Related papers: Complex Equiangular Tight Frames and Erasures
We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions, and that…
We use operators from generalized equiangular measurements to construct positive maps. Their positivity follows from the inequality for indices of coincidence corresponding to few equiangular tight frames. These maps give rise to…
Most objects in the visual world are partially occluded, but humans can recognize them without difficulty. However, it remains unknown whether object recognition models like convolutional neural networks (CNNs) can handle real-world…
Complex-valued neural networks are not a new concept, however, the use of real-valued models has often been favoured over complex-valued models due to difficulties in training and performance. When comparing real-valued versus…
The aim of this paper is twofold. First of all, we confirm a few basic criteria of the finiteness of real forms of a given smooth complex projective variety, in terms of the Galois cohomology set of the discrete part of the automorphism…
We discuss an extension of the almost Hadamard matrix formalism, to the case of complex matrices. Quite surprisingly, the situation here is very different from the one in the real case, and our conjectural conclusion is that there should be…
Full exploitation of emittance exchange (EEX) requires aberration-free performance of a complex imaging system including active radio-frequency (RF) elements which can add temporal distortions. We investigate the performance of an EEX line…
Recent work has found that adversarially-robust deep networks used for image classification are more interpretable: their feature attributions tend to be sharper, and are more concentrated on the objects associated with the image's…
This thesis is a study of large sets of unit vectors in $\cx^n$ such that the absolute value of their standard inner products takes on only a small number of values. We begin with bounds: what is the maximal size of a set of lines with only…
In this paper, we address the open question: "What do adversarially robust models look at?" Recently, it has been reported in many works that there exists the trade-off between standard accuracy and adversarial robustness. According to…
We study Fourier frames of exponentials on fractal measures associated with a class of affine iterated function systems. We prove that, under a mild technical condition, the Beurling dimension of a Fourier frame coincides with the Hausdorff…
Deep learning models are intrinsically sensitive to distribution shifts in the input data. In particular, small, barely perceivable perturbations to the input data can force models to make wrong predictions with high confidence. An common…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…
All varieties, extremal contractions, singularities are divided on exceptional and non-exceptional ones. Roughly speaking, there are the infinite families of non-exceptional varieties, extremal contractions or singularities and only the…
Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional…
We present a generic condition for Lorentzian manifolds to have a barrier that limits the reach of boundary-anchored extremal surfaces of arbitrary dimension. We show that any surface with nonpositive extrinsic curvature is a barrier, in…
We present new numerical results on the space of local, unitary, parity-preserving conformal field theories (CFTs) in three dimensions from the stress tensor bootstrap. In bounds maximizing certain OPE coefficients, we find a plethora of…
We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${\mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element…
We discuss the possible relevance of complex codimension-two extremal surfaces to the the Ryu-Takayanagi holographic entanglement proposal and its covariant Hubeny-Rangamani-Takayanagi (HRT) generalization. Such surfaces live in a…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…