Paper addresses underestimation bias in double Q-learning, proposing a method to improve learning performance.
problem Underestimation bias in double Q-learning leading to non-optimal fixed points.
method Proposes a simple approach using approximate dynamic programming to bound the target value.
result Significant improvement in learning performance over baseline algorithms in Atari benchmark tasks.
Gradient-based optimization methods are the most popular choice for finding local optima for classical minimization and saddle point problems. Here, we highlight a systemic issue of gradient dynamics that arise for saddle point problems, namely the presence of undesired stable stationary points that are no local optima…
New constraints rule out some optimal domains for helicity maximisation.
problem Finding a smooth domain of fixed volume that maximizes helicity.
method Established additional geometric constraints on optimal domains.
result Ruled out the optimality of a broad class of solid tori.
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear whether the fixed point identified by the variational inference algorithm is a local…
We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the well-established common knowledge that using longer price time series provides better, …
The paper classifies circle actions on 6D manifolds with isolated fixed points.
problem Classifying circle actions on 6D manifolds with isolated fixed points.
method Performing equivariant connected sums at fixed points with specific manifolds.
result A sequence of operations can reduce the fixed point data to the empty collection.
Groups with special properties always have fixed points.
problem Groups acting on finite CW-complexes without fixed points.
method Exhibited specific groups with strong fixed-point properties.
result Groups with finite generation and torsion-freeness have global fixed points.
Quantized neural networks can represent all fixed-point functions under certain conditions.
problem Expressive power of quantized neural networks under fixed-point arithmetic.
method Analyzing necessary and sufficient conditions for quantized networks to represent all fixed-point functions.
result Various popular activation functions satisfy the sufficient condition for representing all fixed-point functions.
Study circle actions on unitary manifolds with discrete fixed points.
problem Understanding circle actions on compact unitary manifolds with discrete fixed points.
method Prove relationships between weights at fixed points and derive results regarding the first equivariant Chern class and Hirzebruch χy-genus. result Derive a multigraph encoding fixed point data, leading to new insights into unitary S1-manifolds. Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.
problem Analyzing the growth of derivative maxima for C2 interval diffeomorphisms with parabolic fixed points. method Examining C2 diffeomorphisms with only parabolic fixed points, focusing on tangency and repelling behavior. result Maximal growth of derivative maxima is exactly quadratic for diffeomorphisms with a non-quadratic tangency to identity at a repelling fixed point.
New proof for 6D symplectic manifold with 4 fixed points.
problem Classifying the integral cohomology ring and total Chern class for 6D symplectic manifolds with 4 fixed points.
method New different argument using moment map values and weights of fixed points.
result Determined the sets of weights and global invariants for the manifold.
The paper highlights issues with fixed point claims in digital images.
problem Flaws in published assertions about fixed points in digital images.
method Continues a series of studies examining digital topology.
result Identifies and discusses problems with fixed point claims.
The paper highlights issues in fixed point claims in digital topology.
problem Flaws in published assertions about fixed points in digital metric spaces.
method Continues a series of studies examining these flaws.
result Identifies and discusses problems in fixed point claims.
In this paper, we study a circle action on a compact oriented manifold with a discrete fixed point set. The fixed point data consists of the weights of the S1-representations at the fixed points. We prove various results and properties of the action, in terms of the fixed point data. We show that the manifold can be…
Study fixed point indices and words at infinity for graph selfmaps.
problem Estimate indices of fixed point classes for graph selfmaps.
method Extend attracting fixed words at infinity, use relative train track technique, algebraic approach.
result Upper bound for attracting fixed words of injective endomorphisms of free groups.
Critiques incorrect fixed point assertions in digital topology.
problem Incorrect or incorrectly proven fixed point assertions in digital topology.
method Critical review of existing assertions.
result Identifies and critiques incorrect fixed point assertions.
The paper introduces fixed-point centralities for networks and graphons.
problem Defining network centralities for networks and graphons.
method Fixed-point centralities defined via permutation equivariant mappings and graphons.
result Variation bounds of fixed-point centralities under mild assumptions.
Improved convergence of fixed-point methods using windowed Anderson acceleration.
problem Improving convergence of fixed-point methods for symmetric operators.
method Windowed Anderson acceleration for symmetric fixed-point iterations.
result Windowed Anderson acceleration improves convergence over standard fixed-point methods.
A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regula…
Study circle actions on manifolds with 3 fixed points, finding dimension constraints and unique structures.
problem Characterize circle actions on oriented manifolds with exactly 3 fixed points.
method Analyzes manifold dimensions, isotropy submanifolds, and uses quaternionic projective space as a reference.
result For a manifold with three fixed points, its dimension must be a multiple of 4, and specific weights are unique.
Corrects incorrect assertions about fixed points in digital topology.
problem Incorrect or incorrectly proven assertions about fixed points in digital metric spaces.
method Analysis of existing assertions and proofs.
result Identifies and corrects errors in published assertions.
Paper finds at least 6 fixed points for a specific circle action on a 10D manifold.
problem Finding the minimum number of fixed points for a circle action on a 10D almost complex manifold.
method Established a lower bound by showing the non-existence of a circle action with 4 fixed points.
result There are at least 6 fixed points for a circle action on a 10D compact almost complex manifold.
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find \emph{all} fixed poi…
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect or poorly stated fixed point assertions in digital topology.
method Discussion of problematic publications in digital metric spaces.
result Clarification of incorrect fixed point assertions.
The paper addresses flaws in fixed point assertions for digital images.
problem Deficiencies in previously published works on fixed point assertions for digital images.
method Continues a series of studies to identify and rectify issues in fixed point assertions.
result Identifies and corrects flaws in fixed point assertions for digital images.
Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set MG. We say that M is fixed-point homogeneous if G acts transitively on a normal sphere to some component of MG. Fixed-point homogeneous manifolds with positive sectional curvature have been c…
Fixed point assertions in digital topology are often incorrect or poorly stated.
problem Fixed points in digital metric spaces
method Discussing publications with bad assertions
result Identifying and correcting errors in fixed point assertions
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect, incorrectly proven, or trivial fixed point assertions in digital topology.
method Continues earlier work on identifying and critiquing bad fixed point assertions.
result Clarifies the nature and extent of incorrect fixed point assertions in digital topology.
Improved UCB method for stochastic bandits using distance tuning.
problem Improving performance in stochastic bandit problems.
method Tuning confidence bounds based on bandit distance.
result Empirically shows increased performance compared to existing methods.
This paper provides a new proof of the Lefschetz fixed point formula using groupoids.
problem The Lefschetz fixed point formula for elliptic complexes.
method Defines a relative tangent groupoid and pseudodifferential calculi to prove the formula.
result A new proof of the Lefschetz fixed point formula using groupoids.
Classifies circle actions on 6D manifolds with 4 fixed points.
problem Classifying circle actions on 6D manifolds with specific fixed points.
method Analyzes fixed point data and proves agreement with known actions.
result Agrees with actions on 6-spheres or CP3. In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and typically attains an order of magnitude or better improvement in optimization pe…
Study fixed-point sets of S1-actions on quaternionic manifolds.
problem Characterize fixed-point sets and compatible complex structures on quaternionic manifolds.
method Analyze fixed-point sets and derive equations involving first Chern classes.
result Conditions for the existence of hypercomplex structures on quaternionic manifolds.
Fixed points of nonnegative neural networks are analyzed using fixed point theory.
problem Analyzing fixed points in nonnegative neural networks.
method Fixed point theory, nonlinear Perron-Frobenius theory, monotonic and scalable mappings.
result Conditions for the existence of fixed points in nonnegative neural networks are provided.
We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the existence of a fixed point set for a continuous self-map restricts the map on the c…
Large multi-tenant production clusters often have to handle a variety of jobs and applications with a variety of complex resource usage characteristics. It is non-trivial and non-optimal to manually create placement rules for scheduling that would decide which applications should co-locate. In this paper, we present De…
Let G be a compact Lie group acting effectively by isometries on a compact Riemannian manifold M with nonempty fixed point set Fix(M,G). We say that the action is \emph{fixed point homogeneous} if G acts transitively on a normal sphere to some component of Fix(M,G), equivalently, if Fix(M,G) has codimension…
Upper bounds on fixed points in PWL neural networks with hyperplane analysis.
problem Analyzing the number of fixed points in neural networks with PWL activation.
method Hyperplane arrangements to bound the number of fixed points.
result Upper bounds on the number of fixed points for PWL networks, showing exponential growth in layers.
We investigate the fixed point property of the group actions on a coarse space and its Higson corona. We deduce the coarse version of Brouwer's fixed point theorem.
The author proved that if the circle acts symplectically on a compact, connected symplectic manifold M with three fixed points, then M is equivariantly symplectomorphic to some standard action on CP2. In this paper, we extend the result to a circle action on an almost complex manifold; if the circle act…
We apply fixed-point techniques to compute the coefficient ring of semifree geometric circle-equivariant complex cobordism with isolated fixed points, recovering a 2004 result of Sinha through 19th-century methods.
New proofs in fixed point theory for manifolds and domains.
problem Proving fixed points and isometries for specific geometric structures.
method Topological fixed point theory applied to manifolds and domains.
result Prime divisors of finite group orders are constrained by domain connectivity.
Classifies multigraphs for torus actions on 6D manifolds with isolated fixed points.
problem Classifying torus actions on 6D manifolds with isolated fixed points.
method Associate multigraphs to fixed point data, study operations, and prove classification.
result Classifies multigraphs for 6D manifolds by converting them into the empty graph.
The study proves fixed-point theorems for groups acting on CAT(0) spaces.
problem Finding fixed points for groups acting on CAT(0) spaces.
method Bootstrapping technique with Helly-type theorems to prove intersections of fixed-point sets.
result Lower bounds on the smallest dimension for groups to act on CAT(0) spaces without global fixed points.
We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most pi/2, and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology.
Formula for fixed points on noncompact spaces.
problem Calculating fixed points on noncompact manifolds.
method Equivariant index theorem, localised functional, asymptotically local operators.
result Obtained a new Lefschetz fixed-point formula.
We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry.
Formula estimates pseudo-Anosov maps' fixed points, linking to surface properties.
problem Estimating fixed points of pseudo-Anosov maps.
method Formula using Teichmüller translation length for fixed points of strong irreducible maps.
result Log of fixed points coarsely equals Teichmüller translation length for strong irreducible maps.