Related papers: Pebble minimization: the last theorems
Given a configuration of pebbles on the vertices of a connected graph $G$, a \emph{pebbling move} removes two pebbles from some vertex and places one pebble on an adjacent vertex. The \emph{pebbling number} of a graph $G$ is the smallest…
We study an extension of the well-known red-blue pebble game (RBP) with partial computation steps, inspired by the recent work of Sobczyk. While the original RBP assumes that we need to have all the inputs of an operation in fast memory at…
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…
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…
We study bounded deviation of non-deterministic finite transducers under the Hamming distance: the bounded comparison problem asks, given two transducers and $k \in \mathbb{N}$, whether for every input the two transducers produce words at…
Transformers in their common form are inherently limited to operate on whole token sequences rather than on one token at a time. Consequently, their use during online inference on time-series data entails considerable redundancy due to the…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…
Trace reconstruction considers the task of recovering an unknown string $x \in \{0,1\}^n$ given a number of independent "traces", i.e., subsequences of $x$ obtained by randomly and independently deleting every symbol of $x$ with some…
The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed…
Neural networks have in recent years shown promise for helping software engineers write programs and even formally verify them. While semantic information plays a crucial part in these processes, it remains unclear to what degree popular…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
In contrast to RNNs, which compress their history into a single hidden state, Transformers can attend to all past tokens directly. However, standard Transformers rely solely on the hidden state from the previous layer to represent the…
An up-down chain is a Markov chain in which each transition is a two-step process that moves up to a larger object and then back down to an object of the original size. The first goal of this paper is to present a general framework for…
In recent years it has become popular to study dynamic problems in a sensitivity setting: Instead of allowing for an arbitrary sequence of updates, the sensitivity model only allows to apply batch updates of small size to the original input…
We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…