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Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of…

Targeting to understand the underlying explainable factors behind observations and modeling the conditional generation process on these factors, we connect disentangled representation learning to Diffusion Probabilistic Models (DPMs) to…

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem…

Deep-learning models such as Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) have been successfully used for process-mining tasks. They have achieved better performance for different predictive tasks than traditional…

The Linear Multistep Method Particle Filter (LMM PF) is a method for predicting the evolution in time of a evolutionary system governed by a system of differential equations. If some of the parameters of the governing equations are…

In these notes we review emergent phenomena in complex systems, emphasizing ways to identify potential underlying universal mechanisms that generates complexity. The discussion is centered around the emergence of collective behavior in…

Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically driven, dynamically evolving field from finite…

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to break down complex problems into interpretable intermediate steps, significantly enhancing model transparency and performance in reasoning tasks. However, conventional…

The particle-flow (PF) algorithm is used in general-purpose particle detectors to reconstruct a comprehensive particle-level view of the collision by combining information from different subdetectors. A graph neural network (GNN) model,…

Many disciplines need quantitative models that synthesize experimental data across multiple instances of the same general system. For example, neuroscientists must combine data from the brains of many individual animals to understand the…

Business processes evolve over time to adapt to changing business environments. This requires continuous monitoring of business processes to gain insights into whether they conform to the intended design or deviate from it. The situation…

While large language models (LLMs) have demonstrated remarkable reasoning capabilities, they often struggle with complex tasks that require specific thinking paradigms, such as divide-and-conquer and procedural deduction, \etc Previous…

Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose…

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…

Large language models (LLMs) are often portrayed as merely imitating linguistic patterns without genuine understanding. We argue that recent findings in mechanistic interpretability (MI), the emerging field probing the inner workings of…

Self-explaining models are models that reveal decision making parameters in an interpretable manner so that the model reasoning process can be directly understood by human beings. General Linear Models (GLMs) are self-explaining because the…

Inductive reasoning is an essential capability for large language models (LLMs) to achieve higher intelligence, which requires the model to generalize rules from observed facts and then apply them to unseen examples. We present MIRAGE, a…

Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…

While large language models (LLMs) equipped with techniques like chain-of-thought prompting have demonstrated impressive capabilities, they still fall short in their ability to reason robustly in complex settings. However, evaluating LLM…

Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies…