Related papers: On Redundant Topological Constraints
We study the base distribution in chart-based generative models on Riemannian manifolds. Standard methods sample in Euclidean tangent space and then map the sample to the manifold with a chart. This is convenient, but it changes the meaning…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
The ResNet architecture has been widely adopted in deep learning due to its significant boost to performance through the use of simple skip connections, yet the underlying mechanisms leading to its success remain largely unknown. In this…
We study grammar-constrained decoding (GCD) as a coupling between an autoregressive next-token distribution and a reachability oracle over a pushdown system compiled from a context-free grammar (CFG). We prove an oracle invariance theorem:…
We focus on the commonly used synchronous Gradient Descent paradigm for large-scale distributed learning, for which there has been a growing interest to develop efficient and robust gradient aggregation strategies that overcome two key…
Recursive Conditioning (RC) was introduced recently as the first any-space algorithm for inference in Bayesian networks which can trade time for space by varying the size of its cache at the increment needed to store a floating point…
We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
A Qualitative Constraint Network (QCN) is a constraint graph for representing problems under qualitative temporal and spatial relations, among others. More formally, a QCN includes a set of entities, and a list of qualitative constraints…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
Recurrent neural network (RNN)'s architecture is a key factor influencing its performance. We propose algorithms to optimize hidden sizes under running time constraint. We convert the discrete optimization into a subset selection problem.…
This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its…
We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating…
A general Continuum Approximation (CA) model is proposed for optimizing transit network designs (TND) in grid cities under spatially heterogeneous demand. While conventional studies often assume rigid geometric line configurations (e.g.,…
A method for estimating theoretical predictability of time series is presented, based on information-theoretic functionals---redundancies and surrogate data technique. The redundancy, designed for a chosen model and a prediction horizon,…
This paper considers a resilient high-dimensional constrained consensus problem and studies a resilient distributed algorithm for complete graphs. For convex constrained sets with a singleton intersection, a sufficient condition on…
Let $G$ be a real algebraic group defined over $\mathbb{Q}$, $\Gamma$ be an arithmetic subgroup of $G$, and $T$ be a maximal $\mathbb{R}$-split torus. A trajectory in $G/\Gamma$ is divergent if eventually it leaves every compact subset. In…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…