Related papers: Quantifying the attractor landscape and transition…

The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…

Target search by active agents in rugged energy landscapes has remained a challenge because standard enhanced sampling methods do not apply to irreversible dynamics. We overcome this non-equilibrium rare-event problem by developing an…

In agricultural landscapes, the composition and spatial configuration of cultivated and semi-natural elements strongly impact species dynamics, their interactions and habitat connectivity. To allow for landscape structural analysis and…

In many real-world scenarios, an autonomous agent often encounters various tasks within a single complex environment. We propose to build a graph abstraction over the environment structure to accelerate the learning of these tasks. Here,…

Reservoir computing provides a time and cost-efficient alternative to traditional learning methods.Critical regimes, known as the "edge of chaos," have been found to optimize computational performance in binary neural networks. However,…

The repertoire of neural activity patterns that a cortical network can produce constrains the network's ability to transfer and process information. Here, we measured activity patterns obtained from multi-site local field potential (LFP)…

Understanding emotional processing in the human brain requires examining the complex interactions between different brain regions. While previous studies have identified specific regions involved in emotion processing, a holistic network…

Robots are still poor at traversing cluttered large obstacles required for important applications like search and rescue. By contrast, animals are excellent at doing so, often using direct physical interaction with obstacles rather than…

The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative…

In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize…

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research…

The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems. In the analysis of rare events in stochastic dynamics, it plays a central role in characterizing the statistics of transition…

Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them have been variously…

The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation,…

The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…

Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…

Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…

Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine…

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant…