CRA improves UL-based CO solvers by dynamically smoothing and enforcing discreteness.
problem Local optima and artificial rounding issues in UL-based CO solvers.
method Continuous Relaxation Annealing (CRA) strategy that dynamically shifts from continuous to discrete solutions.
result Significantly enhances UL-based CO solver performance and eliminates artificial rounding.
New ANN method for imputing rounded zeros in compositional data.
problem Imputing missing values in compositional data with rounded zeros.
method Artificial Neural Networks (ANNs) for imputation of compositional data.
result ANNs are competitive or better than conventional methods for imputing rounded zeros.
We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market …
Paper tackles adaptive submodularity in sequential decision making.
problem Maximizing adaptive submodular functions with limited adaptive rounds.
method Proposes an efficient semi-adaptive policy with logarithmic adaptive rounds.
result Achieves an almost tight 1−1/e−ε approximation guarantee. Like many problems in AI in their general form, supervised learning is computationally intractable. We hypothesize that an important reason humans can learn highly complex and varied concepts, in spite of the computational difficulty, is that they benefit tremendously from experienced and insightful teachers. This pape…
We consider learning under the constraint of local differential privacy (LDP). For many learning problems known efficient algorithms in this model require many rounds of communication between the server and the clients holding the data points. Yet multi-round protocols are prohibitively slow in practice due to network …
Paper tackles concept drift in Federated Learning, improving model performance.
problem Concept drift in real-world data makes existing Federated Learning methods ineffective.
method Introduces a multiscale algorithm combining extit{FedAvg} and extit{FedOMD} with non-stationary detection and adaptation.
result Achieves dynamic regret of $\Tilde{\mathcal{O}} ( \min \{ \sqrt{LT} , Δ^{\frac{1}{3}}T^{\frac{2}{3}} + \sqrt{T} \})$ for T rounds. Gradient descent with biased rounding errors converges faster under certain conditions.
problem Stagnation or negative impact of rounding errors in neural network training with low precision.
method Analysis of gradient descent with stochastic fixed-point rounding errors under the Polyak-Lojasiewicz inequality.
result Biased rounding errors can improve convergence rates, especially when the Polyak-Lojasiewicz inequality holds.
AI beats 95% of humans in Rock-Paper-Scissors.
problem Predicting and modeling human behavior in strategic games.
method Used Markov Models of varying memory lengths to compete against humans, introducing a 'focus length' parameter.
result Multi-AI strategy wins over 95% of human opponents in continuous 300-round games.
Round surgery diagrams represent 3-manifolds in S3.
problem Representing and manipulating 3-manifolds in S3. method Introducing round surgery diagrams and defining moves to establish Kirby Calculus.
result Any 3-manifold can be obtained by a round surgery on a framed link in S3. Contact round surgeries on (S3,ξst) help in constructing and understanding contact 3-manifolds.
problem Constructing contact 3-manifolds using Legendrian surgeries.
method Introducing contact round surgeries of indices 1 and 2, and associating them with surgery diagrams.
result Every closed connected contact 3-manifold can be obtained by a sequence of contact round surgeries on Legendrian knots in (S3,ξst). In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create pathological examples of flows. We find a sequence of flows that …
Optimizes sample and round complexity in adaptive sampling from multiple distributions.
problem Adaptive sampling from multiple distributions with limited rounds and samples.
method Introduces OODS framework and analyzes tradeoffs between sample and round complexity.
result Achieves near-optimal sample complexity and sub-polynomial round complexity.
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has r…
New findings show infinitely many knots cannot be smoothly round handle slices.
problem Understanding the smoothability of knots in 4-dimensional space.
method Analyzing the properties of knots under surgery conjectures and cobordism conjectures.
result Infinitely many knots fail to be smoothly round handle slices.
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.
This work investigates how multi-round reasoning improves LLM performance.
problem Improving problem-solving abilities in complex tasks with LLMs.
method Investigates approximation, learnability, and generalization properties of multi-round auto-regressive models.
result Transformers with finite context windows are universal approximators for Turing-computable functions and can approximate any Turing-computable sequence-to-sequence function through multi-round reasoning.
AI learns market manipulation through simulation, suggesting regulation.
problem Regulating AI to prevent market manipulation.
method Used a genetic algorithm in an artificial market simulation.
result AI discovered market manipulation as an optimal strategy.
New findings on κ-solutions with round cylinder as asymptotic shrinker.
problem Characterizing κ-solutions with specific asymptotic behavior. method Analysis of Ricci flow in dimensions n≥4. result Uniformly Positive Isoperimetric Constant (PIC) for κ-solutions. Round balls minimize liquid drop model volumes ≤ 1.
problem Minimizing volumes in liquid drop models.
method Proved uniqueness of minimizers for small volumes.
result Round balls uniquely minimize volumes ≤ 1.
Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.
problem Stagnation of gradient descent in low-precision computation.
method Proposed unbiased stochastic rounding schemes that trade zero bias for larger probability of preserving small gradients.
result Unbiased rounding methods typically improve convergence rate of gradient descent for convex problems.
Round cylinders are rigid in Ricci shrinkers close to the standard product.
problem Proving rigidity of round cylinders in Ricci shrinkers.
method Proving isometry using pointed-Gromov-Hausdorff topology.
result Ricci shrinkers close to Sn−1imesR are isometric to Sn−1imesR. A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.
We show that if the entropy of any closed hypersurface is close to that of a round hyper-sphere, then it is close to a round sphere in Hausdorff distance. Generalizing the result of \cite{BW1} to higher dimensions.
In this paper, we study the limiting behavior of the Brown-York mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined in an intrinsic way. Our results show that the ADM mass of an asymptotically flat 3-manifold can be approximated by some …
The study characterizes round spheres in Euclidean space based on r-mean curvature conditions.
problem Characterizing round spheres in Euclidean space under specific curvature conditions.
method Characterization based on r-mean curvature conditions.
result Characterizes round spheres in Euclidean space under suitable r-mean curvature conditions.
Contact round surgery of contact 3-manifolds is introduced in this paper. By using this method, an alternative proof of the existence of a contact structure on any closed orientable 3-manifold is given. It is also proved that any contact structure on any closed orientable 3-manifold is constructed from the standard con…
In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer Trapped Surface (MOTS), called a quasi-round MOTS. In the first part of this paper, f…
Study cohomology rings of 3D manifolds with round fold maps into the plane.
problem Understanding cohomology rings of 3D manifolds with round fold maps.
method Analyzing cohomology rings of 3D manifolds admitting round fold maps into the plane.
result Explicit new study showing relation between coefficient rings and topological types of round fold maps.
Research explores real algebraic realization of round fold maps of codimension -1.
problem Real algebraic realization of round fold maps of codimension -1.
method Generalizes canonical projections of unit spheres to round fold maps and discusses their real algebraic realization.
result Developed new studies in real algebraic geometry focusing on round fold maps of codimension -1.
New compact mean convex hypersurfaces found for positive λ.
problem Finding compact embedded hypersurfaces for positive λ.
method Constructing compact mean convex hypersurfaces diffeomorphic to spheres.
result No compact convex embedded λ-hypersurfaces except a round sphere for λ > 0.
New Einstein metrics found on a 10-dimensional sphere.
problem Finding non-round Einstein metrics on spheres.
method Proving existence of three new metrics on S10. result Existence of three non-round, non-isometric Einstein metrics with positive scalar curvature on S10. We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.
Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a great deal of samples as well as a large number of features. In this paper, thus…
We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-manifold R constructed from adding round handles to the four ball. A negative answer would contradict the union of the surgery conjecture and th…
We prove that the well-rounded retract of SO_n\SL_n(R) is a minimal SL_n(Z)-invariant spine.
High-frequency traders can act as either small informed traders or round-trippers, affecting price discovery and liquidity.
problem Effects of high-frequency trading on price discovery and liquidity.
method Extended Kyle's model with interactions between large informed traders and high-frequency traders.
result High-frequency traders can act as Small-IT or Round-Tripper, impacting price discovery and liquidity.
Artificial intelligence has impacted many aspects of human life. This paper studies the impact of artificial intelligence on economic theory. In particular we study the impact of artificial intelligence on the theory of bounded rationality, efficient market hypothesis and prospect theory.
One-round FL method improves robustness and reduces communication rounds.
problem Making predictions robust and reducing FL communication rounds in heterogeneous data.
method Bayesian predictive space aggregation of client posteriors in one round.
result One-round FL method outperforms other techniques on heterogeneous settings.
Eigenvalues on spheres are compared to the unit round sphere, proving a sharp bound and equality condition.
problem Comparing eigenvalues of spheres under different metrics.
method Analyzing Laplace eigenvalues and using Alexandrov spaces.
result Equality of eigenvalues forces metrics to be isometric to the unit round sphere.
This paper studies a deformation retraction of Teichmüller space and its analogy with well-rounded retractions.
problem Understanding the well-rounded deformation retraction of Teichmüller space.
method Examining the mapping class group-equivariant deformation retraction of Teichmüller space onto a CW complex and comparing it to well-rounded retractions of other spaces.
result The well-rounded deformation retraction of Teichmüller space is analogous to well-rounded retractions of other spaces.
PAMS is a Python-based platform for simulating artificial markets.
problem Simulating complex market behaviors for research and education.
method Developed as a Python-based simulator with deep learning integration.
result Demonstrated effectiveness through agent price prediction studies.
We consider the problem of learning a general graph G=(V,E) using edge-detecting queries, where the number of vertices ∣V∣=n is given to the learner. The information theoretic lower bound gives mlogn for the number of queries, where m=∣E∣ is the number of edges. In case the number of edges m is also given t…
Proposes rounding method for precise treatment effect estimation under budget constraints.
problem Resource-constrained experimental design for precise treatment effect estimation.
method Dependent randomized rounding procedure to convert assignment probabilities into binary treatment decisions.
result Improved estimator precision through variance reduction and efficient inference.
AdaRound improves post-training quantization of neural networks.
problem Improving the accuracy of quantized weights in neural networks.
method Adaptive rounding mechanism that adapts to data and task loss.
result AdaRound outperforms rounding-to-nearest and achieves state-of-the-art performance.
In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes special generic maps on spheres and such maps have been constructed on smooth bundles …
Proposes a flexible tournament design combining knockout and round-robin.
problem Designing a tournament that eliminates participants linearly.
method Combines knockout and round-robin structures for flexible elimination.
result Flexible tournament design can eliminate participants linearly.
A new algorithm reduces communication rounds for distributed convex optimization.
problem Efficiently solving convex optimization problems in distributed systems.
method Proposes a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization.
result Reduces the number and frequency of communication rounds compared to existing methods.