arXiv research

The paper proves recurrence relations for heat kernels on hyperbolic and spherical spaces.

Recurrent-DBN models dynamic relational data with interpretable latent structures.

Study provides explicit formula for complex 2D Kähler manifold quantization.

The aim of the present paper is to investigate new types of recurrence in Finsler geometry, namely, hyper-generalized recurrence and generalized conharmonic recurrence. The properties of such recurrences and their relations to other Finsler recurrences are studied.

Researchers create a star product on a Grassmannian with separation of variables.

Turning the skein relation for HOMFLY into a Fibonacci recurrence, we prove that there are only three rational specializations of HOMFLY polynomial: Alexander-Conway, Jones, and a new one. Using the recurrence relation, we find general and relative expansion formulae and rational generating functions for Alexander-Conw…

The study finds new infinite dilogarithm identities related to number sequences and continued fractions.

For a knot $K$ in $S^3$, the $sl_2$-colored Jones function $J_K(n)$ is a sequence of Laurent polynomials in the variable $t$, which is known to satisfy non-trivial linear recurrence relations. The operator corresponding to the minimal linear recurrence relation is called the recurrence polynomial of $K$. The AJ conject…

This paper presents a novel latent variable recurrent neural network architecture for jointly modeling sequences of words and (possibly latent) discourse relations between adjacent sentences. A recurrent neural network generates individual words, thus reaping the benefits of discriminatively-trained vector representati…

Using a simple recurrence relation we give a new method to compute Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for Jones polynomials. The method is used to estimate degree of Jones polynomials for some families of braids and to obtain general qualitative re…

A new GRNN tackles multi-relational data learning.

Interstellar searches for recurrent architecture to enhance KG embedding.

The Adomian decomposition method is shown to be equivalent to the Taylor series approach.

We derive formulas for HOMFLY polynomials of torus links using braid groups and linear recurrences.

The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The properties of these special Finsler spaces are studied and the relations betwee…

Bayesian approach improves neural network recurrence.

We study power expansions of the characteristic function of a linear operator $A$ in a $p|q$-dimensional superspace $V$. We show that traces of exterior powers of $A$ satisfy universal recurrence relations of period $q$. `Underlying' recurrence relations hold in the Grothendieck ring of representations of $\GL(V)$. The…

New recursive relation found for a specific torus knot.

Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged autocorrelation function, or disregarded the multi-scaling properties induced by potential…

Study shortest geodesics on flat cone spheres with conical singularities.

Study analyzes stock market dynamics using recurrence measures and transitions.

New differential geometry perspective on orthogonal RNNs.

Study of recurrent Lorentzian Weyl spaces with detailed local and global structures.

Recurrent models can produce infinite sequences, causing bias; new methods prevent this.

End-to-end training of recurrent neural networks for biological sequences.

Text documents are structured on multiple levels of detail: individual words are related by syntax, but larger units of text are related by discourse structure. Existing language models generally fail to account for discourse structure, but it is crucial if we are to have language models that reward coherence and gener…

Enhances graph neural networks with Relational Pooling for better graph classification.

Deep neural nets approximate random dynamical system trajectories uniformly in time.

Improved QA-RNN model with noun-tagging for better accuracy.

New weight systems derived from a specific Lie algebra for knot invariants.

Recently, a technique called Layer-wise Relevance Propagation (LRP) was shown to deliver insightful explanations in the form of input space relevances for understanding feed-forward neural network classification decisions. In the present work, we extend the usage of LRP to recurrent neural networks. We propose a specif…

Although neural machine translation with the encoder-decoder framework has achieved great success recently, it still suffers drawbacks of forgetting distant information, which is an inherent disadvantage of recurrent neural network structure, and disregarding relationship between source words during encoding step. Wher…

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their…

The simplest non-trivial solutions of WDVV equations are A_n and B_n-potentials, which describe metrics of K.Saito on spaces of versal deformation of A_n and B_n-singularities. These are some polynomials, which were known for $n\leqslant$ 4. We find some recurrence relations, which give a possibility to find all A_n an…

A new framework predicts stock movements using news sentiment and relational data.

QLSTM improves speech recognition by considering internal quaternion dependencies.

Unified RNN handles five feature types for better time series modeling.

The polynomial invariants $q_d$ for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the polynomials. As an application, one can read off a lower bound for the genera of embe…

R-SQAIR adds relational bias to sequential object attention models for better object interactions.

Study earthquake deformations on a once-punctured torus.

Paper uses RNNs for more accurate indoor WiFi localization.

New insights on stability in reservoir computing for better performance.

We review ideas on temporal dependences and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework…

New kernel-based models improve on traditional neural methods in sequence modeling.

The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the Baker-Campbell-Hausdorff series.

New analysis explains pathology of deep Gaussian processes.

We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural…

In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.