Related papers: Discrete Signal Processing with Set Functions
Feature Transformation (FT) crafts new features from original ones via mathematical operations to enhance dataset expressiveness for downstream models. However, existing FT methods exhibit critical limitations: discrete search struggles…
Since the evolution of digital computers, the storage of data has always been in terms of discrete bits that can store values of either 1 or 0. Hence, all computer programs (such as MATLAB), convert any input continuous signal into a…
Modulations are a critical part of sound design and music production, enabling the creation of complex and evolving audio. Modern synthesizers provide envelopes, low frequency oscillators (LFOs), and more parameter automation tools that…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
Whenever we have a group acting on a class of functions by translation, the bispectrum offers a principled and lossless way of representing such functions invariant to the action. Unfortunately, computing the bispectrum is often costly and…
Uncertain information is commonplace in real-world data management scenarios. The ability to represent large sets of possible instances (worlds) while supporting efficient storage and processing is an important challenge in this context.…
In this work, we present Point Transformer, a deep neural network that operates directly on unordered and unstructured point sets. We design Point Transformer to extract local and global features and relate both representations by…
Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…
Distributed Stream Processing (DSP) systems enable processing large streams of continuous data to produce results in near to real time. They are an essential part of many data-intensive applications and analytics platforms. The rate at…
We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built…
Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set,…
Many modern datasets are large and carry complex structural relationships. Graph-based methods have traditionally been used to represent networked data, modeling individual elements as nodes and pairwise interactions as edges. Furthermore,…
Determinantal point processes (DPPs) are well known models for diverse subset selection problems, including recommendation tasks, document summarization and image search. In this paper, we discuss a greedy deterministic adaptation of k-DPP.…
We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given…
Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…
In this article, we define the Set Shaping Theory whose goal is the study of the bijection functions that transform a set of strings into a set of equal size made up of strings of greater length. The functions that meet this condition are…
Scene change detection (SCD), a crucial perception task, identifies changes by comparing scenes captured at different times. SCD is challenging due to noisy changes in illumination, seasonal variations, and perspective differences across a…
Perceptual sound matching (PSM) aims to find the input parameters to a synthesizer so as to best imitate an audio target. Deep learning for PSM optimizes a neural network to analyze and reconstruct prerecorded samples. In this context, our…
Machine learning (ML) models frequently experience performance degradation when deployed in new contexts. Such degradation is rarely uniform: some subgroups may suffer large performance decay while others may not. Understanding where and…
We propose a versatile deep image compression network based on Spatial Feature Transform (SFT arXiv:1804.02815), which takes a source image and a corresponding quality map as inputs and produce a compressed image with variable rates. Our…