.12.10 0:00
Time Steps
Look-back window
Predict window
1.75
Ground Truth
TTansformer
ProtoTS
1.25
Timexer
1.00
0.75
0.25
0.00
25.1.28 0:00
25.1.29 0:00
25.1.30 0:00
25.1.31 0:00
25.2.1 0:00
Steps
Figure 6: Result Visualization: The prediction results for four sampled days, consistent with experimental setting: Look-back window is days and Predict window is day, a day consists of 96 time steps. The horizontal axis represents time, and the vertical axis represents the current electricity load. The electricity load values have been normalized, so they are unitless and may include negative values.
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Table 10: Descriptions of the exogenous variables used in the LOF dataset. The table includes each variable's data type, whether it is discrete or continuous, its physical unit (if applicable), and brief description of its meaning and role in the dataset.
Name
Datatype
Type
Unit
Description
Solar year
int
Discrete
gregorian calendar year
Solar month
int
Discrete
gregorian calendar month
Solar day
int
Discrete
gregorian calendar day
Lunar year
int Discrete
chinese lunar calendar year
Lunar month
int Discrete
chinese lunar calendar month
Lunar day
int Discrete
chinese lunar calendar day
Hour
int Discrete
hour of day
Minute
int
Discrete
minute of hour
Skin temperature
float Continuous TC
the temperature of the surface the Earth
Surface pressure
float
Continuous hPa
the temperature of water near the surface
Surface sensible heat flux
float
Continuous Jm 2
the transfer of heat between the Earth's surface and atmosphere through the effects of bulent air motion
Total cloud cover
float
Continuous
%
the proportion of a grid box covered by cloud
Surface net solar radiation
float
Continuous
Jm 2
the amount of solar radiation that reaches a horizontal plane surface the Earth nus the amount reflected by the Earth's 's surface
Total precipitation 4h lead
float
Continuous m
the accumulated liquid and frozen water that falls to the Earth's 's surface
metre wind
float
Continuous ms
maximum second wind at metre height defined
Relative humidity
float
Continuous % the water vapour pressure as a percentage the value at which the air becomes saturated
Is special workday
bool
Discrete
special workday added make up for time lost during an adjusted holiday.
special holiday
bool
Discrete
public holiday mandated by law
Is holiday
bool Discrete
rest day, including weekends and public holi- days
Is workday
bool
Discrete
work day
Day of week
int
Discrete
monday=O, sunday=6
Pricing
float
Continuous
realtime electricity price strategy
21

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Published as a conference paper at ICLR 2026
Table 11: Full results of multivariate time series forecasting task, where the input window is to 96, and the forecast window is set to [96, 192, 336, 720). Results are citepd from TimeXer (Wang 20224, otherwise reproduced, 1st denotes the first count.
Midel
PronttS
Tineke
ParATST
Croas
TirseN
SCTNir
Stativnury
Moni:
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MIE
MiNE
MIE
MAE
0.390
0.388
0
0.582
0.403
0.385
0.415
0.385
0.315
0,414
01419
0:423
0.448
0.479
0.464
0.364
0.402
0.365
0.400
0:654
0,500
0.513
01491
D.449
0.439
0.435
0.441
0.43
0.474
0.925
0.402
0.534
0.504
0.500
0.482
336
0.433
0:440
0.408
0.448
0.487
0.488
0.479
0.446
0,501
0.466
0.570
0.546
0.565
0.515
0-911
0.400
0.481
0.459
0.778
0.009
0.588
0,535
0.521
0.496
0.503
0.621
0.994
0.558
0:43
0.616
0.514
0,512
193
0.770
0.387
0.903
0.789
0. 190
0.000
0.574
0.700
0.388
(1400
0.877
0.066
0.578 11500
0.114
0/477
0.176
0.950 0.000
0.512 01:M3
D4456 0.652
E102
730
0,415
0.431
0
0.408
0.412
0.427
0.445
0.000
0/400
0.431
0.466
1.104 11765
03514 1.679
0-662
0.811
0187
1.349
0.530
0.622 11:00
0,11 0.511
AVG
0.365
0.394
0.30
0.356
0.383
0.407
0.374
0.356
0.307
0.407
0.942
0.664
0661
0.550
0.44
0.457
0.559
0.515
0.954 0.723
0.576 0,516
0.450 0.659
0.304
0.347
0.518
0.716
0.394
0.366
0.951
0.176
0.378
01367
0.991
0:476
0.344 19387
3.375
0.515
0.377
0.418 0.678
0 8:786
01:00
0.506
0.475
0,383
0.387
0.391
0.392
0.451
0.404
0.357
0.441
0.553
336
0,402
0.389
0.345
0.407
0.45
0.420
0.424
0.415
0.399
0.410
0.532
0.515
0/428
0.425
0419
0.411
0.413
0.413
0.445 0.459
0.495
0.464
0/621
0.537
0.441
0.091
0.459
0.450
0:457
0,585
0.516
01671
0.190
0.364
0.182
0,207
0.305
0.187
0.377
0.192
0.274
0.255
0.337
0.255
0.237
0.259
0.250
0.309
0.245
0.304
0.241
0,302
0.414
0.492
0,290
0.364
0.249
0.309
0.284
0.362
0.399
0.445
0.200
0,339
0.251
0.340
0.118
0.011
0.146
0.307
0.142
0.915
01245
0.997
08342
0.577
IA422
0.351
0.969
0.427
0.591
B1314
01301
0.312
0.394
0.310
0.392
0.194
0.422
04407
0,977
0.196
0.922
D.400
1:280
1.022
0333
11324
01405
0.354
0,522
D969
0.:03
BABY
01415
0443
0,422
AVG
0.275
0.312
0.274
0.312
0.288
0.312
0.296
0.327
0.281
0.326
0.757
0.10
0,358
0.404
0.291
0.333
0.359
0.401
0.571
0.537
0.306
0,347
0.327
0.371
0.155
0.297
0.157
0.305
0.134
0.214
0.192
01332
10218
0.558
01230
0.302
0.172
11220
0.195
01225
0.221
0.306
01173
0.223
0.256
0,356
0,312
0.241
2.304
0.247
02221
0.154
0.400
01211
01259
0.306
0.242
1L206
0221
0.251
01231
11200
0.361
01540
B1245
01225
DUSDY 0.567
0.299
0.265
0.261
0.20
0221
01286
0.202
0.208
10.99
0.272
01355
0227
1L335
11306
02283
01.55
0.00V
0.5%
D1321
0,335
DU399 0.395
0.341
0.354
0.349
0.964
0.153
0334
0.998
0418
0333
IL386
01381
0.37V
0.422
8414
0.410
D441 0.426
0.238
0.364
0.211
0.319
0.771
0.701
01781
0.319
8111
0.711
150
03112
0.367
8.788
0.314
5/778 0.187
0.065
0.305
0
0.209
0.085
0.206
0.093
0.217
0.038
0.306
0.256
0.367
0.054
02218
0.107
0.254
0.085
0.218
0.367
0.506
01111
0.257
0.197
0.325
Exehlnne
0.299
0.309
0.177
0.300
0.154
0.307
0.509
0.184
D1307
0344
0.176
0.459
0.219
0.335
0.300 0.309
0.309
0.424
0.5
0.49
0.331
0.417
0.351
0.433
0.301
0.397
1.258
0.83
0.349
0.967
0.688
0.313
0.457
1.324
0.855
0/411
0.476
0.509
0.534
0.714
0.681
0.886
0.714
0,852
0/644
0.766
1.090 0.700
1.447
0.417
0.47
0.360
0.483
0.578
0.370
04413
GALS
0.443
0.354
0.461
0.454
0653 0.599
22


Reviews:
[{"review_id": "7qXJL2qNC6", "reviewer": "Reviewer_cW3t", "summary": "This paper proposes ProtoTS, an interpretable forecasting framework that models hierarchical prototypes to achieve both high accuracy and explainability in time series forecasting. The method builds a hierarchy of prototypes representing multi-scale temporal patterns and incorporates a multi-channel similarity mechanism for heterogeneous inputs. The approach is ambitious and technically solid, aiming to connect interpretable representation learning with practical forecasting performance.", "questions": "Please refer to the weaknesses above.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 4, "contribution": 3, "strengths": "- The paper presents an original attempt to unify interpretability and accuracy through hierarchical prototype learning.\n- It offers a systematic framework combining multi-level structure, prototype reasoning, and human-editable interpretability.\n- The experiments and visual analyses are thorough and insightful.", "weaknesses": "### **Problem & Motivation**\n\n- The motivation to move beyond local or post-hoc explanations toward global interpretable forecasting is strong and well justified.\n\n- However, it remains unclear how this approach differs fundamentally from previous prototype-based or dictionary-learning forecasting methods that already encode recurring temporal patterns.\n\n- The paper could better articulate how hierarchical prototypes specifically enhance interpretability compared to flat prototypes or segment-level reasoning.\n\n- The expert-steering feature is intriguing, but its implementation and scalability remain vague.\n\n---\n\n### **Method**\n\n- It is not clearly explained how prototypes and the model output are computed, given an input $x$. The mechanism by which a new time series sample is assigned to or reconstructed from prototypes is ambiguous.\n\n- The description also leaves uncertainty about whether there is a prototype per sample or whether prototypes are shared across samples in a latent cluster space.\n\n- Since the interactions occur in the latent space, it is unclear how one can meaningfully interpret what each prototype represents in the original time domain. A mapping or visualization process should be clarified.\n\n---\n\n### **Experiments**\n\n- The experimental scope is narrow. All evaluations are performed on a limited set of datasets; broader diversity in data domains (e.g., finance, energy, healthcare) and different lookback windows would make the results more generalizable.\n\n- There is almost no comparison with other ante-hoc or post-hoc XAI models. The paper mainly compares against interpretable models, but not against modern post-hoc explanation techniques that could provide competitive interpretability, while also achieving superior performance.\n\n- The paper should explicitly discuss the trade-off between interpretability and performance, perhaps through a 2D evaluation showing both forecast error and explanation quality.\n\n- It is unclear why models like TimeXer and ITrans are excluded from qualitative comparisons in Table 4. These baselines could offer meaningful insights into representational interpretability.", "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": "ifoZrdjoiK", "reviewer": "Reviewer_AWPh", "summary": "The paper proposes ProtoTS, an interpretable forecasting framework that models prototypical temporal patterns. The weights of these prototypes are determined by measuring the similarity between different prototypes. To balance predictability and interpretability, the authors introduce a hierarchical structure, allowing a root prototype to be split into more detailed child prototypes. The experimental results indicate that ProtoTS achieves strong forecast accuracy while also providing interpretations that can be guided by expert knowledge.", "questions": "**Main concern:** \n\n1. **Variable Interactions**: The paper states that the prototype-instance similarity is computed by \"incorporating a multi-channel embedding and bottleneck fusion mechanism\" to model interactions between input variables. However, the embedding described in Equation (2) appears to be a summation of individual variable embeddings prior to the bottleneck layer. Could the authors elaborate on how this specific architecture facilitates the modeling of interactions between variables?\n\n2. **Entropy Regularization**: In line 300, the stated goal of the entropy term in the loss function is to \"encourage a few main prototypes to cover most predictions.\" Given that negative Shannon entropy is minimized by a discrete uniform distribution, could the authors provide further intuition on how this term achieves the stated objective of encouraging a sparse set of dominant prototypes? Additionally, the inclusion of a tuning parameter (e.g., $\\lambda$) to balance the L1-norm and the regularization term seems warranted and would be a valuable addition.\n\n3. **Scope of Regularization**: The current regularization term appears to only consider the first level of the hierarchical structure. Have the authors considered extending this to other levels of the hierarchy, and what might be the potential impact of such a change?\n\n4. **Choice of L1-Norm**: Could the authors provide the rationale for selecting the L1-norm for the loss function over other metrics such as the L2-norm or domain-specific measures like Dynamic Time Warping?\n\n5. **Prototype Splitting Criteria**: The experiments include a sensitivity analysis on the number of prototypes. However, a more detailed discussion on the rules for splitting prototypes would be beneficial. Have the authors considered implementing a formal rule, such as a threshold-based criterion (e.g., $ f(Z|\\mu)>\\alpha $  or a metric like the Gini index, to guide the splitting process and maintain a robust balance between predictive accuracy and interpretability?\n6. **Simulation for Interpretability**: To further strengthen the claims regarding interpretability, have the authors considered conducting a simulation study? A simulation with a known ground truth for the underlying prototypes and hierarchical structure could provide a more objective evaluation of the model's ability to recover these causal relationships.\n\n**Minor concerns:** \n\n1.\tLine 29: The phrase \"their overall interpretability and their potential\" could be revised for clarity, as the second \"their\" is redundant.\n\n2.\tLine 76: \"input covariates\" is repetitive. Using either \"inputs\" or \"covariates\" would be more concise.\n\n3.\tLine 84: Similarly, \"interactions of covariate combinations\" could be shortened to \"interactions of covariates.\"\n\n4.\tFigure 2 (Similarity Computing): The percentages shown (0.35, 0.65, 0.1) sum to 1.1. Please verify these values.\n\n5.\tLine 208: \"is holiday\" should be corrected to \"holiday.\"\n\n6.\tLine 234: The text states the process is \"along the temporal dimension and then along the feature dimension,\" while Equation (3) suggests the fusion occurs along the feature dimension first. Please clarify this sequence.\n\n7.\tLine 236: The meaning of T in Equation (3) is unclear. Please provide a definition.\n\n8.\tLine 249: For consistency, \\mu should be rendered in boldface.\n\n9.\tLine 303: To be precise, the L1-norm should be denoted with a subscript, for instance, $|| \\cdot ||_1$.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The proposed hierarchical structure, where prototypes are progressively refined into lower levels, offers a compelling approach to managing the trade-off between forecasting accuracy and interpretability.\n\n2. The experiments demonstrate that ProtoTS delivers strong performance on time series forecasting tasks that include exogenous variables.", "weaknesses": "1.\t**Guidance on Hierarchical Structure**: While the hierarchical prototype structure is a key contribution, the paper lacks a formal or suggested methodology for determining the optimal number of leaf-prototypes. Providing a general splitting rule would enhance the practical applicability of the framework.\n2.\t**Clarity of the Loss Function**: The formulation of the loss function, which combines an L1-norm with an entropy regularization term, could be further clarified. Specifically, the intended effect of the entropy regularization on promoting a few dominant prototypes is not immediately apparent.\n3.\t**Validation of Interpretability**: The assessment of interpretability relies on a questionnaire administered to 12 users. While this provides initial evidence, the small sample size and the potential for subjective responses may limit the generalizability of these findings.", "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": "HK7htNylWP", "reviewer": "Reviewer_Tt99", "summary": "This paper introduces ProtoTS, an interpretable time series forecaasting framework that learns hierarchical prototypes. The model combines a multi-channel bottleneck encoder for heterogeneous variables with a hierachical prototype tree for coarse-to-fine interpretability. Experiments on load-forecasting and electricity price datasets show accuracy gains and improved interpretability.", "questions": "Please refer to weaknesses above.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The framework is conceptually novel. The proposed hierarchical prototypes for interpretable time series forecasting is novel and empircally verified. \n- The model design, including multi-channel embedding, bottleneck fusion, is clearly justified and contributes to performance. \n- The case study is intuitive and interesting. It well-demonstrates real-world applicability. \n- The paper is generally well written, equations align with intuition, and the proposed architecture is easy to follow.", "weaknesses": "- Experiments are limited to two datasets within the energy domain. Broader validation on additional domains (e.g., weather, traffic, retail, healthcare) would better demonstrate the generality and adaptability of ProtoTS.\n- Forecasting accuracy is reported only with MAE. Reporting MSE would provide a more comprehensive assessment.\n- Baselines include mainly traditional statistical or early deep models (ARIMA, XGBoost). I suggest comparing with more recent models such as PatchTST and TimesNet, and FEDformer.\n- Reported accuracy gains are not validated by statistical significance tests \n- The relationship with ProseNet (Interpretable and Steerable Sequence Learning via Prototypes, KDD 2019) should be discussed more thoroughly, as both share conceptual similarities in prototype-based interpretability and steering. \n- For quantiative interpretability test, only User Precision and System Usability Score are reported. I suggest considering additional metrics such as fidelity, faithfulness, which do not rely on human judgment.\n- The robustness of learned prototypes could be evaluated by introducing noise or perturbations in the input time series to test whether prototype assignments remain stable.\n- Please clarify whether the 12 participants in the user study were domain experts (e.g., energy analysts) or general users. \n- Also, please justify or discuss whether a sample size of 12 provides sufficient statistical reliability.\n- The case study focuses solely on load forecasting. I suggest adding more case studies on the other dataset as well. I belive this case study is the core result of the paper’s interpretability claim and thus presenting additional case studies (e.g., price forecasting, weather, or traffic datasets) would substantially strengthen the paper.\n- The anonymous GitHub repository provides only minimal instructions. Please add detailed environment setup instructions, data-preprocessing scripts, configuration files, and run commands so that results can be reproduced reliably.", "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": "HpuFZ1VPLR", "reviewer": "Reviewer_Ju6i", "summary": "This paper introduces a hierarchical prototype framework for explainable time series forecasting, combining prototype similarity with multi-channel embeddings to improve forecasting accuracy.", "questions": "The authors could refer to Weakness", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper proposes a clear framework that connects prototype with time series forecasting.\n\n2. Experimental results show competitive accuracy and provide case studies that make it easy to understand.", "weaknesses": "1. The introduction claims that ProtoTS is the first to model prototypical temporal patterns. However, Sec 2 already cites some prototype-based time-series models . It would be clearer if the authors could clarify more explicitly what innovation distinguishes ProtoTS from these prior works.\n\n2. The paper does not clearly explain how the learned prototypes remain semantically meaningful throughout training. The optimization objective lacks explicit constraints ensuring diversity or interpretive consistency among prototypes, which may lead to redundant prototypes.\n\n3. In experiment, adding the discussion of computational cost and complexity analysis would make the performance more convincing.", "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)