EvoTSC: Evolving Feature Learning Models for Time Series Classification via Genetic Programming

Time series classification is an important analytical task across diverse domains. However, its practical application is often hindered by the scarcity of labeled data and the requirement for substantial computational resources. To address these challenges, this paper proposes EvoTSC, a novel genetic programming approach designed to automatically evolve lightweight feature learning models for time series classification. The core of EvoTSC is a carefully designed multi-layer program structure that strategically embeds diverse forms of prior expert knowledge into the evolutionary process, effectively guiding the search toward operations known to be highly effective for time series analysis. To mitigate the common overfitting problem in time series classification, a tailored Pareto tournament selection strategy is proposed to favor models that perform consistently well across varying training data subsets, promoting the discovery of highly generalizable models. Extensive experiments conducted on univariate time series classification datasets demonstrate that EvoTSC significantly outperforms eleven benchmark methods in most comparisons. Further analyses verify the contribution of each component and the resource efficiency of the evolved models.

Learning Time-Inhomogeneous Markov Dynamics in Financial Time Series via Neural Parameterization

Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit, theoretically grounded rules for system evolution, their empirical estimation collapses due to severe data sparsity when applied to high-resolution, high-noise environments. We explore this statistical barrier using financial time series as a canonical, real-world testbed. To overcome the degeneracy of empirical counting, we introduce a framework that utilizes neural networks strictly as parameterization engines to generate explicit, time-varying Markov transition matrices. By constraining the neural network to output its predictions as a formal stochastic operator, we maintain complete structural interpretability. We demonstrate that these learned operators successfully capture complex regime shifts: the state-conditioned model achieves mean row heterogeneity $\barρ = 0.0073$ while the state-free ablation collapses to exactly zero, and operator row entropy correlates with realized variance at $r = -0.62$ ($p \approx 10^{-251}$), revealing that high-volatility regimes homogenize transition dynamics rather than diversify them. Furthermore, rather than enforcing the Chapman-Kolmogorov equations as a rigid structural requirement, we repurpose them as a localized diagnostic tool to pinpoint specific temporal windows where first-order memory assumptions break down. Ultimately, this framework demonstrates how neural networks can be constrained to make rigorous, classical operator analysis viable for complex real-world time series.

Densification and forecasting of Sentinel-2 time series from multimodal SAR and Optical satellite data using deep generative models

Optical satellite image time series are extensively used in many Earth observation applications, including agriculture, climate monitoring, and land surface analysis. However, clouds and swath edges result in irregular sampling along the temporal dimension, limiting continuous monitoring. To address this issue, a growing body of work has focused on temporal densification and reconstruction of satellite image time series, with the objective of filling missing or cloud-contaminated observations within the temporal extent of the available data. While these approaches improve temporal continuity, they are inherently restricted to the reconstruction of the gaps within the observed time periods, and do not address the prediction of future observations. This work proposes a probabilistic deep learning framework for the densification and forecasting of Sentinel-2 time series by generating optical images at arbitrary past or future dates. The approach leverages multimodal satellite data by jointly exploiting Sentinel-2 optical and Sentinel-1 SAR observations. Unlike most existing works, we propose to focus on the uncertainty of the generated images. Experimental results demonstrate effective densification and forecasting, on sparse and temporally misaligned time series.

Enabling Federated Inference via Unsupervised Consensus Embedding

Cooperative inference across independently deployed machine learning models is increasingly desirable in distributed environments, as there is a growing need to leverage multiple models while keeping their data and model parameters private. However, existing cooperative frameworks typically rely on sharing input data, model parameters, or a common encoder, which limits their applicability in privacy-sensitive or cross-organizational settings. To address this challenge, we propose Consensus Embedding-based Federated Inference (CE-FI), a framework that enables pretrained models to cooperate at inference time without sharing model parameters or raw inputs and without assuming a common encoder. CE-FI introduces two components: a Consensus Embedding (CE) layer that maps heterogeneous intermediate representations into a common embedding space, and a Cooperative Output (CO) layer that produces predictions from these embeddings. Both layers are trained using shared unlabeled data only, so the cooperative stage does not require additional labeled data. Experiments on image classification benchmarks -- CIFAR-10 and CIFAR-100 -- under diverse non-IID conditions show that CE-FI consistently outperforms solo inference and performs comparably to conventional methods that require stronger sharing assumptions. Additional evaluations on text and time-series tasks indicate applicability beyond image classification, although performance depends on the ensemble strategy. Further analysis identifies representation alignment as the primary bottleneck.

FinMoji: A Framework for Emoji-driven Sentiment Analysis in Financial Social Media

This paper explores the use of emojis in financial sentiment analysis, focusing on the social media platform StockTwits. Emojis, increasingly prevalent in digital communication, have potential as compact indicators of investor sentiment, which can be critical for predicting market trends. Our study examines whether emojis alone can serve as reliable proxies for financial sentiment and how they compare with traditional text-based analysis. We conduct a series of experiments using logistic regression and transformer models. We further analyze the performance, computational efficiency, and data requirements of emoji-based versus text-based sentiment classification. Using a balanced dataset of about 528,000 emoji-containing StockTwits posts, we find that emoji-only models achieve F1 approximately 0.75, lower than text-emoji combined models, which achieve F1 approximately 0.88, but with far lower computational cost. This is a useful feature in time-sensitive settings such as high-frequency trading. Furthermore, certain emojis and emoji pairs exhibit strong predictive power for market sentiment, demonstrating over 90 percent accuracy in predicting bullish or bearish trends. Finally, our research reveals large statistical differences in emoji usage between financial and general social media contexts, stressing the need for domain-specific sentiment analysis models.

Preliminary Insights in Chronos Frequency Data Understanding and Reconstruction

This paper presents a preliminary analysis of the ability of Chronos foundation model to process and internally represent frequency domain information. Foundation models that process time-series data offer practitioners a unified architecture capable of learning generic temporal representations across diverse tasks and domains, reducing the need for task-specific feature engineering and enabling transfer across signal modalities. Despite their growing adoption, the extent to which such models encode fundamental signal properties remains insufficiently characterised. We address this gap by analysing Chronos under controlled conditions, starting from the simplest class of signals: discrete sinusoids generated at fixed frequencies. Using lightweight online minimum description length probes applied to the decoder architecture, we test for the presence and separability of frequency information in the model's internal representations. The results provide insight into how frequential content is captured across the frequency spectrum and highlight regimes in which representation quality may degrade or require particular care. These findings offer practical guidance for users of Chronos in signal processing and information fusion contexts, and contribute to ongoing efforts to improve the interpretability and evaluation of foundation models for temporal data.

Positivity of a Hadamard Product

A notable difference between the ordinary and Hadamard products is that the Hadamard product of two singular positive semidefinite matrices can be nonsingular, and one of the factors can even be indefinite. We present an eigenvalue lower bound for a Hadamard product that depends on the rank, effective condition number, and diagonal entries of one factor, and the smallest eigenvalues of certain principal submatrices of the other factor. We give numerical examples and discuss its applications in array signal processing and matrix time series analysis.

FinSTaR: Towards Financial Reasoning with Time Series Reasoning Models

Time series (TS) reasoning models (TSRMs) have shown promising capabilities in general domains, yet they consistently fail on financial domain, which exhibit unique characteristics. We propose a general 2x2 capability taxonomy for TSRMs by crossing 1) single-entity vs. multi-entity analysis with 2) assessment of the current state vs. prediction of future behavior. We instantiate this taxonomy in the financial domain -- where the distinction between deterministic assessment and stochastic prediction is particularly critical -- as ten financial reasoning tasks, forming the FinTSR-Bench benchmark based on S&P stocks. To this end, we propose FinSTaR (Financial Time Series Thinking and Reasoning), trained on FinTSR-Bench with distinct chain-of-thought (CoT) strategies tailored to each category. For assessment, which is deterministic (i.e., computable from observable data), we employ Compute-in-CoT, a programmatic CoT that enables models to derive answers directly from raw prices. For prediction, which is inherently stochastic (i.e., subject to unobservable factors), we adopt Scenario-Aware CoT, which generates diverse scenarios before making a judgment, mirroring how financial analysts reason under uncertainty. The proposed method achieves 78.9% average accuracy on FinTSR-Bench, substantially outperforming LLM and TSRM baselines. Furthermore, we show that the four capability categories are complementary and mutually reinforcing through joint training, and that Scenario-Aware CoT consistently improves prediction accuracy over standard CoT. Code is publicly available at: https://github.com/seunghan96/FinSTaR.

Time Series Augmented Generation for Financial Applications

Evaluating the reasoning capabilities of Large Language Models (LLMs) for complex, quantitative financial tasks is a critical and unsolved challenge. Standard benchmarks often fail to isolate an agent's core ability to parse queries and orchestrate computations. To address this, we introduce a novel evaluation methodology and benchmark designed to rigorously measure an LLM agent's reasoning for financial time-series analysis. We apply this methodology in a large-scale empirical study using our framework, Time Series Augmented Generation (TSAG), where an LLM agent delegates quantitative tasks to verifiable, external tools. Our benchmark, consisting of 100 financial questions, is used to compare multiple SOTA agents (e.g., GPT-4o, Llama 3, Qwen2) on metrics assessing tool selection accuracy, faithfulness, and hallucination. The results demonstrate that capable agents can achieve near-perfect tool-use accuracy with minimal hallucination, validating the tool-augmented paradigm. Our primary contribution is this evaluation framework and the corresponding empirical insights into agent performance, which we release publicly to foster standardized research on reliable financial AI.

Fixation Sequences as Time Series: A Topological Approach to Dyslexia Detection

Persistent homology, a method from topological data analysis, extracts robust, multi-scale features from data. It produces stable representations of time series by applying varying thresholds to their values (a process known as a \textit{filtration}). We develop novel filtrations for time series and introduce topological methods for the analysis of eye-tracking data, by interpreting fixation sequences as time series, and constructing ``hybrid models'' that combine topological features with traditional statistical features. We empirically evaluate our method by applying it to the task of dyslexia detection from eye-tracking-while-reading data using the Copenhagen Corpus, which contains scanpaths from dyslexic and non-dyslexic L1 and L2 readers. Our hybrid models outperform existing approaches that rely solely on traditional features, showing that persistent homology captures complementary information encoded in fixation sequences. The strength of these topological features is further underscored by their achieving performance comparable to established baseline methods. Importantly, our proposed filtrations outperform existing ones.