arXiv research

Study finds methods to learn multiple solutions from single task in offline RL.

Proves $C^{1,1}$ regularity for multiple membrane solutions.

Study finds multiple solutions for Gross-Pitaevskii equations on curved spaces.

We show that strictly stable components of Allen-Cahn minimal hypersurfaces always occur with multiplicity one. We also establish the uniqueness of solutions converging to nondegenerate hypersurfaces with multiplicity one. Our results work in all dimensions and without variational assumptions on the Allen-Cahn solution…

This paper solves the multiple reference model problem in RLHF with exact solutions and sample complexity guarantees.

Solutions to a quadratic matrix equation are linked to strongly regular graphs and multiplicative characters.

GEMSS discovers multiple sparse solutions in high-dimensional data.

Solves optimal control for trading multiple mean-reverting assets.

Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and …

Neural framework learns one solution from multiple for combinatorial problems.

New technique for multiple-source adaptation without density estimation.

The Allen-Cahn system on manifolds yields multiple phase distributions.

Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate expressions for variables h(t) and u(t). We provide here condition for the unique…

Regression problems that have closed-form solutions are well understood and can be easily implemented when the dataset is small enough to be all loaded into the RAM. Challenges arise when data is too big to be stored in RAM to compute the closed form solutions. Many techniques were proposed to overcome or alleviate the…

Study on solutions of Yamabe-type equations on projective spaces.

There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutions are constructed in all dimensions and solutions are classified in d…

Proves existence of multiple solutions to a multiphasic equation on manifolds.

Study hexagonal network evolution under curvature flow.

Study finds multiple periodic solutions to ODEs related to curvature problems.

The paper proves solutions for Yamabe equations on manifolds with boundary.

This work analyzes two methods for combining multiple binary labels in bipartite ranking.

In this paper we consider the functional whose critical points are solutions of the fractional CR Yamabe type equation on the sphere. We firstly study the behavior of the Palais-Smale sequences characterizing the bubbling phenomena and therefore we prove a multiplicity type result by showing the existence of infinitely…

In this paper we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the epsilon-Dirichlet problem obtained as a variational problem for the SU(2)-epsilon-Yang Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem fo…

In this paper we provide a general solution for the dividend discount model in order to compute the intrinsic value of a common stock that allows for multiple stage growth rates of any predetermined number of periods. A mathematical proof is provided for the suggested general solution. A numerical application is also p…

This work includes a number of novel contributions for the multiple-source adaptation problem. We present new normalized solutions with strong theoretical guarantees for the cross-entropy loss and other similar losses. We also provide new guarantees that hold in the case where the conditional probabilities for the sour…

On a Riemannian compact manifold, we give existence and multiplicity results for solutions of elliptic PDE by introducing isometry invariances. When the groups we used have finite orbits, we get multiplicity results for equations with the classical critical Sobolev exponent, for instance the Yamabe equation. When there…

Unified DNN-based precoder for MIMO networks with multiple objectives.

We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for existence and uniqueness of the solution and give a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustra…

In this paper, we study multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.

Paper proposes S-BOMM for optimization with multiple models, focusing on consistency.

The existence of Dirichlet minimizing multiple-valued functions for given boundary data has been known since pioneering work of F. Almgren. Here we prove a multiple-valued analogue of the classical Plateau problem of the existence of area-minimizing mappings of the disk. Specifically, we find, for $K \in \mathbb N,$ $k…

We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $α^j$ plus a minimum jumping rate $η$. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean …

Neural networks solve SPDEs using Wiener chaos expansion.

MKLpy simplifies Multiple Kernel Learning in Python.

Using the method of Nehari manifold, we prove the existence of at least two distinct weak solutions to elliptic equation of four order with singulatities and with critical Sobolev growth.

A new method improves recommendation accuracy by learning from multiple networks and time-dependent user preferences.

Solution to sparse PCA tuning problem using Empirical Bayes.

Study learning from multiple thinkers providing step-by-step solutions to problems.

Gradient Descent (GD) approximators often fail in the solution space with multiple scales of convexities, i.e., in subspace learning and neural network scenarios. To handle that, one solution is to run GD multiple times from different randomized initial states and select the best solution over all experiments. However,…

This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a suitable manifold.In the case of constant coefficients we obtain the existence of tree …

Deep learning approximates SPDE solutions from noise trajectories.

We give existence and nonuniqueness results for simple planar curves with prescribed geodesic curvature.

We prove that a sequence of solutions of the Seiberg-Witten equation with multiple spinors in dimension three can degenerate only by converging (after rescaling) to a Fueter section of a bundle of moduli spaces of ASD instantons.

We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.

We consider a closed Riemannian manifold $(M^n ,g)$ of dimension $n\geq 3$ and study positive solutions of the equation $-Δ_g u + λu = λu^q$, with $λ>0$, $q>1$. If $M$ supports a proper isoparametric function with focal varieties $M_1$, $M_2$ of dimension $d_1 \geq d_2$ we show that for any $q<\frac{ n-d_2+2 }{n - d_2…

Study optimal partition problem for Q-curvature equations on Einstein manifolds.

Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices using the floating point Intel Pentium SIMD (Single Instruction Multiple Data) a…

Study optimal reinsurance pricing under model uncertainty for multiple insurers.