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We study a random walk model in which the jumping probability to a site is dependent on the number of previous visits to the site, as a model of the mobility with memory. To this end we introduce two parameters called the memory parameter…
Learning depends on the ability to acquire and assimilate new information. This ability depends---somewhat counterintuitively---on the ability to forget. In particular, effective forgetting requires the ability to recognize and utilize new…
In the human brain, internal states are often correlated over time (due to local recurrence and other intrinsic circuit properties), punctuated by abrupt transitions. At first glance, temporal smoothness of internal states presents a…
Catastrophic forgetting - the tendency of neural networks to forget previously learned data when learning new information - remains a central challenge in continual learning. In this work, we adopt a behavioral approach, observing a…
Resource constraints can fundamentally change both learning and decision-making. We explore how memory constraints influence an agent's performance when navigating unknown environments using standard reinforcement learning algorithms.…
Large language models (LLMs) suffer from forgetting of upstream knowledge when fine-tuned. Despite efforts on mitigating forgetting, few have investigated how forgotten upstream examples are dependent on newly learned tasks. Insights on…
In this paper, we introduce a variation of the elephant random walk whose steps are polynomially decaying. At each time $k$, the walker's step size is $k^{-\gamma}$ with $\gamma>0$. We investigate effects of the step size exponent $\gamma$…
We investigate the role of stochastic resetting in non-Markovian systems, where memory effects arise due to slow relaxation, rugged energy landscapes, disordered environments, and molecular crowding. Using the celebrated continuous-time…
Spaced repetition is among the most studied learning strategies in the cognitive science literature. It consists in temporally distributing exposure to an information so as to improve long-term memorization. Providing students with an…
Model-based next state prediction and state value prediction are slow to converge. To address these challenges, we do the following: i) Instead of a neural network, we do model-based planning using a parallel memory retrieval system (which…
Spaced repetition is a technique for efficient memorization which uses repeated, spaced review of content to improve long-term retention. Can we find the optimal reviewing schedule to maximize the benefits of spaced repetition? In this…
Lifelong learning capabilities are crucial for artificial autonomous agents operating on real-world data, which is typically non-stationary and temporally correlated. In this work, we demonstrate that dynamically grown networks outperform…
Deep reinforcement learning methods exhibit impressive performance on a range of tasks but still struggle on hard exploration tasks in large environments with sparse rewards. To address this, intrinsic rewards can be generated using forward…
Consider $N$ points randomly distributed along a line segment of unitary length. A walker explores this disordered medium moving according to a partially self-avoiding deterministic walk. The walker, with memory $\mu$, leaves from the…
Self-avoidance is a common mechanism to improve the efficiency of a random walker for covering a spatial domain. However, how this efficiency decreases when self-avoidance is impaired or limited by other processes has remained largely…
We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous…
Continual learning of partially similar tasks poses a challenge for artificial neural networks, as task similarity presents both an opportunity for knowledge transfer and a risk of interference and catastrophic forgetting. However, it…
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite…
We study the fate of a forager who searches for food performing a random walk on lattices. The forager consumes the available food on the site it visits and leaves it depleted but can survive up to $S$ steps without food. We introduce the…
The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of…