Developed algorithms to compute three polynomial invariants of veering triangulations.
problem Computing polynomial invariants of veering triangulations.
method Introduced and used algorithms for taut, veering, and Teichmüller polynomials based on upper and lower tracks of veering triangulations.
result Proved that the lower and upper taut polynomials are equal but the veering polynomials can differ.
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.
The paper provides an almost optimal learning and testing algorithm for sparse polynomials.
problem Learning and testing sparse multivariate polynomials efficiently.
method The paper presents an algorithm with sublinear query complexity in 1/ε and almost linear in s for learning and testing s-sparse polynomials. result The algorithm achieves almost optimal query complexity, making it the first of its kind.
This paper studies a specific blow-up algorithm for sop polynomials and their RLCT.
problem Determining the RLCT of sum-of-products polynomials through blow-up.
method Investigates a specific blow-up algorithm for sop polynomials to resolve their singularities.
result It is possible to resolve the singularities of sop polynomials using a specific blow-up algorithm.
Strongly polynomial algorithm for approximate Forster transforms and halfspace learning.
problem Computing approximate Forster transforms and halfspace learning.
method Strongly polynomial time algorithm for approximate Forster transforms and halfspace learning.
result First strongly polynomial time algorithm for distribution-free PAC learning of halfspaces.
Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.
problem Matching vertices in two correlated Erdős-Rényi graphs.
method Iterative matching algorithm for correlated Gaussian Wigner matrices.
result First polynomial time algorithm for graph matching with arbitrarily small constant correlation.
New algorithm speeds up polynomial kernel approximations.
problem Efficiently approximating polynomial kernels of high degree.
method Oblivious sketching combined with novel sampling.
result Polynomial factor slowdown removed in running time.
Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.
problem Matching correlated random graphs with non-vanishing edge correlation.
method Iterative algorithm for polynomial-time recovery of latent matching.
result Algorithm succeeds in recovering latent matching as long as edge correlation is non-vanishing.
We propose an algorithm which allows to derive the generalized Alexander polynomial invariants of knots and links with the help of the q,p-numbers, appearing in bosonic two-parameter quantum algebra. These polynomials turn into HOMFLY ones by applying special parametrization. The Jones polynomials can be also obtained …
New algorithm speeds up knot polynomial calculations.
problem Computing Reshetikhin--Turaev knot polynomials efficiently.
method Fixed-parameter tractable computation via tensor networks.
result Knot polynomial computations are fixed-parameter tractable.
Algorithm learns halfspaces with Tsybakov noise in polynomial time.
problem PAC learning halfspaces with adversarial noise.
method Reduction to certifying non-optimality, iterative process, warm-start algorithm.
result First polynomial-time algorithm for learning halfspaces with Tsybakov noise.
Algorithm classifies surface homeomorphisms with polynomial time complexity.
problem Classifying surface homeomorphisms with polynomial time complexity.
method Algorithm to compute curve distances and decide Nielsen-Thurston types.
result Polynomial time classification of surface homeomorphisms.
Polynomial algorithm for multiplication on one-hole torus skein algebra.
problem Complexity of multiplicative structure in skein algebra.
method Provided a polynomial algorithm for one-hole torus.
result Closed form formulas for multiplication of curves with low crossing number.
Polynomial-time methods count and sample DAGs from equivalence classes.
problem Counting and sampling DAGs from Markov equivalence classes.
method Polynomial-time algorithms for DAGs.
result Counting and sampling can be done in polynomial time.
Predicts the number of polynomial additions in Buchberger's algorithm using machine learning.
problem Predict the number of polynomial additions in Buchberger's algorithm.
method Multiple linear regression and recursive neural network models trained on ideal generator statistics.
result Machine learning can predict the number of polynomial additions in Buchberger's algorithm.
Polynomial-time algorithm learns causal graphs without parametric assumptions.
problem Learning causal graphs from data without assuming linearity or parametric forms.
method Model-free polynomial-time algorithm with finite-sample guarantees.
result Algorithm achieves linear cost in dimension and samples compared to optimal.
This study limits the number of pretzel links with a specific Jones polynomial span.
problem Determining the number of pretzel links with a given Jones polynomial span.
method Developed an algorithm to decide if a knot is pretzel and used it to identify all pretzel knots up to nine crossings.
result Identified all pretzel knots up to nine crossings, proving 812 is not pretzel. Machine learning improves Buchberger's algorithm for polynomial systems.
problem Optimizing S-pair selection in Buchberger's algorithm for polynomial systems.
method Reinforcement learning agents trained with PPO to select S-pairs.
result Trained model outperforms existing heuristics in polynomial additions.
In this paper we study the adaptive learnability of decision trees of depth at most d from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^…
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.
We describe the polynomial time complexity algorithm for computing first coefficients of the skein (Homflypt) and Kauffman polynomial invariants of links, discovered by D.Vertigan in 1992 but never published.
SURF simplifies distribution estimation with simple, robust, and fast algorithms.
problem Efficient and accurate distribution estimation in statistics and machine learning.
method Piecewise polynomial approximation using empirical probability interpolation and divide-and-conquer merging.
result Surpassing state-of-the-art algorithms in efficiency and accuracy, SURF estimates distributions robustly and quickly.
Algorithm samples from Bingham distribution efficiently.
problem Sampling from the Bingham distribution on a sphere.
method Rejection sampling with polynomial approximation.
result Exact samples from Bingham distribution in polynomial time.
Algorithm learns polynomial transformations of Gaussian distributions.
problem Learning high-dimensional polynomial transformations of Gaussian distributions.
method Polynomial-time algorithms for smoothed settings, tensor ring decomposition.
result First end-to-end guarantees for learning pushforwards under neural networks.
New algorithm recovers sparse measures in polynomial time.
problem Recovering sparse measures from Fourier moments.
method Polynomial-time recovery method inspired by mean-field theory.
result Improves upon convex relaxation methods in specific parameter regime.
EKM solves the K-medoids problem in polynomial time.
problem The K-medoids problem in data analysis. method EKM is a novel algorithm using transformational programming and combinatorial generation.
result EKM solves the K-medoids problem in worst-case $O\left(N^{K+1}
ight)$ time complexity. We explain an algorithm for finding a boundary link Seifert matrix for a given Alexander polynomial. The algorithm depends on several choices and therefore makes it possible to find non-equivalent Seifert matrices for a given Alexander polynomial.
This paper gives a generalization of the AJL algorithm and unitary braid group representation for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle of the Jones parameter. We show that our 3-strand algorithm for the Jones polynomial is a special case of this generalization of…
Polynomial-time algorithm learns high-dimensional halfspaces without labels.
problem Learning high-dimensional halfspaces with margins in polynomial time.
method Contrastive moments and polynomial-time algorithm.
result Establishes the unique and efficient identifiability of the hidden halfspace.
In this paper we give a quantum statistical interpretation for the bracket polynomial state sum <K> and for the Jones polynomial. We use this quantum mechanical interpretation to give a new quantum algorithm for computing the Jones polynomial. This algorithm is useful for its conceptual simplicity, and it applies to al…
New algorithm learns ReLU networks efficiently using Schur polynomials.
problem PAC learning a linear combination of ReLU activations under Gaussian distribution.
method Uses tensor decomposition and Schur polynomials to identify and analyze higher-order moments.
result Near-optimal sample and computational complexity for learning ReLU networks.
Algorithm calculates Jones polynomial from Goeritz matrix.
problem Calculating Jones polynomial from link diagrams.
method Explicit algorithm using Goeritz matrices.
result Jones polynomial can be recovered from orientable checkerboard surfaces.
The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along a braid model of the colored Jones polynomial that was refined by Armond from th…
We give a simple algorithm that determines whether a given post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm produces the Hubbard tree; otherwise, the algorithm produces the canonical obstruction. Our approach is rooted in geometric group theory, using iterati…
We give an algorithm for computing the Teichmüller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such links distinguished by the Teichmüller polynomial.
New algorithm learns decision trees faster than before.
problem Properly learning decision trees in polynomial time.
method Membership query algorithm with nO(loglogn) time complexity. result Achieved faster learning time for decision trees.
Algorithm distinguishes Gaussian mixtures from pure Gaussians in quasi-polynomial time.
problem Distinguishing mixtures of Gaussian components from pure Gaussians, especially when components are well-separated.
method Sum-of-Squares method, quasi-polynomial time algorithm, bipartitioning sample to separate components.
result Algorithm can reliably distinguish between mixtures and pure Gaussians in quasi-polynomial time.
Polynomial-time DP algorithm for learning Gaussians with matching sample complexity.
problem Learning Gaussian distributions while maintaining privacy.
method General framework for reducing DP estimation to non-private, polynomial-time algorithm for Gaussian learning.
result Matching sample complexity to information-theoretic upper bound for Gaussian learning.
Abstract reviews algorithms for multi-index models, focusing on polynomial-time methods and their limitations.
problem Estimating the index space in multi-index models efficiently and accurately.
method Polynomial-time algorithms in Gaussian space, nonparametric gradient estimation, and neural network fitting.
result A gap exists between computationally efficient methods and information-theoretical minimum.
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. The Teichmueller polynomial of a fibered 3-manifold plays a useful role in the construction of mapping class having small stretch factor. We provide an algorithm that computes this polynomial of the fibered face associated to a pseudo-Anosov mapping class of a disc homeomorphism. As a byproduct, our algorithm allows us…
We show that the standard stochastic gradient decent (SGD) algorithm is guaranteed to learn, in polynomial time, a function that is competitive with the best function in the conjugate kernel space of the network, as defined in Daniely, Frostig and Singer. The result holds for log-depth networks from a rich family of ar…
Simple proof of knot genus theorem using Alexander polynomial.
problem Proving the genus of an alternating knot equals half the breadth of its Alexander polynomial.
method Elementary, self-contained proof using Seifert's algorithm.
result Minimal genus surface obtained from any alternating knot diagram.
In their precedent work, the authors constructed closed oriented hyperbolic surfaces with pseudo-Anosov homeomorphisms from certain class of integral matrices. In this paper, we present a very simple algorithm to compute the Teichmueller polynomial corresponding to those surface homeomorphisms by first constructing an …
A new method builds sparse polynomial chaos expansions for models with dependent inputs.
problem Quantifying uncertainty in models with dependent inputs.
method Data-driven approach to construct orthonormal polynomials recursively based on input correlations.
result Reduces the number of observations and improves numerical stability and computational efficiency.
We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For example, we can use these geodesics to compute the asymptotic translation length, Ni…
Optimizes algorithms for non-concave bandit problems.
problem Optimizing algorithms for non-concave bandit problems.
method Unified zeroth-order optimization paradigm.
result Minimax-optimal algorithms in the dimension for low-rank generalized linear bandit problems.
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.