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Persistent neural activity associated with working memory (WM) lasts for a limited time duration. Current theories suggest that its termination is \textit{actively} obtained via inhibitory currents, and there is currently no theory…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
Forgetting is often seen as an unwanted characteristic in both human and machine learning. However, we propose that forgetting can in fact be favorable to learning. We introduce "forget-and-relearn" as a powerful paradigm for shaping the…
The $\mathbb{Z}_2$ lattice gauge model, as the simplest realization of a lattice gauge theory, exhibits rich and unconventional physics. One of its most remarkable features is disorder-free localization, where localization emerges not from…
Continual learning is considered a promising step towards next-generation Artificial Intelligence (AI), where deep neural networks (DNNs) make decisions by continuously learning a sequence of different tasks akin to human learning…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
A central challenge in continual learning is forgetting, the loss of performance on previously learned tasks induced by sequential adaptation to new ones. While forgetting has been extensively studied empirically, rigorous theoretical…
The acoustic cues used by humans and other animals to localise sounds are subtle, and change during and after development. This means that we need to constantly relearn or recalibrate the auditory spatial map throughout our lifetimes. This…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
Despite their success in image generation, diffusion models can memorize training data, raising serious privacy and copyright concerns. Although prior work has sought to characterize, detect, and mitigate memorization, the fundamental…
We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…
Humans learn adaptively and efficiently throughout their lives. However, incrementally learning tasks causes artificial neural networks to overwrite relevant information learned about older tasks, resulting in 'Catastrophic Forgetting'.…
Memory and forgetting constitute two sides of the same coin, and although the first has been rigorously investigated, the latter is often overlooked. A number of experiments under the realm of psychology and experimental neuroscience have…
What happens when a language model thinks without words? Standard reasoning LLMs verbalize intermediate steps as chain-of-thought; latent reasoning transformers (LRTs) instead perform deliberation entirely in continuous hidden space. We…
We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
Humans are skillful navigators: We aptly maneuver through new places, realize when we are back at a location we have seen before, and can even conceive of shortcuts that go through parts of our environments we have never visited. Current…
Continual learning algorithms strive to acquire new knowledge while preserving prior information. Often, these algorithms emphasise stability and restrict network updates upon learning new tasks. In many cases, such restrictions come at a…
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these…