ALER-TI: Aligned Latent Embedding Retrieval for Time Series Imputation Xuan-Thong Truong1 , Trung-Kien Le1 , Tung Kieu2 , Thi-Thu Nguyen1 , Nhat-Hai Nguyen1,*
arXiv:2607.07640v1 [cs.LG] 8 Jul 2026
1
School of Computer Science, Hanoi University of Science and Technology, Hanoi, Vietnam 2 Department of Computer Science, Aalborg University, Aalborg, Denmark * Corresponding author: [email protected]
Abstract—Deep learning has significantly advanced time series imputation, yet most existing architectures primarily rely on localized temporal context within the corrupted input sequence. This reliance can be limiting in real-world scenarios, where time series often exhibit non-stationary dynamics, weak temporal correlations, and infrequent patterns that are difficult to reconstruct from nearby observations alone. In this paper, we propose ALER-TI, Aligned Latent Embedding Retrieval for Time Series Imputation, a retrieval-augmented framework that explicitly leverages historical patterns to supplement degraded local context for more reliable missing-value reconstruction. The core of ALER-TI is Latent Embedding Alignment (LEA), which mitigates the representation mismatch between corrupted queries and complete historical candidates. By applying post-hoc masking in the latent space, LEA aligns candidates with the query’s missingness pattern while allowing historical embeddings to be pre-computed and cached for efficient retrieval. ALER-TI is model-agnostic and can be integrated with various imputation backbones through a lightweight adaptation module. Extensive experiments on six real-world datasets under different missing rates demonstrate that ALER-TI consistently improves strong baseline models and enhances robustness across diverse imputation settings. Index Terms—Time series imputation, retrieval-augmented learning, model-agnostic framework, contrastive learning.
I. I NTRODUCTION Time series data collected from real-world sensors and monitoring systems are frequently affected by missing values due to sensor malfunctions, transmission failures, or human errors [11]. Since many downstream analytical models require complete data matrices as inputs, missing observations can severely undermine the reliability of critical applications, ranging from healthcare monitoring [5], [19] and financial forecasting [1] to industrial anomaly detection [4]. To address this challenge, various deep learning architectures have been developed for time series imputation, including CNN-based models [18], [22], Transformer variants [8], [17], and decomposition-based networks [23], [26]. Despite their different architectural designs, these methods mainly rely on the localized temporal context within the corrupted input sequence to reconstruct missing observations. However, real-world time series often exhibit complex and non-stationary dynamics driven by non-deterministic processes, where temporal correlations may weaken over time [17], [24]. Such dynamics can lead to infrequent patterns and distributional variations, making it difficult for models to infer missing values from the observed local context alone. This limitation is
Pre-computed embeddings
Pre-computed embeddings
Pre-computed embeddings
Representation alignment
Representation alignment
Representation alignment
Top-k Candidates
Top-k Candidates
Top-k Candidates
Similarity Estimation
Similarity Estimation
Similarity Estimation
Query Encoder
Candidate Encoder
Query Encoder
Candidate Encoder
Post-hoc Masking Query Encoder
Early Masking
Missing Query
Historical Database
Asymmetric Retrieval (AR)
Missing Query
Historical Database
On-the-fly Masking (OM) Re-compute
Missing Query
Candidate Encoder
Historical Database
Latent Embedding Alignment (LEA)
Pre-compute
Fig. 1: Comparison of retrieval strategies for time-series imputation. (a) Asymmetric Retrieval (AR): Encodes the query and candidates independently, with candidates represented as fully observed trajectories. (b) On-the-fly Masking (OM): Applies masking before encoding to align candidate representations with the query pattern, but requires online re-encoding at inference time. (c) LEA (Ours): Uses mask-agnostic encoding and performs masking in latent space, enabling reuse of pre-computed embeddings while preserving query-aware alignment.
especially problematic when the corrupted segment corresponds to a rare event or when nearby observations provide insufficient correlated information for reliable reconstruction. A promising direction is to leverage historical patterns through retrieval-augmented mechanisms, a paradigm that has recently shown strong potential in time series forecasting [7], [16], [20]. For imputation, retrieval is especially appealing because it provides explicit reference patterns at inference time, complementing the information stored implicitly in model parameters. When the local context around missing values is weak, ambiguous, or affected by non-stationary dynamics, similar historical segments may offer useful structural evidence for reconstruction. Retrieval can also help reuse rare but relevant temporal patterns when similar situations reappear, which is difficult for fixed-parameter models to achieve when such patterns occur only sparsely in the training data [2], [29]. However, retrieval for time series imputation is fundamentally different from retrieval for forecasting. In forecasting, the query sequence is usually fully observed, so similarity can be estimated from a complete input context. In imputation, by
contrast, the query itself is corrupted. Missing values directly distort the query representation and make it difficult to compare the query with complete historical candidates. Therefore, the key challenge is not merely how to retrieve historical patterns, but how to measure similarity between a corrupted query and clean candidates in a representation space that is both aligned and efficient. As illustrated in Fig. 1(a), a naive Asymmetric Retrieval strategy encodes the corrupted query and complete candidates independently. This design allows candidate embeddings to be pre-computed, but it creates a representation mismatch: the query encoder is affected by missingness artifacts, whereas the candidate encoder processes fully observed trajectories. Consequently, the resulting similarity scores may not reflect the true structural relationship between signals, causing the retriever to select irrelevant historical patterns. A more aligned alternative is On-the-fly Masking, shown in Fig. 1(b), which applies the query-specific mask to each candidate before encoding. Although this strategy reduces the representation gap, it destroys the efficiency of cached retrieval because candidate representations become query-dependent and must be recomputed online. To address these challenges, we propose ALER-TI, a retrievalaugmented framework for time series imputation centered on Latent Embedding Alignment (LEA). As illustrated in Fig. 1(c), LEA adopts a mask-agnostic encoding paradigm that shifts the interaction with missingness patterns from raw input encoding to a downstream latent alignment stage. This design allows historical candidates to be encoded and cached offline, while LEA applies post-hoc masking and context-aware interaction to align corrupted queries with the pre-indexed candidate space during retrieval. In this way, ALER-TI preserves the efficiency of cached retrieval while mitigating the representation mismatch between corrupted queries and clean historical references. We further design ALER-TI as a model-agnostic framework that can be integrated with various time series imputation backbones, such as ModernTCN [18], TimesNet [22], and SAITS [8]. By augmenting local-context models with relevant historical patterns, ALER-TI provides additional global evidence for reconstruction and improves imputation performance across different sequence lengths and missing rates. Our primary contributions are summarized as follows: We propose Latent Embedding Alignment (LEA), a retrieval mechanism that mitigates the representation mismatch between corrupted queries and clean historical candidates while avoiding the computational bottleneck of online database re-encoding. • We introduce ALER-TI, a model-agnostic retrievalaugmented framework for time series imputation that integrates relevant historical patterns with existing backbone models through a lightweight adaptation module. • Extensive experiments on multiple real-world benchmarks demonstrate that ALER-TI consistently improves strong imputation backbones and remains robust across diverse sequence lengths and missing rates.
•
II. R ELATED W ORK Deep Learning for Time Series Imputation Time series imputation has been studied through a wide range of deep learning architectures designed to capture complex temporal dependencies. CNN-based methods extract local temporal patterns, with recent models such as TimesNet [22] transforming 1D sequences into 2D representations to capture multi-periodic variations, while ModernTCN [18] employs largekernel convolutions to enhance temporal feature modeling. Following the success of self-attention, Transformer-based architectures have also been widely adopted for modeling longrange dependencies. For example, PatchTST [21] uses patchlevel representations to preserve local semantic information, whereas SAITS [8] employs diagonal-masked self-attention blocks trained with a joint-optimization strategy to directly target missing entries. In parallel, recent studies show that simpler architectures can also be highly effective. DLinear [26] decomposes time series into trend and seasonal components, while RLinear [15] combines linear mapping with reversible instance normalization to alleviate non-stationary distribution shifts. Despite these advances, most existing models perform imputation primarily based on the corrupted local context within the input sequence. As a result, they may underutilize informative historical patterns, especially when the observed context is insufficient, weakly correlated, or affected by non-stationary dynamics. In contrast, ALER-TI introduces a retrieval-based framework that explicitly extracts relevant historical subsequences and uses them as auxiliary evidence for reconstructing missing values. This design supplements local-context modeling with long-term historical information, thereby improving reconstruction when the current sequence alone provides limited guidance. Retrieval-Augmented Models Retrieval-augmented generation (RAG), originally developed in Natural Language Processing, has become an effective paradigm for alleviating the information bottleneck of fixed-parameter models by retrieving relevant instances from external databases [10], [14]. In the temporal domain, recent studies have mainly explored retrieval-augmented forecasting, where similar historical patterns are retrieved to provide long-term context for future trend estimation [12], [16], [19], [20]. Rather than requiring the model to memorize every possible temporal variation in its parameters, retrieval allows relevant historical sequences to be accessed explicitly, improving the model’s ability to handle complex or infrequent patterns. However, directly applying retrieval to time series imputation is challenging because the query sequence is itself corrupted by missing values. A naive retrieval strategy that matches a corrupted query against complete historical candidates can create a substantial representation mismatch, while dynamically masking and re-encoding every candidate at inference time is computationally expensive. To address this challenge, we introduce ALER-TI, a retrieval-augmented framework tailored for time series imputation. To the best of our knowledge,
ALER-TI is among the first frameworks to explicitly formulate deep time series imputation as a retrieval-augmented task, with a dedicated latent alignment mechanism for handling missing-query and complete-candidate mismatch. Its core component, Latent Embedding Alignment, aligns corrupted queries and clean historical candidates within a shared latent space through post-hoc masking and candidate-guided query encoding strategies, enabling both robust retrieval and efficient cached inference.
Feature similarity Cross Attention
... Multi-view extractor
Fusion Aggregator Backbone imputation
Temporal Embedding
Given a complete time series Y ∈ RC×L with C channels and length L, missing values are indicated by a binary mask M ∈ {0, 1}C×L , where Mc,l = 1 means that the entry at channel c and timestamp l is observed, and Mc,l = 0 means that it is missing. The partially observed input sequence is denoted as X, which contains the observed entries of Y under the mask M. The goal of time series imputation is to estimate the missing entries of Y from the incomplete observation X and the mask M. Specifically, the model is expected to reconstruct the unobserved values indicated by (1 − M) while preserving consistency with the observed values indicated by M. B. Framework Overview ALER-TI extends standard time series imputation by incorporating retrieval-augmented historical references. Given a historical time series repository S ∈ RC×T from the training split, we construct a candidate pool Dtrain by extracting subsequences of length L. For each incomplete query X with mask M, ALER-TI retrieves the top-k most relevant historical subsequences P = pi , i = 1 . . . k from Dtrain and uses them as auxiliary evidence for reconstruction. The reconstruction is produced by a model-agnostic framework: (1)
The final imputed output preserves the observed values and replaces only the missing entries: (2)
where ⊙ denotes element-wise multiplication. As shown in Fig. 2, ALER-TI follows a two-stage design. In the first stage, we train the Latent Embedding Alignment (LEA) module to align corrupted queries with clean historical candidates in a shared latent space. Historical candidates are encoded independently of query-specific masks and cached as latent representations, enabling efficient retrieval during inference. In the second stage, the retrieved subsequences are integrated with the output of a frozen backbone imputation model through a lightweight adapter. This design allows ALER-TI to supplement local-context reconstruction with relevant historical patterns while remaining compatible with different imputation backbones.
Top-k candidates
Masked Transformer Encoder Transformer Encoder
A. Problem Formulation
Ȳ = M ⊙ X + (1 − M) ⊙ X̄,
MLP
Keys
Masking
III. M ETHODOLOGY
X̄ = Fθ (X, M, P).
Score
Query
Backbone
Temporal Embedding
Retrieve
Latent Embedding Alignment
Database
Retrieval-augmented Imputation
Fig. 2: Overview of the ALER-TI pipeline. (Left) LEA aligns corrupted queries with clean candidates through late-stage masking and candidate-guided query encoding. (Right) The retrieved historical signals are integrated with the output of a frozen backbone model through lightweight fusion, followed by a MLP-based block for refined reconstruction.
C. Latent Embedding Alignment (LEA) 1) LEA Architecture: The Latent Embedding Alignment (LEA) module is designed to retrieve structurally relevant historical subsequences for corrupted queries while avoiding the cost of re-encoding the entire database for every query. As illustrated in Fig. 2, LEA adopts a dual-stream architecture consisting of a candidate stream and a query stream. The candidate stream supports offline caching, while the query stream performs mask-aware interaction with cached candidate representations. 2) Candidate Encoding: For each historical candidate pi ∈ Dtrain , LEA first encodes the complete sequence using a Transformer encoder fθ . Importantly, the query-specific mask M is not applied before candidate encoding. Instead, the candidate is encoded in a mask-agnostic manner, and the interaction with the query mask is postponed to the latent stage. This design allows all candidate representations to be pre-computed and cached offline, avoiding repeated online encoding of the historical database. The cached candidate representation is denoted as zci = fθ (pi ).
(3)
3) Candidate-Guided Query Encoding: For a corrupted query X, LEA extracts multiple contextual views from the observed tokens. Let U denote the index set of observed query tokens after applying the mask M, and let hj , j ∈ U be their latent representations from the query stream. We introduce m learnable query codes qr , r = 1 . . . m, where m ≪ L, to summarize the observed query context: √ X exp(q⊤ r hj / d) √ , zq r = αrj hj , αrj = P (4) ⊤ h / d) exp(q u r u∈U j∈U
where d denotes the latent dimension. These m contextual 4) Contrastive Objective: Given a corrupted query, its vectors provide multiple views of the observed query. To com- positive reference p+ , and a set of hard negatives N − , LEA pare the query with the i-th candidate, LEA further aggregates is trained with an InfoNCE-style contrastive objective: these contextual views using the candidate representation zci exp(s(X, p+ )/τ ) X LLEA = − log , as guidance: exp(s(X, p− )/τ ) exp(s(X, p+ )/τ ) + √ m X p− ∈N − exp(z⊤ ci zqr / d) √ . (5) zqi = βir zqr , βir = Pm (10) ⊤ v=1 exp(zci zqv / d) r=1 where s(·, ·) denotes the LEA similarity function and τ is a temperature parameter. The same missingness pattern M The similarity between the corrupted query and the i-th is applied through the post-hoc masking procedure when candidate is then computed as comparing the query with positive and negative samples, ⊤ si = zqi zci . (6) ensuring that similarities are computed in an aligned latent space. Since this interaction is performed only at the top latent E. Retrieval-Augmented Time Series Imputation layer and uses a small number of query codes, LEA improves After LEA is trained, ALER-TI uses it to retrieve relevant representation alignment while maintaining efficient retrieval. historical subsequences and integrate them with the output of a backbone imputation model. D. Data Construction and Contrastive Training 1) Retrieval Module: We first build a persistent latent index 1) Candidate Pool Generation: We construct the candidate by pre-computing candidate representations: pool from the training split of the historical repository S by DV = zci = fθ (pi ) (11) extracting subsequences of length L using a sliding window For a corrupted query X with mask M, LEA computes with unit stride, where Dtrain = {pi }N i=1 , pi = Si:i+L , and N = T − L + 1 for a single training series of length T ; for similarity scores si with i = 1 . . . N between the query and multiple training series, N denotes the total number of extracted all cached candidates. The top-k candidates are selected as subsequences. To reduce distribution shifts across different time retrieved references: periods, each candidate is processed using reversible instance K = Top-k(si ), P = pi | i ∈ K, (12) normalization (RevIN) [13] before being encoded and cached. where Top-k(·) returns the indices of the k largest similarity 2) Positive Sample Construction: During training, the comscores. Because candidate embeddings are cached offline, plete ground truth Y is available and is used only to construct retrieval only requires query encoding and lightweight latentsupervision for the retriever. To encourage LEA to focus on space matching during inference. stable temporal structures rather than stochastic fluctuations, 2) Lightweight Adapter: The retrieved candidates P are intewe apply seasonal-trend decomposition (STL) [6] to Y: grated with the prediction from a frozen backbone imputation Y = Ytr + Ysea + Yres , (7) model. Let zbb denote the backbone output representation. To mitigate distribution shifts between the current query where Ytr , Ysea , and Yres denote the trend, seasonal, and and retrieved references, we apply RevIN to both zbb and residual components, respectively. The positive reference is the retrieved candidates. The normalized candidates are then aggregated into a retrieval representation zre by average pooling constructed from the deterministic components: over the top-k references. p+ = Ytr + Ysea . (8) To adaptively combine the backbone output with the retrieval representation, we compute a gating matrix: This encourages the retriever to align corrupted observations g = σ(MLPg (zbb )), (13) with the underlying structural pattern of the target sequence. 3) Hard Negative Mining: Selecting informative negatives where σ(·) denotes the sigmoid activation. The fused represenis important because randomly sampled subsequences may be tation is obtained as too dissimilar and provide weak training signals. We therefore zf = g ⊙ zbb + (1 − g) ⊙ zre . (14) evaluate the Pearson correlation between the ground truth Y The fused representation is further refined by a residual MLP: and each candidate pi ∈ Dtrain : zimp = zf + MLPr (zf ). (15) ρi = Pearson(Y, pi ). (9) Finally, the denormalization step restores zimp to the original High-correlation but non-positive candidates are sampled as scale and produces the reconstruction X̄. Since the backbone hard negatives. These samples are close enough to challenge the is frozen, the additional trainable parameters introduced by retriever but do not correspond to the target structural reference, ALER-TI mainly come from the two compact MLPs in the encouraging LEA to learn fine-grained discriminative features adapter, making the framework lightweight and easy to integrate beyond simple linear similarity. with different imputation backbones.
3) Imputation Training Objective: The adapter is optimized using the mean squared error over the missing entries: Limp =
|(1 − M) ⊙ (Y − Ȳ)|2F , |1 − M|1
(16)
where | · |F and | · |1 denote the Frobenius norm and ℓ1 norm, respectively. This objective ensures that learning focuses directly on the missing entries while the final output keeps the observed values unchanged. IV. E XPERIMENTS A. Experimental Setup
configurations of each backbone unchanged, consulting TimeSeries-Library1 when needed. Thus, any performance difference between a backbone and its augmented version can be attributed to ALER-TI rather than backbone-specific retuning. All experiments are conducted on a single NVIDIA GeForce RTX 5090 GPU. The source code is available at https://anonymous.4open.science/r/Time-series-0142/. 4) Evaluation: We use MSE and MAE as evaluation metrics. To assess robustness under different levels of information loss, we evaluate four missing rates r ∈ {0.125, 0.25, 0.375, 0.5} and four input lengths L ∈ {96, 192, 336, 720}. Each configuration is repeated with three random seeds, and we report the average result.
1) Datasets: Following established time series benchmarks [18], [22], [29], we evaluate ALER-TI on six widely B. Overall Results used real-world datasets. The ETT benchmark [29] contains Table I summarizes the relative MSE improvement obtained four subsets, ETTh1, ETTh2, ETTm1, and ETTm2, which by adding ALER-TI to different backbones across all datasets record electricity-transformer oil temperature and load at and missing rates. Overall, ALER-TI improves nearly all hourly or 15-minute granularity. Electricity [9] contains evaluated configurations, with only one marginal degradation. hourly electricity consumption from 321 clients over three This demonstrates that the proposed retrieval-augmented mechyears. Weather [29] contains 21 meteorological variables anism is broadly effective rather than being tied to a specific recorded every 10 minutes throughout 2020. Together, these architecture or dataset. datasets cover diverse temporal patterns, sampling granularities, Several observations can be made. First, the gains are and distributional changes. For all datasets, we follow the particularly clear for linear backbones such as DLinear and same preprocessing and train/validation/test splits used by the RLinear. This suggests that explicit historical retrieval can baseline benchmarks to ensure a fair comparison. compensate for the limited capacity of simple parametric 2) Baseline Methods: To evaluate whether ALER-TI can models by providing useful non-parametric context. Second, serve as a model-agnostic enhancement, we instantiate it Transformer-based models also benefit substantially, indicatwith seven general-purpose backbones from three architec- ing that retrieval remains helpful even when the backbone tural families: CNN-based models, including ModernTCN [18] already has strong temporal modeling ability. Third, recent and TimesNet [22]; Transformer-based models, including competitive architectures such as ModernTCN and TimesNet PatchTST [21], Crossformer [28], and Autoformer [23]; still obtain consistent improvements, showing that ALER-TI and Linear/MLP-based models, including DLinear [26] and can enhance strong local-context models without modifying RLinear [15]. These backbones cover a broad range of their internal structures. temporal modeling mechanisms, including multi-scale conWe also observe that ALER-TI is compatible with imputationvolution, patch-wise attention, decomposition, and linear specialized methods and concurrent model-agnostic traintemporal projection. We compare each backbone with its ing paradigms. In particular, applying ALER-TI on top of ALER-TI-augmented counterpart to isolate the benefit of Glocal-IB-trained backbones still brings further improveretrieval-enhanced historical context. We further include three ment, suggesting that retrieval-based context enrichment and imputation-specialized baselines: SAITS [8] and Helix [27] objective-level regularization are complementary. These results are dedicated imputation architectures, while Glocal-IB [25] support the main claim that ALER-TI serves as a general is a concurrent model-agnostic training paradigm that augments plug-and-play module for time series imputation. Full MSE backbone objectives with a global alignment loss derived and MAE results are reported in Table XI and Table XII, from the Information Bottleneck framework. This separation respectively. allows us to assess ALER-TI across both general-purpose and imputation-specialized settings. C. Model Analysis 3) Implementation Details: We train LEA with a batch size 1) Influence of Retrieval Mechanisms: We first examine of 16. The query set contains m = 16 codes, each represented whether the observed gains come from meaningful retrieval by a 64-dimensional vector. The learning rate is set to 0.001. rather than simply adding extra historical sequences. Table II The temperature parameter is initialized as τ = ln(1/0.07) and compares ALER-TI with random retrieval, metric-based reis learned during training. This initialization yields a sufficiently trieval, and two embedding-based alternatives. Random retrieval sharp initial softmax distribution for the contrastive objective provides little benefit and can even hurt performance, showing while allowing the scaling factor to adapt to each dataset. that retrieval quality is critical for time-series imputation. We integrate ALER-TI with each backbone and optimize Metric-based criteria, such as Pearson correlation and DTW the adapter using Adam and the MSE loss. For fairness, 1 https://github.com/thuml/Time-Series-Library we keep the official training pipeline and hyperparameter
Table I: MSE improvement (%) obtained by adding ALER-TI to ten baselines on six datasets. Higher values indicate larger improvements. Results are averaged over four input lengths L ∈ {96, 192, 336, 720} for each missing rate r ∈ {0.125, 0.25, 0.375, 0.5}. Imputation-specialized Helix SAITS Glocal-IB
Baseline type Dataset r
ModernTCN
TimesNet
General-purpose CrossformerAutoformer PatchTST
DLinear
RLinear
ETTh1
0.125 0.25 0.375 0.5
10.26 0.00 4.73 5.59
19.91 7.93 7.83 12.36
13.05 8.63 10.90 11.01
8.11 10.87 5.17 8.22
6.90 8.90 10.60 12.80
49.14 41.67 38.00 28.82
24.62 27.71 24.53 21.71
35.90 33.85 27.46 25.45
33.02 33.57 31.03 28.10
27.10 27.34 24.28 21.63
ETTh2
0.125 0.25 0.375 0.5
5.50 2.44 3.19 1.63
9.56 13.13 8.45 12.07
15.98 10.54 11.05 6.84
2.50 2.27 2.08 8.77
5.10 6.30 7.10 8.30
29.51 26.62 21.52 17.49
8.33 9.26 6.56 4.05
3.13 1.45 4.05 1.25
24.53 26.09 27.22 24.50
14.91 24.06 25.16 23.78
ETTm1
0.125 0.25 0.375 0.5
6.98 4.00 7.02 12.07
23.46 15.52 23.81 18.95
9.05 6.90 8.16 5.22
10.53 12.50 15.38 7.14
2.50 3.40 3.60 4.10
21.15 20.37 13.56 15.63
44.44 40.98 49.37 46.59
41.79 42.42 43.84 34.94
43.40 39.44 34.07 20.19
43.40 40.00 34.83 44.77
ETTm2
0.125 0.25 0.375 0.5
14.29 0.00 10.53 8.70
20.73 15.38 15.44 10.62
18.06 15.80 6.92 6.78
0.00 4.76 4.00 -3.85
2.00 2.20 2.40 2.70
16.42 17.50 13.95 12.00
24.59 24.62 8.89 6.67
6.25 5.71 2.70 7.50
21.88 22.62 13.33 20.47
19.67 20.25 17.89 20.54
0.125 0.25 Electricity 0.375 0.5
12.75 3.70 3.31 3.17
7.35 8.33 11.06 12.27
7.89 5.89 5.70 2.71
7.14 8.33 3.70 6.74
9.80 9.50 9.70 10.00
10.29 11.88 11.30 16.28
6.52 7.97 8.28 8.61
10.99 5.68 5.32 1.83
17.46 19.42 17.19 18.06
19.05 18.09 17.39 15.94
0.125 0.25 Weather 0.375 0.5
14.81 6.45 11.76 10.53
6.90 10.34 11.11 8.33
13.29 6.08 6.96 7.24
10.34 3.33 3.03 0.00
2.70 3.20 3.60 3.80
10.53 5.26 7.14 9.09
18.75 16.22 12.12 16.00
14.71 23.91 15.38 27.78
15.79 19.15 23.64 21.88
15.79 19.15 22.22 22.58
Table II: Ablation study of retrieval criteria on ETTh1 and Weather with missing rate r = 0.25. Results are averaged over four input lengths L ∈ {96, 192, 336, 720}. The entry “-” denotes the vanilla baseline without retrieval augmentation, while other entries represent the specific methods used for candidate selection. Best results are in bold. Dataset
ETTh1
Model
ModernTCN
DLinear
Weather ModernTCN
DLinear
MAE MSE MAE MSE MAE MSE MAE MSE -
0.149 0.046 0.261 0.140 0.058 0.030 0.107 0.047
Random 0.158 0.052 0.258 0.136 0.067 0.035 0.113 0.048 Metric
Pearson 0.135 0.042 0.218 0.099 0.059 0.030 0.096 0.043
based
DTW
0.146 0.044 0.244 0.127 0.058 0.032 0.093 0.045
AR
0.136 0.044 0.217 0.103 0.060 0.032 0.094 0.042
OM
0.132 0.041 0.214 0.094 0.054 0.029 0.085 0.040
Embedding based
ALER-TI 0.133 0.041 0.211 0.093 0.056 0.029 0.084 0.038
after linear interpolation, provide stronger candidates than random retrieval but remain limited because they mainly capture surface-level similarity. Among embedding-based methods, AR supports offline candidate encoding but suffers from a representation mismatch between masked queries and complete historical candidates. OM reduces this mismatch by encoding candidates under the
Table III: Ablation study of the candidate-guided query encoding in MSE. Dataset
w/o Interaction
ALER-TI
Prm. (∆%)
ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity
0.128 0.082 0.068 0.040 0.109 0.046
0.123 0.079 0.060 0.037 0.107 0.039
3.91% 3.66% 11.76% 7.50% 1.83% 15.22%
query-specific mask, but this requires online candidate reencoding and therefore becomes expensive when the retrieval database is large. LEA offers a more favorable trade-off: it preserves offline candidate pre-computation while using latent interaction to align masked queries with historical candidates. As a result, ALER-TI achieves performance comparable to or better than OM, while avoiding its online encoding bottleneck. 2) Importance of Candidate-Guided Query Encoding: As illustrated in Fig. 2 (Left), we evaluate the candidate-guided query encoding mechanism in LEA through an ablation study against a Bi-Encoder baseline. This baseline retains the latestage masking pipeline but restricts the query representation, thereby collapsing the dynamic cross-attention process into non-interactive embedding alignment. As summarized in Table III, removing this mechanism
Table IV: Ablation study evaluating different fusion strategies (MSE). Bold indicates the optimal configuration. “+Cross-attn” denotes the cross-attention fusion and “+AF” denotes our ALER-TI’s Fusion. Dataset
Crossformer
+Linear
+Cross-attn
+AF
ETTh1 ETTm1 Weather Electricity
0.170 0.064 0.129 0.044
0.156 0.063 0.117 0.046
0.158 0.061 0.112 0.048
0.121 0.054 0.108 0.043
Table V: Ablation study on different components of the ALER-TI mechanism. We evaluate the impact of the gating module, RevIN, and the baseline imputation on final performance. Dataset
ETTh1
Weather
Metric
MAE
MSE
MAE
MSE
Autoformer Autoformer +ALER-TI w/o gate g w/o RevIN
0.211 0.191 0.202 0.209
0.097 0.081 0.095 0.098
0.126 0.102 0.118 0.121
0.051 0.040 0.053 0.049
consistently degrades performance across all benchmarks, with especially clear drops on Electricity and ETTm1. These results confirm that jointly encoding the masked query with candidate information helps extract richer contextual representations, leading to more accurate imputation. We further place the contextual views on the input query branch rather than the candidate branch. If the multi-view representation were deployed on the candidate side, the cached representation of each candidate would need to pass through multiple attention layers and an additional cross-attention block during online candidate encoding. This design would substantially increase inference latency, especially when scaling to large historical databases. 3) Effectiveness of ALER-TI’s Fusion: To assess the design of ALER-TI’s Fusion (AF) mechanism, we compare it with two alternative integration strategies on Crossformer under r = 0.5: (i) Linear Fusion, which projects the concatenation of the backbone output and retrieved references through a static linear layer; and (ii) Cross-attention Fusion, which computes attention weights to dynamically align the backbone output with the top-k retrieved candidates. As shown in Table IV, AF consistently achieves the lowest MSE across the evaluated datasets. Linear Fusion, despite its simplicity, relies on static parameterization and cannot sufficiently capture sample-specific retrieval patterns. Crossattention Fusion is more expressive, but it introduces additional parameter overhead and may overfit, notably degrading performance on Electricity compared with the standalone backbone. In contrast, AF avoids both limitations through a lightweight, instance-dependent gating mechanism that dynamically calibrates the retrieved context against the backbone output with minimal additional parameters. 4) Ablation Study on Component Contributions: We investigate the individual contributions of two key components in ALER-TI: the gating matrix g and the RevIN module for mitigating distribution shift. As summarized in Table V, removing
Table VI: Detailed MSE results of sensitivity analysis under varying numbers of retrieved candidates (k). Dataset
k=1
k=2
k=3
k=5
k=10
ETTh1 ETTh2 ETTm1 ETTm2 Weather Electricity
0.124 0.078 0.062 0.040 0.107 0.041
0.123 0.081 0.062 0.040 0.109 0.038
0.123 0.079 0.060 0.037 0.107 0.039
0.125 0.081 0.063 0.037 0.110 0.041
0.124 0.082 0.061 0.039 0.114 0.043
either component consistently degrades performance and, in some cases, even performs worse than the vanilla backbone. Specifically, the gating mechanism acts as a dynamic filter that selectively integrates retrieved historical patterns, preventing irrelevant context from distorting the current reconstruction. RevIN further mitigates distribution shift between historical references and the current input, enabling stable and scaleinvariant imputation under non-stationary temporal dynamics. 5) Influence of the Number of Retrieved Candidates k: We analyze the sensitivity of imputation performance to the number of retrieved candidates k ∈ 1, 2, 3, 5, 10 across six benchmark datasets, as shown in Table VI. ALER-TI remains stable across the evaluated range, reducing the need for exhaustive hyperparameter search. While a small value such as k = 1 is sufficient for datasets with simpler temporal patterns, it can be insufficient for datasets with more complex dynamics, where richer contextual information is beneficial. Conversely, excessively large values may introduce noise from less relevant candidates and slightly degrade performance. Overall, the best results are typically achieved around k ∈ 2, 3. We therefore fix k = 3 as the default setting for all experiments. 6) Theoretical Complexity Analysis: To characterize the computational cost of LEA, we compare its theoretical complexity with the embedding-based retrieval paradigms introduced in Fig. 1, namely AR and OM, across different operational phases. Table VII summarizes the theoretical bounds. Given a missing rate r, where r′ = 1 − r denotes the observed ratio, a standard Transformer backbone processing the observed tokens requires O(L2 r′2 d + Lr′ d2 ) operations per block, accounting for both quadratic self-attention and latent linear projections. The OM strategy incurs high online inference cost because its dynamic coupling mechanism requires the query mask to guide the encoding of historical candidates. As a result, candidate representations must be recomputed online, leading to an overhead of O(N (L2 r′2 d+Lr′ d2 )), which scales linearly with the database size N and quadratically with the observed sequence length Lr′ . LEA mitigates this bottleneck through post-hoc masking. The expensive sequence encoding can be shifted to the offline phase, with complexity O(N (L2 d + Ld2 )). During online retrieval, LEA reduces candidate encoding to O(N Lr′ d). Although LEA introduces an additional similarity-estimation cost of O(N m(Lr′ + 1)d) due to candidate-guided query encoding, this term remains efficient because the number of query codes is small, i.e., m ≪ L. Therefore, LEA preserves the efficiency
Table VII: Theoretical complexity comparison of retrieval strategies for time-series imputation. N : database size, L: sequence length, d: latent dimension, m: number of query codes (m ≪ L), and r′ = 1 − r, where r denotes the missing rate. Phase / Strategy
AR
OM
LEA (Ours)
Offline Embedding
O(N (L2 d + Ld2 ))
0 (Cannot)
O(N (L2 d + Ld2 ))
O(L2 r′2 d + Lr′ d2 )
O(L2 r′2 d + Lr′ d2 )
Online Query Encoding
O(L2 r′2 d + Lr′ d2 )
Online Candidate Encoding
O(1)
O(N (L2 r′2 d + Lr′ d2 ))
O(N Lr′ d)
Similarity Estimation
O(N d)
O(N d)
O(N m(Lr′ + 1)d)
of offline-indexed retrieval while improving representation consistency under dynamic masking. Table VIII: Efficiency comparison of baseline models and their ALER-TI-enhanced versions on Weather under r = 0.375 and L = 192. Best results are bolded. Model
Trainable Params
Train Time (s)
ModernTCN +ALER-TI TimesNet +ALER-TI PatchTST +ALER-TI DLinear +ALER-TI
5.9454M 0.0022M 4.6933M 0.0022M 0.9898M 0.0022M 0.2265M 0.0022M
544.1 175.4 498.3 158.7 321.1 131.2 275.3 114.9
Const. RDB Time (s) 921.7 921.7 921.7 921.7
Inference Time (ms)
Table IX: Robustness analysis of ALER-TI under temporal distribution shift. MSE results are obtained using PatchTST as the backbone with a missing rate r = 0.5, averaged across four sequence lengths 96, 192, 336, 720. Best results are bolded. Dataset ETTh1 ETTm2
6.1 7.3 5.9 6.9 5.4 6.2 1.3 2.1
7) Inference Latency and Empirical Scalability: While ALER-TI reduces training cost by freezing the backbone parameters and optimizing only a lightweight adapter, its retrieval mechanism introduces a small inference overhead. As reported in Table VIII, this overhead is consistently limited across the evaluated architectures and remains small in absolute terms. This observation is consistent with the theoretical analysis in Table VII. The additional cost mainly comes from candidate-guided query encoding and similarity matching against the pre-computed candidate embedding database. Importantly, the latency remains bounded in practice. The post-hoc masking and aggregation design of LEA restricts online candidate encoding to O(N Lr′ d), avoiding the quadratic cost of conventional dynamic retrieval approaches. Even for lightweight backbones, where the relative overhead is more visible, the absolute inference time remains modest. These results show that ALER-TI achieves a favorable tradeoff between retrieval-augmented accuracy and computational efficiency. 8) ALER-TI Remains Helpful under Temporal Distribution Shift: We evaluate the resilience of ALER-TI under temporal distribution shift by restricting the training data to 25% and 50% of the full training set. Since these datasets are chronologically ordered, limiting the training window to earlier segments creates a challenging setting where the retrieval database is temporally separated from the test period. As shown in Table IX, ALER-TI matches or outperforms the standalone PatchTST baseline across all datasets and data
Weather Electricity
Model
25%
50%
100%
PatchTST +ALER-TI PatchTST +ALER-TI PatchTST +ALER-TI PatchTST +ALER-TI
0.204 0.173 0.059 0.055 0.134 0.134 0.071 0.060
0.188 0.157 0.051 0.046 0.121 0.120 0.062 0.056
0.165 0.123 0.040 0.037 0.109 0.107 0.054 0.039
Table X: Imputation performance in terms of MSE under varying degrees of pattern rarity in the training set. Results are averaged across 360 independent evaluation segments. Best results are bolded. Pattern occurrences
1
2
4
DLinear +ALER-TI TimesNet +ALER-TI PatchTST +ALER-TI
0.191 0.164 0.127 0.116 0.141 0.120
0.180 0.163 0.109 0.103 0.133 0.118
0.168 0.159 0.104 0.099 0.128 0.115
regimes, with the only tie occurring on Weather under the 25% setting. Even in the most constrained setting, LEA recovers useful structural patterns from limited historical memory. Under the 50% setting, ALER-TI continues to provide consistent improvements. With the full training set, the gains become more pronounced, suggesting that the framework can effectively leverage a denser retrieval repository to improve imputation accuracy. 9) Robustness to Infrequent Temporal Patterns: Parametric deep networks can underrepresent long-tail temporal behaviors because their parameters are primarily optimized toward dominant global trajectories. ALER-TI addresses this limitation through an explicit non-parametric retrieval mechanism, enabling the reconstruction of localized dynamics even when their morphological signatures are rare. We validate this property on synthetic time series embedded with sparse, event-driven anomalies. a) Synthetic Data Generation: The evaluation sequences superimpose deterministic global trajectories, including sinusoidal trend and seasonality, with localized low-frequency structural anomalies modeled by a Time-Varying Autoregressive
Table XI: Detailed MSE results for ten baselines with and without ALER-TI. Lower metric values indicate better performance and best performances are bolded. The missing rates are set as r ∈ {0.125, 0.25, 0.375, 0.5}. The final results are averaged across four different sequence lengths L ∈ {96, 192, 336, 720}. * represents variants with the “former” suffix. Imputation-specialized
Baseline type Dataset
ETTh1
ETTh2
ETTm1
ETTm2
Electricity
Weather
r
General-purpose
Helix +ALER-TI SAITS +ALER-TI Glocal-Ib +ALER-TI ModernTCN +ALER-TI TimesNet +ALER-TI Cross* +ALER-TI Auto* +ALER-TI PatchTST +ALER-TI DLinear +ALER-TI RLinear +ALER-TI
0.125
0.117
0.105
0.226
0.181
0.212
0.184
0.037
0.034
0.069
0.064
0.116
0.059
0.065
0.049
0.117
0.075
0.106
0.071
0.107
0.078
0.25
0.137
0.137
0.290
0.267
0.277
0.253
0.046
0.041
0.089
0.081
0.132
0.077
0.083
0.060
0.130
0.086
0.140
0.093
0.139
0.101
0.375
0.148
0.141
0.332
0.306
0.342
0.305
0.058
0.055
0.106
0.095
0.150
0.093
0.106
0.080
0.142
0.103
0.174
0.120
0.173
0.131
0.5
0.179
0.169
0.437
0.383
0.423
0.376
0.073
0.067
0.128
0.112
0.170
0.121
0.129
0.101
0.165
0.123
0.210
0.151
0.208
0.163
0.125
0.109
0.103
0.251
0.227
0.145
0.122
0.040
0.039
0.051
0.048
0.122
0.086
0.048
0.044
0.064
0.062
0.106
0.080
0.104
0.088
0.25
0.082
0.080
0.259
0.225
0.316
0.283
0.044
0.043
0.063
0.059
0.139
0.102
0.054
0.049
0.069
0.068
0.138
0.102
0.133
0.101
0.375
0.094
0.091
0.296
0.271
0.260
0.231
0.048
0.047
0.071
0.066
0.158
0.124
0.061
0.057
0.074
0.071
0.169
0.123
0.159
0.119
0.5
0.123
0.121
0.323
0.284
0.407
0.379
0.057
0.052
0.083
0.076
0.183
0.151
0.074
0.071
0.080
0.079
0.200
0.151
0.185
0.141
0.125
0.043
0.040
0.081
0.062
0.120
0.109
0.019
0.017
0.025
0.024
0.052
0.041
0.054
0.030
0.067
0.039
0.053
0.030
0.053
0.030
0.25
0.050
0.048
0.116
0.098
0.161
0.150
0.024
0.021
0.034
0.033
0.054
0.043
0.037
0.022
0.066
0.038
0.071
0.043
0.070
0.042
0.375
0.057
0.053
0.147
0.112
0.208
0.191
0.026
0.022
0.036
0.035
0.059
0.051
0.079
0.040
0.073
0.041
0.091
0.060
0.089
0.058
0.5
0.058
0.051
0.190
0.154
0.262
0.248
0.028
0.026
0.041
0.039
0.064
0.054
0.088
0.047
0.083
0.054
0.117
0.093
0.106
0.059
0.125
0.021
0.018
0.082
0.065
0.052
0.043
0.021
0.021
0.020
0.020
0.067
0.056
0.061
0.046
0.032
0.030
0.064
0.050
0.061
0.049
0.25
0.021
0.021
0.104
0.088
0.075
0.063
0.021
0.020
0.022
0.022
0.080
0.066
0.065
0.049
0.035
0.033
0.084
0.065
0.079
0.063
0.375
0.019
0.017
0.136
0.115
0.120
0.112
0.025
0.024
0.024
0.023
0.086
0.074
0.045
0.041
0.037
0.036
0.105
0.091
0.095
0.078
0.5
0.023
0.021
0.113
0.101
0.327
0.305
0.026
0.027
0.027
0.026
0.100
0.088
0.045
0.042
0.040
0.037
0.127
0.101
0.112
0.089
0.125
0.102
0.089
0.204
0.189
0.313
0.288
0.056
0.052
0.098
0.088
0.068
0.061
0.138
0.129
0.091
0.081
0.063
0.052
0.063
0.051
0.25
0.108
0.104
0.204
0.187
0.320
0.301
0.072
0.066
0.095
0.086
0.101
0.089
0.138
0.127
0.088
0.083
0.103
0.083
0.094
0.077
0.375
0.121
0.117
0.208
0.185
0.329
0.310
0.081
0.078
0.097
0.088
0.115
0.102
0.145
0.133
0.094
0.089
0.128
0.106
0.115
0.095
0.5
0.126
0.122
0.220
0.193
0.338
0.329
0.089
0.083
0.100
0.090
0.129
0.108
0.151
0.138
0.109
0.107
0.155
0.127
0.138
0.116
0.125
0.027
0.023
0.029
0.027
0.080
0.069
0.029
0.026
0.027
0.026
0.038
0.034
0.032
0.026
0.034
0.029
0.038
0.032
0.038
0.032
0.25
0.031
0.029
0.029
0.026
0.091
0.085
0.030
0.029
0.032
0.031
0.038
0.036
0.037
0.031
0.046
0.035
0.047
0.038
0.047
0.038
0.375
0.034
0.030
0.072
0.064
0.133
0.124
0.033
0.032
0.036
0.035
0.042
0.039
0.066
0.058
0.039
0.033
0.055
0.042
0.054
0.042
0.5
0.038
0.034
0.036
0.033
0.179
0.166
0.036
0.036
0.038
0.037
0.044
0.040
0.050
0.042
0.054
0.039
0.064
0.050
0.062
0.048
Table XII: Detailed MAE results for ten baselines with and without ALER-TI. Lower metric values indicate better performance and best performances are bolded. The missing rates are set as r ∈ {0.125, 0.25, 0.375, 0.5}. The final results are averaged across four different sequence lengths L ∈ {96, 192, 336, 720}. * represents variants with the “former” suffix. Imputation-specialized
Baseline type Dataset
ETTh1
ETTh2
ETTm1
ETTm2
Electricity
Weather
r
General-purpose
Helix +ALER-TI SAITS +ALER-TI Glocal-Ib +ALER-TI ModernTCN +ALER-TI TimesNet +ALER-TI Cross* +ALER-TI Auto* +ALER-TI PatchTST +ALER-TI DLinear +ALER-TI RLinear +ALER-TI
0.125
0.220
0.209
0.311
0.249
0.302
0.261
0.134
0.127
0.177
0.171
0.236
0.170
0.176
0.146
0.224
0.182
0.227
0.184
0.228
0.193
0.25
0.241
0.238
0.348
0.301
0.347
0.311
0.149
0.133
0.202
0.196
0.253
0.194
0.198
0.162
0.236
0.196
0.261
0.211
0.261
0.217
0.375
0.251
0.242
0.383
0.342
0.389
0.347
0.166
0.159
0.221
0.215
0.271
0.213
0.225
0.188
0.249
0.214
0.290
0.239
0.289
0.245
0.5
0.273
0.256
0.436
0.361
0.433
0.380
0.184
0.174
0.241
0.237
0.291
0.243
0.246
0.211
0.265
0.233
0.318
0.267
0.316
0.273
0.125
0.234
0.226
0.343
0.288
0.262
0.229
0.131
0.127
0.152
0.145
0.231
0.202
0.147
0.148
0.167
0.165
0.220
0.197
0.218
0.218
0.25
0.202
0.195
0.350
0.313
0.433
0.387
0.138
0.135
0.171
0.159
0.249
0.219
0.156
0.157
0.172
0.170
0.253
0.222
0.249
0.223
0.375
0.220
0.214
0.372
0.329
0.370
0.335
0.143
0.142
0.182
0.169
0.267
0.240
0.165
0.167
0.179
0.174
0.280
0.244
0.273
0.242
0.5
0.254
0.253
0.396
0.338
0.478
0.428
0.159
0.152
0.196
0.185
0.290
0.265
0.183
0.184
0.186
0.187
0.306
0.269
0.296
0.263
0.125
0.124
0.117
0.181
0.150
0.220
0.201
0.093
0.088
0.099
0.095
0.160
0.148
0.158
0.114
0.170
0.114
0.158
0.121
0.157
0.122
0.25
0.136
0.131
0.209
0.167
0.250
0.236
0.103
0.097
0.111
0.111
0.163
0.128
0.131
0.115
0.171
0.126
0.184
0.145
0.183
0.144
0.375
0.146
0.142
0.233
0.202
0.281
0.264
0.106
0.098
0.122
0.119
0.171
0.164
0.189
0.132
0.180
0.137
0.209
0.171
0.207
0.167
0.5
0.147
0.140
0.267
0.211
0.314
0.287
0.118
0.110
0.145
0.136
0.192
0.176
0.196
0.154
0.190
0.150
0.226
0.205
0.215
0.179
0.125
0.102
0.096
0.199
0.176
0.164
0.141
0.088
0.087
0.085
0.084
0.174
0.163
0.157
0.143
0.112
0.125
0.168
0.150
0.165
0.149
0.25
0.095
0.094
0.217
0.189
0.198
0.175
0.089
0.087
0.091
0.090
0.187
0.173
0.154
0.141
0.117
0.113
0.195
0.172
0.189
0.171
0.375
0.094
0.091
0.244
0.209
0.250
0.237
0.098
0.097
0.096
0.095
0.192
0.181
0.136
0.132
0.122
0.119
0.218
0.197
0.209
0.186
0.5
0.103
0.098
0.229
0.207
0.445
0.403
0.100
0.102
0.104
0.106
0.206
0.194
0.139
0.134
0.128
0.124
0.241
0.215
0.227
0.205
0.125
0.191
0.177
0.309
0.278
0.381
0.354
0.166
0.159
0.217
0.203
0.184
0.169
0.258
0.216
0.222
0.214
0.176
0.151
0.176
0.148
0.25
0.197
0.192
0.305
0.279
0.387
0.353
0.191
0.181
0.211
0.207
0.228
0.209
0.256
0.221
0.219
0.202
0.231
0.202
0.219
0.187
0.375
0.211
0.206
0.307
0.278
0.394
0.366
0.202
0.200
0.212
0.206
0.244
0.215
0.263
0.227
0.227
0.220
0.258
0.215
0.244
0.212
0.5
0.218
0.211
0.314
0.281
0.401
0.381
0.211
0.204
0.218
0.213
0.260
0.221
0.267
0.232
0.245
0.241
0.286
0.241
0.269
0.238
0.125
0.048
0.041
0.039
0.035
0.115
0.108
0.054
0.052
0.056
0.055
0.093
0.079
0.067
0.058
0.064
0.056
0.088
0.071
0.089
0.072
0.25
0.052
0.049
0.040
0.039
0.132
0.125
0.058
0.056
0.065
0.063
0.095
0.088
0.078
0.069
0.086
0.060
0.107
0.084
0.106
0.084
0.375
0.062
0.056
0.047
0.041
0.181
0.167
0.063
0.061
0.071
0.072
0.104
0.095
0.118
0.106
0.071
0.064
0.120
0.091
0.118
0.091
0.5
0.067
0.062
0.049
0.045
0.238
0.221
0.068
0.067
0.075
0.074
0.105
0.099
0.099
0.087
0.095
0.070
0.133
0.103
0.129
0.100
(TV-AR) [3] process: xt =
p X
φi (t), xt−i + ϵt ,
i=1
where p = 30, ϵt ∼ U(−0.05, 0.05), and φi (t) changes abruptly to define the rare anomaly morphology within a fixed window of 192 time steps. To enforce data scarcity, TV-AR segments are injected into the training set with exactly 1, 2, and 4 occurrences. b) Empirical Evaluation: Table X reports the imputation performance. Standalone parametric baselines degrade as the pattern frequency decreases from 4 to 1, indicating their difficulty in modeling rare temporal patterns. In contrast, ALER-TI mitigates this degradation across all backbones, and its relative gains become larger as the pattern becomes scarcer. For example, ALER-TI reduces DLinear’s MSE by 14.1% with one occurrence, compared with 5.3% with four occurrences. These results confirm that non-parametric retrieval provides explicit temporal context that helps overcome the data-scarcity bottleneck of purely parametric models. D. Detailed Results Tables XI and XII report the full MSE and MAE results for all ten baselines and their ALER-TI-augmented counterparts across six datasets, four missing rates, and four sequence lengths, confirming the consistent gains summarized in Table I. V. C ONCLUSION We proposed ALER-TI, a retrieval-augmented framework for time series imputation. ALER-TI addresses the limitation of relying only on corrupted local context by retrieving relevant historical patterns to support missing-value reconstruction. Its core component, Latent Embedding Alignment (LEA), mitigates the representation mismatch between corrupted queries and clean historical candidates while maintaining efficient cached retrieval. Through a lightweight model-agnostic adapter, ALER-TI can be integrated with different imputation backbones. Experiments on multiple real-world benchmarks show that ALER-TI consistently improves strong baseline models across different sequence lengths and missing rates. In future work, we plan to explore more efficient retrieval strategies for large-scale historical databases. We also aim to extend ALER-TI to more challenging missingness patterns, such as block missingness and sensor-level failures. R EFERENCES [1] Y. S. Abu-Mostafa and A. F. Atiya, “Introduction to financial forecasting,” Appl. Intell., vol. 6, no. 3, pp. 205–213, 1996. [2] D. Arpit, S. Jastrzebski, N. Ballas, D. Krueger, E. Bengio, M. S. Kanwal, T. Maharaj, A. Fischer, A. C. Courville, Y. Bengio, and S. Lacoste-Julien, “A closer look at memorization in deep networks,” in Proc. ICML, 2017, pp. 233–242. [3] L. F. Bringmann, E. L. Hamaker, D. E. Vigo, A. Aubert, D. Borsboom, and F. Tuerlinckx, “Changing dynamics: Time-varying autoregressive models using generalized additive modeling.” Psychological methods, vol. 22, no. 3, p. 409, 2017. [4] M. Canizo, I. Triguero, A. Conde, and E. Onieva, “Multi-head CNNRNN for multi time series anomaly detection: An industrial case study,” Neurocomputing, vol. 363, pp. 246–260, 2019.
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