arXiv subjects

Amit Boyarski

Publications and source records attributed to Amit Boyarski.

5 recordsLinked to original sources

arXiv2022

Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings

Graph isomorphism testing is usually approached via the comparison of graph invariants. Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the Weisfeiler-Leman (WL) test) and spectral invariants. While the exact power of the latter is still an open question, the former is regularly criticized for its limited power, when a standard configuration of uniform pre-coloring is used. This drawback hinders the applicability of Message Passing Graph Neural Networks (MPGNNs), whose expressive power is upper bounded by the WL test. Relaxing the assumption of uniform pre-coloring, we show that one can increase the expressive power of the WL test ad infinitum. Following that, we propose an efficient pre-coloring based on spectral features that provably increase the expressive power of the vanilla WL test. The above claims are accompanied by extensive synthetic and real data experiments. The code to reproduce our experiments is available at https://github.com/TPFI22/Spectral-and-Combinatorial

cs.LG↗

arXiv2021

Spectral Geometric Matrix Completion

Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix. In this work we interpret the DMF model through the lens of spectral geometry. This allows us to incorporate explicit regularization without breaking the DMF structure, thus enjoying the best of both worlds. In particular, we focus on matrix completion problems with underlying geometric or topological relations between the rows and/or columns. Such relations are prevalent in matrix completion problems that arise in many applications, such as recommender systems and drug-target interaction. Our contributions enable DMF models to exploit these relations, and make them competitive on real benchmarks, while exhibiting one of the first successful applications of deep linear networks.

cs.LG↗

arXiv2017

Efficient Deformable Shape Correspondence via Kernel Matching

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We provide preliminary theoretical analysis and several interpretations of the method.

cs.CV↗

arXiv2017

Subspace Least Squares Multidimensional Scaling

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a \textit{shape from metric} algorithm, consisting of finding a configuration of points in the Euclidean space that realize, as isometrically as possible, some given distance structure. In the present work we cast the least squares variant of MDS (LS-MDS) in the spectral domain. This uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings.

cs.CG↗

arXiv2017

Inspiring Computer Vision System Solutions

The "digital Michelangelo project" was a seminal computer vision project in the early 2000's that pushed the capabilities of acquisition systems and involved multiple people from diverse fields, many of whom are now leaders in industry and academia. Reviewing this project with modern eyes provides us with the opportunity to reflect on several issues, relevant now as then to the field of computer vision and research in general, that go beyond the technical aspects of the work. This article was written in the context of a reading group competition at the week-long International Computer Vision Summer School 2017 (ICVSS) on Sicily, Italy. To deepen the participants understanding of computer vision and to foster a sense of community, various reading groups were tasked to highlight important lessons which may be learned from provided literature, going beyond the contents of the paper. This report is the winning entry of this guided discourse (Fig. 1). The authors closely examined the origins, fruits and most importantly lessons about research in general which may be distilled from the "digital Michelangelo project". Discussions leading to this report were held within the group as well as with Hao Li, the group mentor.

cs.CV↗