Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved hidden drivers on the observed dynamics. This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems, whether deterministic or stochastic. Notably, the method also uncovers hidden common causes beyond the observed variables. By analyzing the degrees of freedom in the system, our approach provides a more comprehensive understanding of both causal influence and hidden confounders. This unified framework is validated through theoretical models and simulations, demonstrating its robustness and potential for broader application.

Today's best language models still struggle with hallucinations: factually incorrect generations, which impede their ability to reliably retrieve information seen during training. The reversal curse, where models cannot recall information when probed in a different order than was encountered during training, exemplifies this in information retrieval. We reframe the reversal curse as a factorization curse - a failure of models to learn the same joint distribution under different factorizations. Through a series of controlled experiments with increasing levels of realism including WikiReversal, a setting we introduce to closely simulate a knowledge intensive finetuning task, we find that the factorization curse is an inherent failure of the next-token prediction objective used in popular large language models. Moreover, we demonstrate reliable information retrieval cannot be solved with scale, reversed tokens, or even naive bidirectional-attention training. Consequently, various approaches to finetuning on specialized data would necessarily provide mixed results on downstream tasks, unless the model has already seen the right sequence of tokens. Across five tasks of varying levels of complexity, our results uncover a promising path forward: factorization-agnostic objectives can significantly mitigate the reversal curse and hint at improved knowledge storage and planning capabilities.

Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to position C of White, position C of White is preferable to position D of Black, but position D of Black is preferable to position A of White. Intransitivity of winningness of positions of chess players is considered to be a consequence of complexity of the chess environment -- in contrast with simpler games with transitive positions only. The space of relations between winningness of positions of chess players is non-Euclidean. The Zermelo-von Neumann theorem is complemented by statements about possibility vs. impossibility of building pure winning strategies based on the assumption of transitivity of positions of chess players. Questions about the possibility of intransitive positions of players in other positional games are raised.

Time-Series Forecasting is a powerful data modeling discipline that analyzes historical observations to predict future values of a time-series. It has been utilized in numerous applications, including but not limited to economics, meteorology, and health. In this paper, we use time-series forecasting techniques to model and predict the future incidence of chickenpox. To achieve this, we implement and simulate multiple models and data preprocessing techniques on a Hungary-collected dataset. We demonstrate that the LSTM model outperforms all other models in the vast majority of the experiments in terms of county-level forecasting, whereas the SARIMAX model performs best at the national level. We also demonstrate that the performance of the traditional data preprocessing method is inferior to that of the data preprocessing method that we have proposed.

Recurrent graph convolutional neural networks are highly effective machine learning techniques for spatiotemporal signal processing. Newly proposed graph neural network architectures are repetitively evaluated on standard tasks such as traffic or weather forecasting. In this paper, we propose the Chickenpox Cases in Hungary dataset as a new dataset for comparing graph neural network architectures. Our time series analysis and forecasting experiments demonstrate that the Chickenpox Cases in Hungary dataset is adequate for comparing the predictive performance and forecasting capabilities of novel recurrent graph neural network architectures.

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold-adaptive Farahmand-Szepesv\'ari-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected-median-FSA estimator with kNN estimators: maximum likelihood (ML, Levina-Bickel) and two implementations of DANCo (R and matlab). We show that corrected-median-FSA estimator beats the ML estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.