Related papers: The Structure of In-Place Space-Bounded Computatio…
In this paper, we present a novel variation of the coded matrix multiplication problem which we refer to as fully private grouped matrix multiplication (FPGMM). In FPGMM, a master wants to compute a group of matrix products between two…
Let C be a closed subset of a topological space X, and let f : C --> X. Let us assume that f is continuous and f(x) lies in C for every x in the boundary of C. How many times can one iterate f? This paper provides estimates on the number of…
Data protection across organizations is limiting the application of centralized learning (CL) techniques. Federated learning (FL) enables multiple participants to build a learning model without sharing data. Nevertheless, there are very few…
For $0\le k\le n$, write $\binom nk=uv$ where the primes dividing $u$ are at most $k$ and the primes dividing $v$ exceed $k$, and let $f(n)$ be the least $k$ with $u>n^2$; Erd\H{o}s problem 684 asks for bounds on $f(n)$. We resolve the…
The aim of this paper is twofold. First, we study the number of partitions of a positive integer $m$ into at most $n$ parts in a given set $A$. We prove that such a number is bounded by the $n$-th Fibonacci number $F(n)$ for any $m$ and…
Let $D\in\mathbb{N}$, let $A>D+1$, and let $Q\geqslant3$. Consider the class of multiplicative functions $f:\mathbb{N}\to\mathbb{C}$ such that $|\sum_{n\leqslant x}f(n)|\le x(\log Q)^{A-D-1}/(\log x)^A$ for all $x\geqslant Q$, and such that…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
Research in robotic planning with temporal logic specifications, such as Linear Temporal Logic (LTL), has relied on single formulas. However, as task complexity increases, LTL formulas become lengthy, making them difficult to interpret and…
Federated learning (FL) is a distributed machine learning paradigm that enables multiple clients to collaboratively train a shared model without disclosing their local data. To address privacy issues of gradient, several privacy-preserving…
A factored Nonlinear Program (Factored-NLP) explicitly models the dependencies between a set of continuous variables and nonlinear constraints, providing an expressive formulation for relevant robotics problems such as manipulation planning…
We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…
With the explosive growth of data and wireless devices, federated learning (FL) over wireless medium has emerged as a promising technology for large-scale distributed intelligent systems. Yet, the urgent demand for ubiquitous intelligence…
A language is said to be in catalytic logspace if we can test membership using a deterministic logspace machine that has an additional read/write tape filled with arbitrary data whose contents have to be restored to their original value at…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Federated Learning (FL) is a distributed machine learning paradigm that addresses privacy concerns in machine learning and still guarantees high test accuracy. However, achieving the necessary accuracy by having all clients participate in…
Federated Learning (FL) is an upcoming technology that is increasingly applied in real-world applications. Early applications focused on cross-device scenarios, where many participants with limited resources train machine learning (ML)…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
Kolmogorov famously proved that multivariate continuous functions can be represented as a superposition of a small number of univariate continuous functions, $$ f(x_1,\dots,x_n) = \sum_{q=0}^{2n+1} \chi^q \left( \sum_{p=1}^n \psi^{pq}(x_p)…