AXIS: Explainable Time Series Anomaly Detection with Large Language Models

## Abstract

Abstract Time-series anomaly detection (TSAD) increasingly demands explanations that articulate not only if an anomaly occurred, but also what pattern it exhibits and why it is anomalous. Leveraging the impressive explanatory capabilities of Large Language Models (LLMs), recent works have attempted to treat time series as text for explainable TSAD. However, this approach faces a fundamental challenge: LLMs operate on discrete tokens and struggle to directly process long, continuous signals. Consequently, naïve time-to-text serialization suffers from a lack of contextual grounding and representation alignment between the two modalities. To address this gap, we introduce AXIS, a framework that conditions a frozen LLM for nuanced time-series understanding. Instead of direct serialization, AXIS enriches the LLM’s input with three complementary hints derived from the series: (i) a symbolic numeric hint for numerical grounding, (ii) a context-integrated, step-aligned hint distilled from a pretrained time-series encoder to capture fine-grained dynamics, and (iii) a task-prior hint that encodes global anomaly characteristics. Furthermore, to facilitate robust evaluation of explainability, we introduce a new benchmark featuring multi-format questions and rationales that supervise contextual grounding and pattern-level semantics. Extensive experiments, including both LLM-based and human evaluations, demonstrate that AXIS yields explanations of significantly higher quality and achieves competitive detection accuracy compared to general-purpose LLMs, specialized time-series LLMs, and time-series Vision Language Models.

## 1 Introduction

Figure: Figure 1: Deep learning method for TSAD: (a) Opaque anomaly scores fail to explain why; (b) XAI features lack intuitive semantics;
Refer to caption: x1.png

Time Series Anomaly Detection (TSAD) is essential for safeguarding critical systems across domains (Iqbal et al., 2019; Zeufack et al., 2021; Hundman et al., 2018). While deep learning models can detect anomalies with high accuracy (Fig. [1](https://arxiv.org/html/2509.24378v1#S1.F1)(a)), their adoption in real-world systems is limited by two challenges. First, their reasoning process is essentially a black box. Experts remain in the dark when asking the most practical question: why was this anomaly flagged? Post-hoc attribution methods such as SHAP (Fig. [1](https://arxiv.org/html/2509.24378v1#S1.F1)(b)) attempt to fill this void, but they merely repackage correlations into statistical features. Such attributions reveal what inputs influenced the model, but they stop short of offering why the underlying anomaly event occurred. Second, these models are brittle. Trained narrowly - often on a single dataset - they capture dataset-specific features rather than generalizable patterns. In fast-changing environments where anomalies manifest in diverse forms, this rigidity is crippling: models must be retrained at high cost, yet still fail to transfer across domains. What is missing is the ability to handle anomalies universally—to recognize and adapt across diverse failure patterns without exhaustive retraining.

Figure: Figure 2: Bridging the Semantic Gap in Time Series Anomaly Explanation. (a) Current LLM-based methods fail due to: (i) poor Contextual Grounding, where observing a local pattern (e.g., the ”V-shape”) in isolation prevents a meaningful diagnosis; and (ii) Representation Misalignment, where inputs of abstract statistics (e.g., ”variance increased”) lead to uninformative, circular explanations. (b) Our approach overcomes these limitations by producing contextualized, pattern-level explanations that align with expert reasoning.
Refer to caption: x2.png

In response to these limitations, the community has turned to Large Language Models (LLMs), celebrated for their fluency and generalization. Yet critical obstacles remain: LLMs operate on discrete tokens, making them ill-suited for the long, continuous nature of time series  (Dong et al., 2024). Attempting to fit these signals into tokenized inputs often incurs lossy serialization, forcing workarounds that undercut the LLM’s capabilities. Common strategies—feeding isolated fragments or pre-aggregated statistics—reduce the model to a mere post-hoc translator. As our motivating example illustrates (Fig. [2](https://arxiv.org/html/2509.24378v1#S1.F2)(a)), this naive approach, however, suffers a critical semantic gap, driven by two fundamental failures.

The first is a lack of Contextual Grounding. By analyzing only a narrow snippet of the series, the LLM is deprived of the broader temporal context required to discern whether a local pattern is genuinely anomalous or merely a benign fluctuation. The second is a failure of Representation Alignment, which creates a chasm between the model’s analytical basis and human intuition. When an LLM is fed abstract statistical summaries instead of the data’s intrinsic shape, its explanations degenerate into shallow echoes of its inputs, failing to provide the qualitative, pattern-level insights that domain experts require to understand what truly happened in the data.

Overcoming these failures requires a paradigm shift. Explanations must move beyond statistical paraphrasing toward a native integration of temporal dynamics and linguistic reasoning. This reduces to two core challenges: the Contextual Grounding Challenge, which demands interpreting local events in the context of the full series to explain not only what the data looks like but why it is abnormal; and the Representation Alignment Challenge, which requires bridging the semantic gap between low-level numerical signals and the rich, shape-based concepts underlying human reasoning.

In this paper, we introduce AXIS, a framework designed to address these challenges and unlock the explanatory potential of LLMs for TSAD. Our approach rest on two synergistic contributions. First, to establish the necessary semantic foundation, we construct a novel benchmark with pattern-level labels and rich contextual cues, providing the semantic foundation essential for both grounding and alignment. Second, at the core of our framework is a Hint Tuner that systematically tackles both challenges. For contextual grounding, it distills global time-series information into a compact, informative ”hint.” For representation alignment, it maps this temporal hint into the LLM’s native semantic space. This integrated design transforms a frozen, general-purpose LLM into a context-aware diagnostic expert, capable of generating correct and high reasonal quality answers for TSAD, as illustrated in Fig. [2](https://arxiv.org/html/2509.24378v1#S1.F2)(b). In summary, our main contributions are threefold:

- •
A Benchmark for Semantic Explanations: To bridge the “semantic gap” between raw time series signals and linguistic concepts, we construct the first benchmark dedicated to semantic time series anomaly explanation. This benchmark ensures both anomaly diversity and explanation fidelity, providing a principled testbed for evaluating the semantic explainability of TSAD.
- •
A Novel Cross-Modal Alignment Framework: We present AXIS, a framework that aligns a frozen LLM with time-series dynamics. It conditions the LLM on three synergistic inputs: a symbolic numeric hint for numerical grounding, a context-integrated step-aligned hint for fine-grained dynamics, and a task-prior hint for global task priors.
- •
Extensive Empirical Validation: Comprehensive experiments show that AXIS establishes a new state of the art in semantic anomaly explanation, substantially outperforming strong baselines including general LLM, specialized time-series LLM, time series VLM.

## 2 Related Work

##### State-of-the-Art TSAD Models and Interpretability Challenges

Classical and statistical methods remain competitive baselines yet produce pointwise scores with weak semantics and limited support for multivariate structure (Liu et al., 2008; Yeh et al., 2016). Deep TSAD improves accuracy via reconstruction (Audibert et al., 2020; Su et al., 2019; Zhang et al., 2019), prediction-residual modeling (Tuli et al., 2022), and attention-centric architectures (Xu et al., 2021; Yang et al., 2023; Shen et al., 2020; Lan et al., 2025a), with recent work exploring unified/foundation-style formulations (Shentu et al., 2024; Gao et al., 2024) and diffusion-based detectors (Wang et al., 2025b). Explanations, however, are largely post hoc and tied to low-level contributions (e.g., time-step or feature importance), limiting mechanism-oriented diagnosis. Time-series XAI extends attribution (Bento et al., 2021) and investigates prototype/shapelet/motif views and counterfactual recourse (Bahri et al., 2022; Yeh et al., 2016), but explanations remain grounded in signal-level statistics rather than pattern-level concepts. This motivates treating TSAD explainability as a semantic alignment problem.

##### Large Language Models for TSAD

LLMs can function as zero-shot anomaly detectors under appropriate prompting and input scaling (Alnegheimish et al., 2024; Dong et al., 2024; Zhou & Yu, 2024; Wang et al., 2025a). Performance degrades on long-horizon series due to context-length limits, lossy time-to-text serialization, and chunked inference, which together induce memory decay and boundary artifacts. A complementary line uses LLMs as post-hoc reasoners that verbalize anomaly scores, SHAP attributions, or raw subsequences, or coordinate multi-agent annotation (Liu et al., 2025; Lin et al., 2024). In both paradigms, LLMs act mainly as summarizers of low-level signals, yielding descriptive rather than semantically grounded explanations. Our approach directly aligns temporal representations with language via soft-prompt-based conditioning, aiming for faithful, pattern-level explanations.

##### Benchmarks for TSAD

Existing benchmarks for time-series question answering, which are adjacent to our task, can be broadly categorized into two paradigms. The first relies on fully synthetic data generation, where normal time series are composed from trends, seasonality, and noise, after which localized anomalies are injected to generate templated or LLM-augmented labels (Cai et al., 2024; Xie et al., 2024; Wang et al., 2025a; Kong et al., 2025). The second paradigm uses real-world datasets, pairing authentic time-series data with corresponding semantic information to create evaluation suites (Kim et al., 2024; Cai et al., 2025; Liu et al., 2024a; Williams et al., 2024; Chen et al., 2025). However, synthetic benchmarks often lack the contextual richness required for robust grounding and representation alignment, while real-world data yields domain-specific explanations that limit model generalizability. To our knowledge, a dedicated benchmark for semantic time series anomaly explanation has remained a critical gap, which our work directly addresses by introducing a benchmark designed for this task.

## 3 Methodology

This section presents our AXIS framework for the semantic anomaly explanation task.
We begin by formalizing the task in Sec. [3.1](https://arxiv.org/html/2509.24378v1#S3.SS1).
Next, we introduce the core architecture in Sec. [3.2](https://arxiv.org/html/2509.24378v1#S3.SS2).
Sec. [3.3](https://arxiv.org/html/2509.24378v1#S3.SS3) describes the two-phase training paradigm—encoder pretraining followed by hint tuning with the LLM frozen—and the inference procedure.
Finally, to enable systematic supervision, we synthesize a benchmark with pattern-level annotations in Sec. [3.4](https://arxiv.org/html/2509.24378v1#S3.SS4).

### 3.1 Problem Formulation

Conventional TSAD methods typically output point-wise anomaly scores for a series of length $T$, but such signals rarely provide human-understandable insights. In practice, anomalies often span contiguous intervals rather than isolated timestamps, and users are chiefly concerned with understanding why an interval is anomalous. To address this, we reformulate the task by introducing a target interval $(s,e)$ and defining the goal as generating a natural-language explanation for it. This window-based formulation respects the temporal continuity of anomalies and makes the explanation task well-posed by localizing reasoning to a specific region within the series. We formalize the problem as follows:

### 3.2 AXIS Framework

We now propose our novel framework called AXIS for semantic anomaly explanation task. AXIS conditions a frozen LLM through three representation pathways: symbolic numeric hint, context-integrated step-aligned hint, and task-prior hint. The overall framework is shown in Fig. [3](https://arxiv.org/html/2509.24378v1#S3.F3). We instantiate this conditioning through three pathways that jointly provide numeric grounding, step-aligned dynamics under global context, and compact task-level priors, without expanding the context length or modifying the LLM.

Figure: Figure 3: AXIS constructs the prompt by three representation pathways: (i) symbolic numeric grounding via window values, (ii) context-integrated local dynamics through step-aligned hints to capture contextual information, and (iii) task-prior hints encoding global priors.
Refer to caption: x3.png

##### Symbolic Numeric Hint.

LLMs possess native reasoning capabilities over discrete numerals when presented symbolically, even in zero-shot settings. To exploit this capability without exhausting the context budget, we textualize only the target window $[s,e)$ after Z-score normalization of the full series $\mathbf{x}_{1:T}$. Values are scaled by a factor $r$ (default $r{=}100$) to preserve precision while avoiding decimal tokens (Liu et al., 2024b), rounded to integers, and serialized as a delimiter-separated string (e.g., “123, 124, 127, 128”) to constitute {time_series_tokens}.
This pathway is compact—its position cost scales as $\alpha(e-s)+c$ where $\alpha$ is the average subword tokens per integer and $c$ the delimiter overhead—yet it preserves step-wise numeric grounding.

##### Context-Integrated Step-aligned Hint.

While the above textualization provides direct numeric access, it cannot capture long-range dependencies essential for TSAD such as regime shifts, seasonality interactions, and boundary effects. We therefore condense global information into step-aligned local representations via a pretrained time-series encoder and a *Hint Tuner*, in the spirit of (Jin et al., 2023). A Transformer encoder $f_{\theta}$ consumes $\mathbf{x}_{1:T}$ and outputs embeddings $\mathbf{H}_{1:T}\in\mathbb{R}^{T\times d_{\text{proj}}}$ where $d_{\text{proj}}$ is the projection dimension (the details are shown in Appx. [B.1](https://arxiv.org/html/2509.24378v1#A2.SS1)). We slice $\mathbf{H}_{s:e}$ and map it into the LLM space using cross-attention over a prototype bank derived from the LLM vocabulary: $\mathbf{S}_{\text{proto}}=\mathbf{M}\mathbf{E}_{\text{vocab}}$ where $\mathbf{E}_{\text{vocab}}\in\mathbb{R}^{|\mathcal{V}|\times d_{h}}$ is fixed word embeddings and $\mathbf{M}\in\mathbb{R}^{P\times|\mathcal{V}|}$ is a learnable linear projection. Queries $\mathbf{W}_{q}\,\mathbf{H}_{s:e}$ attend to this bank:
$\tilde{\mathbf{H}}_{s:e}=\mathrm{Attn}\!\big(\mathbf{W}_{q}\,\mathbf{H}_{s:e},\,\mathbf{S}_{\text{proto}},\,\mathbf{S}_{\text{proto}}\big)\ \in\ \mathbb{R}^{(e-s)\times d_{h}}.$
The resulting $\tilde{\mathbf{H}}_{s:e}$ acts as step-aligned local hints that inject global context and temporal structure into the LLM embedding space while keeping both the LLM and $f_{\theta}$ frozen. This pathway adds $(e-s)$ positions linearly while supplying detailed global context and temporal alignment.

##### Task-Prior Hint.

To regularize decoding and inject task-level priors that remain stable across instances, we introduce a small set of shared queries $\mathbf{P}_{\text{fix}}\in\mathbb{R}^{K\times d_{h}}$ that attend to the same prototype source:
$\tilde{\mathbf{F}}=\mathrm{Attn}\!\big(\mathbf{P}_{\text{fix}},\,\mathbf{S}_{\text{proto}},\,\mathbf{S}_{\text{proto}}\big)\ \in\ \mathbb{R}^{K\times d_{h}}.$

##### Final Prompt.

The three hint pathways are integrated into a unified prompt that conditions the frozen LLM, as illustrated in Fig. [3](https://arxiv.org/html/2509.24378v1#S3.F3). The final input sequence is constructed from a template containing the user’s query $q$, the textualized window values, and special placeholder tokens. At input time, the embeddings for the $K$ task-prior hints ($\tilde{\mathbf{F}}$) and the $(e-s)$ step-aligned hints ($\tilde{\mathbf{H}}_{s:e}$) replace the embeddings of $K+(e-s)$ placeholder tokens. The symbolic numeric hint is inserted directly as text. This process yields a single, coherent input sequence for the LLM that combines natural language with rich, multi-faceted temporal information, all without requiring architectural changes to the base model.

### 3.3 Training Objective and Inference

Our method is trained in two phases. First, we pretrain the time-series encoder $f_{\theta}$ with a joint objective of masked reconstruction and anomaly classification with an additional linear head, then freeze its weights. Second, keeping both the encoder and the LLM frozen, we train only the Hint Tuner and its associated parameters ($\mathbf{M}$, $\mathbf{P}_{\text{fix}}$). This phase optimizes a next-token prediction loss to generate the explanation $\mathbf{y}$ conditioned on the query and all three hint pathways. The detailed training process is given in Appx. [B.2](https://arxiv.org/html/2509.24378v1#A2.SS2).

### 3.4 A Benchmark for semantic time series anomaly explanation

Existing methods reveal a foundational limitation: the community lacks a benchmark that teaches models to speak the language of temporal patterns. To address both the contextual grounding and representation alignment challenges outlined earlier, we synthesize a benchmark specifically designed to train models to reason about anomalies like human experts. Rather than a mere collection of time series, our benchmark constitutes a carefully curated curriculum built around three core design principles.

##### Pattern-Level Anomaly Vocabulary.

To address the representation alignment challenge, we introduce a procedural engine that moves beyond abstract statistical deviations to a vocabulary of interpretable, pattern-level anomalies using the procedure of Lan et al. (2025b). As illustrated in Figure [4](https://arxiv.org/html/2509.24378v1#S3.F4), our engine synthetically composes canonical anomaly primitives—such as sudden spikes, level shifts, and periodicity breaks—onto clean baseline series. A key advantage of our approach is the generation of paired time series: for every abnormal series created, a corresponding normal counterpart is preserved. This methodology establishes an unambiguous, verifiable link between anomaly time series and its linguistic label, forming the bedrock for teaching models to reason about the semantics of temporal events.

Figure: Figure 4: The architecture of our procedural engine for generating context-aware and comparative anomaly explanation benchmarks.
Refer to caption: x4.png

##### Contextual and Comparative Reasoning.

To overcome the contextual grounding challenge, we designed our benchmark to compel models to reason about local events within a global and comparative framework. Naively presenting isolated time-series windows is insufficient. Instead, our engine first generates a global descriptor, a textual summary of the series’ overall dynamics (e.g., trends, seasonality), which provides essential context. Second, we employ a comparative windowing strategy. A model is presented not only with a window containing a potential anomaly but also with the corresponding temporal window from its “healthy” paired series. This core design choice is a significant advantage, as it inherently frames the task as a discriminative one: the model must learn to articulate why a specific pattern deviates from an explicit, provided norm, rather than merely describing a segment in isolation.

##### LLM-Powered Explanation Generation.

Building on this structured foundation, we leverage LLMs to generate high-quality, multi-format supervision signals. As depicted in our pipeline, this is a multi-agent process. One LLM agent uses the global descriptor to formulate a targeted diagnostic question. A second, more powerful agent is then tasked with answering this question, conditioned on the global descriptor, the abnormal and normal window data. The primary motivation here is to generate rich, conceptual explanations. Our prompts are meticulously engineered to discourage superficial strategies (e.g., quoting raw values) and instead elicit reasoning based on the intrinsic, morphological characteristics of the anomaly. This process yields a diverse and consistent set of questions and detailed rationales, creating a powerful supervisory signal for training.

##### Ensuring Benchmark Integrity.

To guarantee the scientific utility and integrity of our benchmark, we implement a rigorous quality control pipeline. This process verifies the agreement between ground-truth labels and generated answers, enforces stylistic consistency, and filters potential redundancies. We provide comprehensive dataset statistics and are releasing all generation metadata to ensure the full reproducibility of our benchmark. The result is not merely a dataset but a robust training environment engineered to finally bridge the semantic gap in time series anomaly explanation. Some examples of the generated Q&A pairs are given in Appx. [C.2](https://arxiv.org/html/2509.24378v1#A3.SS2).

## 4 Experiments

To validate the effectiveness of AXIS, we conduct a series of experiments designed to answer three central research questions: RQ1: Explanation Quality. How does AXIS compare against state-of-the-art LLM-based methods in generating high-quality, semantic anomaly explanations? RQ2: Component Importance. How do the core components of our framework—the symbolic numeric hint, the context-integrated step-aligned hint, and the task-prior hint—contribute to the final explanation quality? RQ3: Architectural Generality. How robust is the AXIS framework when applied to different underlying frozen LLMs? Finally, in Appx. [B.2](https://arxiv.org/html/2509.24378v1#A2.SS2), we demonstrate that our Phase I TSAD model achieves results comparable to state-of-the-art methods on real-world public TSAD datasets.

### 4.1 Experimental Setup

##### Dataset.

All experiments are conducted on our newly created Semantic Anomaly Benchmark (detailed in Sec. [3.4](https://arxiv.org/html/2509.24378v1#S3.SS4)). This benchmark is specifically designed for the task of semantic time series anomaly explanation, containing diverse anomaly patterns, multi-format questions (Multiple Choice, True/False, Open-Ended), and detailed, pattern-level ground-truth explanations. The all hyperparameters for AXIS is given in Appx. [B.3](https://arxiv.org/html/2509.24378v1#A2.SS3).

##### Baselines.

We compare AXIS with a comprehensive set of strong baselines, categorized as follows:
Timeseries VLM:(He et al., 2025) Image LLM is supported by gpt-4o, which analyzes plots of the full time series with highlighted window, treating the explanation task as a visual reasoning problem. Specialized TS-LLM Methods: We include several recent models designed for time series analysis with LLMs: ChatTS (Xie et al., 2024), LLMAD (Liu et al., 2025), ChatTime (Wang et al., 2025a), and AnomLLM (Dong et al., 2024). We evaluate AnomLLM in two settings: providing the full series (AnomLLM(Full)) and providing only the target window (AnomLLM(Window)).

##### Evaluation Metrics.

Following recent work on evaluating LLM-generated content, we use an LLM-as-a-judge approach, specifically G-eval (Liu et al., 2023) with Gemini-2.5 as the arbiter. The quality of explanations is assessed across multiple dimensions tailored to each question type, including Correctness (Corr.), Reasoning Quality (Rsn. Qual.), Accuracy (Acc.), Completeness (Comp.), Relevance (Rel.), and Justification Quality (Justif.). A final, holistic score (Final) is also computed. The detailed definition for evaluation metrics is given in Appx. [E](https://arxiv.org/html/2509.24378v1#A5)

### 4.2 Main Results: Explanation Quality (RQ1)

Table [1](https://arxiv.org/html/2509.24378v1#S4.T1) presents the main results comparing our model, AXIS, against all baselines. Our method demonstrates superior performance across all metrics and question types, establishing a new state-of-the-art for the task.

Specifically, AXIS achieves the highest final scores on Multiple Choice (4.19), Open-Ended (3.02), and True/False (3.65) questions. This consistent top-ranking performance highlights its robust ability to generate accurate, complete, and well-reasoned explanations regardless of the question format. Compared to specialized TS-LLM baselines like ChatTS and the AnomLLM variants, our method shows a significant improvement, underscoring the effectiveness of our proposed hint-based conditioning strategy. The strong performance against the Image LLM baseline further suggests that our multi-pathway representation provides richer, more aligned signals for the LLM than raw visual serialization.

**Table 1: Main Results: AXIS vs Baselines**
|  | Multiple Choice | Open Ended | True False |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Model | Final | Corr. | Rsn. Qual. | Final | Acc. | Comp. | Rel. | Final | Corr. | Justif. |
| AXIS | 4.19 | 4.21 | 4.14 | 3.02 | 2.87 | 2.93 | 3.31 | 3.65 | 3.60 | 3.74 |
| Image LLM | 4.09 | 4.12 | 4.02 | 2.68 | 2.53 | 2.49 | 3.07 | 2.64 | 2.57 | 2.74 |
| ChatTS | 3.29 | 3.40 | 3.05 | 2.19 | 1.67 | 2.13 | 2.87 | 2.79 | 2.76 | 2.83 |
| LLMAD | 2.73 | 2.70 | 2.79 | 2.09 | 2.09 | 1.89 | 2.31 | 2.49 | 2.52 | 2.43 |
| ChatTime | 1.33 | 1.49 | 0.98 | 0.96 | 0.95 | 0.98 | 0.95 | 1.04 | 1.07 | 1.00 |
| AnomLLM(Full) | 3.13 | 2.98 | 3.49 | 2.86 | 2.53 | 2.89 | 3.20 | 2.88 | 2.60 | 3.31 |
| AnomLLM(Window) | 3.78 | 3.81 | 3.70 | 2.84 | 2.78 | 2.55 | 3.24 | 3.32 | 3.45 | 3.12 |

##### Visualization.

To qualitatively illustrate these performance gains, Fig. [5](https://arxiv.org/html/2509.24378v1#S4.F5) presents a comparative case study. In the Fig. [5](https://arxiv.org/html/2509.24378v1#S4.F5)(a), the target window (steps 444 to 473) exhibits pronounced oscillations. AXIS correctly contextualizes these dynamics against the broader series, identifying them as part of a normal periodic pattern and concluding there is no anomaly. In stark contrast, a baseline like AnomLLM or ChatTS, when limited to the window view, lacks this broader context and erroneously flags the internal deviations as potential outliers. In Fig. [5](https://arxiv.org/html/2509.24378v1#S4.F5)(b), AXIS provides a precise characterization by explicitly identifying the brief increase at steps 6–7 (2.27, 1.73, 2.38) and correctly interpreting it as a transient fluctuation rather than a sustained anomaly, concluding that the pattern is stable and anomaly-free. In contrast, alternative approaches tend to give vague or generalized descriptions, often noting fluctuations or moderate oscillations without distinguishing whether they indicate normal behavior or anomalies. This comparison highlights that our representation alignment framework enables fine-grained, context-aware interpretation of time series behavior, avoiding ambiguous assessments and ensuring robust anomaly detection.

##### Human evaluation.

To further validate these quantitative results from a human-centric perspective, we also performed a statistical analysis based on expert rankings of the model-generated explanations. We conducted a survey where human evaluators were asked to rank the outputs from all competing models for each question type. Fig. [6](https://arxiv.org/html/2509.24378v1#S4.F6) corroborates the findings from Table [1](https://arxiv.org/html/2509.24378v1#S4.T1)(We remove the ChatTime for poor performance). Our model, AXIS, consistently achieves the best (lowest) average rank across all three tasks, positioning it furthest to the right. The details for experiment setup and results are shown in Appx. [F](https://arxiv.org/html/2509.24378v1#A6).

Figure: Figure 5: Visualization of (a) contextual grounding and (b) representation alignment ability
Refer to caption: x5.png

Figure: Figure 6: Critical Difference diagrams illustrating the statistical comparison of model performance based on human rankings for (a) Multiple Choice, (b) Open-Ended, and (c) True/False questions.
Refer to caption: x6.png

**Table 2: Ablation Studies of Hint Components**
|  | Multiple Choice | Open Ended | True False |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Model | Final | Corr. | Rsn. Qual. | Final | Acc. | Comp. | Rel. | Final | Corr. | Justif. |
| AXIS | 4.19 | 4.21 | 4.14 | 3.02 | 2.87 | 2.93 | 3.31 | 3.65 | 3.60 | 3.74 |
| w/o-task-hint | 3.82 | 3.93 | 3.56 | 2.33 | 2.13 | 2.22 | 2.69 | 3.25 | 3.31 | 3.17 |
| w/o-context-hint | 4.09 | 4.16 | 3.91 | 2.75 | 2.56 | 2.58 | 3.16 | 2.44 | 2.48 | 2.38 |
| w/o-windows | 3.95 | 4.00 | 3.84 | 2.41 | 2.00 | 2.36 | 2.95 | 2.87 | 2.83 | 2.93 |

**Table 3: AXIS variants across LLM families and settings (standardized naming: family + size + variant; Instruct denotes instruction-tuned, Coder denotes code-pretrained**
|  |  | Multiple Choice | Open Ended | True False |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Family | Variant | Final | Corr. | Rsn. Qual. | Final | Acc. | Comp. | Rel. | Final | Corr. | Justif. |
| Deepseek-Llama | 8B (Instruct) | 4.28 | 4.30 | 4.23 | 3.02 | 2.84 | 2.84 | 3.45 | 3.64 | 3.55 | 3.79 |
| Deepseek-Qwen | 14B (Instruct) | 4.31 | 4.28 | 4.37 | 3.03 | 2.80 | 2.93 | 3.42 | 3.60 | 3.55 | 3.69 |
| Deepseek-Qwen | 7B (Instruct) | 4.19 | 4.21 | 4.14 | 3.02 | 2.87 | 2.93 | 3.31 | 3.65 | 3.60 | 3.74 |
| Deepseek-Qwen | 1.5B (Instruct) | 4.07 | 4.12 | 3.95 | 2.72 | 2.65 | 2.55 | 3.00 | 3.18 | 3.17 | 3.19 |
| Qwen2.5 | 7B (Coder) | 4.40 | 4.40 | 4.42 | 2.72 | 2.64 | 2.58 | 2.98 | 2.96 | 2.98 | 2.93 |
| Qwen2.5 | 7B (Base) | 4.30 | 4.37 | 4.12 | 2.75 | 2.73 | 2.45 | 3.13 | 3.66 | 3.69 | 3.62 |
| Qwen2.5 | 7B (Instruct) | 4.17 | 4.22 | 4.06 | 3.08 | 2.80 | 3.00 | 3.50 | 3.11 | 3.00 | 3.27 |
| Mistral | 7B (Base) | 2.97 | 3.05 | 2.79 | 2.89 | 2.69 | 2.82 | 3.20 | 2.69 | 2.55 | 2.90 |
| Mistral | 7B (Instruct) | 3.36 | 3.33 | 3.44 | 2.77 | 2.58 | 2.45 | 3.35 | 3.27 | 3.17 | 3.43 |

### 4.3 Ablation Studies (RQ2)

To understand the contribution of each component in AXIS, we conducted an ablation study, with results summarized in Table [2](https://arxiv.org/html/2509.24378v1#S4.T2). The study confirms that all three input pathways are crucial for optimal performance. Removing the context-integrated step-aligned hint (‘w/o-context-hint‘) degrades performance most severely on True/False questions (Final score drops from 3.65 to 2.44), confirming that binary judgments rely on precise, step-aligned temporal cues. In contrast, Open-Ended questions are most sensitive to the symbolic numeric hint from the window (‘w/o-windows‘); without it, accuracy drops markedly (2.00 vs 2.87) and overall quality declines (Final 2.41 vs 3.02), indicating that direct numeric access provides the fine-grained grounding needed for detailed answers. Eliminating the task-prior hint (‘w/o-task-hint‘) also substantially harms Open-Ended completeness and relevance (2.22/2.69 vs 2.93/3.31), suggesting that these global priors help structure the explanation and ensure comprehensive coverage. The full model consistently yields the best scores, validating our design choices. Additional experiments for causal contribution of hints are given in Appx. [G](https://arxiv.org/html/2509.24378v1#A7).

### 4.4 Analysis of Architectural Variants (RQ3)

To assess its generality, we instantiated AXIS across multiple LLM families and settings, using a standardized *Family + Size + Variant* naming scheme and a fixed data schedule (R1) to isolate architectural effects. As shown in Table [3](https://arxiv.org/html/2509.24378v1#S4.T3), our framework demonstrates robust cross-family adaptation (Qwen, Llama, Mistral) and its performance scales with model size (e.g., Qwen-14B $>$ 7B $>$ 1.5B). The results also reveal complementary strengths among model variants: code-pretrained models like Qwen2.5-7B Coder excel at structured discrimination tasks, achieving the highest Multiple Choice score (4.40), whereas instruction-tuned versions such as Qwen2.5-7B Instruct lead in free-form explanatory quality, with top scores in Open-Ended relevance and completeness (3.50/3.00). This highlights that AXIS not only universally enhances different base models but also allows for trade-offs between discriminative and explanatory objectives through strategic variant selection.

## 5 Conclusion

We introduce a novel cross-modal framework that effectively adapts frozen Large Language Models for semantic time series anomaly explanation. By using a three-stream conditioning strategy that combines a symbolic numeric hint, a context-integrated step-aligned hint, and a task-prior hint, our method achieves strong performance in both detection accuracy and explanation quality. Future work will explore incorporating domain-specific knowledge graphs to enhance causal reasoning and generating multi-modal explanations that include visualizations alongside text.

## Ethics statement

This work focuses on explainable time series anomaly detection and does not involve personally identifiable information or other sensitive attributes. Our benchmark primarily uses procedurally synthesized data and publicly available datasets; no private logs are collected, and no re-identification is attempted. Human evaluation was conducted with informed consent, anonymized responses, and fair compensation in line with institutional guidelines, without storing any personally identifying information.

## Reproducity statement

We aim for full reproducibility. Upon publication, we will release code, configuration files, and scripts to reproduce: (i) the benchmark synthesis pipeline (including prompts, fixed random seeds, and parameter settings); (ii) Phase I encoder pretraining and Phase II hint tuning with exact hyperparameters, token budgets, and training schedules (see Appendix [B.2](https://arxiv.org/html/2509.24378v1#A2.SS2) and Appendix [B.3](https://arxiv.org/html/2509.24378v1#A2.SS3)); and (iii) evaluation pipelines, including baseline configurations, G-Eval judge prompts, scoring scripts, and human-evaluation materials. We will provide model checkpoints where licensing permits or otherwise specify exact model identifiers and initialization procedures.

## References

- Alnegheimish et al. (2024)
Sarah Alnegheimish, Linh Nguyen, Laure Berti-Equille, and Kalyan Veeramachaneni.
Can large language models be anomaly detectors for time series?
In *2024 IEEE 11th International Conference on Data Science and Advanced Analytics (DSAA)*, pp. 1–10. IEEE, 2024.
- Ansari et al. (2024)
Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, et al.
Chronos: Learning the language of time series.
*arXiv preprint arXiv:2403.07815*, 2024.
- Audibert et al. (2020)
Julien Audibert, Pietro Michiardi, Frédéric Guyard, Sébastien Marti, and Maria A Zuluaga.
Usad: Unsupervised anomaly detection on multivariate time series.
In *Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining*, pp. 3395–3404, 2020.
- Bahri et al. (2022)
Omar Bahri, Soukaina Filali Boubrahimi, and Shah Muhammad Hamdi.
Shapelet-based counterfactual explanations for multivariate time series.
*arXiv preprint arXiv:2208.10462*, 2022.
- Bento et al. (2021)
João Bento, Pedro Saleiro, André F Cruz, Mário AT Figueiredo, and Pedro Bizarro.
Timeshap: Explaining recurrent models through sequence perturbations.
In *Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining*, pp. 2565–2573, 2021.
- Breunig et al. (2000)
Markus M Breunig, Hans-Peter Kriegel, Raymond T Ng, and Jörg Sander.
Lof: identifying density-based local outliers.
In *Proceedings of the 2000 ACM SIGMOD international conference on Management of data*, pp. 93–104, 2000.
- Cai et al. (2024)
Yifu Cai, Arjun Choudhry, Mononito Goswami, and Artur Dubrawski.
Timeseriesexam: A time series understanding exam.
*arXiv preprint arXiv:2410.14752*, 2024.
- Cai et al. (2025)
Yifu Cai, Xinyu Li, Mononito Goswami, Michał Wiliński, Gus Welter, and Artur Dubrawski.
Timeseriesgym: A scalable benchmark for (time series) machine learning engineering agents.
*arXiv preprint arXiv:2505.13291*, 2025.
- Chen et al. (2025)
Jialin Chen, Aosong Feng, Ziyu Zhao, Juan Garza, Gaukhar Nurbek, Cheng Qin, Ali Maatouk, Leandros Tassiulas, Yifeng Gao, and Rex Ying.
Mtbench: A multimodal time series benchmark for temporal reasoning and question answering.
*arXiv preprint arXiv:2503.16858*, 2025.
- Das et al. (2024)
Abhimanyu Das, Weihao Kong, Rajat Sen, and Yichen Zhou.
A decoder-only foundation model for time-series forecasting.
In *Forty-first International Conference on Machine Learning*, 2024.
- Dong et al. (2024)
Manqing Dong, Hao Huang, and Longbing Cao.
Can llms serve as time series anomaly detectors?
*arXiv preprint arXiv:2408.03475*, 2024.
- Ekambaram et al. (2025)
Vijay Ekambaram, Subodh Kumar, Arindam Jati, Sumanta Mukherjee, Tomoya Sakai, Pankaj Dayama, Wesley M Gifford, and Jayant Kalagnanam.
Tspulse: Dual space tiny pre-trained models for rapid time-series analysis.
*arXiv preprint arXiv:2505.13033*, 2025.
- Gao et al. (2024)
Shanghua Gao, Teddy Koker, Owen Queen, Tom Hartvigsen, Theodoros Tsiligkaridis, and Marinka Zitnik.
Units: A unified multi-task time series model.
*Advances in Neural Information Processing Systems*, 37:140589–140631, 2024.
- Goswami et al. (2024)
Mononito Goswami, Konrad Szafer, Arjun Choudhry, Yifu Cai, Shuo Li, and Artur Dubrawski.
Moment: A family of open time-series foundation models.
*arXiv preprint arXiv:2402.03885*, 2024.
- He et al. (2025)
Zelin He, Sarah Alnegheimish, and Matthew Reimherr.
Harnessing vision-language models for time series anomaly detection.
*arXiv preprint arXiv:2506.06836*, 2025.
- Hundman et al. (2018)
Kyle Hundman, Valentino Constantinou, Christopher Laporte, Ian Colwell, and Tom Soderstrom.
Detecting spacecraft anomalies using lstms and nonparametric dynamic thresholding.
In *Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery & data mining*, pp. 387–395, 2018.
- Iqbal et al. (2019)
Rahat Iqbal, Tomasz Maniak, Faiyaz Doctor, and Charalampos Karyotis.
Fault detection and isolation in industrial processes using deep learning approaches.
*IEEE Transactions on Industrial Informatics*, 15(5):3077–3084, 2019.
- Jin et al. (2023)
Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y Zhang, Xiaoming Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, et al.
Time-llm: Time series forecasting by reprogramming large language models.
*arXiv preprint arXiv:2310.01728*, 2023.
- Kim et al. (2024)
Kai Kim, Howard Tsai, Rajat Sen, Abhimanyu Das, Zihao Zhou, Abhishek Tanpure, Mathew Luo, and Rose Yu.
Multi-modal forecaster: Jointly predicting time series and textual data.
*arXiv preprint arXiv:2411.06735*, 2024.
- Kong et al. (2025)
Yaxuan Kong, Yiyuan Yang, Yoontae Hwang, Wenjie Du, Stefan Zohren, Zhangyang Wang, Ming Jin, and Qingsong Wen.
Time-mqa: Time series multi-task question answering with context enhancement.
*arXiv preprint arXiv:2503.01875*, 2025.
- Lan et al. (2025a)
Tian Lan, Yifei Gao, Yimeng Lu, and Chen Zhang.
Cicada: Cross-domain interpretable coding for anomaly detection and adaptation in multivariate time series.
*arXiv preprint arXiv:2505.00415*, 2025a.
- Lan et al. (2025b)
Tian Lan, Hao Duong Le, Jinbo Li, Wenjun He, Meng Wang, Chenghao Liu, and Chen Zhang.
Towards foundation models for zero-shot time series anomaly detection: Leveraging synthetic data and relative context discrepancy.
*arXiv preprint arXiv:2509.21190*, 2025b.
- Lin et al. (2024)
Minhua Lin, Zhengzhang Chen, Yanchi Liu, Xujiang Zhao, Zongyu Wu, Junxiang Wang, Xiang Zhang, Suhang Wang, and Haifeng Chen.
Decoding time series with llms: A multi-agent framework for cross-domain annotation.
*arXiv preprint arXiv:2410.17462*, 2024.
- Liu et al. (2008)
Fei Tony Liu, Kai Ming Ting, and Zhi-Hua Zhou.
Isolation forest.
In *2008 eighth ieee international conference on data mining*, pp. 413–422. IEEE, 2008.
- Liu et al. (2024a)
Haoxin Liu, Shangqing Xu, Zhiyuan Zhao, Lingkai Kong, Harshavardhan Prabhakar Kamarthi, Aditya Sasanur, Megha Sharma, Jiaming Cui, Qingsong Wen, Chao Zhang, et al.
Time-mmd: Multi-domain multimodal dataset for time series analysis.
*Advances in Neural Information Processing Systems*, 37:77888–77933, 2024a.
- Liu et al. (2025)
Jun Liu, Chaoyun Zhang, Jiaxu Qian, Minghua Ma, Si Qin, Chetan Bansal, Qingwei Lin, Saravan Rajmohan, and Dongmei Zhang.
Large language models can deliver accurate and interpretable time series anomaly detection.
In *Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2*, pp. 4623–4634, 2025.
- Liu et al. (2024b)
Qingxiang Liu, Xu Liu, Chenghao Liu, Qingsong Wen, and Yuxuan Liang.
Time-ffm: Towards lm-empowered federated foundation model for time series forecasting.
*Advances in Neural Information Processing Systems*, 37:94512–94538, 2024b.
- Liu et al. (2023)
Yang Liu, Dan Iter, Yichong Xu, Shuohang Wang, Ruochen Xu, and Chenguang Zhu.
G-eval: Nlg evaluation using gpt-4 with better human alignment.
*arXiv preprint arXiv:2303.16634*, 2023.
- Shen et al. (2020)
Lifeng Shen, Zhuocong Li, and James Kwok.
Timeseries anomaly detection using temporal hierarchical one-class network.
*Advances in neural information processing systems*, 33:13016–13026, 2020.
- Shentu et al. (2024)
Qichao Shentu, Beibu Li, Kai Zhao, Yang Shu, Zhongwen Rao, Lujia Pan, Bin Yang, and Chenjuan Guo.
Towards a general time series anomaly detector with adaptive bottlenecks and dual adversarial decoders.
*arXiv preprint arXiv:2405.15273*, 2024.
- Su et al. (2019)
Ya Su, Youjian Zhao, Chenhao Niu, Rong Liu, Wei Sun, and Dan Pei.
Robust anomaly detection for multivariate time series through stochastic recurrent neural network.
In *Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining*, pp. 2828–2837, 2019.
- Tuli et al. (2022)
Shreshth Tuli, Giuliano Casale, and Nicholas R Jennings.
Tranad: deep transformer networks for anomaly detection in multivariate time series data.
*Proceedings of the VLDB Endowment*, 15(6):1201–1214, 2022.
- Wang et al. (2025a)
Chengsen Wang, Qi Qi, Jingyu Wang, Haifeng Sun, Zirui Zhuang, Jinming Wu, Lei Zhang, and Jianxin Liao.
Chattime: A unified multimodal time series foundation model bridging numerical and textual data.
In *Proceedings of the AAAI Conference on Artificial Intelligence*, volume 39, pp. 12694–12702, 2025a.
- Wang et al. (2025b)
Tao Wang, Cong Zhang, Xingguang Qu, Kun Li, Weiwei Liu, and Chang Huang.
Diffad: A unified diffusion modeling approach for autonomous driving.
*arXiv preprint arXiv:2503.12170*, 2025b.
- Williams et al. (2024)
Andrew Robert Williams, Arjun Ashok, Étienne Marcotte, Valentina Zantedeschi, Jithendaraa Subramanian, Roland Riachi, James Requeima, Alexandre Lacoste, Irina Rish, Nicolas Chapados, et al.
Context is key: A benchmark for forecasting with essential textual information.
*arXiv preprint arXiv:2410.18959*, 2024.
- Xiaoming et al. (2025)
Shi Xiaoming, Wang Shiyu, Nie Yuqi, Li Dianqi, Ye Zhou, Wen Qingsong, and Ming Jin.
Time-moe: Billion-scale time series foundation models with mixture of experts.
In *ICLR 2025: The Thirteenth International Conference on Learning Representations*. International Conference on Learning Representations, 2025.
- Xie et al. (2024)
Zhe Xie, Zeyan Li, Xiao He, Longlong Xu, Xidao Wen, Tieying Zhang, Jianjun Chen, Rui Shi, and Dan Pei.
Chatts: Aligning time series with llms via synthetic data for enhanced understanding and reasoning.
*arXiv preprint arXiv:2412.03104*, 2024.
- Xu et al. (2021)
Jiehui Xu, Haixu Wu, Jianmin Wang, and Mingsheng Long.
Anomaly transformer: Time series anomaly detection with association discrepancy.
*arXiv preprint arXiv:2110.02642*, 2021.
- Yang et al. (2023)
Yiyuan Yang, Chaoli Zhang, Tian Zhou, Qingsong Wen, and Liang Sun.
Dcdetector: Dual attention contrastive representation learning for time series anomaly detection.
In *Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining*, pp. 3033–3045, 2023.
- Yeh et al. (2016)
Chin-Chia Michael Yeh, Yan Zhu, Liudmila Ulanova, Nurjahan Begum, Yifei Ding, Hoang Anh Dau, Diego Furtado Silva, Abdullah Mueen, and Eamonn Keogh.
Matrix profile i: all pairs similarity joins for time series: a unifying view that includes motifs, discords and shapelets.
In *2016 IEEE 16th international conference on data mining (ICDM)*, pp. 1317–1322. Ieee, 2016.
- Zeufack et al. (2021)
Vannel Zeufack, Donghyun Kim, Daehee Seo, and Ahyoung Lee.
An unsupervised anomaly detection framework for detecting anomalies in real time through network system’s log files analysis.
*High-Confidence Computing*, 1(2):100030, 2021.
- Zhang et al. (2019)
Chuxu Zhang, Dongjin Song, Yuncong Chen, Xinyang Feng, Cristian Lumezanu, Wei Cheng, Jingchao Ni, Bo Zong, Haifeng Chen, and Nitesh V Chawla.
A deep neural network for unsupervised anomaly detection and diagnosis in multivariate time series data.
In *Proceedings of the AAAI conference on artificial intelligence*, volume 33, pp. 1409–1416, 2019.
- Zhou & Yu (2024)
Zihao Zhou and Rose Yu.
Can llms understand time series anomalies?
*arXiv preprint arXiv:2410.05440*, 2024.

## Appendix A Use of LLMs

Our manuscript preparation involved the use of large language models (LLMs) primarily for refining language, improving grammar, readability, and stylistic elements. Crucially, LLMs also constituted a core component of our research process. They were leveraged as agents to participate in data generation, established as benchmarks for experimental baselines, and contributed to the comprehensive evaluation of experimental results. For a detailed account of LLMs’ specific applications within our methodology, please refer to Section  [3.4](https://arxiv.org/html/2509.24378v1#S3.SS4) and Section  [4](https://arxiv.org/html/2509.24378v1#S4). We confirm that the contributions of LLMs, whether in writing or research, do not impede the reproducibility of our reported findings.

## Appendix B Details for AXIS

### B.1 Time-Series Encoder Details

This section details the architecture of the time-series encoder $f_{\theta}$ used in AXIS. The overall structure is shown in Fig. [7](https://arxiv.org/html/2509.24378v1#A2.F7).

Figure: Figure 7: The structure of time-series encoder.
Refer to caption: x7.png

##### Patchify.

Let $P$ denote the patch size. We pad $\mathbf{x}_{1:T}$ to length $T^{\prime}=\lceil T/P\rceil P$ with zeros and form $N=T^{\prime}/P$ contiguous, non-overlapping patches:

$$ $\mathbf{X}^{(n)}=[x_{(n-1)P+1},\dots,x_{nP}]\in\mathbb{R}^{P},\quad n=1,\dots,N.$ $$

Stacking yields $\mathbf{X}_{p}\in\mathbb{R}^{N\times P}$. The patch-level attention mask is obtained by aggregating the step mask: a patch is valid if it contains at least one valid step,

$$ $\mathbf{m}^{\text{patch}}_{n}=\mathbb{I}\Big(\sum_{t=(n-1)P+1}^{nP}m_{t}>0\Big),\quad n=1,\dots,N.$ $$

##### Patch Embedding.

Each patch is projected to the model dimension $d_{\text{model}}$ with a linear layer

$$ $\mathbf{Z}=\mathbf{X}_{p}\mathbf{W}_{e}+\mathbf{1}\,\mathbf{b}_{e}^{\top}\in\mathbb{R}^{N\times d_{\text{model}}},\quad\mathbf{W}_{e}\in\mathbb{R}^{P\times d_{\text{model}}}.$ $$

##### Positional Encoding via RoPE.

The encoder uses rotary positional encoding (RoPE) applied *inside* self-attention to the query and key of each head. Concretely, for a sequence of $N$ patch tokens, RoPE generates frequency pairs that rotate the $d_{\text{model}}$ channels in 2D subspaces, providing translation-friendly relative position information.

##### Transformer Encoder (Non-causal).

We stack $L$ pre-norm Transformer encoder layers. Each layer comprises: (i) multi-head self-attention with $H$ heads and head dimension $d_{\text{head}}=d_{\text{model}}/H$; (ii) an MLP block of the LLaMA style with gated GELU activation. RMSNorm is used before attention and MLP. Attention is *non-causal* and operates over all $N$ patches, enabling global context aggregation. The attention mask derived from $\mathbf{m}^{\text{patch}}$ prevents padded tokens from contributing. In the univariate case there is no inter-feature bias term; the attention is standard scaled dot-product with RoPE.

##### UnPatchify and Projection to Step Alignment.

The encoder output $\mathbf{U}\in\mathbb{R}^{N\times d_{\text{model}}}$ is mapped to a patch-level representation of size $P\times d_{\text{proj}}$ through a linear projection

$$ $\mathbf{Y}=\mathbf{U}\mathbf{W}_{p}\in\mathbb{R}^{N\times(P\,d_{\text{proj}})},\quad\mathbf{W}_{p}\in\mathbb{R}^{d_{\text{model}}\times(P\,d_{\text{proj}})}.$ $$

Reshaping and reordering yield step-aligned embeddings $\tilde{\mathbf{H}}\in\mathbb{R}^{T^{\prime}\times d_{\text{proj}}}$. We finally drop the padded tail to obtain

$$ $\mathbf{H}_{1:T}=\tilde{\mathbf{H}}_{1:T}\in\mathbb{R}^{T\times d_{\text{proj}}}.$ $$

### B.2 Training Process Details

Our model is trained in a two-phase process designed to first build a robust time-series representation and then align it with the frozen LLM’s semantic space.

#### B.2.1 Phase I: Time-Series Encoder Pretraining

In the first phase, we pretrain the time-series encoder $f_{\theta}$ to learn a versatile representation of temporal dynamics. This is achieved by optimizing a joint objective function that combines masked reconstruction and anomaly classification. The encoder is a Transformer-based architecture that processes the entire input time series $\mathbf{x}_{1:T}$.

##### Masked Reconstruction.

Following the principles of self-supervised learning for sequential data, we employ a masked reconstruction objective. A portion of the input time series is randomly masked, and the encoder is tasked with reconstructing the masked values. Let $\mathbf{x}$ be the input series and $\mathbf{m}$ be a binary mask where $m_{i}=1$ if the $i$-th timestep is masked and 0 otherwise. The encoder $f_{\theta}$, followed by a reconstruction head $g_{\psi}$, outputs a reconstructed series

$$ $\hat{\mathbf{x}}=g_{\psi}\big(f_{\theta}(\mathbf{x}\odot(\mathbf{1}-\mathbf{m}))\big).$ $$

The reconstruction loss is the Mean Squared Error (MSE) over the masked timesteps:

$$ $\mathcal{L}_{\text{recon}}=\frac{1}{\sum_{i}m_{i}}\sum_{i=1}^{T}m_{i}(x_{i}-\hat{x}_{i})^{2}.$ $$

This objective forces the encoder to learn the underlying patterns and dependencies within the time series.

##### Anomaly Classification.

To explicitly teach the encoder to distinguish between normal and anomalous patterns. Given a time series $\mathbf{x}$ and its corresponding binary anomaly label $\mathbf{l}\in\{0,1\}^{T}$, the model predicts the probability of an anomaly $\hat{\mathbf{l}}_{t}=h_{\zeta}(f_{\theta}(\mathbf{x}))$. We use the BCE loss:

$$ $\mathcal{L}_{\text{class}}=-\sum_{t=1}^{T}\big(l_{t}\log(\hat{l}_{t})+(1-l_{t})\log(1-\hat{l}_{t})\big).$ $$

##### Joint Objective.

The total loss for the pretraining phase is a weighted sum of the reconstruction and classification losses:

$$ $\mathcal{L}_{\text{pretrain}}=\lambda_{\text{recon}}\mathcal{L}_{\text{recon}}+\lambda_{\text{class}}\mathcal{L}_{\text{class}},$ $$

where $\lambda_{\text{recon}}$ and $\lambda_{\text{class}}$ are hyperparameters that balance the two objectives. After this phase, the weights of the encoder $f_{\theta}$ are frozen (only $f_{\theta}$ is retained for the next phase).

#### B.2.2 Phase II: Hint Tuner Training

In the second phase, we focus on aligning the pretrained time-series representations with the LLM. Both the time-series encoder $f_{\theta}$ and the LLM are kept frozen to maintain their powerful, pre-existing capabilities. The only trainable components are the Hint Tuner and its associated parameters, namely the prototype bank selection matrix $\mathbf{M}$ and the learnable task-prior queries $\mathbf{P}_{\text{fix}}$.

The goal of this phase is to train the model to generate a natural language explanation $\mathbf{y}=(y_{1},y_{2},\dots,y_{N})$ conditioned on the time series $\mathbf{x}$, the query $q$, and the derived hints. The training objective is a standard causal language modeling loss, which maximizes the likelihood of the ground-truth explanation.

Specifically, the input to the LLM is constructed by embedding the query $q$, the symbolic-numeric hint, and replacing placeholder token embeddings with the outputs of the Hint Tuner ($\tilde{\mathbf{H}}_{s:e}$ and $\tilde{\mathbf{F}}$). Here, $s$ and $e$ denote the start and end indices of the selected window within the full series $\mathbf{x}_{1:T}$. The model then autoregressively predicts the next token in the explanation sequence. The loss function is the negative log-likelihood of the target sequence:

$$ $\mathcal{L}_{\text{LM}}=-\sum_{i=1}^{N}\log P\big(y_{i}\mid y_{<i},q,\tilde{\mathbf{H}}_{s:e},\tilde{\mathbf{F}}\big).$ $$

By optimizing this objective, the Hint Tuner learns to map temporal features from the frozen encoder into meaningful ”soft prompts” that effectively guide the frozen LLM to generate accurate and relevant explanations for the given time-series window. During this phase, gradients update only the Hint Tuner and its associated parameters ($\mathbf{M}$ and $\mathbf{P}_{\text{fix}}$); both $f_{\theta}$ and all LLM parameters remain frozen.

### B.3 AXIS Hyperparameter Configuration

This section provides a comprehensive specification of the hyperparameter configuration used in our AXIS framework. The architecture consists of two primary components: the time-series encoder and the hint tuner, each with distinct parameter settings optimized through systematic ablation studies.

##### Time-Series Encoder Configuration.

The time-series encoder $f_{\theta}$ employs a Transformer-based architecture with patch-based tokenization. The patch size $P$ is set to 16, enabling efficient processing of long sequences while preserving temporal granularity. The encoder utilizes $L=6$ transformer layers, each with a model dimension $d_{\text{model}}=512$ and $H=8$ attention heads, resulting in a head dimension $d_{\text{head}}=64$. The projection dimension $d_{\text{proj}}$ is configured to 256.

##### Hint Tuner Architecture.

The Perceiver-based hint tuner serves as the cross-modal alignment module between time-series representations and the frozen LLM embedding space. The prototype bank consists of $P=1024$ prototype embeddings derived from the LLM vocabulary through a learned linear mapping. The number of fixed task-prior tokens $K$ is set to 8, providing sufficient capacity for global task-level priors while maintaining computational efficiency. The cross-attention mechanism within the hint tuner employs 8 attention heads, matching the encoder configuration for architectural consistency.

##### Language Model Integration.

Our framework supports multiple LLM families with varying parameter scales. The experiments primarily utilize Qwen2.5-7B-Instruct as the base model, with the hidden dimension $d_{h}=4096$ for the 7B variant. The vocabulary size varies by model family, typically ranging from 32,000 to 152,000 tokens. Special tokens 
 and 
 are added to the vocabulary for hint injection, with corresponding token IDs dynamically assigned during initialization.

##### Training Configuration.

The two-phase training procedure employs distinct hyperparameter settings for each phase. During Phase I (encoder pretraining), the reconstruction loss weight $\lambda_{\text{recon}}$ and classification loss weight $\lambda_{\text{class}}$ are both set to 1.0, providing balanced supervision across objectives. The masking ratio for reconstruction is configured to 0.25, following established practices in self-supervised time-series learning. Phase II (hint tuner training) utilizes standard causal language modeling with a learning rate of $2\times 10^{-4}$ and weight decay of 0.01, applied exclusively to the trainable parameters of the hint tuner and prototype bank.

##### Inference Parameters.

During generation, the model employs beam search with 5 beams and a repetition penalty of 1.15 to ensure diverse and coherent explanations. The maximum generation length is capped at 1000 tokens to accommodate detailed explanations while preventing excessive verbosity. No-repeat n-gram size is set to 3 to avoid repetitive patterns, and length penalty is maintained at 1.0 to balance explanation completeness with conciseness.

## Appendix C Prompt Templates and Q&A Exemplars

### C.1 Prompt Templates

#### C.1.1 Question Generation Prompt

#### C.1.2 Answer Generation Prompt

### C.2 Q&A Exemplars

#### C.2.1 Multiple Choice

#### C.2.2 True/False

#### C.2.3 Open-ended

## Appendix D Phase I TSAD results

##### Datasets.

We benchmark nine public univariate time-series anomaly detection corpora: IOPS, MGAB, NAB, NEK, Power, SED, TODS, UCR, and YAHOO. These datasets span industrial KPIs, synthetic chaotic dynamics, web traffic, power consumption, network/system logs, and curated mixed-domain series. Each series is standardized via z-score normalization using training-set statistics.

##### Baselines.

The comparison covers classical, deep generative, and foundation-style models. IForest (Liu et al., 2008) and LOF (Breunig et al., 2000) serve as nonparametric unsupervised baselines. OmniAnomaly (Su et al., 2019), USAD (Audibert et al., 2020), and TranAD (Tuli et al., 2022) represent deep unsupervised anomaly detectors. DADA (Shentu et al., 2024) and TSPulse (Ekambaram et al., 2025), MOMENT_ZS (Goswami et al., 2024), Chronos (Ansari et al., 2024), TimesFM (Das et al., 2024), and Time_MOE (Xiaoming et al., 2025) are pretrained time-series models evaluated in zero-shot or lightly adapted settings. AXIS denotes a semantic representation-based detector. Implementations follow public releases or authors’ configurations when feasible.

##### Metrics.

We report three standard metrics. (i) PA-F1: the point-adjusted F1 that credits a hit if any point within an anomalous window is flagged, computed from precision and recall after point adjustment; threshold for PA-F1 is selected on a validation split when available, or via an unsupervised percentile heuristic on training scores. (ii) AUC-ROC: area under the receiver operating characteristic, threshold-free and aggregated over all test points. (iii) AUC-PR: area under the precision–recall curve, which is more informative under severe class imbalance. Higher values indicate better performance for all metrics.

**Table 4: Model Performance Comparison Across All Datasets**
|  |  | Foundation Models | Deep Learning | Classical |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Dataset | Metric | AXIS | Chronos | DADA | MOMENT_ZS | TS_Pulse | Time_MOE | TimesFM | OmniAnomaly | TranAD | USAD | IForest | LOF |
| IOPS | PA-F1 | 57.19 | 64.17 | 55.52 | 44.76 | 50.59 | 41.58 | 87.89 | 53.50 | 53.04 | 41.24 | 15.31 | 41.38 |
| AUC-ROC | 71.13 | 72.16 | 78.61 | 82.67 | 49.71 | 61.87 | 70.12 | 80.89 | 69.44 | 81.31 | 48.29 | 66.80 |  |
| AUC-PR | 18.13 | 25.65 | 29.59 | 22.45 | 1.65 | 24.15 | 28.33 | 41.63 | 25.51 | 21.96 | 6.49 | 25.63 |  |
| MGAB | PA-F1 | 7.13 | 10.16 | 3.11 | 2.90 | 11.39 | 2.64 | 7.74 | 7.62 | 7.80 | 3.49 | 5.85 | 12.31 |
| AUC-ROC | 69.97 | 50.78 | 54.12 | 47.47 | 49.94 | 37.73 | 49.97 | 60.15 | 61.04 | 51.12 | 43.88 | 50.27 |  |
| AUC-PR | 0.55 | 0.31 | 0.31 | 0.25 | 0.27 | 0.20 | 0.27 | 0.41 | 0.42 | 1.74 | 0.24 | 0.34 |  |
| NAB | PA-F1 | 93.73 | 97.08 | 96.18 | 94.61 | 97.76 | 90.48 | 99.09 | 98.02 | 97.93 | 93.42 | 42.81 | 86.79 |
| AUC-ROC | 51.79 | 53.82 | 56.23 | 64.01 | 50.28 | 50.82 | 53.33 | 56.26 | 54.33 | 73.09 | 55.26 | 49.93 |  |
| AUC-PR | 21.00 | 20.62 | 21.87 | 42.73 | 13.91 | 20.32 | 21.12 | 24.87 | 21.92 | 53.14 | 20.48 | 18.55 |  |
| NEK | PA-F1 | 87.19 | 98.44 | 98.68 | 81.10 | 88.14 | 50.82 | 98.79 | 88.50 | 86.78 | 66.26 | 72.47 | 87.35 |
| AUC-ROC | 53.28 | 57.60 | 82.51 | 92.02 | 53.94 | 37.41 | 62.64 | 88.85 | 81.25 | 91.65 | 85.66 | 81.38 |  |
| AUC-PR | 30.32 | 30.63 | 44.90 | 55.75 | 16.34 | 7.13 | 34.05 | 73.10 | 57.39 | 52.91 | 52.76 | 55.63 |  |
| Power | PA-F1 | 98.94 | 95.97 | 89.53 | 90.25 | 98.77 | 83.29 | 97.58 | 86.66 | 87.51 | 68.06 | 0.00 | 87.92 |
| AUC-ROC | 62.47 | 48.82 | 46.19 | 43.23 | 50.68 | 38.92 | 46.78 | 59.88 | 57.05 | 66.46 | 50.00 | 38.93 |  |
| AUC-PR | 20.52 | 10.44 | 10.07 | 10.68 | 11.09 | 9.01 | 9.98 | 13.64 | 12.37 | 17.30 | 10.97 | 8.98 |  |
| SED | PA-F1 | 93.59 | 38.77 | 18.69 | 1.92 | 70.26 | 33.29 | 32.49 | 2.25 | 4.49 | 0.00 | 31.62 | 0.00 |
| AUC-ROC | 96.35 | 53.03 | 14.85 | 1.43 | 49.23 | 69.08 | 29.64 | 28.93 | 12.89 | 10.71 | 27.96 | 27.35 |  |
| AUC-PR | 73.76 | 4.80 | 2.77 | 2.57 | 4.95 | 7.45 | 3.26 | 3.35 | 2.78 | 2.68 | 3.26 | 3.25 |  |
| TODS | PA-F1 | 77.50 | 83.40 | 61.20 | 26.86 | 53.03 | 44.92 | 81.26 | 38.82 | 40.31 | 40.86 | 33.25 | 54.62 |
| AUC-ROC | 92.40 | 68.45 | 68.16 | 46.17 | 50.20 | 51.68 | 72.96 | 49.69 | 48.87 | 53.92 | 51.16 | 53.12 |  |
| AUC-PR | 68.20 | 35.60 | 20.33 | 10.03 | 6.98 | 10.36 | 36.69 | 6.89 | 6.74 | 17.37 | 7.43 | 19.74 |  |
| UCR | PA-F1 | 47.58 | 43.71 | 34.90 | 25.55 | 56.57 | 31.63 | 60.88 | 31.44 | 32.67 | 22.57 | 23.02 | 32.43 |
| AUC-ROC | 79.34 | 55.79 | 56.27 | 54.92 | 50.57 | 55.38 | 57.21 | 50.67 | 50.64 | 53.74 | 51.93 | 55.86 |  |
| AUC-PR | 24.06 | 6.11 | 2.19 | 6.92 | 0.85 | 2.12 | 6.35 | 2.91 | 2.32 | 8.08 | 2.54 | 2.50 |  |
| YAHOO | PA-F1 | 53.88 | 54.09 | 50.82 | 12.54 | 7.99 | 21.39 | 87.18 | 18.66 | 8.09 | 7.40 | 2.86 | 29.78 |
| AUC-ROC | 96.55 | 94.64 | 95.95 | 74.37 | 49.02 | 63.08 | 96.35 | 77.71 | 56.47 | 62.54 | 48.90 | 72.85 |  |
| AUC-PR | 86.07 | 70.75 | 76.66 | 4.84 | 1.49 | 22.08 | 79.23 | 16.28 | 2.90 | 3.72 | 1.66 | 44.26 |  |
| Overall | Avg. Rank | 3.81 | 4.74 | 5.52 | 7.48 | 7.70 | 8.70 | 4.41 | 5.48 | 7.00 | 6.78 | 9.07 | 7.30 |

##### Results.

The experimental results, summarized in Table [4](https://arxiv.org/html/2509.24378v1#A4.T4), demonstrate that our proposed AXIS model achieves competitive performance across the nine public benchmarks. When compared against a variety of SOTA methods, including recent time-series foundation models, AXIS consistently ranks as a top performer on several datasets such as SED, TODS, UCR, and YAHOO, achieving the best results on multiple metrics. This validates the effectiveness of our approach for time-series anomaly detection and shows its potential to match or even exceed the current state of the art.

## Appendix E Detailed Procedure for G-eval

This appendix documents the evaluation methodology, criteria, and prompts used by our G-Eval variant.

### E.1 Methodological Overview

We adopt an advanced G-Eval judge that evaluates system answers along multiple dimensions and calibrates discrete scores using token-level log-probabilities. For each question-answer instance:

- 1.
Determine the question type (e.g., multiple choice, open-ended, true/false) and instantiate the corresponding set of evaluation dimensions.
- 2.
For each dimension, query a LLM judge with a criterion-specific instruction (see the exact prompt in Appx.) to produce a reasoning-based assessment and a final integer score $s\in\{1,2,3,4,5\}$. If score extraction is ambiguous, a conservative default is used.
- 3.
Obtain token-level probabilities assigned to the score tokens $\{1,\dots,5\}$. Exponentiate and normalize these probabilities to construct a score distribution. Use its expectation as a log-probability-weighted score and compute a confidence via normalized entropy (Appx. [E.3](https://arxiv.org/html/2509.24378v1#A5.SS3)).

### E.2 Evaluation Criteria and Weights

For each question_type, the evaluator applies a fixed set of dimensions with 5-point guidelines and combines them via type-specific weights:

**Table 5: Dimension Weights by Question Type.**
| multiple_choice | correctness: 0.70, reasoning_quality: 0.30 |
| --- | --- |
| open_ended | relevance: 0.30, completeness: 0.35, accuracy: 0.35 |
| true_false | correctness: 0.60, justification_quality: 0.40 |

The dimension descriptions and scoring guidelines (1–5) are:

##### multiple_choice

- •
correctness: How accurate is the generated response compared to the expected answer?
–
5: Perfect match, completely correct
–
4: Mostly correct; minor deviations not affecting core meaning
–
3: Partially correct; captures some key aspects but misses important details
–
2: Somewhat relevant but with significant errors or omissions
–
1: Incorrect or completely irrelevant
- •
reasoning_quality: How well does the response demonstrate logical reasoning and explanation?
–
5: Clear, logical, comprehensive reasoning fully explains the choice
–
4: Good reasoning with minor gaps
–
3: Adequate reasoning; lacks depth or has inconsistencies
–
2: Weak reasoning; significant gaps or flawed logic
–
1: No clear reasoning or completely flawed logic

##### open_ended

- •
relevance: How relevant and on-topic is the generated response?
–
5: Completely relevant; directly addresses all aspects
–
4: Highly relevant; minor omissions
–
3: Moderately relevant; addresses core aspects but misses details
–
2: Somewhat relevant; off-topic content or key omissions
–
1: Irrelevant or off-topic
- •
completeness: How complete and comprehensive is the response?
–
5: Fully comprehensive; covers all necessary aspects
–
4: Mostly complete; minor gaps
–
3: Adequately complete; missing some important details
–
2: Incomplete; significant information missing
–
1: Very incomplete
- •
accuracy: How factually accurate is the response?
–
5: Completely accurate; no factual errors
–
4: Mostly accurate; very minor inaccuracies
–
3: Generally accurate; some notable errors
–
2: Several factual errors affecting reliability
–
1: Major factual errors or mostly inaccurate

##### true_false

- •
correctness: How correct is the T/F judgment and supporting explanation?
–
5: Perfect judgment; excellent supporting explanation
–
4: Correct judgment; good explanation
–
3: Correct judgment; adequate explanation
–
2: Incorrect judgment; reasonable attempt at explanation
–
1: Incorrect judgment; poor or no explanation
- •
justification_quality: How well does the response justify the decision?
–
5: Excellent justification with clear evidence and reasoning
–
4: Good justification with solid evidence
–
3: Adequate justification with some evidence
–
2: Weak justification with little evidence
–
1: No meaningful justification

### E.3 Advanced Scoring From Log-Probabilities

Let $s\in\{1,2,3,4,5\}$ denote the raw score extracted from the LLM’s evaluation output. We also obtain token-level log-probabilities for score tokens $\{1,\dots,5\}$. The evaluator constructs a distribution over scores by exponentiating and normalizing these log-probabilities:

$$ $p(s)\propto\exp(\log p_{s}),\quad\tilde{p}(s)=\frac{\exp(\log p_{s})}{\sum_{k=1}^{5}\exp(\log p_{k})}.$ $$

The weighted score is the expectation under $\tilde{p}$:

$$ $\mathrm{WeightedScore}=\sum_{s=1}^{5}s\cdot\tilde{p}(s).$ $$

### E.4 Advanced G-Eval Prompt

### E.5 Detailed results of G-eval

Figures [8](https://arxiv.org/html/2509.24378v1#A5.F8) to [10](https://arxiv.org/html/2509.24378v1#A5.F10) present forest plots to visually summarize the pairwise model performance comparisons from Tables [1](https://arxiv.org/html/2509.24378v1#S4.T1) to [3](https://arxiv.org/html/2509.24378v1#S4.T3). The confidence intervals are calculated from the variance of the pairwise total scores.

As shown in Fig. [8](https://arxiv.org/html/2509.24378v1#A5.F8), our AXIS model demonstrates a strong performance. On Multiple-choice questions, it significantly outperforms all models except for Image-LLM and Anon-LLM(Window). For True/False questions, AXIS significantly surpasses all other models, highlighting its advantage in objective answering. Furthermore, on Open-Ended questions, AXIS outperforms other models while achieving performance comparable to the General LLM (AnomLLM).

Fig. [9](https://arxiv.org/html/2509.24378v1#A5.F9) details an ablation study of our proposed AXIS model. The results demonstrate that AXIS consistently and significantly outperforms its variants (”w/o-windows”, ”w/o-task-hint”, and ”w/o-context-hint”) across all three question categories. The confidence intervals for the mean paired difference are entirely below zero in all subplots, indicating that the removal of any of these components leads to a statistically significant degradation in performance. This underscores the integral contribution of each component to the overall efficacy of the AXIS model.

Fig. [10](https://arxiv.org/html/2509.24378v1#A5.F10) provides a comparative analysis of various open-source models against the Deepseek Llama 8B (Inst) baseline. In multiple-choice questions, Deepseek Llama 8B shows a significant performance advantage over the Mistral 7B models, while its performance is statistically comparable to the Qwen2.5 7B series. For open-ended and true/false questions, Deepseek Llama 8B shows comparable performance to most Qwen and Deepseek-Qwen variants, showing that the robustness of our AXIS design.

Figure: Figure 8: Comparative analysis of baseline models against AXIS via forest plot. Each horizontal line represents the 95% bootstrap confidence interval for the mean paired score difference relative to the AXIS baseline. The central dot marks the point estimate of the mean difference. The vertical red dashed line at zero indicates no difference; confidence intervals crossing this line suggest that the model’s performance is not statistically different from the baseline.
Refer to caption: x8.png

Figure: Figure 9: Forest plot comparing AXIS variants against the AXIS baseline. The plot displays the mean paired score difference and the 95% bootstrap confidence interval for each variant. The vertical red line at zero indicates no performance difference relative to AXIS.
Refer to caption: x9.png

Figure: Figure 10: Forest plot for ablation studies, benchmarked against AXIS. This plot illustrates the mean paired score difference and the corresponding 95% bootstrap confidence interval for each ablated variant. The vertical red line at zero serves as the reference for no difference from the baseline.
Refer to caption: x10.png

## Appendix F Procedure and detail results for Human-based evaluation

### F.1 Designs of questionnaire

Our human expert questionnaire is systematically designed to evaluate model explanations across multiple dimensions. Each questionnaire includes: (1) Question Information: the original question, expected answer, and question type classification (multiple choice, open-ended, or true/false); (2) Time Series Visualization: a plot showing the full time series with the target window highlighted to provide visual context; (3) Model Responses: all baseline model outputs presented in a randomized order to minimize bias; (4) Evaluation Criteria: dimension-specific scoring guidelines adapted from G-Eval methodology, with 5-point scales for correctness, reasoning quality, relevance, completeness, accuracy, and justification quality depending on question type; (5) Scoring Tables: structured evaluation forms for each criterion; (6) Model Ranking: comparative ranking of all models with justifications.

For our study, a total of 140 unique questions were assessed. To ensure robust and unbiased evaluation, we collected 280 completed questionnaires, ensuring that each question was independently evaluated by two human experts under a double-blind protocol. This comprehensive design guarantees systematic and unbiased human evaluation, capturing both quantitative scores and rich qualitative insights from domain experts.

### F.2 Detailed results for Human evaluation

Fig. [11](https://arxiv.org/html/2509.24378v1#A6.F11) provides a criterion-level breakdown of human evaluation across the three question types. AXIS ranks first consistently. On Multiple Choice questions, it achieves the best scores in both *Correctness* and *Reasoning Quality*, with a clear margin over the next best visual baseline. This indicates that our hint-based conditioning not only selects the right option but also articulates concise, logically grounded rationale.

For Open-Ended questions, AXIS leads on *Relevance*, *Completeness*, and *Accuracy*, reflecting faithful, fully supported explanations rather than surface descriptors. On True/False questions, it also tops both *Correctness* and *Justification Quality*, showing strong calibration and evidence-backed decisions. Overall, these results demonstrate that the proposed three-pathway design (symbolic numeric grounding, context-integrated local hints, and task-prior hints) confers robust advantages across formats—surpassing specialized TS-LLMs and multimodal vision–language approaches in both accuracy and human-judged explanatory quality.

Figure: Figure 11: The mean scores by human evaluation for (a) multiple choice question, (b) open ended questions and (c) true/false questions
Refer to caption: x11.png

## Appendix G Causal Ablation Analysis for Hint Tokens

To analyze the individual contribution of each local hint token to the model’s generation quality, we implement a causal ablation study. This method systematically removes or modifies specific hint tokens to quantify their importance in producing accurate explanations.

Given hint embeddings $\tilde{\mathbf{H}}_{s:e}\in\mathbb{R}^{(e-s)\times d_{h}}$, we measure the contribution of each local hint token at position $i$ within the target window $[s,e)$ through the following procedure:

##### Baseline Computation.

First, we compute the baseline log-likelihood using the complete hint embeddings:

$$ $\mathcal{L}_{\text{baseline}}=-\log P(\mathbf{y}|\tilde{\mathbf{H}}_{s:e},q,\tilde{\mathbf{F}}),$ $$

where $\mathbf{y}$ is the target explanation, $q$ is the query, and $\tilde{\mathbf{F}}$ represents the task-prior hints.

##### Ablation Methods.

For each position $i\in[s,e)$, we create an ablated version of the hint embeddings $\tilde{\mathbf{H}}_{s:e}^{(i)}$ using Zero Replacement: $\tilde{\mathbf{H}}_{s:e}^{(i)}[i-s]=\mathbf{0}$.

##### Contribution Score.

The contribution score for position $i$ is computed as:

$$ $C_{i}=\mathcal{L}_{\text{baseline}}-\mathcal{L}_{\text{ablated}}^{(i)},$ $$

where $\mathcal{L}_{\text{ablated}}^{(i)}=-\log P(\mathbf{y}|\tilde{\mathbf{H}}_{s:e}^{(i)},q,\tilde{\mathbf{F}})$. A positive $C_{i}$ indicates that removing the hint at position $i$ degrades the model’s performance, suggesting that this position contributes positively to explanation generation.

##### Validation of Context-Integrated Hints via Causal Ablation Analysis.

As depicted in Fig. [12](https://arxiv.org/html/2509.24378v1#A7.F12) and Fig. [13](https://arxiv.org/html/2509.24378v1#A7.F13), the causal ablation analysis provides empirical evidence for the efficacy of our proposed hint mechanism. A predominant observation across both examples is that the majority of the contribution scores, denoted by $C_{i}$, are positive ($C_{i}>0$). According to the formulation presented in Appx. [G](https://arxiv.org/html/2509.24378v1#A7), a positive $C_{i}$ indicates that ablating the hint token at position $i$ degrades the model’s performance, as measured by an increase in the negative log-likelihood of the target explanation. This finding strongly supports our hypothesis that the context-integrated, step-aligned hints furnish valuable guidance for the model, making a net positive contribution to the generation of high-quality answers.

Furthermore, a more nuanced pattern emerges from the results. We observe that in regions where the time series exhibits significant volatility or sharp fluctuations, the corresponding contribution scores are comparatively lower. This suggests that the inherent complexity and unpredictability of volatile segments in the time series can diminish the marginal utility of individual hint tokens. In essence, while the hints remain beneficial overall, their directional impact is partially mitigated by the increased difficulty of the task in these challenging temporal regions.

Figure: Figure 12: Causal Ablation Analysis of Step-Aligned Hint Tokens. The figure visualizes the contribution score $C_{i}$ for each hint token, computed via our causal ablation method, alongside the original input time series.
Refer to caption: x12.png

Figure: Figure 13: Causal Ablation Analysis of Step-Aligned Hint Tokens. The figure visualizes the contribution score $C_{i}$ for each hint token, computed via our causal ablation method, alongside the original input time series.
Refer to caption: x13.png

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 4
presentation: 2
questions: 1. Training objectives and hyperparameters.  
    Please include explicit formulas/weights for the two stages (masking strategy, classification head details), and list key hyperparameters for Stage-II NTP (LR/steps/batch sizes) plus stabilization tricks.
    
2. Prototype bank and attention implementation.  
    What are $P$ (prototype count), initialization/regularization for $M$, and the exact shape of $W_q$? Do you use multi-head attention with scaled dot-product? How are head count and $d_h$ matched?
    
3. Question-type sensitivity.  
    Why is the context hint nearly useless for MC but critical for TF? Can you ablate distractor quality, window length, and prototype size to produce sensitivity curves per question type?
    
4. External benchmarks and real-world cases.  
    Can you report explanation quality (blind human evaluation + reliability coefficients) on 2–3 public TSAD datasets and provide at least one real operational log case study (with cost/latency)?
    
5. Judge robustness.  
    Beyond the current judge, can you add a second LLM-judge and a human subset, reporting Kendall/Spearman correlations and statistical significance?
soundness: 2
strengths: - Clear problem reformulation. Recasts TSAD from point-wise scoring to a window-level explanation problem, formalizing $G:(x_{1:T},q,s,e)\mapsto y$, which aligns with practical interpretability needs.
- Frozen-LLM practicality. All hints operate with a frozen backbone LLM, lowering deployment cost and risk.
- Clean unification interface. $\tilde H_{s:e}$, $\tilde F$, and the numeric string are fused in a single prompt, keeping the injection interface modular and reusable.
- Paired controls and multi-format evaluation. The benchmark includes normal/abnormal pairs and multiple question formats, plus human/CD-style summaries—useful for qualitative diagnosis.
summary: This paper presents AXIS, a framework for semantic time-series anomaly explanation that conditions a frozen LLM via three complementary hint pathways:
1. Symbolic Numeric hint.    
2. Context-Integrated, Step-Aligned hint  
3. Task-Prior hint. 

In the final prompt, $\tilde F$ and $\tilde H_{s:e}$ replace the embeddings of $K+(e-s)$ placeholder tokens, while the numeric string is injected verbatim into the text; the LLM then generates an explanation $y$. Training is two-stage: (i) pretrain $f_\theta$ with a joint objective (masked reconstruction + anomaly classification) and freeze it; (ii) optimize only the hint tuner (including $M$ and $P_{\text{fix}}$) with a next-token prediction loss, keeping the LLM and encoder frozen. The paper also builds a paired-window, explanation-oriented benchmark with normal/abnormal pairs and multi-format questions (MC/True-False/Open-Ended) plus human/LLM judgments.
weaknesses: 1. Math/training under-specification (reproducibility risk).  
    The main text omits explicit forms and weights for the pretraining joint loss; Stage II is only described as NTP. The paper should state, for example,  
$$  
    L_{\text{pretrain}}=L_{\text{recon}}+\lambda,L_{\text{cls}},  
    $$  with $\lambda$ values, and define $L_{\text{NTP}}$ precisely. Dimensional alignment for prototype attention is incomplete (exact shape of $W_q$; whether multi-head is used; scaling/normalization). Currently $\operatorname{Attn}(Q,K,V)$ inputs are given without implementation details.
    
2. Evidence chain leans on the self-built benchmark.  
    Core results are on synthetic/self-constructed data; statements like “comparable on real TSAD datasets” are relegated to the appendix without prominent tables and significance/variance reporting. Public datasets with explanation-quality metrics should appear in the main paper.
    
3. LLM-as-a-Judge dependence and reporting.  
    Although CD plots are reported, there is no systematic inter-rater reliability across judges/models. The text mentions removing a baseline due to very poor performance, which risks selection bias; either keep it with a discussion of why it fails or re-run under controlled, equal-resource settings.
    
4. Uneven ablation interpretation.  
    In the ablation, the context hint yields minimal gain on Multiple Choice (e.g., $4.19\to4.09$, $-0.10$), yet has a large impact on True/False (e.g., $3.65\to2.44$). The paper does not analyze why different formats exhibit such divergent sensitivities (e.g., distractor design, window length, prototype size).
    
5. Missing equal-resource comparisons to strong baselines.  
    Direct, matched-budget comparisons to alternative routes—image-VLM, ChatTS-style multimodal alignment, Time-LLM-style reprogramming—are limited or absent in the main text, hindering external validity claims.

---

confidence: 3
contribution: 3
initial_rating: 4
presentation: 3
questions: Q1: Did you evaluate AXIS’s explanations using multiple LLM judges and report inter-judge agreement? Were any controls applied to mitigate position, verbosity, or stylistic biases—such as randomized output order or style-normalized prompts?

Q2: What are the inter-rater agreement statistics (e.g., Fleiss’ κ or Kendall’s W) for the 280 annotated questionnaires? How were the human experts recruited and compensated, and what were their domain backgrounds? (Appendix F could provide more transparency here.)

Q3: How does the step-aligned hint extend to multivariate time-series inputs, considering dimensionality and cross-channel dependencies? Are there any preliminary results or ablations on multivariate benchmarks to demonstrate scalability?

Q4: Could you report the average token counts and generation latencies per question type and time-window size? This would help clarify the computational overhead of AXIS relative to simpler baselines.
soundness: 3
strengths: S1: The paper clearly articulates why existing anomaly detectors and post-hoc attribution methods fall short in answering the question “why was this flagged?”, and proposes a principled remedy centered on contextual grounding and representation alignment.

S2: The combination of the step-aligned hint, task-prior hint, and symbolic numeric hint forms a well-motivated triad; employing a Perceiver-style cross-attention mechanism to map time-series features into the LLM token space is technically sound and aligns with prior work on prefix and prompt tuning, here innovatively adapted for TSAD explanation.

S3: The experimental comparisons are comprehensive, covering classical and deep baselines, time-series foundation models (e.g., Chronos, TimesFM, MOMENT), specialized TS-LLMs (e.g., ChatTS, AnomLLM, ChatTime), and a plot-based VLM baseline, demonstrating broad empirical coverage.
summary: The paper presents AXIS, a framework for explainable time-series anomaly detection (TSAD) that conditions a frozen large language model (LLM) to tackle two key challenges (1) contextual grounding and representation alignment (2) and contrasts its design with naive time-to-text serialization approaches. AXIS leverages three complementary types of hints: (i) a symbolic numeric hint that exposes the raw values within the queried time window, (ii) a context-integrated, step-aligned hint distilled from a pretrained time-series encoder to capture local and fine-grained temporal dynamics, and (iii) a task-prior hint that encodes global anomaly characteristics.

For evaluation, the authors (a) construct a multi-format QA benchmark of anomaly-centric questions paired with human-written rationales, (b) assess explanation quality using a G-Eval-style LLM-as-a-judge pipeline, and (c) conduct a human study comparing model outputs. Overall, AXIS achieves improved semantic anomaly explanation performance, outperforming LLMAD and several other baselines. Ablation studies further verify that all three types of hints contribute substantially to the model’s effectiveness.
weaknesses: W1: The main explanation results rely on a single LLM judge (Gemini-2.5) using a G-Eval-style rubric. Prior studies have documented systematic biases in such setups—e.g., position and authority effects, prompt sensitivity, and reproducibility drift as models evolve. This raises concerns about the robustness and fairness of evaluation, suggesting that reliance on a single evaluator may overstate performance consistency.

W2: The proposed benchmark is procedurally generated. While the design encourages morphology-level reasoning, it risks inheriting the authors’ priors or artifacts from the data generation pipeline, particularly since similar classes of LLMs appear both in benchmark creation and evaluation. Although the paper mentions “benchmark integrity” checks, the description is brief and lacks sufficient transparency for reproducibility.

W3: The benchmark and Phase-I experiments appear limited to univariate settings, whereas many real-world TSAD applications involve multivariate signals with exogenous features. Recent TS-LLM and TS-VLM efforts (e.g., ChatTS, ChatTime, VLM-based TSAD) have begun addressing such multivariate reasoning.

---

confidence: 3
contribution: 3
initial_rating: 4
presentation: 3
questions: - My primary concern relates to the generation process and overall quality of the proposed benchmark, as discussed in the weaknesses section. I would be inclined to increase my evaluation score if the paper provided additional analyses or evidence validating the reliability and soundness of the benchmark.
soundness: 2
strengths: - The proposed problem definition is novel and conceptually appealing. In particular, the formulation based on intervals rather than single points is well motivated, as anomalies in real-world time series typically extend over contiguous intervals instead of isolated timestamps. Furthermore, framing the task as generating explanations adds interpretability and makes the objective of the model more aligned with practical anomaly analysis needs.

- The paper clearly articulates one of the key challenges in applying LLMs to time-series data: LLMs operate on discrete tokens and therefore struggle to directly process long, continuous temporal signals. To address this issue, the authors propose a novel prompt construction strategy within the AXIS framework, which integrates three complementary representation pathways:
    - a symbolic numeric hint, providing numerical grounding for continuous values;
    - a context-integrated, step-aligned hint, distilled from a pre-trained time-series encoder to capture fine-grained temporal dynamics; and
    - a task-prior hint, encoding global anomaly characteristics and prior knowledge relevant to the task.

- The experimental results presented in Table 1 demonstrate that the proposed AXIS framework outperforms baseline methods on the newly introduced benchmark.

- The ablation study reported in Table 2 provides evidence that the proposed prompt design contributes significantly to performance improvements, confirming the effectiveness of the multi-hint representation strategy.

- The model architecture analysis in Table 3 indicates that the proposed approach is relatively robust across different LLM architectures, although performance variations are observed among specific models.

- Overall, the paper is clearly written and well structured. It provides sufficient background and motivation to understand the problem setting and the contributions. Figure 2 offers a concise and informative summary of the differences between the proposed approach and existing LLM-based methods for time-series anomaly detection.
summary: This paper presents a novel approach to the time-series anomaly detection problem. The authors reformulate the task by focusing on interval-based anomalies rather than point-based ones, motivated by the observation that anomalies in real-world time series often occur over contiguous intervals instead of isolated timestamps. The problem is defined as follows: given a univariate time series and a natural-language query specifying an interval, the goal is to determine whether the interval is anomalous and to provide an explanation for this decision. To address this problem, the authors propose AXIS, an LLM-based framework designed to handle continuous time-series data. Since standard LLMs are not well-suited for processing continuous signals, AXIS introduces three complementary representation pathways, referred to as hints: the symbolic numerical hint, the context-integrated step-aligned hint, and the task-prior hint. These pathways aim to bridge the gap between time-series representations and language-based reasoning. The training process consists of two phases. In the first phase, the time-series encoder used in the context-integrated step-aligned hint is pre-trained to capture temporal dependencies. In the second phase, both the encoder and the LLM are kept frozen while the remaining parameters are optimized to align the representations with the anomaly explanation task. The paper also introduces a new benchmark for semantic time-series anomaly explanation, designed to evaluate both detection and interpretability. Experimental results show that AXIS outperforms baseline methods on this benchmark. Additionally, an ablation study is conducted to assess the contributions of individual components, providing evidence for the effectiveness of the proposed design choices.
weaknesses: - The main concern lies in the generation process and overall quality of the proposed benchmark. Although the paper introduces a new semantic anomaly explanation benchmark, its characteristics are not thoroughly analyzed. For instance, the paper could include descriptive statistics of the datasets, such as the number of samples, anomaly distributions, and interval lengths. It would also be useful to report how simple baseline heuristics perform on these datasets to better contextualize the difficulty and validity of the benchmark. Since all experimental results are evaluated exclusively on this benchmark, a more detailed analysis is crucial to assess the reliability and generalizability of the reported findings.

- The justification for the two-phase training strategy remains unclear. The paper would benefit from a more detailed explanation, supported by either theoretical reasoning or empirical evidence, to demonstrate why this specific training scheme is necessary or advantageous compared to alternative training strategies.

- The paper does not discuss how robust the proposed model is to input noise or data corruption. It would be valuable to analyze the model’s sensitivity to noise in the time series, such as testing whether performance remains stable when individual values or small segments are perturbed or corrupted. Such an analysis would provide additional insight into the robustness and practical applicability of the proposed approach.


Decision: Reject