arXiv research

A novel transformer model improves classification of partially ordered sequences.

New algorithm minimizes expert selection regret in partial bandit feedback.

Bayesian method detects Markov order in network paths more reliably.

Partial AHS-structures extend G-structures and Cartan geometries to manifolds with involutive distributions.

We present the Insertion Transformer, an iterative, partially autoregressive model for sequence generation based on insertion operations. Unlike typical autoregressive models which rely on a fixed, often left-to-right ordering of the output, our approach accommodates arbitrary orderings by allowing for tokens to be ins…

New statistical models for predicting ranked preferences from partial orders.

We present a recurrent neural network memory that uses sparse coding to create a combinatoric encoding of sequential inputs. Using several examples, we show that the network can associate distant causes and effects in a discrete stochastic process, predict partially-observable higher-order sequences, and enable a DQN a…

Method preserves order in hierarchical clustering of ordered data.

Time series models generalize ARMA and ARFIMA with non-Gaussian dependence.

We provide necessary and sufficient conditions on the derived type of a vector field distribution $\Cal V$ in order that it be locally equivalent to a partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from $\Bbb R$ to $\Bbb R^q$, $q\geq 1$. This result fully genera…

The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc. In this paper we give new and much simpler proofs for the whole theory using Fock…

Conditions for curves on a torus with specific pairwise intersections.

New non-Kähler manifolds constructed with specific properties.

In sequence learning tasks such as language modelling, Recurrent Neural Networks must learn relationships between input features separated by time. State of the art models such as LSTM and Transformer are trained by backpropagation of losses into prior hidden states and inputs held in memory. This allows gradients to f…

Let $\CV$ be a vector field distribution on manifold $M$. We give an efficient algorithm for the construction of local coordinates on $M$ such that $\CV$ may be locally expressed as some partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from $\Bbb R$ to $\Bbb R^q$,…

Ribbon cobordism forms a partial order in 3-manifolds.

The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation…

Ribbon cobordisms form a partial order on 3-manifolds.

Predicts node sequences in graphs using multi-order network models.

Constructs Serre spectral sequence for bounded cohomology.

Generalizes results for Riemannian manifolds with boundary to those without.

The paper solves complex swing option pricing equations with numerical methods.

Generative model simulates financial market price variations from order flow.

Prove strong ribbon concordance induces a partial order on links, certify minimality for a handful of knots, and find minimal ribbon minimal knots.

Rational homology ribbon cobordism defines a partial order on 3-manifolds.

Differentiable relaxation for inferring partial orders from noisy linear data.

Study of split Nakamura manifolds and their automorphisms.

We propose a Hodge theory for the spaces $E_2^{p,\,q}$ featuring at the second step either in the Frölicher spectral sequence of an arbitrary compact complex manifold $X$ or in the spectral sequence associated with a pair $(N,\,F)$ of complementary regular holomorphic foliations on such a manifold. The main idea is to …

Calculates knot $X$-torsion order using spectral sequences.

A convolutional sequence to sequence non-intrusive load monitoring model is proposed in this paper. Gated linear unit convolutional layers are used to extract information from the sequences of aggregate electricity consumption. Residual blocks are also introduced to refine the output of the neural network. The partiall…

Partial coverings of hyperbolic surfaces equidistribute with geodesics.

The paper uses belief propagation to analyze rankings and partial orders from partial information.

We discuss intrinsic aspects of Krupka's approach to finite-order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite-order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite-order (short exact) variational sequence which i…

Paper proposes methods to learn DAGs from partial orderings.

This paper proposes a new estimation algorithm for the parameters of an HMM as to best account for the observed data. In this model, in addition to the observation sequence, we have \emph{partial} and \emph{noisy} access to the hidden state sequence as side information. This access can be seen as "partial labeling" of …

Algorithm improves reinforcement learning in MDPs with partial order policies.

In this paper, we introduce a partial order on neighborhood equivalence classes of maximally spread essential multibranched surfaces embedded in a 3-manifold. We show that if a maximally spread essential multibranched surface is atoroidal and acylindrical, then its equivalence class is minimal with respect to the parti…

It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear …

The paper proves a logarithmic partial derivative lemma and applies it to several geometric problems.

Hierarchical Partial-Order Models for Ranking

Study optimal liquidation strategies under partial information in high-frequency trading.

A method for finding most influential sets reduces a complex problem to a sequence of simpler top-$k$ problems.

We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We…

Čech cohomology $H^n(X)$ of a separable metrizable space $X$ is defined in terms of cohomology of its nerves (or ANR neighborhoods) $P_β$ whereas Steenrod-Sitnikov homology $H_n(X)$ is defined in terms of homology of compact subsets $K_α\subset X$. We show that one can also go vice versa: in a sense, $H^n(X)$ can be re…

Let $S$ be a rank-one symmetric space of non-compact type and let $X$ be a $\text{CAT}(-1)$ space. A well-known result by Bourdon states that if a topological embedding $\varphi: \partial_\infty S \rightarrow \partial_\infty X$ respects cross ratios, that means $\text{cr}_S( ξ_0,η_0,ξ_1,η_1)=\text{cr}_X( \varphi(ξ_0),\…

In this thesis, we show the existence of a sequence of differential operators starting with with the Dirac operator in k Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\sum_j e_j\cdot \partial_{ij}: C^\infty((\R^n)^k,§)\to C^\infty((\R^n)^k,§)$ ($§$ is the spinor module). This operator is the Cauchy-Riemann operato…

Graphical estimation of count time series dependencies.