grangersearch: An R Package for Exhaustive Granger Causality Testing with Tidyverse Integration

This paper introduces grangersearch, an R package for performing exhaustive Granger causality searches on multiple time series. The package provides: (1) exhaustive pairwise search across multiple variables, (2) automatic lag order optimization with visualization, (3) tidyverse-compatible syntax with pipe operators and non-standard evaluation, and (4) integration with the broom ecosystem through tidy() and glance() methods. The package wraps the vars infrastructure while providing a simple interface for exploratory causal analysis. We describe the statistical methodology, demonstrate the package through worked examples, and discuss practical considerations for applied researchers.

LDLT L-Lipschitz Network Weight Parameterization Initialization

We analyze initialization dynamics for LDLT-based $\mathcal{L}$-Lipschitz layers by deriving the exact marginal output variance when the underlying parameter matrix $W_0\in \mathbb{R}^{m\times n}$ is initialized with IID Gaussian entries $\mathcal{N}(0,σ^2)$. The Wishart distribution, $S=W_0W_0^\top\sim\mathcal{W}_m(n,σ^2 \boldsymbol{I}_m)$, used for computing the output marginal variance is derived in closed form using expectations of zonal polynomials via James' theorem and a Laplace-integral expansion of $(α\boldsymbol{I}_m+S)^{-1}$. We develop an Isserlis/Wick-based combinatorial expansion for $\operatorname{\mathbb{E}}\left[\operatorname{tr}(S^k)\right]$ and provide explicit truncated moments up to $k=10$, which yield accurate series approximations for small-to-moderate $σ^2$. Monte Carlo experiments confirm the theoretical estimates. Furthermore, empirical analysis was performed to quantify that, using current He or Kaiming initialization with scaling $1/\sqrt{n}$, the output variance is $0.41$, whereas the new parameterization with $10/ \sqrt{n}$ for $α=1$ results in an output variance of $0.9$. The findings clarify why deep $\mathcal{L}$-Lipschitz networks suffer rapid information loss at initialization and offer practical prescriptions for choosing initialization hyperparameters to mitigate this effect. However, using the Higgs boson classification dataset, a hyperparameter sweep over optimizers, initialization scale, and depth was conducted to validate the results on real-world data, showing that although the derivation ensures variance preservation, empirical results indicate He initialization still performs better.

What makes for an enjoyable protagonist? An analysis of character warmth and competence

Drawing on psychological and literary theory, we investigated whether the warmth and competence of movie protagonists predict IMDb ratings, and whether these effects vary across genres. Using 2,858 films and series from the Movie Scripts Corpus, we identified protagonists via AI-assisted annotation and quantified their warmth and competence with the LLM_annotate package ([1]; human-LLM agreement: r = .83). Preregistered Bayesian regression analyses revealed theory-consistent but small associations between both warmth and competence and audience ratings, while genre-specific interactions did not meaningfully improve predictions. Male protagonists were slightly less warm than female protagonists, and movies with male leads received higher ratings on average (an association that was multiple times stronger than the relationships between movie ratings and warmth/competence). These findings suggest that, although audiences tend to favor warm, competent characters, the effects on movie evaluations are modest, indicating that character personality is only one of many factors shaping movie ratings. AI-assisted annotation with LLM_annotate and gpt-4.1-mini proved effective for large-scale analyses but occasionally fell short of manually generated annotations.

Domain Generalization for Time Series: Enhancing Drilling Regression Models for Stick-Slip Index Prediction

This paper provides a comprehensive comparison of domain generalization techniques applied to time series data within a drilling context, focusing on the prediction of a continuous Stick-Slip Index (SSI), a critical metric for assessing torsional downhole vibrations at the drill bit. The study aims to develop a robust regression model that can generalize across domains by training on 60 second labeled sequences of 1 Hz surface drilling data to predict the SSI. The model is tested in wells that are different from those used during training. To fine-tune the model architecture, a grid search approach is employed to optimize key hyperparameters. A comparative analysis of the Adversarial Domain Generalization (ADG), Invariant Risk Minimization (IRM) and baseline models is presented, along with an evaluation of the effectiveness of transfer learning (TL) in improving model performance. The ADG and IRM models achieve performance improvements of 10% and 8%, respectively, over the baseline model. Most importantly, severe events are detected 60% of the time, against 20% for the baseline model. Overall, the results indicate that both ADG and IRM models surpass the baseline, with the ADG model exhibiting a slight advantage over the IRM model. Additionally, applying TL to a pre-trained model further improves performance. Our findings demonstrate the potential of domain generalization approaches in drilling applications, with ADG emerging as the most effective approach.

A Mechanistic Analysis of Transformers for Dynamical Systems

Transformers are increasingly adopted for modeling and forecasting time-series, yet their internal mechanisms remain poorly understood from a dynamical systems perspective. In contrast to classical autoregressive and state-space models, which benefit from well-established theoretical foundations, Transformer architectures are typically treated as black boxes. This gap becomes particularly relevant as attention-based models are considered for general-purpose or zero-shot forecasting across diverse dynamical regimes. In this work, we do not propose a new forecasting model, but instead investigate the representational capabilities and limitations of single-layer Transformers when applied to dynamical data. Building on a dynamical systems perspective we interpret causal self-attention as a linear, history-dependent recurrence and analyze how it processes temporal information. Through a series of linear and nonlinear case studies, we identify distinct operational regimes. For linear systems, we show that the convexity constraint imposed by softmax attention fundamentally restricts the class of dynamics that can be represented, leading to oversmoothing in oscillatory settings. For nonlinear systems under partial observability, attention instead acts as an adaptive delay-embedding mechanism, enabling effective state reconstruction when sufficient temporal context and latent dimensionality are available. These results help bridge empirical observations with classical dynamical systems theory, providing insight into when and why Transformers succeed or fail as models of dynamical systems.

DecoKAN: Interpretable Decomposition for Forecasting Cryptocurrency Market Dynamics

Accurate and interpretable forecasting of multivariate time series is crucial for understanding the complex dynamics of cryptocurrency markets in digital asset systems. Advanced deep learning methodologies, particularly Transformer-based and MLP-based architectures, have achieved competitive predictive performance in cryptocurrency forecasting tasks. However, cryptocurrency data is inherently composed of long-term socio-economic trends and local high-frequency speculative oscillations. Existing deep learning-based 'black-box' models fail to effectively decouple these composite dynamics or provide the interpretability needed for trustworthy financial decision-making. To overcome these limitations, we propose DecoKAN, an interpretable forecasting framework that integrates multi-level Discrete Wavelet Transform (DWT) for decoupling and hierarchical signal decomposition with Kolmogorov-Arnold Network (KAN) mixers for transparent and interpretable nonlinear modeling. The DWT component decomposes complex cryptocurrency time series into distinct frequency components, enabling frequency-specific analysis, while KAN mixers provide intrinsically interpretable spline-based mappings within each decomposed subseries. Furthermore, interpretability is enhanced through a symbolic analysis pipeline involving sparsification, pruning, and symbolization, which produces concise analytical expressions offering symbolic representations of the learned patterns. Extensive experiments demonstrate that DecoKAN achieves the lowest average Mean Squared Error on all tested real-world cryptocurrency datasets (BTC, ETH, XMR), consistently outperforming a comprehensive suite of competitive state-of-the-art baselines. These results validate DecoKAN's potential to bridge the gap between predictive accuracy and model transparency, advancing trustworthy decision support within complex cryptocurrency markets.

Learning to be Reproducible: Custom Loss Design for Robust Neural Networks

To enhance the reproducibility and reliability of deep learning models, we address a critical gap in current training methodologies: the lack of mechanisms that ensure consistent and robust performance across runs. Our empirical analysis reveals that even under controlled initialization and training conditions, the accuracy of the model can exhibit significant variability. To address this issue, we propose a Custom Loss Function (CLF) that reduces the sensitivity of training outcomes to stochastic factors such as weight initialization and data shuffling. By fine-tuning its parameters, CLF explicitly balances predictive accuracy with training stability, leading to more consistent and reliable model performance. Extensive experiments across diverse architectures for both image classification and time series forecasting demonstrate that our approach significantly improves training robustness without sacrificing predictive performance. These results establish CLF as an effective and efficient strategy for developing more stable, reliable and trustworthy neural networks.

The Procrustean Bed of Time Series: The Optimization Bias of Point-wise Loss

Optimizing time series models via point-wise loss functions (e.g., MSE) relying on a flawed point-wise independent and identically distributed (i.i.d.) assumption that disregards the causal temporal structure, an issue with growing awareness yet lacking formal theoretical grounding. Focusing on the core independence issue under covariance stationarity, this paper aims to provide a first-principles analysis of the Expectation of Optimization Bias (EOB), formalizing it information-theoretically as the discrepancy between the true joint distribution and its flawed i.i.d. counterpart. Our analysis reveals a fundamental paradigm paradox: the more deterministic and structured the time series, the more severe the bias by point-wise loss function. We derive the first closed-form quantification for the non-deterministic EOB across linear and non-linear systems, and prove EOB is an intrinsic data property, governed exclusively by sequence length and our proposed Structural Signal-to-Noise Ratio (SSNR). This theoretical diagnosis motivates our principled debiasing program that eliminates the bias through sequence length reduction and structural orthogonalization. We present a concrete solution that simultaneously achieves both principles via DFT or DWT. Furthermore, a novel harmonized $\ell_p$ norm framework is proposed to rectify gradient pathologies of high-variance series. Extensive experiments validate EOB Theory's generality and the superior performance of debiasing program.

On the Identifiability of Regime-Switching Models with Multi-Lag Dependencies

Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting. For SDSs, we establish identifiability of the latent variables up to permutation and scaling via temporal structure, which in turn yields conditions for identifiability of regime-dependent latent causal graphs (up to regime/node permutations). Our results hold in a fully unsupervised setting through architectural and noise assumptions that are directly enforceable via neural network design. We complement the theory with a flexible variational estimator that satisfies the assumptions and validate the results on synthetic benchmarks. Across real-world datasets from neuroscience, finance, and climate, identifiability leads to more trustworthy interpretability analysis, which is crucial for scientific discovery.

Empirical Mode Decomposition and Graph Transformation of the MSCI World Index: A Multiscale Topological Analysis for Graph Neural Network Modeling

This study applies Empirical Mode Decomposition (EMD) to the MSCI World index and converts the resulting intrinsic mode functions (IMFs) into graph representations to enable modeling with graph neural networks (GNNs). Using CEEMDAN, we extract nine IMFs spanning high-frequency fluctuations to long-term trends. Each IMF is transformed into a graph using four time-series-to-graph methods: natural visibility, horizontal visibility, recurrence, and transition graphs. Topological analysis shows clear scale-dependent structure: high-frequency IMFs yield dense, highly connected small-world graphs, whereas low-frequency IMFs produce sparser networks with longer characteristic path lengths. Visibility-based methods are more sensitive to amplitude variability and typically generate higher clustering, while recurrence graphs better preserve temporal dependencies. These results provide guidance for designing GNN architectures tailored to the structural properties of decomposed components, supporting more effective predictive modeling of financial time series.