Dynamical Systems Analysis Reveals Functional Regimes in Large Language Models

Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal interventions, leaving temporal structure largely unexplored. Drawing on neuroscience, where temporal integration and metastability are core markers of neural organisation, we adapt these concepts to transformer models and discuss a composite dynamical metric, computed from activation time-series during autoregressive generation. We evaluate this metric in GPT-2-medium across five conditions: structured reasoning, forced repetition, high-temperature noisy sampling, attention-head pruning, and weight-noise injection. Structured reasoning consistently exhibits elevated metric relative to repetitive, noisy, and perturbed regimes, with statistically significant differences confirmed by one-way ANOVA and large effect sizes in key comparisons. These results are robust to layer selection, channel subsampling, and random seeds. Our findings demonstrate that neuroscience-inspired dynamical metrics can reliably characterise differences in computational organisation across functional regimes in large language models. We stress that the proposed metric captures formal dynamical properties and does not imply subjective experience.

Interpretability-Guided Bi-objective Optimization: Aligning Accuracy and Explainability

This paper introduces Interpretability-Guided Bi-objective Optimization (IGBO), a framework that trains interpretable models by incorporating structured domain knowledge via a bi-objective formulation. IGBO encodes feature importance hierarchies as a Directed Acyclic Graph (DAG) via Central Limit Theorem-based construction and uses Temporal Integrated Gradients (TIG) to measure feature importance. To address the Out-of-Distribution (OOD) problem in TIG computation, we propose an Optimal Path Oracle that learns data-manifold-aware integration paths. Theoretical analysis establishes convergence properties via a geometric projection mapping $\mathcal{P}$ and proves robustness to mini-batch noise. Central Limit Theorem-based construction of the interpretability DAG ensures statistical validity of edge orientation decisions. Empirical results on time-series data demonstrate IGBO's effectiveness in enforcing DAG constraints with minimal accuracy loss, outperforming standard regularization baselines.

Trustworthy Data-Driven Wildfire Risk Prediction and Understanding in Western Canada

In recent decades, the intensification of wildfire activity in western Canada has resulted in substantial socio-economic and environmental losses. Accurate wildfire risk prediction is hindered by the intrinsic stochasticity of ignition and spread and by nonlinear interactions among fuel conditions, meteorology, climate variability, topography, and human activities, challenging the reliability and interpretability of purely data-driven models. We propose a trustworthy data-driven wildfire risk prediction framework based on long-sequence, multi-scale temporal modeling, which integrates heterogeneous drivers while explicitly quantifying predictive uncertainty and enabling process-level interpretation. Evaluated over western Canada during the record-breaking 2023 and 2024 fire seasons, the proposed model outperforms existing time-series approaches, achieving an F1 score of 0.90 and a PR-AUC of 0.98 with low computational cost. Uncertainty-aware analysis reveals structured spatial and seasonal patterns in predictive confidence, highlighting increased uncertainty associated with ambiguous predictions and spatiotemporal decision boundaries. SHAP-based interpretation provides mechanistic understanding of wildfire controls, showing that temperature-related drivers dominate wildfire risk in both years, while moisture-related constraints play a stronger role in shaping spatial and land-cover-specific contrasts in 2024 compared to the widespread hot and dry conditions of 2023. Data and code are available at https://github.com/SynUW/mmFire.

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.

Predicting Time Pressure of Powered Two-Wheeler Riders for Proactive Safety Interventions

Time pressure critically influences risky maneuvers and crash proneness among powered two-wheeler riders, yet its prediction remains underexplored in intelligent transportation systems. We present a large-scale dataset of 129,000+ labeled multivariate time-series sequences from 153 rides by 51 participants under No, Low, and High Time Pressure conditions. Each sequence captures 63 features spanning vehicle kinematics, control inputs, behavioral violations, and environmental context. Our empirical analysis shows High Time Pressure induces 48% higher speeds, 36.4% greater speed variability, 58% more risky turns at intersections, 36% more sudden braking, and 50% higher rear brake forces versus No Time Pressure. To benchmark this dataset, we propose MotoTimePressure, a deep learning model combining convolutional preprocessing, dual-stage temporal attention, and Squeeze-and-Excitation feature recalibration, achieving 91.53% accuracy and 98.93% ROC AUC, outperforming eight baselines. Since time pressure cannot be directly measured in real time, we demonstrate its utility in collision prediction and threshold determination. Using MTPS-predicted time pressure as features, improves Informer-based collision risk accuracy from 91.25% to 93.51%, approaching oracle performance (93.72%). Thresholded time pressure states capture rider cognitive stress and enable proactive ITS interventions, including adaptive alerts, haptic feedback, V2I signaling, and speed guidance, supporting safer two-wheeler mobility under the Safe System Approach.

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.

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.

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.