Study finds methods to learn multiple solutions from single task in offline RL.
problem Learning multiple solutions from a single task in offline RL.
method Proposed algorithms for offline RL.
result Empirical results show learning of multiple solutions in offline RL.
Proves C1,1 regularity for multiple membrane solutions.
problem Stationary C1,α solutions to the multiple membrane problem. method Uses C1,1-regularity estimate. result Proves C1,1 regularity for stationary solutions. Study finds multiple solutions for Gross-Pitaevskii equations on curved spaces.
problem Finding multiple solutions for Gross-Pitaevskii equations on Riemannian manifolds.
method Critical point theory and Γ-convergence for Ginzburg-Landau functionals, plus new isoperimetric results.
result Lower bounds on the multiplicity of solutions in terms of the topology of the velocity set.
Strictly stable Allen-Cahn hypersurfaces have multiplicity one.
problem Understanding the multiplicity of stable hypersurfaces in Allen-Cahn equations.
method Analyzing strictly stable components without variational assumptions.
result Strictly stable components occur with multiplicity one.
This paper solves the multiple reference model problem in RLHF with exact solutions and sample complexity guarantees.
problem Limitations of single reference models in aligning LLMs with human feedback.
method Integrates multiple reference models into RLHF frameworks, addressing theoretical challenges with exact solutions and sample complexity guarantees.
result First exact solution to the multiple reference model problem in reverse KL-regularized RLHF.
Solutions to a quadratic matrix equation are linked to strongly regular graphs and multiplicative characters.
problem Solving a specific quadratic matrix equation in Riemannian geometry.
method Constructing nonzero solutions using group rings and multiplicative characters of finite fields.
result Solutions relate to strongly regular graphs and multiplicative characters of finite fields.
GEMSS discovers multiple sparse solutions in high-dimensional data.
problem Identifying multiple sparse feature combinations in high-dimensional, underdetermined systems.
method GEMSS (Gaussian Ensemble for Multiple Sparse Solutions) uses a structured spike-and-slab prior, mixture of Gaussians, and Jaccard-based penalty to optimize a single objective function via stochastic gradient descent.
result GEMSS consistently outperforms five feature selection methods on 128 experiments and real-world datasets.
Solves optimal control for trading multiple mean-reverting assets.
problem How to construct a portfolio from mean-reverting assets.
method Optimal control problem for power utility agent.
result Nearly explicit solution with properties of optimal solution.
DMClusts discovers multiple clusterings from multi-view data.
problem Finding multiple meaningful and diverse clusterings from multi-view data.
method Deep matrix factorization to gradually factorize multi-view data into representational subspaces and generate one clustering per layer, enforcing diversity through proximity minimization.
result DMClusts outperforms state-of-the-art multiple clustering solutions.
Neural framework learns one solution from multiple for combinatorial problems.
problem Finding any one of many possible solutions for combinatorial problems.
method Adapts existing prediction networks to handle solution multiplicity using a selection module trained via RL.
result Framework significantly improves accuracy in solving combinatorial problems.
New technique for multiple-source adaptation without density estimation.
problem Multiple-source adaptation problem.
method Discriminative technique that uses conditional probabilities from unlabeled data.
result Our technique outperforms previous generative solutions and other domain adaptation baselines.
The Allen-Cahn system on manifolds yields multiple phase distributions.
problem Finding the number of solutions to the Allen-Cahn system on manifolds.
method Volume-fixing variations approach to classify isoperimetric clusters.
result The number of solutions is bounded by topological invariants for parallelizable manifolds.
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.
problem Existence and multiplicity of solutions of Yamabe-type equations on projective spaces.
method Investigation of solutions invariant under cohomogeneity one actions of U(n) and Sp(n).
result Existence of degenerate solutions 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.
problem Existence of multiple solutions to a multiphasic equation with a small volume constraint.
method Lusternik-Schnirelmann and infinite-dimensional Morse theories, combined with isoperimetric theory and transversality theorem.
result Lower bound for the number of solutions depending on topological invariants.
Study hexagonal network evolution under curvature flow.
problem Understanding hexagonal network evolution under curvature flow.
method Proved local existence of classical solutions and classified homothetically shrinking solutions.
result Provided an example of network shrinking to a segment with multiplicity two.
Study finds multiple periodic solutions to ODEs related to curvature problems.
problem Finding multiple positive periodic solutions to quasilinear ODEs.
method Global bifurcation techniques applied to second order quasilinear ODEs.
result Bifurcation-theoretic proof of nonuniqueness for conformal metrics with constant scalar curvature.
The paper proves solutions for Yamabe equations on manifolds with boundary.
problem Existence and multiplicity of positive solutions for Yamabe equations.
method Use of isoparametric functions to prove existence and multiplicity results.
result Existence and multiplicity results for positive solutions of Yamabe equations.
This work analyzes two methods for combining multiple binary labels in bipartite ranking.
problem Combining multiple binary labels for optimal bipartite ranking.
method Loss aggregation vs. label aggregation approaches.
result Label aggregation is preferable to loss aggregation due to label dictatorship issues.
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.
problem Optimizing data transmission, energy harvesting, and security in MIMO networks.
method Rotation-based precoding and DNN for multi-objective optimization.
result DNN-based precoder reduces computational complexity and achieves near-optimal performance.
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.
problem Optimization challenges with multiple models of varying fidelity and accuracy.
method Set-Based Optimization with Multiple Models (S-BOMM) focusing on model consistency.
result Empirical results show S-BOMM's effectiveness in identifying good solutions across multiple models.
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∈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 αj 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.
problem Solving stochastic partial differential equations (SPDEs) numerically.
method Using neural networks in the truncated Wiener chaos expansion.
result Approximation rates for learning SPDE solutions with noise.
MKLpy simplifies Multiple Kernel Learning in Python.
problem Learning optimal kernel functions from data.
method Python-based framework for Multiple Kernel Learning algorithms.
result Maximizes usability and simplifies development of novel solutions.
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.
problem Incomplete user profiles and dynamic user preferences degrade recommender quality.
method A cross-network time-aware recommender that learns from multiple source networks and develops current user models.
result The proposed solution achieves superior performance in accuracy, novelty, and diversity.
Solution to sparse PCA tuning problem using Empirical Bayes.
problem Sparse PCA multiple tuning problem (MTP).
method Empirical Bayes covariance decomposition for penalized PCA.
result Empirical Bayes approach efficiently solves MTP in sparse PCA.
Study learning from multiple thinkers providing step-by-step solutions to problems.
problem Learning from multiple, possibly different, thinkers providing step-by-step solutions to problems.
method Active learning algorithm that uses CoT data from multiple thinkers and end-result data.
result Learning can be hard from CoT supervision provided by two or a few different thinkers, but a generic algorithm can learn efficiently.
Paper speeds up matrix multiplication on Intel PIII using SIMD.
problem Efficiently multiplying large matrices for faster algorithm performance.
method Implemented matrix-matrix multiply using Intel Pentium SIMD architecture.
result Average performance 2.09 times faster than public domain routines.
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,…
Deep learning approximates SPDE solutions from noise trajectories.
problem Approximating solutions to stochastic partial differential equations (SPDEs).
method Uses neural networks to approximate SPDE solutions based on noise realizations.
result Accurately estimates SPDE solutions and functionals like mean and variance.
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 …
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 (Mn,g) of dimension n≥3 and study positive solutions of the equation −Δgu+λu=λuq, with λ>0, q>1. If M supports a proper isoparametric function with focal varieties M1, M2 of dimension d1≥d2 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.
problem Optimal partition problem for prescribed Q-curvature equation.
method Cohomogeneity one actions, higher order conformal operators, weakly coupled elliptic systems.
result Existence and multiplicity of least energy symmetric and sign-changing solutions.
Study optimal reinsurance pricing under model uncertainty for multiple insurers.
problem Optimal reinsurance pricing in the presence of multiple sources of model uncertainty.
method Solves a continuous-time Stackelberg game for general reinsurance contracts, considering entropy penalties and ambiguity in insurers' models.
result Reinsurer prices under a distortion of the barycentre of insurers' models, maximizing expected wealth with an entropy penalty.