Related papers: Lost in Self-stabilization
A theory of self-propelled particles is developed in two dimensions assuming that the particles can be deformed from a circular shape when the propagating velocity is increased. A coupled set of equations in terms of the velocity and a…
The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…
We consider a mixed formulation of parametrized elasticity problems in terms of stress, displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce conservation of linear and angular momentum. Due to the…
The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…
This article studies routes to chaos occurring within a resonance wedge for a 3-parametric family of differential equations acting on a 3-sphere. Our starting point is an autonomous vector field whose flow exhibits a weakly attracting…
Relating formal grammars is a hard problem that balances between language equivalence (which is known to be undecidable) and grammar identity (which is trivial). In this paper, we investigate several milestones between those two extremes…
While language progresses through a sequence of semantic states, the underlying dynamics of this progression remain elusive. Here, we treat the semantic progression of written text as a stochastic trajectory in a high-dimensional state…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
Robots that can manipulate objects in unstructured environments and collaborate with humans can benefit immensely by understanding natural language. We propose a pipelined architecture of two stages to perform spatial reasoning on the text…
Math word problems (MWPs) is a task that automatically derives solution expression from a giving math problems in text. The previous studies suffer from spurious correlations between input text and output expression. To mitigate this issue,…
Consider an agent acting to achieve its temporal goal, but with a "trembling hand". In this case, the agent may mistakenly instruct, with a certain (typically small) probability, actions that are not intended due to faults or imprecision in…
We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…
Automatic spelling and grammatical correction systems are one of the most widely used tools within natural language applications. In this thesis, we assume the task of error correction as a type of monolingual machine translation where the…
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group…
It has recently been argued that AI models' representations are becoming aligned as their scale and performance increase. Empirical analyses have been designed to support this idea and conjecture the possible alignment of different…
Various natural language processing tasks are structured prediction problems where outputs are constructed with multiple interdependent decisions. Past work has shown that domain knowledge, framed as constraints over the output space, can…
We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the…
An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it…
We propose a communicationally and computationally efficient algorithm for high-dimensional distributed sparse learning. At each iteration, local machines compute the gradient on local data and the master machine solves one shifted $l_1$…
The cornerstone of multilingual neural translation is shared representations across languages. Given the theoretically infinite representation power of neural networks, semantically identical sentences are likely represented differently.…