Related papers: Sparsity in the numerical six-point bootstrap
We study a new class of codes for Gaussian multi-terminal source and channel coding. These codes are designed using the statistical framework of high-dimensional linear regression and are called Sparse Superposition or Sparse Regression…
This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fractional objective function can be replaced by a parametric family…
We show that conformal blocks simplify greatly when there is a large difference between two of the scaling dimensions for external operators. In particular the spacetime dimension only appears in an overall constant which we determine via…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
Foundational optimization embeddings have recently emerged as powerful pre-trained representations for mixed-integer programming (MIP) problems. These embeddings were shown to enable cross-domain transfer and reduce reliance on…
Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Interpolation of sparse pixel information towards a dense target resolution finds its application across multiple disciplines in computer vision. State-of-the-art interpolation of motion fields applies model-based interpolation that makes…
Many neuroimaging studies focus on the cortex, in order to benefit from better signal to noise ratios and reduced computational burden. Cortical data are usually projected onto a reference mesh, where subsequent analyses are carried out.…
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
In semidefinite programming (SDP), a number of pre-processing techniques have been developed including chordal-completion procedures, which reduce the dimension of individual constraints by exploiting sparsity therein, and facial reduction,…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown non-trivial conformal field theories (CFTs). Here we investigate the extent to which…
We study numerically the 6D (2,0) superconformal bootstrap using the soft-Actor-Critic (SAC) algorithm as a stochastic optimizer. We focus on the four-point functions of scalar superconformal primaries in the energy-momentum multiplet.…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…