The paper calculates the Kobayashi-Royden metric on a punctured sphere and finds rational coefficients.
problem Calculating the Kobayashi-Royden metric on a punctured sphere.
method Explicit formula and asymptotic expansion using exponential Bell polynomials.
result The coefficients in the asymptotic expansion of the Kobayashi-Royden metric on the punctured sphere are rational numbers.
Investigates differential smoothness of 3D skew polynomial rings.
problem Differential smoothness of 3D skew polynomial rings.
method Analyzes Bell and Smith's characterization of 3D skew polynomial rings.
result Provides insights into the differential smoothness of these rings.
We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. We define the concept of the variation of a…
Bell's theorem shows quantum correlations can't be explained by classical causal models, even with some measurement dependence.
problem Quantum correlations violate classical causal models.
method Using causal networks, the study bounds the level of measurement dependence and derives nonlinear Bell inequalities.
result Quantum correlations can't be explained by classical causal models even with some measurement dependence.
In \cite{Ka14} we produced an algorithm for deciding whether or not an element φ∈Out(FN) is an iwip ("fully irreducible") automorphism. At several points that algorithm was rather inefficient as it involved some general enumeration procedures as well as running several abstract processes in parallel. In this pape…
Soft diamond regularizers improve deep learning performance and sparsity.
problem Improving deep learning performance and sparsity of trained weights.
method New soft diamond synaptic weight priors based on thick-tailed symmetric alpha stable probability curves.
result Soft diamond regularizers outperform state-of-the-art methods in deep learning tasks.
Quantum theory challenges traditional cause-effect relations, showing causal influences even without Bell inequality violations.
problem Challenging traditional concepts of cause-effect relations in quantum mechanics.
method Introducing a general framework to estimate causal influences without interventions or classical/quantum assumptions.
result Every pure bipartite entangled state violates classical bounds on causal influence, negating the idea that Bell inequalities are the only signature of incompatibility.
This work develops efficient methods for computing moments of Gaussian mixtures.
problem Efficient computation of moments for Gaussian mixtures with large dimensions.
method Theory and numerical methods for implicit computations with moment tensors of Gaussian mixtures.
result Reduced computational and storage costs for moment tensors of Gaussian mixtures.
It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations, quantum correlations and other kinds of correlations on any directed acyclic graph,…
The paper constructs denoisers that recover the Brenier map from higher-order score functions.
problem Estimating the Brenier map from noisy data.
method Constructs a hierarchy of denoisers using higher-order score functions.
result The T∞ denoiser recovers the Brenier map from the additive Gaussian model. Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.
problem Improving estimator efficiency in non-asymptotic settings.
method Incorporates curvature-aware corrections based on extrinsic geometry of statistical model manifold.
result Meaningful tightening of estimator variance bounds.
Generative Adversarial Networks generate PXD background noise efficiently.
problem Efficiently generate statistically independent PXD background noise samples.
method Conditional Generative Adversarial Networks (GANs) with contrastive learning.
result On-demand PXD background generator reduces storage requirements.
New bounds for score matching in polynomial exponential families.
problem Understanding the sample complexity of score matching for polynomial exponential families.
method Non-asymptotic sample complexity analysis for score matching.
result First finite sample bounds for score matching in polynomial exponential families.
Study online learning of quantum processes, showing feasibility for certain types.
problem Learning quantum processes adaptively, especially for bounded gate complexity and Pauli channels.
method Online learning, mistake-bounded model, multiplicative weights update algorithm, Bell sampling.
result Online learning feasible for quantum channels of bounded gate complexity and Pauli channels.
Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.
problem Characterizing ancient solutions on an infinite strip with polynomial and exponential growth.
method Analyzing parabolic equations on an infinite strip, proving properties of ancient solutions.
result Ancient solutions on the strip are constant if they grow polynomially, and have a finite-dimensional space for slower exponential growth.
Study shows exponential growth of knot polynomial tied to Chern-Simons invariant.
problem Asymptotic behavior of colored Jones polynomials of figure-eight knot.
method Analyzes growth rate of polynomial evaluated at specific points.
result Growth rate determined by Chern-Simons invariant of an affine representation.
The ability to witness non-local correlations lies at the core of foundational aspects of quantum mechanics and its application in the processing of information. Commonly, this is achieved via the violation of Bell inequalities. Unfortunately, however, their systematic derivation quickly becomes unfeasible as the scena…
The cost-benefit analysis formulates the holy trinity of objectives of project management - cost, schedule, and benefits. As our previous research has shown, ICT projects deviate from their initial cost estimate by more than 10% in 8 out of 10 cases. Academic research has argued that Optimism Bias and Black Swan Blindn…
Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that mod…
This work improves polynomial approximations for functions with asymmetric behavior.
problem Efficiently approximating functions with asymmetric behavior, especially those growing unbounded on one side.
method Introduces weighted deep polynomial approximants that combine learnable deep polynomials with one-sided weights.
result Weighted deep polynomial approximants outperform existing methods in approximating functions with asymmetric behavior.
Develops polynomial diffusion models for multi-factor commodity futures dynamics.
problem Modeling futures prices using latent state variables for short and long-term stochastic factors.
method Polynomial diffusion models to incorporate non-linear effects, two filtering methods for estimation.
result Accurate estimation of futures prices despite parameter identification issues in polynomial diffusion models.
Investigates polynomial time algorithms for computing Khovanov homology of braids.
problem Computing Khovanov homology for general braids is intractable.
method Examines polynomial time algorithms for 3-braids and a variation of the scanning algorithm for more general braids.
result Shows that for 3-braids, Khovanov homology can be computed in polynomial time, while for more general braids, it can be computed in polynomial time for bounded homological degrees.
Bayesian tensor network reduces conditional probability calculation to polynomial time.
problem Exponential cost of calculating conditional probabilities for multiple events.
method Bayesian tensor network (BTN) with polynomial complexity.
result Competitive performance in image recognition with simple tree structures.
Polynomial-time algorithm estimates mean with bounded covariance using differential privacy.
problem Estimating mean of a d-variate distribution with differential privacy constraints.
method Sum of Squares (SoS) exponential mechanism for polynomial-time differentially private estimation.
result First polynomial-time algorithm with O(d) samples for mean estimation under pure differential privacy. New algorithm speeds up learning of graphical models.
problem Learning graphical models with sparse structure efficiently.
method Vertex-greedy score-based algorithm for learning DAGs.
result Polynomial runtime for learning DAG models.
Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allo…
Analytic networks with bounded coefficients can't outperform polynomial approximations.
problem Approximation limits of neural networks with analytic activation functions under coefficient constraints.
method Deterministic analysis using comparison argument and Bernstein-type estimates.
result Networks with analytic activation functions and controlled coefficients cannot outperform classical polynomial approximation rates on non-analytic targets.
Given an automorphism of a free group Fn, we consider the following invariants: e is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); d is the maximal degree of polynomial growth of conjugacy classes; R is the rank of the fixed subgrou…
This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently computable. We propose a variant to the original speed prior (Schmidhuber, 2002),…
Parallel algorithm speeds up Jones polynomial computation.
problem Efficient computation of knot complexity measures.
method First parallel algorithm for exact Jones polynomial computation.
result Reduces computational time by an exponential factor.
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…
Efficiently optimizes boolean functions using multilinear polynomials and exponential weight updates.
problem Optimizing boolean functions over the boolean hypercube with high computational cost.
method Proposes a computationally efficient algorithm using multilinear polynomials and exponential weight updates.
result Improves computational time up to several orders of magnitude compared to state-of-the-art algorithms.
Quantifies polynomial approximation rates for smooth functions under various distributions.
problem Approximating smooth functions with polynomials under different distributional constraints.
method Develops a quantitative analogue of Carleman's theorem using complex analysis.
result Establishes superexponential rates of approximation for certain function classes over general distributions.
Adaptive algorithm identifies best arm with abstention, showing phase transition from polynomial to exponential error probability.
problem Bayesian best-arm identification with abstention to reduce undetected error.
method Adaptive algorithm PGWS that optimally uses abstention budget.
result Introducing any positive abstention budget induces an exponential decay in undetected error probability.
Polynomial-time algorithm for near-optimal community detection in graphs.
problem Node-private community estimation in stochastic block models.
method Explicit Lipschitz surrogate and accept-reject algorithm for sampling community labels.
result Achieves minimax rates for exact recovery with polynomial-time runtime and logarithmic privacy parameter.
Thompson Sampling shows polynomial regret for combinatorial semi-bandits with subgaussian rewards.
problem Finding optimal solutions in combinatorial semi-bandits with suboptimal sampling.
method Proposes Thompson Sampling with polynomial regret for linear combinatorial semi-bandits.
result Demonstrates 'mismatched sampling paradox' where knowing distributions can lead to worse performance.
Graphical notation simplifies complex polynomial constraints in linear models.
problem Complex polynomial constraints in linear structural equation models are impractical.
method Developed a graphical notation to represent these constraints.
result The graphical notation simplifies the representation of many polynomial constraints.
The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;C) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2*Pi*I. On the other hand if the absolute v…
Polynomial delay algorithm tests causal models with hidden variables.
problem Testing causal models with hidden variables in polynomial delay.
method c-component local Markov property (C-LMP) and polynomial delay algorithm.
result First algorithm for poly-delay testing of CIs in causal graphs with hidden variables.
Polynomial-time algorithm estimates edge density of random graphs with privacy and robustness.
problem Estimating edge density of random graphs while maintaining privacy and robustness.
method Sum-of-squares algorithm for robust edge density estimation and reduction from privacy to robustness.
result Optimal error rate up to logarithmic factors, matching theoretical lower bounds.
The volume conjecture and its generalization state that the series of certain evaluations of the colored Jones polynomials of a knot would grow exponentially and its growth rate would be related to the volume of a three-manifold obtained by Dehn surgery along the knot. In this paper, we show that for the figure-eight k…
A new machine learning model uses matrix exponentials for universal approximation.
problem Developing a robust and efficient machine learning model.
method Introduces a novel architecture using matrix exponentials as the only nonlinearity.
result The model achieves universal approximation properties and outperforms other models on benchmark tasks.
Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of th…
Detects changes in global financial networks before crashes.
problem Financial contagion and crashes across global markets.
method Sequential change point detection in dynamic networks.
result Can detect changes in network behavior before stock market crashes.
Estimates support in distributions with sampling artifacts and errors.
problem Support estimation in the presence of sampling artifacts and errors.
method Regularized weighted Chebyshev approximations with Touchard polynomials, discretized semi-infinte programming.
result Significant improvements over noiseless support estimation methods.
Time homogeneous polynomial processes are Markov processes whose moments can be calculated easily through matrix exponentials. In this work, we develop a notion of time inhomogeneous polynomial processes where the coeffiecients of the process may depend on time. A full characterization of this model class is given by m…
We study the growth of the order of torsion subgroups of the homology in a tower of finite abelian coverings. In particular, we prove that it is exponential for when the tower converges to the maximal free abelian cover of a link complement when the first nonzero Alexander polynomial has positive logarithmic Mahler mea…
Holomorphic actions on complex spaces for nilpotent groups.
problem Understanding polynomial actions on complex spaces for nilpotent groups.
method Explicit construction of biholomorphisms by polynomial maps.
result Simply connected nilpotent Lie groups are biholomorphic to Cn.