Related papers: Extracting low-dimensional dynamics from multiple …
In unsupervised learning, dimensionality reduction is an important tool for data exploration and visualization. Because these aims are typically open-ended, it can be useful to frame the problem as looking for patterns that are enriched in…
A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
The success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…
We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…
Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
Networked dynamic systems are ubiquitous in various domains, such as industrial processes, social networks, and biological systems. These systems produce high-dimensional data that reflect the complex interactions among the network nodes…
We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…
Ecologists are interested in modeling the population growth of species in various ecosystems. Studying population dynamics can assist environmental managers in making better decisions for the environment. Traditionally, the sampling of…
Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to…
We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…
Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks…
Evaluating the causal impacts of possible interventions is crucial for informing decision-making, especially towards improving access to opportunity. However, if causal effects are heterogeneous and predictable from covariates, personalized…
In this study, we propose an innovative dynamic classification algorithm aimed at achieving zero missed detections and minimal false positives,acritical in safety-critical domains (e.g., medical diagnostics) where undetected cases risk…