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Prior work on perceptual effectiveness has decomposed visualizations into smaller common units (e.g., channels such as angle, position, and length) to establish rankings. While useful, these decompositions lack the computational structure…
Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence…
In this article, we consider the decoding problem of affine Grassmann codes over nonbinary fields. We use matrices of different ranks to construct a large set consisting of parity checks of affine Grassmann codes, which are orthogonal with…
Question answering models struggle to generalize to novel compositions of training patterns, such to longer sequences or more complex test structures. Current end-to-end models learn a flat input embedding which can lose input syntax…
Whereas chord transcription has received considerable attention during the past couple of decades, far less work has been devoted to transcribing and encoding the rhythmic patterns that occur in a song. The topic is especially relevant for…
A methodology based upon recurrence quantification analysis is proposed for the study of orthographic structure of written texts. Five different orthographic data sets (20th century Italian poems, 20th century American poems, contemporary…
Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty…
In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting…
Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for both unique string…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
Simple continued fractions, base-b expansions, Dedekind cuts and Cauchy sequences are common notations for number systems. In this note, first, it is proven that both simple continued fractions and base-b expansions fail to denote real…
It has been a long standing problem to find good symbolic codings for translations on the $d$-dimensional torus that enjoy the beautiful properties of Sturmian sequences like low factor complexity and good local discrepancy properties.…
The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…
How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis…
We present a hierarchical neuro-symbolic control framework that tightly couples a classical symbolic planner with a transformer-based policy to address long-horizon decision-making under uncertainty. At the high level, the planner assembles…
Spoken language understanding (SLU) systems can be trained on two types of labelled data: aligned or unaligned. Unaligned data do not require word by word annotation and is easier to be obtained. In the paper, we focus on spoken language…
We consider a symbolic coding of linear trajectories in the regular octagon with opposite sides identified (and more generally in regular 2n-gons). Each infinite trajectory gives a cutting sequence corresponding to the sequence of sides…
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…
Systems which incrementally create 3D semantic maps from image sequences must store and update representations of both geometry and semantic entities. However, while there has been much work on the correct formulation for geometrical…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…