相关论文: Mapping Equivalence for Symbolic Sequences: Theory…
In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error…
We introduce a general method for the study of memory in symbolic sequences based on higher-order Markov analysis. The Markov process that best represents a sequence is expressed as a mixture of matrices of minimal orders, enabling the…
Motivation: Most existing methods for DNA sequence analysis rely on accurate sequences or genotypes. However, in applications of the next-generation sequencing (NGS), accurate genotypes may not be easily obtained (e.g. multi-sample…
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…
We introduce the concept of a \textbf{neuro-symbolic pair} -- neural and symbolic approaches that are linked through a common knowledge representation. Next, we present \textbf{taxonomic networks}, a type of discrimination network in which…
We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For…
Reconstructing low-dimensional truth labels from high-dimensional experimental data is a central challenge in any scenario that relies on robust mappings across this so-called domain gap, from multi-particle final states in high-energy…
Much of the on-going statistical analysis of DNA sequences is focused on the estimation of characteristics of coding and non-coding regions that would possibly allow discrimination of these regions. In the current approach, we concentrate…
This paper introduces a new similarity measure, the covering similarity, that we formally define for evaluating the similarity between a symbolic sequence and a set of symbolic sequences. A pair-wise similarity can also be directly derived…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
The human ability to flexibly reason using analogies with domain-general content depends on mechanisms for identifying relations between concepts, and for mapping concepts and their relations across analogs. Building on a recent model of…
Neuro-symbolic artificial intelligence is a novel area of AI research which seeks to combine traditional rules-based AI approaches with modern deep learning techniques. Neuro-symbolic models have already demonstrated the capability to…
Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. A particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. An…
How we choose to represent our data has a fundamental impact on our ability to subsequently extract information from them. Machine learning promises to automatically determine efficient representations from large unstructured datasets, such…
Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…
The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable…
Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…