Time-series Foundation Models (TSFMs) have recently emerged as a universal paradigm for learning across diverse temporal domains. However, despite their empirical success, the internal mechanisms by which these models represent fundamental time-series concepts remain poorly understood. In this work, we undertake a systematic investigation of concept interpretability in TSFMs. Specifically, we examine: (i) which layers encode which concepts, (ii) whether concept parameters are linearly recoverable, (iii) how representations evolve in terms of concept disentanglement and abstraction across model depth, and (iv) how models process compositions of concepts. We systematically probe these questions using layer-wise analyses, linear recoverability tests, and representation similarity measures, providing a structured account of TSFM semantics. The resulting insights show that early layers mainly capture local, time-domain patterns (e.g., AR(1), level shifts, trends), while deeper layers encode dispersion and change-time signals, with spectral and warping factors remaining the hardest to recover linearly. In compositional settings, however, probe performance degrades, revealing interference between concepts. This highlights that while atomic concepts are reliably localized, composition remains a challenge, underscoring a key limitation in current TSFMs' ability to represent interacting temporal phenomena.

Time series data is widely used in various fields, such as finance, economics, and engineering. One of the key challenges when working with time series data is detecting level shifts. A level shift occurs when the time series' mean and/or variance changes abruptly. These shifts can significantly impact the analysis and forecasting of the time series and must be detected and handled properly. One popular method for detecting level shifts is using an Autoregressive Moving Average (ARMA) time series model.

Change detection involves segmenting sequential data such that observations in the same segment share some desired properties. Multivariate change detection continues to be a challenging problem due to the variety of ways change points can be correlated across channels and the potentially poor signal-to-noise ratio on individual channels. In this paper, we are interested in locating additive outliers (AO) and level shifts (LS) in the unsupervised setting. We propose ABACUS, Automatic BAyesian Changepoints Under Sparsity, a Bayesian source separation technique to recover latent signals while also detecting changes in model parameters. Multi-level sparsity achieves both dimension reduction and modeling of signal changes. We show ABACUS has competitive or superior performance in simulation studies against state-of-the-art change detection methods and established latent variable models. We also illustrate ABACUS on two real application, modeling genomic profiles and analyzing household electricity consumption.

Adaptive Filter for Automatic Identification of Multiple Faults in a Noisy OTDR Profile Jean Pierre von der Weid, Mario H. Souto, Joaquim D. Garcia, and Gustavo C. Amaral November 7, 2018 Abstract We present a novel methodology able to distinguish meaningful level shifts from typical signal fluctuations. A two-stage regularization filtering can accurately identify the location of the significant level-shifts with an efficient parameter-free algorithm. The developed methodology demands low computational effort and can easily be embedded in a dedicated processing unit. Our case studies compare the new methodology with current available ones and show that it is the most adequate technique for fast detection of multiple unknown level-shifts in a noisy OTDR profile. 1 Introduction The central problem in fiber monitoring is the detection of small faults or losses most commonly performed by inspecting the trace of an Optical Time Domain Reflectometer (OTDR) [1]. These faults appear as small level shifts in a slowly varying backscattered optical power, eventually masked by the detector noise. Averaging over many OTDR shots is usually required to get access to the information needed. However, measurement time is of paramount importance in network monitoring, so that signal processing and filtering is a fundamental tool to improve time and sensitivity of the overall process. Moreover, in the case of wavelength multiplexed optical networks (WDM-PON) the problem is still worse because coherent backscattered power fluctuations (CRN) cannot be averaged out by summing up many OTDR shots [2].