Related papers: Set Shaping Theory and the Foundations of Redundan…
In developing locally testable codes, information is added to the coded message by creating redundancy in the codewords. In this article, we propose an alternative method in which redundancy is introduced on the message that must be…
Set Shaping Theory (SST) moves beyond the classical fixed-space model by constructing bijective mappings the original sequence set into structured regions of a larger sequence space. These shaped subsets are characterized by a reduced…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
The task of learning to map an input set onto a permuted sequence of its elements is challenging for neural networks. Set-to-sequence problems occur in natural language processing, computer vision and structure prediction, where…
The Transformer model has a tendency to overfit various aspects of the training data, such as the overall sequence length. We study elementary string edit functions using a defined set of error indicators to interpret the behaviour of the…
Sequence-to-sequence models have achieved impressive results on various tasks. However, they are unsuitable for tasks that require incremental predictions to be made as more data arrives or tasks that have long input sequences and output…
This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different…
Abstract: In this article, we will analyze in detail the coding limit of an individual sequence by introducing the latest developments brought by the Set Shaping Theory. This new theory made us realize that there is a huge difference…
Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…
Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The $\ell$-th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping…
In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with…
We revisit the problem of statistical sequence matching initiated by Unnikrishnan (TIT 2015) and derive theoretical performance guarantees for sequential tests that have bounded expected stopping times. Specifically, in this problem, one is…
Recurrent Neural Networks can be trained to produce sequences of tokens given some input, as exemplified by recent results in machine translation and image captioning. The current approach to training them consists of maximizing the…
In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…
Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…
Systematic compositionality is an essential mechanism in human language, allowing the recombination of known parts to create novel expressions. However, existing neural models have been shown to lack this basic ability in learning symbolic…