QPLEX learns efficient multi-agent Q-values by enforcing IGM principle.
problem Scalable multi-agent reinforcement learning with IGM consistency.
method Dueling duplex network architecture to enforce IGM principle.
result QPLEX achieves high sample efficiency and benefits from offline data.
The paper explores when and why value decomposition algorithms work in cooperative multi-agent reinforcement learning.
problem The applicability and convergence properties of value decomposition algorithms in cooperative multi-agent reinforcement learning are unclear.
method The paper introduces decomposable games and proves that applying the multi-agent fitted Q-Iteration algorithm leads to an optimal Q-function in these games.
result The paper offers theoretical insights into when and why value decomposition algorithms converge in cooperative multi-agent reinforcement learning.
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of complicated datasets and sampling from them. The proposed algorithm is based on a f…
This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponential-Blurring-Mean-Sh…
Implicit Generative Models (IGMs) such as GANs have emerged as effective data-driven models for generating samples, particularly images. In this paper, we formulate the problem of learning an IGM as minimizing the expected distance between characteristic functions. Specifically, we minimize the distance between charact…
A new flow optimizes synthetic data alignment for generative modeling.
problem Optimizing synthetic data to match target distributions.
method Score difference (SD) flow to reduce KL divergence.
result SD flow provides a theoretical link between generative models.
21cmEMU speeds up EoR simulations by 10^4x, predicting key observables with sub-percent accuracy.
problem Efficiently simulating and inferring Epoch of Reionization properties from limited computational resources.
method Developed an emulator for 21cmFAST simulation outputs, reducing computational cost by 10^4x.
result Sub-percent accurate predictions of 6 key observables from EoR simulations.
ScoreGAN uses GANs with IGM to detect bot-generated reviews based on text and scores.
problem Lack of labeled data and bot-generated reviews in fraud review detection.
method ScoreGAN incorporates review text and scores into a GAN framework for data augmentation and detection.
result ScoreGAN outperforms existing methods by 7% and 5% on Yelp and TripAdvisor datasets.
Research examines how Islamic banking principles spread among managers and scholars.
problem Diffusion of Islamic banking principles among managers and scholars.
method Literature review focusing on knowledge diffusion and Islamic banking governance principles.
result Emergence of common Islamic banking governance principles from diverse knowledge streams.
The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
problem Maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
method Established generalized maximum principles and proved stochastic completeness equivalence.
result Stochastic completeness for the heat semigroup is equivalent to generalized maximum principles.
The h-principle helps solve complex geometric problems.
problem Solving complex geometric problems using the h-principle.
method Developed from the Oka-Grauert principle and Gromov's theory, the h-principle is applied to Oka manifolds and maps.
result Recent developments and applications of the h-principle in complex analysis and geometry.
The study establishes uncertainty principles on harmonic manifolds of rank one.
problem Developing uncertainty principles for harmonic manifolds of rank one.
method Derivation of various uncertainty principles including Heisenberg, Morgen, Schrödinger, and Hömanders principles.
result Generalization of Hausdorff-Young inequality to harmonic manifolds of rank one.
Conditions for polynomial to be isometry of lattice, answering Hasse principles.
problem Conditions for integral polynomials to be characteristic polynomials of isometries of lattices.
method Necessary and sufficient conditions derived from lattice isometries and Hasse principles.
result Proved a Hasse principle for signatures of knots.
Shows flexible sheaves as fibrant objects for Gromov's h-principle.
problem Applying the h-principle to partial differential relations.
method Interprets flexible sheaves as fibrant objects in a model structure.
result Flexible sheaves can be understood as fibrant objects.
A new method to break down insurance costs into risk and uncertainty.
problem Understanding and quantifying insurance costs in uncertain environments.
method An axiomatic approach to decompose premium principles into risk and deviation measures.
result Maximal risk and minimal deviation measures can be uniquely identified in decompositions.
Study on maximum principles for nonlinear equations on Riemannian manifolds.
problem Investigating strong maximum principles for fully nonlinear equations on Riemannian manifolds.
method Analyzing scaling conditions and applying to various nonlinear operators.
result Established new strong comparison principles for second order uniformly elliptic problems.
Derives Fredholm criteria for isotypical components from a Simonenko principle.
problem Finding Fredholm conditions for isotypical components of invariant pseudodifferential operators.
method General Simonenko's local principle and equivariant local principle for restriction to isotypical components.
result Full proof of equivariant local principle and extension of results.
Establishes a boundary maximum principle for varifolds with fixed contact angle.
problem Boundary behavior of varifolds with contact angle constraints.
method Maximum principle for stationary pairs of varifolds with fixed contact angle condition.
result Boundary maximum principle proven for stationary varifolds.
Study proves Maximum Principles for unbounded Riemannian domains.
problem Proving Maximum Principles for unbounded Riemannian domains.
method Examines both ambient manifold and differential operator assumptions.
result Valid Maximum Principles established for unbounded domains.
A pricing principle is introduced for non-attainable claims in incomplete markets.
problem Pricing non-attainable contingent claims in incomplete markets.
method Distorted Radon-Nikodym derivative and Tsallis relative entropy over a family of equivalent martingale measures.
result The pricing principle is closely related to backward stochastic differential equations and is arbitrage-free and time-consistent.
We show that a well known uncertainty principle for functions on the circle can be derived from an uncertainty principle for the Euclidean motion group.
Proves a principle for one-phase Bernoulli problem minimizers.
problem One-phase Bernoulli problem minimizers.
method Strong maximum principle, Alt-Caffarelli functional, Hardt-Simon-type foliation.
result Constructs a foliation for global minimizers.
New method proves h-principles for stable forms on manifolds.
problem Proving h-principles for stable forms on manifolds. method Convex integration applied to stable forms.
result Proved h-principles for 4 classes of stable forms. We give a version of the comparison principle from pluripotential theory where the Monge-Ampère measure is replaced by the Bergman kernel and use it to derive a maximum principle
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is o…
Note establishes a local maximum principle for Ricci flow under curvature conditions.
problem Preserving nonnegativity of curvature along Ricci flow with unbounded curvature.
method Combining scaling invariant curvature condition with Dirichlet heat kernel estimates.
result Unified and more direct proof of localized maximum principle.
The Weyl principle holds in some Finsler settings despite general failure.
problem Applying the Weyl principle to Finsler manifolds.
method Investigation of the Weyl principle in Finsler geometry.
result A weak form of the Weyl principle persists in certain Finsler settings.
Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very use…
Derives time-averaged active inference from control principles.
problem Finite-horizon or discounted-surprise problems in active inference.
method Derives infinite-horizon, average-surprise active inference from optimal control principles.
result Unified objective functional for sensorimotor control.
New principle for harmonic maps helps study higher-dimensional submanifolds.
problem Understanding unboundedness of totally geodesic projections in higher codimension.
method Introducing a flexible notion of convexity and applying it to harmonic and conformal maps.
result New maximum principle for harmonic maps applicable to various geometric settings.
In this paper we give three applications of a method to prove h-principles on closed manifolds. Under weaker conditions this method proves a homological h-principle, under stronger conditions it proves a homotopical one. The three applications are as follows: a homotopical version of Vassiliev's h-principle, the contra…
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving …
3-manifolds study Hasse norm principle, akin to number fields.
problem Topological analog of Hasse norm principle for 3-manifolds.
method Analogy with number fields and finite cyclic coverings.
result Showed topological Hasse norm principle for 3-manifolds.
New equivalences found linking parabolicity, comparison principle, and capacity on Riemannian manifolds.
problem Understanding parabolicity and related concepts on Riemannian manifolds.
method Establishing new equivalences between parabolicity, comparison principle, and capacity.
result Equivalence between p-parabolicity and the comparison principle for the p-Laplace equation. Maps to manifolds transverse to certain distributions satisfy an h-principle.
problem Maps to manifolds transverse to certain distributions.
method Proving the complete h-principle for transverse maps. result Maps to manifolds transverse to certain distributions satisfy the h-principle. Paper proves h-principles for symplectic structures and foliations.
problem Existence of conformal symplectic structures and foliations.
method Application of h-principles and foliated Morse theory.
result Linear deformation of foliations to contact structures.
Previous studies have shown that deep neural networks (DNNs) with common settings often capture target functions from low to high frequency, which is called Frequency Principle (F-Principle). It has also been shown that F-Principle can provide an understanding to the often observed good generalization ability of DNNs. …
Study shows strong min-max principle for phase transitions.
problem Understanding nodal sets near minimal hypersurfaces.
method Analogous to White's principle, applies to Allen-Cahn energy.
result Strong min-max principle for phase transitions.
We prove that for an algebraic curvature tensor on a pseudo-Euclidean space, the Jordan-Osserman condition implies the Rakić duality principle, and that the Osserman condition and the duality principle are equivalent in the diagonalisable case.
Why deep neural networks (DNNs) capable of overfitting often generalize well in practice is a mystery [#zhang2016understanding]. To find a potential mechanism, we focus on the study of implicit biases underlying the training process of DNNs. In this work, for both real and synthetic datasets, we empirically find that a…
Photography method solves manifold invariants.
problem Constructing invariants of manifolds.
method General principle of photography, dealing with various data and data transmission.
result Dijkgraaf-Witten invariants are a specific application of the photography principle.
New distance comparison principle for curve shortening flow in higher dimensions.
problem Understanding curve shortening flow in higher dimensions.
method Established a variant of Huisken's distance comparison principle.
result Symmetric curve shortening flow with one-to-one convex projection develops Type I singularities and becomes asymptotically circular.
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the transformation group principle (smooth geometric objects and their discretizations are invar…
The net-premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, an insurance company, applying the net-premium principle, goes bankrupt with probability one in the long run, even if the company covers its entire costs by collecting the respective fees from i…
Study h-principles for non-integrable distributions on manifolds.
problem Existence and classification of maximally non-integrable distributions of derived length one.
method Introduced formal structures and used h-principles to discuss existence and classification.
result Discussed existence and classification of maximally non-integrable distributions of derived length one.
Study shows distance to boundary is always attained on varifolds with bounded curvature.
problem Understanding varifolds with bounded mean curvature in Riemannian manifolds.
method Proves a barrier principle at infinity using sharp maximum principles.
result Distance to boundary is always attained on varifolds with bounded curvature.
We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz func…