Related papers: The memory centre
We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…
The source-coding problem with side information at the decoder is studied subject to a constraint that the encoder---to whom the side information is unavailable---be able to compute the decoder's reconstruction sequence to within some…
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a…
A lower time bound $\Omega(\min(\nu(x), n-\nu(x))$ for counting the number of ones in a binary input word $x$ of length $n$ is presented, where $\nu(x)$ is the number of ones. The operations available are increment, decrement, bit-wise…
A binary code Enc$:\{0,1\}^k \to \{0,1\}^n$ is $(0.5-\epsilon,L)$-list decodable if for all $w \in \{0,1\}^n$, the set List$(w)$ of all messages $m \in \{0,1\}^k$ such that the relative Hamming distance between Enc$(m)$ and $w$ is at most…
We study the complexity of estimating the partition function $\mathsf{Z}(\beta)=\sum_{x\in\chi} e^{-\beta H(x)}$ for a Gibbs distribution characterized by the Hamiltonian $H(x)$. We provide a simple and natural lower bound for quantum…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
An agent who lacks preferences and instead makes decisions using criteria that are costly to create should select efficient sets of criteria, where the cost of making a given number of choice distinctions is minimized. Under mild…
Non-deterministic random bits are needed in many scientific fields. Unfortunately today's computers are very limited in ability to produce them. We present here a method for extraction of non-deterministic random bits from random physics…
We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…
An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal…
An algorithm is presented for error correction in the surface code quantum memory. This is shown to correct depolarizing noise up to a threshold error rate of 18.5%, exceeding previous results and coming close to the upper bound of 18.9%.…
In this work we introduce malware detection from raw byte sequences as a fruitful research area to the larger machine learning community. Building a neural network for such a problem presents a number of interesting challenges that have not…
A classic result in algorithmic information theory is that every infinite binary sequence is computable from a Martin-Loef random infinite binary sequence. Proved independently by Kucera and Gacs, this result answered a question by Charles…
In this paper, we derive an expression for the expected number of runs in a trace of a binary sequence $x \in \{0,1\}^n$ obtained by passing $x$ through a deletion channel that independently deletes each bit with probability $q$. We use…
We consider the problem of encoding a set of vectors into a minimal number of bits while preserving information on their Euclidean geometry. We show that this task can be accomplished by applying a Johnson-Lindenstrauss embedding and…
Recovering high-level type information in binaries is a key task in reverse engineering and binary analysis. Binaries contain very little explicit type information. The structure of binary code is incredibly flexible allowing for ad-hoc…
In this work we consider a generalization of the well-studied problem of coding for ``stuck-at'' errors, which we refer to as ``strong stuck-at'' codes. In the traditional framework of stuck-at codes, the task involves encoding a message…
High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for…