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Recent years have seen significant advancements in foundation models through generative pre-training, yet algorithmic innovation in this space has largely stagnated around autoregressive models for discrete signals and diffusion models for…

In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…

Mathematical and computational tools have proven to be reliable in decision-making processes. In recent times, in particular, machine learning-based methods are becoming increasingly popular as advanced support tools. When dealing with…

In recent years, pre-trained large language models (LLMs) have demonstrated remarkable efficiency in achieving an inference-time few-shot learning capability known as in-context learning. However, existing literature has highlighted the…

Programming a robot manipulator should be as intuitive as possible. To achieve that, the paradigm of teaching motion skills by providing few demonstrations has become widely popular in recent years. Probabilistic versions thereof take into…

Inference-time scaling (ITS) in latent reasoning models typically relies on heuristic perturbations, such as dropout or fixed Gaussian noise, to generate diverse candidate trajectories. However, we show that stronger perturbations do not…

Using Gaussian Mixture Model (GMM) and Expectation Maximization Algorithm, we perform an analysis of time duration ($T_{90}$) for \textit{CGRO}/BATSE, \textit{Swift}/BAT and \textit{Fermi}/GBM Gamma-Ray Bursts. The $T_{90}$ distributions of…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…

In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…

Large Language Models (LLMs) are increasingly being used to simulate human-like decision making in agent-based financial market models (ABMs). As models become more powerful and accessible, researchers can now incorporate individual LLM…

Generative models, particularly diffusion models, have achieved remarkable success in density estimation for multimodal data, drawing significant interest from the reinforcement learning (RL) community, especially in policy modeling in…

The dynamics of simple two-alternative forced-choice (2AFC) decisions are well-modeled by a class of random walk models (e.g. Laming, 1968; Ratcliff, 1978; Usher & McClelland, 2001; Bogacz et al., 2006). However, in real-life, even simple…

LLMs face significant challenges in systematic generalization, particularly when dealing with reasoning tasks requiring compositional rules and handling out-of-distribution examples. To address these challenges, we introduce an in-context…

The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random…

Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial…

Large language models (LLMs) are powerful tools that, in a number of settings, overlap with the results of human pattern recognition and reasoning. Retrieval-augmented generation (RAG) further allows LLMs to produce tailored output…

Cognitive biases often shape human decisions. While large language models (LLMs) have been shown to reproduce well-known biases, a more critical question is whether LLMs can predict biases at the individual level and emulate the dynamics of…

In this paper we study the kinetics of diffusion-limited, pseudo-first-order A + B -> B reactions in situations in which the particles' intrinsic reactivities vary randomly in time. That is, we suppose that the particles are bearing "gates"…

Piecewise Diffusion Markov Processes (PDifMPs) are valuable for modelling systems where continuous dynamics are interrupted by sudden shifts and/or changes in drift and diffusion. The first-passage time (FPT) in such models plays a central…