Markov reads Pushkin, again: A statistical journey into the poetic world of Evgenij Onegin

This study applies symbolic time series analysis and Markov modeling to explore the phonological structure of Evgenij Onegin-as captured through a graphemic vowel/consonant (V/C) encoding-and one contemporary Italian translation. Using a binary encoding inspired by Markov's original scheme, we construct minimalist probabilistic models that capture both local V/C dependencies and large-scale sequential patterns. A compact four-state Markov chain is shown to be descriptively accurate and generative, reproducing key features of the original sequences such as autocorrelation and memory depth. All findings are exploratory in nature and aim to highlight structural regularities while suggesting hypotheses about underlying narrative dynamics. The analysis reveals a marked asymmetry between the Russian and Italian texts: the original exhibits a gradual decline in memory depth, whereas the translation maintains a more uniform profile. To further investigate this divergence, we introduce phonological probes-short symbolic patterns that link surface structure to narrative-relevant cues. Tracked across the unfolding text, these probes reveal subtle connections between graphemic form and thematic development, particularly in the Russian original. By revisiting Markov's original proposal of applying symbolic analysis to a literary text and pairing it with contemporary tools from computational statistics and data science, this study shows that even minimalist Markov models can support exploratory analysis of complex poetic material. When complemented by a coarse layer of linguistic annotation, such models provide a general framework for comparative poetics and demonstrate that stylized structural patterns remain accessible through simple representations grounded in linguistic form.

Conditional Attribution for Root Cause Analysis in Time-Series Anomaly Detection

Root cause analysis (RCA) for time-series anomaly detection is critical for the reliable operation of complex real-world systems. Existing explanation methods often rely on unrealistic feature perturbations and ignore temporal and cross-feature dependencies, leading to unreliable attributions. We propose a conditional attribution framework that explains anomalies relative to contextually similar normal system states. Instead of using marginal or randomly sampled baselines, our method retrieves representative normal instances conditioned on the anomalous observation, enabling dependency-preserving and operationally meaningful explanations. To support high-dimensional time-series data, contextual retrieval is performed in learned low-dimensional representations using both variational autoencoder latent spaces and UMAP manifold embeddings. By grounding the retrieval process in the system's learned manifold, this strategy avoids out-of-distribution artifacts and ensures attribution fidelity while maintaining computational efficiency. We further introduce confidence-aware and temporal evaluation metrics for assessing explanation reliability and responsiveness. Experiments on the SWaT and MSDS benchmarks demonstrate that the proposed approach consistently improves root-cause identification accuracy, temporal localization, and robustness across multiple anomaly detection models. These results highlight the practical utility of conditional attribution for explainable anomaly diagnosis in complex time-series systems. Code and models will be publicly released.

On Solving the Multiple Variable Gapped Longest Common Subsequence Problem

This paper addresses the Variable Gapped Longest Common Subsequence (VGLCS) problem, a generalization of the classical LCS problem involving flexible gap constraints between consecutive solutions' characters. The problem arises in molecular sequence comparison, where structural distance constraints between residues must be respected, and in time-series analysis where events are required to occur within specified temporal delays. We propose a search framework based on the root-based state graph representation, in which the state space comprises a generally large number of rooted state subgraphs. To cope with the resulting combinatorial explosion, an iterative beam search strategy is employed, dynamically maintaining a global pool of promising candidate root nodes, enabling effective control of diversification across iterations. To exploit the search for high-quality solutions, several known heuristics from the LCS literature are utilized into the standalone beam search procedure. To the best of our knowledge, this is the first comprehensive computational study on the VGLCS problem comprising 320 synthetic instances with up to 10 input sequences and up to 500 characters. Experimental results show robustness of the designed approach over the baseline beam search in comparable runtimes.

FLUID: Continuous-Time Hyperconnected Sparse Transformer for Sink-Free Learning

Continuous-time (CT) Transformers improve irregular and long-range modeling over CT-RNNs by exploiting inputs or outputs embeddings with continuous dynamics. However, the core scaled-dot-product-attention (SDPA) mechanism remains inherently discrete. We propose FLUID (Flexible Unified Information Dynamics), a CT Transformer that incorporates continuous dynamics directly into the attention computation by replacing it with Liquid Attention Network (LAN). LAN reinterprets attention logits as continuous dynamical system and reformulates them as the solution to a linear ODE modulated by input-dependent nonlinear recurrent gates. Theoretically, we establish stability guarantees for LAN dynamics and show that it serves as an interpolating middle ground between SDPA and CT-RNNs, recovering each as special case under well-defined parameterization of its gating functions. LAN also introduces an explicit attention-sink gate to eliminate disproportionate attention mass on uninformative nodes. FLUID replaces standard residual connections with input-dependent Liquid Hyper-Connections to adaptively regulate interlayer information flow. Empirically, we evaluate FLUID on a broad set of learning tasks, including (i) irregular time-series, (ii) long-range modeling, (iii) lane-keeping control of autonomous vehicles, and (iv) learning physical dynamics under a scarce data regime. Across all the tasks, FLUID consistently matches or outperforms CT baselines, achieving improvements of up to 47% in certain scenarios and enhancing generalization under distributional shifts. Additionally, FLUID demonstrates superior noise robustness and a self-correcting inductive bias in autonomous vehicle control. We also provide a detailed analysis of key hyperparameters to guide tuning and show that FLUID occupies an intermediate position among competing approaches in terms of runtime and memory efficiency.

RamanBench: A Large-Scale Benchmark for Machine Learning on Raman Spectroscopy

Machine Learning (ML) has transformed many scientific fields, yet key applications still lack standardized benchmarks. Raman spectroscopy, a widely used technique for non-invasive molecular analysis, is one such field where progress is limited by fragmented datasets, inconsistent evaluation, and models that fail to capture the structure of spectral data. We introduce RamanBench, the first large-scale, fully reproducible benchmark for ML on Raman spectroscopy, consisting of streamlined data access, evaluation protocols and code, as well as a live leaderboard. It unifies 74 datasets (including 16 first released with this benchmark) across four domains, comprising 325,668 spectra and spanning classification and regression tasks under diverse experimental conditions. We benchmark 28 models under a standardized protocol, including classical methods (e.g., PLS), Raman-specific (e.g., RamanNet), Tabular Foundation Model (TFM) (e.g., TabPFN), and time-series approaches (e.g., ROCKET). TFM consistently outperform domain-specific and gradient boosting baselines, while time-series models remain competitive. However, no method generalizes across datasets, revealing a fundamental gap. Therefore, we invite the community to contribute new approaches to our living benchmark, with the potential to accelerate advances in critical applications such as medical diagnostics, biological research, and materials science.

ESN-DAGMM: A Lightweight Framework for Unsupervised Time-Series Data Monitoring in 5G O-RAN Networks

Open Radio Access Network (O-RAN) is an important 5G network architecture enabling flexible communication with adaptive strategies for different verticals. However, testing for O-RAN deployments involve massive volumes of time-series data (e.g., key performance indicators), creating critical challenges for scalable, unsupervised monitoring without labels or high computational overhead. To address this, we present ESN-DAGMM, a lightweight adaptation of the Deep Autoencoding Gaussian Mixture Model (DAGMM) framework for time series analysis. Our model utilizes an Echo State Network (ESN) to efficiently model temporal dependencies, proving effective in O-RAN networks where training samples are highly limited. Combined with DAGMM's integratation of dimensionality reduction and density estimation, we present a scalable framework for unsupervised monitoring of high volume network telemetry. When trained on only 10% of an O-RAN video-streaming dataset, ESN-DAGMM achieved on average 269.59% higher quality clustering than baselines under identical conditions, all while maintaining competitive reconstruction error. By extending DAGMM to capture temporal dynamics, ESN-DAGMM offers a practical solution for time-series analysis using very limited training samples, outperforming baselines and enabling operator's control over the clustering-reconstruction trade-off.

AdaMamba: Adaptive Frequency-Gated Mamba for Long-Term Time Series Forecasting

Accurate long-term time series forecasting (LTSF) requires the capture of complex long-range dependencies and dynamic periodic patterns. Recent advances in frequency-domain analysis offer a global perspective for uncovering temporal characteristics. However, real-world time series often exhibit pronounced cross-domain heterogeneity where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Existing frequency-based LTSF methods often rely on implicit assumptions of cross-domain homogeneity, which limits their ability to adapt to such intricate variability. To effectively integrate frequency-domain analysis with temporal dependency learning, we propose AdaMamba, a novel framework that endogenizes adaptive and context-aware frequency analysis within the Mamba state-space update process. Specifically, AdaMamba introduces an interactive patch encoding module to capture inter-variable interaction dynamics. Then, we develop an adaptive frequency-gated state-space module that generates input-dependent frequency bases, and generalizes the conventional temporal forgetting gate into a unified time-frequency forgetting gate. This allows dynamic calibration of state transitions based on learned frequency-domain importance, while preserving Mamba's capability in modeling long-range dependencies. Extensive experiments on seven public LTSF benchmarks and two domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art methods in forecasting accu racy while maintaining competitive computational efficiency. The code of AdaMamba is available at https://github.com/XDjiang25/AdaMamba.

Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting

Existing theory suggests that Kolmogorov-Arnold Networks (KANs) can overcome the spectral bias commonly observed in neural networks under the assumption that inputs are statistically independent. However, this assumption does not hold in time series forecasting (TSF), where inputs are lagged observations with strong temporal autocorrelation. Through theoretical analysis and empirical validation, we obtain an unexpected finding: temporal autocorrelation reintroduces spectral bias in KANs, and the bias becomes increasingly pronounced as the degree of autocorrelation increases. This suggests that standard KANs may face substantial difficulties in TSF with strongly autocorrelated inputs. To address this problem, we introduce the Discrete Cosine Transform (DCT) to reduce the correlations among the network inputs. As expected, experimental results reveal that DCT preprocessing substantially reduces the observed low-frequency preference in TSF. This result also corroborates that the spectral bias of KANs in TSF tasks is indeed induced by the autocorrelation among input variables.

DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency. This work proposes DecompKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function over learned patch-embedding coordinates that can be directly visualized. On standard benchmarks, DecompKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar -17%, ECL -10% vs. iTransformer, Weather) and physiological time series. Visualization of learned edge functions reveals qualitatively different latent nonlinearities across domains. Ablation analysis shows that the architectural pipeline (decomposition, patching, normalization) drives performance more than the choice of nonlinear layer, while the KAN formulation enables inspection of learned latent transformations.

HELIX: Hybrid Encoding with Learnable Identity and Cross-dimensional Synthesis for Time Series Imputation

Time series imputation benefits from leveraging cross-feature correlations, yet existing attention-based methods re-discover feature relationships at each layer, lacking persistent anchors to maintain consistent representations. To address this, we propose HELIX, which assigns each feature a learnable feature identity, a persistent embedding that captures intrinsic semantic properties throughout the network. Unlike graph-based methods that rely on predefined topology and assume homogeneous spatial relationships, HELIX learns arbitrary feature dependencies end-to-end from temporal co-variation, naturally handling datasets where features mix spatial locations with semantic variables. Integrated with hybrid temporal-feature attention, HELIX achieves the state-of-the-art performance, surpassing all 16 baselines on 5 public datasets across 21 experimental settings in our evaluation. Furthermore, our mechanistic analysis reveals that HELIX aligns learned feature identities and dependencies with latent physical and semantic structure progressively across layers, demonstrating that it more effectively translates cross-feature structure into imputation accuracy.