Pseudo-Alignment is a pervasive challenge in many large language models for time series (LLM4TS) models, often causing them to underperform compared to linear models or randomly initialised backbones. However, there is limited discussion in the community for the reasons that pseudo-alignment occurs. In this work, we conduct a thorough investigation into the root causes of pseudo-alignment in LLM4TS and build a connection of pseudo-alignment to the cone effect in LLM. We demonstrate that pseudo-alignment arises from the interplay of cone effect within pretrained LLM components and the intrinsically low-dimensional manifold of time-series data. In addition, we also introduce TimeSUP, a novel technique designed to mitigate this issue and improve forecast performance in existing LLM4TS approaches. TimeSUP addresses this by increasing the time series manifold to more closely match the intrinsic dimension of language embeddings, allowing the model to distinguish temporal signals clearly while still capturing shared structures across modalities. As a result, representations for time and language tokens remain distinct yet exhibit high cosine similarity, signifying that the model preserves each modality's unique features while learning their commonalities in a unified embedding space. Empirically, TimeSUP consistently outperforms state-of-the-art LLM4TS methods and other lightweight baselines on long-term forecasting performance. Furthermore, it can be seamlessly integrated into four existing LLM4TS pipelines and delivers significant improvements in forecasting performance.

Kolmogorov-Arnold Networks (KANs) are neural architectures inspired by the Kolmogorov-Arnold representation theorem that leverage B-spline parameterizations for flexible, locally adaptive function approximation. Although KANs can capture complex nonlinearities beyond those modeled by standard Multi-Layer Perceptrons (MLPs), they frequently exhibit miscalibrated confidence estimates-manifesting as overconfidence in dense data regions and underconfidence in sparse areas. In this work, we systematically examine the impact of four critical hyperparameters -- Layer Width, Grid Order, Shortcut Function, and Grid Range -- on the calibration of KANs. Furthermore, we introduce a novel Temperature-Scaled Loss (TSL) that integrates a temperature parameter directly into the training objective, dynamically adjusting the predictive distribution during learning. Both theoretical analysis and extensive empirical evaluations on standard benchmarks demonstrate that TSL significantly reduces calibration errors, thereby improving the reliability of probabilistic predictions. Overall, our study provides actionable insights into the design of spline-based neural networks and establishes TSL as a robust, loss-agnostic solution for enhancing calibration.

Classical overlap metrics such as Dice or IoU quantify where a medical-image segmentation falls short but say nothing about the confidence of each prediction. Over-confident errors are particularly dangerous in clinical practice, where a single false-positive voxel may trigger an unnecessary biopsy. We introduce three contributions that jointly address spatial precision and reliability. (i) Signed-Distance Calibration (SDC) loss couples cross-entropy, local calibration and a differentiable signed-distance penalty, enforcing boundary accuracy while moderating confidence. (ii) A Spatially Adaptive Margin (SAM) module applies lightweight morphological transforms to ground-truth masks before computing the local target, sharpening ambiguous edges. (iii) Pixel-wise Expected Calibration Error (pECE) extends ECE to millions of voxels and penalises high-confidence false positives. Across four public datasets (ACDC, FLARE, BraTS, PROSTATE) and two back-bones (U-Net, nnU-Net), SDC improves Dice by up to 4 percentage points and halves ECE compared with the state of the art, without sacrificing runtime. Code is available on: https://github.com/EagleAdelaide/SDC-Loss.

Kolmogorov-Arnold Neural Networks (KANs) have recently attracted significant attention in the machine learning community. However, their practical implementation often faces challenges such as poor training stability and a large number of trainable parameters. Moreover, the behavior of learnable activation functions based on B-splines remains insufficiently understood. In this work, we analyze KANs through the lens of spline knot behavior and derive lower and upper bounds on the number of knots in B-spline-based KANs. To address the existing limitations, we propose a novel KAN-based approach, which improves upon the original KAN by reducing the number of trainable parameters to match the scale of standard Multi-Layer Perceptrons (MLPs), while enhancing overall performance. Additionally, we introduce a new training strategy that enforces C2 continuity in the learnable splines, leading to smoother activation functions and improved training stability via range expansion. We evaluate our method across eight diverse datasets encompassing image, text, time series, multimodal, and function approximation tasks. The promising results demonstrate the feasibility of KAN-based architectures and the effectiveness of our proposed enhancements. The proposed method implementation is released in https://github.com/IcurasLW/FR-KAN.git

Large Language Models (LLMs) have demonstrated impressive performance in time series analysis and seems to understand the time temporal relationship well than traditional transformer-based approaches. However, since LLMs are not designed for time series tasks, simpler models-like linear regressions can often achieve comparable performance with far less complexity. In this study, we perform extensive experiments to assess the effectiveness of applying LLMs to key time series tasks, including forecasting, classification, imputation, and anomaly detection. We compare the performance of LLMs against simpler baseline models, such as single-layer linear models and randomly initialized LLMs. Our results reveal that LLMs offer minimal advantages for these core time series tasks and may even distort the temporal structure of the data. In contrast, simpler models consistently outperform LLMs while requiring far fewer parameters. Furthermore, we analyze existing reprogramming techniques and show, through data manifold analysis, that these methods fail to effectively align time series data with language and display ''pseudo-alignment'' behavior in embedding space. Our findings suggest that the performance of LLM-based methods in time series tasks arises from the intrinsic characteristics and structure of time series data, rather than any meaningful alignment with the language model architecture. We release the code for experiments here: https://github.com/IcurasLW/Official-Repository_Understanding_LLM_for_Time_Series_Analysis.git

Irregular Time Series Data (IRTS) has shown increasing prevalence in real-world applications. We observed that IRTS can be divided into two specialized types: Natural Irregular Time Series (NIRTS) and Accidental Irregular Time Series (AIRTS). Various existing methods either ignore the impacts of irregular patterns or statically learn the irregular dynamics of NIRTS and AIRTS data and suffer from limited data availability due to the sparsity of IRTS. We proposed a novel transformer-based framework for general irregular time series data that treats IRTS from four views: Locality, Time, Spatio and Irregularity to motivate the data usage to the highest potential. Moreover, we design a sophisticated irregularity-gate mechanism to adaptively select task-relevant information from irregularity, which improves the generalization ability to various IRTS data. We implement extensive experiments to demonstrate the resistance of our work to three highly missing ratio datasets (88.4%, 94.9%, 60% missing value) and investigate the significance of the irregularity information for both NIRTS and AIRTS by additional ablation study. We release our implementation in https://github.com/IcurasLW/MTSFormer-Irregular_Time_Series.git.