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.
We present the strongest known knot invariant that can be computed effectively (in polynomial time).
Polynomial-time method solves complex combinatorial semi-bandits.
problem Optimal strategies for combinatorial semi-bandits with uncorrelated Gaussian rewards.
method Proposes a polynomial-time method to solve the Graves-Lai optimization problem for various combinatorial structures.
result First known approach to implement asymptotically optimal algorithms in polynomial time for combinatorial semi-bandits.
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.
Paper extends Cohen's method to compute Jones polynomial for certain braid subfamilies.
problem Computing Jones polynomial for specific knot families.
method Using weighted adjacency matrices and determinants for certain subfamilies of braid groups.
result Jones polynomial can be computed in polynomial time for certain subfamilies of braid groups.
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),…
Algorithm creates polynomials for knotted surfaces, with bounds on degree.
problem Creating polynomials for knotted surfaces with constraints.
method Algorithm constructs polynomials based on loop braids and surface braids.
result Upper bounds on the degree of polynomials for knotted surfaces.
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.
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.
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.
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…
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.
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 reachability for LTI systems with TLL NN controllers is achieved.
problem Bounding the reachable set of LTI systems controlled by TLL NN controllers.
method Polynomial-time computation of exact one-step reachable set and tight bounding box via two methods.
result Exact reachability computation in polynomial time for TLL NN controllers.
New algorithms explain Naive Bayes classifiers in polynomial time and delay.
problem Computing explanations for Naive Bayes classifiers efficiently.
method Developed log-linear time and polynomial delay algorithms for PI-explanations.
result Efficiently computed PI-explanations for linear classifiers.
New polynomial-time solutions found for training ReLU networks, mirroring Max-Cut complexity.
problem Training two-layer ReLU neural networks with weight decay regularization.
method Developed a convex formulation and randomized algorithm to find approximate global optimizers.
result First polynomial-time approximation guarantees and hardness of approximation results for regularized ReLU networks.
Polynomial-time methods count and sample DAGs from Markov classes.
problem Counting and sampling Markov equivalent DAGs.
method Polynomial-time algorithms for DAGs from Markov classes.
result Long-standing open problem solved, making practical infeasible strategies feasible.
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.
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. 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.
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.
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this pap…
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…
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.
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^…
Ancient caloric functions on manifolds with polynomial growth are studied under volume doubling barrier.
problem Analyzing ancient caloric functions on manifolds beyond volume doubling.
method Time polynomial structure result on ancient caloric functions with polynomial growth.
result Finiteness result for ancient caloric functions is essentially sharp, except for multi-end cases.
Following the recent work by Chan, and by Morton and Hadji on the Homflypt polynomials of some generalized Hopf links, we investigate the Kauffman polynomials of generalized Hopf links. By studying the Kauffman skein module of the solid torus S^1\times D^2, we establish a similar skein map on the Kauffman skein module …
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.
Novel knot polynomials from Gaussian calculus show half vanish and determine Jones polynomials.
problem Understanding and characterizing knot polynomials from Gaussian calculus.
method Gaussian calculus of generating series for noncommutative algebras, connected sum of knots.
result Half of the polynomials vanish and three polynomials are explicitly given.
Study shows polynomial-width neural networks can closely approximate infinite-width networks in polynomial time.
problem Approximating dynamics of polynomial-width neural networks with infinite-width networks.
method Bounding approximation gap through a differential equation governed by mean-field dynamics, considering local Hessian.
result Polynomially many neurons are sufficient to closely approximate mean-field dynamics.
Bounds on knot polynomials for Lie superalgebras of type I.
problem Determining genus bounds for knot polynomials colored by Lie superalgebra representations.
method Proved bounds on the t-degree of knot polynomials, relating it to the number of odd roots and the genus of the knot. result Proved bounds on knot polynomials for Lie superalgebras of type I, showing equality for certain knots.
Polynomial-time algorithm for clustering mixtures with separation Δ=Ω(√(log k)).
problem Clustering mixtures of mean-separated Gaussians in high dimensions.
method Polynomial-time algorithm using implicit moment estimation.
result Achieves almost optimal clustering guarantee with separation Δ=Ω(√(log k)).
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics, making them especially challenging. Standard approaches, often relying on ADP, dualit…
Computes Kauffman bracket polynomial for specific 2-tangle shadows.
problem Calculating Kauffman bracket polynomial for complex tangle structures.
method Computed Kauffman bracket polynomial for specific 2-tangle shadows with up to 4 crossings.
result Computed polynomial for specific 2-tangle shadows.
Polynomial-time algorithm solves random parity games with high probability.
problem Solving random parity games efficiently.
method SWCP algorithm based on cycles in subgraphs.
result Polynomial-time solution for large-degree games with high probability.
New moving average adapts weight dynamically based on polynomial and wavefunction.
problem Lagging traditional moving averages in adjusting to changes in data.
method Develops a moving average with weight as a polynomial of a wavefunction from an eigenproblem.
result Immediate 'switch' without lag, adapting to changes in data.
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.
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.
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.
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.
Polynomial-time algorithm learns ReLU networks without assumptions.
problem Learning linear combinations of ReLU activations with Gaussian inputs.
method Random contractions of moment tensors and multi-scale analysis.
result First polynomial-time algorithm without additional assumptions.
In this article, we explore a class of tractable interest rate models that have the property that the price of a zero-coupon bond can be expressed as a polynomial of a state diffusion process. Our results include a classification of all such time-homogeneous single-factor models in the spirit of Filipovic's maximal deg…
Homology handles with trivial Alexander polynomial bound a 3D sphere.
problem Understanding when homology handles bound 3D spheres.
method Using Freedman and Quinn's result for Z-homology 3-spheres. result A distinguished homology handle with trivial Alexander polynomial bounds a homology S1imesD3. 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 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.
Detecting correlated trees helps align sparse graphs.
problem Detecting correlation between trees for sparse random graphs.
method MPAlign message-passing algorithm for graph alignment.
result MPAlign succeeds in polynomial time for partial alignment.
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.
New upper bound on Jones polynomial for fibered positive links.
problem Classifying positive and non-positive knots of crossing number ≤ 12.
method Proved a new upper bound on the maximum degree of Jones polynomial for fibered positive knots.
result Maximum degree of Jones polynomial for fibered positive knots is at most four times the minimum degree.