arXiv research

Study shows how transformers classify symbols without naming them, proving a margin-versus-collision criterion.

Classifies generalized Seifert fiber spaces and their branched covers.

New algorithm improves interpretability in sequence classification.

The paper classifies symbols of differential operators on vector bundles.

Recurrent Neural Networks (RNN) are a type of statistical model designed to handle sequential data. The model reads a sequence one symbol at a time. Each symbol is processed based on information collected from the previous symbols. With existing RNN architectures, each symbol is processed using only information from th…

The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. The research focus has mostly been on improving the accuracy and efficiency of classifiers, while their interpretability has been somewhat neglected. Classifier interpretabil…

ECSEL learns signomial equations for explainable classification.

Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Dee…

Many real-world domains can be expressed as graphs and, more generally, as multi-relational knowledge graphs. Though reasoning and learning with knowledge graphs has traditionally been addressed by symbolic approaches, recent methods in (deep) representation learning has shown promising results for specialized tasks su…

Quantum $6j$-symbols linked to tetrahedra angles and volumes.

OccamNet finds interpretable symbolic fits to data efficiently.

New linear models improve time series classification efficiency and interpretability.

RED CoMETS improves multivariate time series classification accuracy.

In this paper, we consider the problem of event classification with multi-variate time series data consisting of heterogeneous (continuous and categorical) variables. The complex temporal dependencies between the variables combined with sparsity of the data makes the event classification problem particularly challengin…

Co-eye combines multiple symbolic representations to improve time series classification accuracy.

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An…

Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.

Enhances neural networks with logical knowledge for better performance.

This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.

Relational data mining is becoming ubiquitous in many fields of study. It offers insights into behaviour of complex, real-world systems which cannot be modeled directly using propositional learning. We propose Symbolic Graph Embedding (SGE), an algorithm aimed to learn symbolic node representations. Built on the ideas …

We study the varieties of invariant totally geodesic submanifolds of isometries of the spherical, Euclidean and hyperbolic spaces in each finite dimension. We show that the dimensions of the connected components of these varieties determine the orbit type (or the z-class) of the isometry. For this purpose, we introduce…

Fink AGN classifier achieves high accuracy in classifying active galactic nuclei.

One computes the cohomology of the projective embedding of sl(m+1,R) acting on the differential operators on densities on R^m of various weights. This cohomology is non vanishing only for some special critical values of the weights. This allows us first to explain some strange feature pointed out by Gargoubi in his cla…

VaSST uses soft symbolic trees for probabilistic symbolic regression.

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots code…

Random forests classify Pokemon names based on evolutionary status.

We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…

Paper closes neural-symbolic learning loop with grammar model and back-search algorithm.

Reinforcement learning and symbolic planning have both been used to build intelligent autonomous agents. Reinforcement learning relies on learning from interactions with real world, which often requires an unfeasibly large amount of experience. Symbolic planning relies on manually crafted symbolic knowledge, which may …

For an arbitrary Riemannian manifold $X$ and Hermitian vector bundles $E$ and $F$ over $X$ we define the notion of the normal symbol of a pseudodifferential operator $P$ from $E$ to $F$. The normal symbol of $P$ is a certain smooth function from the cotangent bundle $T^*X$ to the homomorphism bundle $Hom (E,F)$ and dep…

Based on the ideas of Optimal Control, we introduce the new basic characteristic of a bracket generating distribution, the Jacobi symbol. In contrast to the classical Tanaka symbol, the set of Jacobi symbols is discrete and classifiable. We give an explicit and unified algebraic procedure for the construction of the ca…

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…

A formula for Rademacher symbols in triangle groups is provided.

The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Ou…

Complex $b$-$6j$ symbols relate to hyperbolic tetrahedron volumes and determinants.

NeSS combines neural and symbolic approaches for better compositional generalization.

Defines transverse symbols for foliated manifolds and proves their K-homology class.

A new method for spotting symbols in CAD images reduces annotation costs and improves accuracy.

Paper proposes a bijective approach for signal/symbol translation using variational auto-encoders.

The Wodzicki residue and the cut-off integral extend to classical symbol-valued forms. We show that they obey a Stokes' type property and that the extended Wodzicki residue can be interpreted as a complex residue like the ordinary one. In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact forms) o…

We show some fundamental results concerning $3$-dimensional foliated dynamical systems (FDS$^3$ for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS$^3$, which yields a classification of FDS$^3$'s. Secondly, for each type of the classification, we construct concrete examples of FDS$^3$…

Bayesian symbolic regression automates model discovery from data.

Symbolic regression finds simple formulas for implied volatility.

S2KAN integrates symbolic primitives into neural network activations for improved interpretability.

Symbolic LSTM improves time series forecasting by reducing hyperparameter sensitivity.

Introduces canonical connections for sub-Riemannian manifolds with constant symbol.

Distributions of Monge type are a class of strongly regular bracket-generating distributions introduced by I. Anderson, Zh. Nie and P. Nurowski. Their symbol algebras prolong to simple graded Lie algebras, thus allowing one to associate a parabolic geometry to any given Monge distribution. This article is devoted to th…

Meta-learning symbolic default hyperparameters from dataset properties.