Related papers: Symmetries: From Proofs To Algorithms And Back
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
Symmetry is an important inductive bias that can improve model robustness and generalization across many deep learning domains. In multi-agent settings, a priori known symmetries have been shown to address a fundamental coordination failure…
We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…
Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in…
The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the…
Given values of a piecewise smooth function $f$ on a square grid within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. Standard approximation techniques achieve reduced approximation orders near the boundary of…
When the inverse of an algorithm is well-defined -- that is, when its output can be deterministically transformed into the input producing it -- we say that the algorithm is invertible. While one can describe an invertible algorithm using a…
Image inpainting consists of filling holes or missing parts of an image. Inpainting face images with symmetric characteristics is more challenging than inpainting a natural scene. None of the powerful existing models can fill out the…
We show that any sequence of measurements on a permutationally-symmetric (pure or mixed) multi-qubit string leaves the unmeasured qubit substring also permutationally-symmetric. In addition, we show that the measurement probabilities for an…
We present the concept of the \emph{information efficiency of functions} as a technique to understand the interaction between information and computation. Based on these results we identify a new class of objects that we call…
The online bipartite matching problem, extensively studied in the literature, deals with the allocation of online arriving vertices (items) to a predetermined set of offline vertices (agents). However, little attention has been given to the…
If $\sigma$ is a symmetric mean and $f$ is an operator monotone function on $[0, \infty)$, then $$f(2(A^{-1}+B^{-1})^{-1})\le f(A\sigma B)\le f((A+B)/2).$$ Conversely, Ando and Hiai showed that if $f$ is a function that satisfies either one…
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
For more than a century and a half it has been widely-believed (but was never rigorously shown) that the physics of diffraction imposes certain fundamental limits on the resolution of an optical system. However our understanding of what…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
The Fisher-Yates shuffle is a well-known algorithm for shuffling a finite sequence, such that every permutation is equally likely. Despite its simplicity, it is prone to implementation errors that can introduce bias into the generated…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
Here we present an algorithm to procedurally remap spectral contents of natural signals. The algorithm takes in two inputs: a signal whose spectral component needs to be remapped and a warping or remapping function. The algorithm generates…