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Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
Learning high-performance control policies that remain consistent with expert behavior is a fundamental challenge in robotics. Reinforcement learning can discover high-performing strategies but often departs from desirable human behavior,…
There has been much recent interest in the necessity of an observer degree of freedom in the description of local algebras in semiclassical gravity. In this work, we describe an example where the observer can be constructed intrinsically…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
Exceptional points are special degeneracy points in parameter space that can arise in (effective) non-Hermitian Hamiltonians describing open quantum and wave systems. At an n-th order exceptional point, n eigenvalues and the corresponding…
The prevailing graph neural network models have achieved significant progress in graph representation learning. However, in this paper, we uncover an ever-overlooked phenomenon: the pre-trained graph representation learning model tested…
This paper investigates the necessary conditions of optimality for uni- formly overtaking optimal control on infinite horizon with free right endpoint. Clarke's form of the Pontryagin Maximum Principle is proved without the as- sumption on…
We describe an apparatus for subgradient-following of the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence needs…
Since their introduction by Kipf and Welling in $2017$, a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within a single observed graph and its feature matrix. Despite the…
Graph convolution is a fundamental building block for many deep neural networks on graph-structured data. In this paper, we introduce a simple, yet very effective graph convolutional network with skip connections for semi-supervised anomaly…
The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or…
We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and,…
Deviations from Fermi liquid behavior are well documented in the normal state of the cuprate superconductors, and some of these differences are possibly related to pre-formed pairs appearing at temperatures above T_c. In order to test these…
Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $\beta_2$ near…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
We present a method for learning unknown parametric constraints from locally-optimal input-output trajectory data. We assume the data is generated by rollouts of stochastic nonlinear dynamics, under a single state or output feedback law and…
A generalization of implicit conservative numerics to multiple dimensions requires advanced concepts of tensor analysis and differential geometry and hence a more thorough dedication to mathematical fundamentals than maybe expected at first…
Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's…
In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols,…
We compare higher order gravity models to observational constraints from magnitude-redshift supernova data, distance to the last scattering surface of the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed systematic…