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The long-term memory of most connectionist systems lies entirely in the weights of the system. Since the number of weights is typically fixed, this bounds the total amount of knowledge that can be learned and stored. Though this is not…
The memory and rejuvenation aspects of intermittent heat transport are explored theoretically and by numerical simulation for Ising spin glasses with short-ranged interactions. The theoretical part develops a picture of non-equilibrium…
We investigate long and short memory in $\alpha$-stable moving averages and max-stable processes with $\alpha$-Fr\'echet marginal distributions. As these processes are heavy-tailed, we rely on the notion of long range dependence suggested…
Neuronal networks provide living organisms with the ability to process information. They are also characterized by abundant recurrent connections, which give rise to strong feedback that dictates their dynamics and endows them with fading…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
Neural Turing Machines (NTM) contain memory component that simulates "working memory" in the brain to store and retrieve information to ease simple algorithms learning. So far, only linearly organized memory is proposed, and during…
This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…
Inspired by the cognitive science theory of the explicit human memory systems, we have modeled an agent with short-term, episodic, and semantic memory systems, each of which is modeled with a knowledge graph. To evaluate this system and…
The persistence exponent, which characterises the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large…
A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of {\em…
It is not uncommon in analysis that existence of extremal objects is obtained via an iterative procedure: we start from a given admissible object, then modify it, then modify again etc... If being extremal means maximimizing a real valued…
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…
Extremal Optimization, a recently introduced meta-heuristic for hard optimization problems, is analyzed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin…
Large reasoning models (LRMs) achieve strong accuracy through test-time scaling, generating longer chains of thought or sampling multiple solutions, but at steep costs in tokens and latency. We argue that memory is a core ingredient for…
Language Models (LMs) are important components in several Natural Language Processing systems. Recurrent Neural Network LMs composed of LSTM units, especially those augmented with an external memory, have achieved state-of-the-art results.…
We consider the dynamic range minimum problem on the ultra-wide word RAM model of computation. This model extends the classic $w$-bit word RAM model with special ultrawords of length $w^2$ bits that support standard arithmetic and boolean…
The behavior of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for…
The ability to learn in dynamic, nonstationary environments without forgetting previous knowledge, also known as Continual Learning (CL), is a key enabler for scalable and trustworthy deployments of adaptive solutions. While the importance…