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Due to their capacity to generate novel and high-quality samples, diffusion models have attracted significant research interest in recent years. Notably, the typical training objective of diffusion models, i.e., denoising score matching,…
Memorization in language models is widely studied but remains difficult to isolate and control. Understanding when and what models memorize is essential for explaining their predictions, yet existing approaches are post-hoc: they can detect…
Memory is often defined as the mental capacity of retaining information about facts, events, procedures and more generally about any type of previous experience. Memories are remembered as long as they influence our thoughts, feelings, and…
In this paper the modification of the method conventionally used for the modeling of the massive fermions production and decays is proposed. The step by step algorithm is presented. Under the strict conditions the proposed method of…
The paper describes the application of some numerical techniques to analyze and to characterize the observed dynamical behaviour of fluidized bed systems. The preliminary results showed clearly that the dynamics of the considered process…
We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, the dynamics is governed by equations that usually describe food search of…
An external description for aperiodically sampled MIMO linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use of…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
To produce accurate predictions, language models (LMs) must balance between generalization and memorization. Yet, little is known about the mechanism by which transformer LMs employ their memorization capacity. When does a model decide to…
Motivated by recent experimental studies, we derive and analyze a twodimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a model of an active poroelastic two-phase…
As Large Language Models (LLMs) become widely adopted, understanding how they learn from, and memorize, training data becomes crucial. Memorization in LLMs is widely assumed to only occur as a result of sequences being repeated in the…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
Procedural planning, which entails decomposing a high-level goal into a sequence of temporally ordered steps, is an important yet intricate task for machines. It involves integrating common-sense knowledge to reason about complex and often…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
Three abilities - the ability to recognize sounds, the ability to visually recognize movement and the ability to keep an upright standing position - can function only with using precise measurements of the short time intervals. Other…
We explore a simplified class of models we call swarms, which are inspired by the collective behavior of social insects. We perform a mean-field stability analysis and perform numerical simulations of the model. Several interesting types of…
We propose a minimal yet intriguing model for a relationship between two individuals. The feeling of an individual is modeled by a complex variable and hence has two degrees of freedom. The effect of memory of other individual's behavior in…
Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details.…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been…