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We present studies of the potential energy landscape of selected binary Lennard-Jones thirteen atom clusters. The effect of adding selected impurity atoms to a homogeneous cluster is explored. We analyze the energy landscapes of the studied…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High…
We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations…
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…
One of the most common problem-solving heuristics is by analogy. For a given problem, a solver can be viewed as a strategic walk on its fitness landscape. Thus if a solver works for one problem instance, we expect it will also be effective…
We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the…
Conventional jet algorithms are based on a deterministic view of the underlying hard scattering process. Each outgoing parton from the hard scattering is associated with a hard, well separated jet. This approach is very successful because…
We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (R. C. Heitmann, C.…
Energy landscape approaches have become increasingly popular for analysing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study the natural gradient method for learning in deep Bayesian networks, including neural networks. There are two natural geometries associated with such learning systems consisting of visible and hidden units. One geometry is related…
This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…
Two-dimensional architected materials are often realized as periodic grids of elastic beams. Conventional homogenization methods represent these structures as equivalent elastic solids but neglect shear deformation in the constituent beams.…
We characterize the generating function of bipartite planar maps counted according to the degree distribution of their black and white vertices. This result is applied to the solution of the hard particle and Ising models on random planar…
Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…
While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent works have shown that they suffer from lack of diversity or mode collapse. The theoretical work…
Deterministic complex networks that use iterative generation algorithms have been found to more closely mirror properties found in real world networks than the traditional uniform random graph models. In this paper we introduce a new,…
This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…