Solves natural PDE system for minimal surfaces in 4D Euclidean space.
problem Determining minimal surfaces in 4D Euclidean space.
method Explicitly solves the system of natural PDE's using two holomorphic functions.
result Expresses any solution of the system of natural PDE's by two holomorphic functions in the Gauss plane.
Deeper neural networks can better approximate certain natural functions than shallower ones.
problem Approximating natural functions with neural networks.
method Depth-based separation results for feed-forward neural networks.
result Deeper networks can better approximate certain types of functions than shallower ones.
Solves natural PDEs for minimal Lorentz surfaces in 4D spacetime.
problem Natural PDEs for minimal Lorentz surfaces in R24. method Weierstrass type representations and canonical coordinates.
result Explicit solution of the system of natural PDEs.
Paper extends option-critic architecture to estimate natural gradient for reinforcement learning.
problem Estimating natural gradient in hierarchical reinforcement learning.
method Introduces natural option critic algorithm to estimate natural gradient for option's policy and termination function.
result Improves over vanilla gradient approach in experimental results.
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to …
New algorithm for online convex minimization over integer lattice.
problem Online decision-making with nonlinear combinatorial objectives.
method Introduces online Latural-convex minimization and proposes efficient algorithms. result Tight regret bound for full information setting algorithm.
Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.
problem Local elliptic regularity for operators with low regularity coefficients in Sobolev-type spaces.
method Rescaling estimates and multiplication results for function spaces.
result Unified set of interior estimates and regularity inference for operators with Sobolev-type coefficients.
Natural gradient improves deep Q-learning performance.
problem Improving deep Q-learning stability and performance.
method Integrates natural-gradient techniques into deep Q-learning.
result Natural-gradient deep Q-learning (NGDQN) outperforms standard DQN without target networks and performs similarly to DQN with target networks.
A new black-box optimizer using implicit natural gradient.
problem Efficient optimization for complex, computationally intensive problems.
method Stochastic update with implicit natural gradient of an exponential-family distribution.
result Theoretical convergence rate for convex functions and continuous non-differentiable functions.
Trust-region methods and natural gradients are equivalent in certain policy search scenarios.
problem Improving policy search methods in continuous control tasks.
method Introducing compatible policy search (COPOS) that uses natural parameterization and compatible value function approximation to control entropy loss.
result COPOS yields state-of-the-art results in challenging tasks and reduces entropy loss.
Natural gradient learning improves synaptic plasticity in spiking neurons.
problem Parametrization dependence leads to inconsistencies in classical synaptic plasticity theories.
method Proposes natural gradient descent in Riemannian geometry for spiking neurons.
result Derives a synaptic learning rule that explains biological phenomena.
Entropy-regularized NPG converges linearly with linear function approximation.
problem Analyzing convergence of entropy-regularized NPG with function approximation.
method Established finite-time convergence analyses with entropy regularization and linear function approximation.
result Entropy-regularized NPG achieves linear convergence up to a function approximation error.
The author studies regions foliated by 1D families of functions and their applications.
problem Understanding regions represented as foliated forms and natural smooth maps onto them.
method Investigates natural smooth maps respecting canonical projections and moment maps, focusing on foliated regions.
result Discusses the 1st derivative of functions and critical sets in foliated regions.
Meta-Gradient RL adapts return nature online for improved performance.
problem Estimating and optimizing value functions without a true value function oracle.
method Gradient-based meta-learning algorithm that adapts return nature online.
result Achieved new state-of-the-art performance on 57 Atari 2600 games.
Improved activation function NLReLU boosts neural network performance.
problem Performance issues with ReLU activation function.
method NLReLU uses parametric natural logarithmic transform to improve ReLU.
result NLReLU provides higher accuracy than ReLU in various neural networks.
The paper characterizes conditions for convergence of RL methods with linear approximations.
problem Characterizing non-uniqueness issues for reinforcement learning algorithms with linear function approximation.
method Proves a condition on features that determines convergence or non-uniqueness of natural algorithms.
result Natural algorithms converge to the correct solution if and only if value functions in the approximation space satisfy a certain shape.
Study of circle arrangements related to Morse-Bott functions.
problem Understanding the geometry and singularity theory of Morse-Bott functions.
method Systematic construction of circle arrangements centered at existing circles, studying local changes in Reeb graphs.
result Reeb graphs of Morse-Bott functions are spaces of all components of preimages of single points.
Survey of deep learning methods for fMRI natural image reconstruction.
problem Reconstructing natural images from fMRI brain activity.
method Survey of deep learning approaches, including architectural design, datasets, and evaluation metrics.
result Performance evaluation across standardized metrics.
Defines manifolds of mappings between function spaces and discusses their properties.
problem Defining smooth manifolds of mappings between function spaces.
method Defines a smooth manifold structure on sets of continuous mappings and discusses properties of natural mappings.
result Properties of spaces of sections and smoothness of natural mappings between spaces of mappings.
Modified training direction reduces generalization error in neural networks.
problem Reducing generalization error in neural networks.
method Theoretical analysis of modified natural gradient descent in function space.
result Modifying training direction in function space reduces total generalization error.
Unified model for attention in NLP defined.
problem Lack of systematic overview of attention mechanisms in NLP.
method Unified model and taxonomy of attention models.
result First extensive categorization of NLP attention literature.
Given a knot K in the 3-sphere, consider a singular disk bounded by K and the intersections of K with the interior of the disk. The absolute number of intersections, minimised over all choices of singular disk with a given algebraic number of intersections, defines the framing function of the knot. We show that the fra…
The paper introduces various canonical parameterizations for 2D-curved shapes.
problem Comparing unparameterized simple curves in the plane.
method Proposes diverse canonical parameterizations, including arc-length and curvature-based.
result Natural parameterizations correspond to physical movements and are geometric invariants.
New method improves value function estimation in noisy environments.
problem High variance in value-based reinforcement learning methods.
method Introduce Recurrent Value Functions (RVFs) to estimate value function of current state using past states.
result RVFs show robustness and improved performance in noisy environments.
Constructs real algebraic functions with specified preimages.
problem Reconstructing smooth functions with prescribed preimages.
method Using real algebraic functions and techniques from singularity theory and differential topology.
result Constructs examples of real algebraic functions with specified preimages.
Lueck expressed the Gromov norm of a knot complement in terms of an infinite series that can be computed from a presentation of the fundamental group of the knot complement. In this note we show that Lueck's formula, applied to torus knots, yields surprising power series expansions for the logarithm function. This gene…
The natural gradient allows for more efficient gradient descent by removing dependencies and biases inherent in a function's parameterization. Several papers present the topic thoroughly and precisely. It remains a very difficult idea to get your head around however. The intent of this note is to provide simple intuiti…
Solves PDE system for minimal space-like surfaces in Minkowski space-time.
problem Solving the system of natural PDE's for minimal space-like surfaces.
method Using canonical Weierstrass representations, solves the system explicitly.
result Expresses solutions by means of two holomorphic functions.
New method converts natural language commands into reward functions for robots.
problem Creating effective reward functions for autonomous machines.
method Language-conditioned reward learning (LC-RL) using inverse reinforcement learning.
result Model learns transferable rewards from natural language commands.
The study finds a special type of smooth function on connected sums of manifolds.
problem Finding smooth functions that are Morse on preimages of non-extrema values.
method Investigates internally Morse (I-Morse) and neat with respect to Reeb graph (N-Reeb) functions.
result Constructs an IN-Morse-Reeb function on a connected sum of given manifolds.
Natural experiment dataset reveals inconsistent treatment effect estimators.
problem Inconsistent results from over 20 estimators on a new dataset.
method Created a benchmark to evaluate estimator accuracy, derived variance formula, introduced new estimator.
result Doubly robust estimators outperform others by orders of magnitude.
Challenge evaluates semantic code search using annotated corpus.
problem Evaluating relevant code from natural language queries.
method Release of CodeSearchNet Corpus and expert annotations.
result 99 queries with 4k relevance annotations for evaluation.
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. In this paper, we define naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. We investigate the properties of these mappin…
Efficient estimator for two-sample functionals improves on oracle performance.
problem Estimating two-sample integral functionals efficiently.
method Weighted nearest neighbour estimator, central limit theorem.
result The estimator can outperform the oracle in certain cases.
Demand functions for goods are generally cyclical in nature with characteristics such as trend or stochasticity. Most existing demand forecasting techniques in literature are designed to manage and forecast this type of demand functions. However, if the demand function is lumpy in nature, then the general demand foreca…
Bound critical points for minimal Radó functions.
problem Counting interior critical points for minimal Radó functions.
method Bounding critical points in terms of boundary data and domain Euler characteristic.
result Bound the number of interior critical points.
We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides with the well studied functional which is the integration over the manifold of the k-symmetric function of the Schouten tensor of…
Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting substantially of a vertical contraction factor function and nonlinear transform…
We produce examples of groups of type F_3 with 2-dimensional Dehn functions of the form exp^n(x) (a tower of exponentials of height n), where n is any natural number.
On any space-like W-surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as …
Study of energy functional on Deligne-Hitchin moduli space sections.
problem Understanding energy functionals on sections of Deligne-Hitchin moduli space.
method Generalizes energy of equivariant harmonic maps to holomorphic sections, links to meromorphic connections, and uses Willmore energy analogy.
result Shows functional is essentially Willmore energy for certain sections, distinguishes new components from twistor lines.
This paper introduces the Metric-Free Natural Gradient (MFNG) algorithm for training Boltzmann Machines. Similar in spirit to the Hessian-Free method of Martens [8], our algorithm belongs to the family of truncated Newton methods and exploits an efficient matrix-vector product to avoid explicitely storing the natural g…
Paper defines Farey Recursive Functions and explores their properties.
problem Understanding recursive functions on rationals.
method Defined and studied Farey Recursive Functions using Farey graph.
result Farey Recursive Functions naturally connect to 2-bridge knots and links.
We have performed detailed multifractal analysis on the minutely volatility of two indexes and 1139 stocks in the Chinese stock markets based on the partition function approach. The partition function χq(s) scales as a power law with respect to box size s. The scaling exponents τ(q) form a nonlinear function of …
Defines 'nowhere coexpanding functions' and studies their fixed points.
problem Understanding fixed points of nowhere coexpanding functions.
method Defines and studies C1 nowhere coexpanding functions, including C3 functions with non-positive Schwarzian derivative. result Establishes results on the number and nature of fixed points, generalizing Singer's result.
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. A symplectic abelian Chern-Simons partition functi…
A method for diffusion on probability simplex for generative models.
problem Tension between continuous and discrete data in diffusion models.
method Proposes using softmax function applied to Ornstein-Uhlenbeck Process on probability simplex.
result Method extends to bounded image generation.
This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.