Reduced parameter space improves neural network training efficiency.
problem Training efficiency and optimization in neural networks.
method Training weights on a unit sphere and thresholds in a bounded interval.
result Equivalent performance with reduced parameter space.
New analysis shows black-box methods outperform action space methods in certain scenarios.
problem Comparing black-box methods vs. action space methods in exploration.
method Theoretical analyses and empirical comparisons of simple methods on various problems.
result Complexity of exploration in parameter space depends on parameter space dimensionality, while action space complexity depends on both action space and horizon length.
Paper reduces movement primitive dimensionality in parameter space.
problem High dimensionality of movement primitives makes policy optimization expensive.
method Investigates dimensionality reduction in parameter space, identifying principal movements.
result Dimensionality reduction in parameter space is more effective than in configuration space.
Algorithm learns optimal parameters from infinite space for computational resource optimization.
problem Finding nearly-optimal parameters from an infinite space of tunable parameters.
method Learn a finite set of promising parameters from an infinite set using a data-independent discretization approach.
result Algorithm can help compile a configuration portfolio or select input to a configuration algorithm for finite parameter spaces.
We study the Euler-Lagrange equations for a parameter dependent G-invariant Lagrangian on a homogeneous G-space. We consider the pullback of the parameter dependent Lagrangian to the Lie group G, emphasizing the special invariance properties of the associated Euler-Poincaré equations with advected parameters.
Gradient flow in parameters equals linear interpolation in outputs.
problem Understanding and optimizing training algorithms in deep learning.
method Proving equivalence between gradient flow in parameter space and linear interpolation in output space, and deriving formulas for global minima.
result Gradient flow in parameters can be transformed into linear interpolation in outputs, leading to global minima.
Combines NES and PPO to enhance exploration in various environments.
problem Improving exploration in reinforcement learning environments.
method Parameter transfer and parameter space noise methods for combining NES and PPO.
result PPO benefits from both NES methods in discrete and continuous control tasks.
Empirical study shows removing neural parameter symmetries impacts model performance.
problem Understanding the impact of neural parameter symmetries on model performance.
method Developed two methods to reduce parameter space symmetries in neural networks.
result Removing parameter symmetries can lead to faster and more effective Bayesian neural network training.
The paper defines and studies canonical parameters on surfaces in 4D space.
problem Understanding surfaces in 4D space without minimal points.
method Defining and proving existence of canonical principal parameters.
result Surfaces in 4D space are uniquely determined by four functions satisfying partial differential equations.
Sharp bounds on hyperbolic metrics in Ptolemaic spaces are derived.
problem Finding sharp bounds on hyperbolic metrics in Ptolemaic spaces.
method Construction of metrics on open subsets of Ptolemaic spaces.
result Sharp parameter bounds for hyperbolic and strongly hyperbolic metrics are derived.
Improved Bayesian optimization for conditional parameter spaces.
problem Efficient global optimization of expensive-to-evaluate functions in conditional parameter spaces.
method Additive tree-structured covariance function for conditional parameter optimization.
result Significantly improved sample-efficiency and wider applicability compared to existing methods.
The paper introduces canonical parameters for marginally trapped surfaces in Minkowski space.
problem Determining marginally trapped surfaces in Minkowski space.
method Introducing canonical parameters and proving existence and uniqueness theorems.
result Every marginally trapped surface is determined by three smooth functions.
Study geometric flows with varying parameters and prove continuous dependence.
problem Continuous dependence of flows on parameters in geometric settings.
method Derived suitable topologies for vector fields and flows, proved new continuous dependence.
result Proved continuous dependence of flows on parameters in a general topological space.
A new method reduces high-dimensional parameter spaces for faster numerical tasks.
problem Efficiently reducing high-dimensional parameter spaces for numerical tasks.
method Local Active Subspaces (LAS) combining active subspaces with clustering techniques.
result Significant speed-up in numerical tasks through efficient dimension reduction.
Study of metric spaces and group actions using Vietoris-Rips and Čech complexes.
problem Understanding the homotopy type of quotient spaces under group actions.
method Intermediate scale parameters for Vietoris-Rips and Čech complexes.
result First scale parameter where homotopy type of projective spaces changes.
Conditions for uniquely identifying parameters of deep ReLU networks.
problem Characterizing networks whose parameters can be uniquely identified.
method Conditions on deep fully-connected feedforward ReLU neural networks.
result Parameters of the network are uniquely identified under certain conditions.
A new exploration method for RL using parameter space noise.
problem Improving exploration in deep reinforcement learning.
method Switching isotropic and directional exploration in parameter space with parameter space noise.
result The proposed method achieves competitive results and better performance in sparse reward environments.
We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.
Gaussian kernel fails on circle and related spaces.
problem Gaussian kernel's positive definiteness on non-Euclidean spaces.
method Analyzing the Gaussian kernel on the circle and related metric spaces.
result Gaussian kernel is not positive definite on the circle or spaces admitting circle embeddings.
This paper proves Hitchin moduli spaces are ALG gravitational instantons.
problem Proving Hitchin moduli spaces are ALG gravitational instantons.
method Computing Torelli parameters for each Hitchin moduli space corresponding to different parabolic data.
result All Hitchin moduli spaces studied are ALG-D4 gravitational instantons. Study singularity structures in finite mixtures affecting parameter estimation rates.
problem Understanding how singularity structures impact parameter estimation in finite mixtures.
method Developed a general framework to identify singularity structures in finite mixtures and studied their effects on convergence rates and minimax lower bounds.
result Established convergence rates for finite mixtures of skew-normal distributions, revealing complex asymptotic behaviors.
The monster tower's spaces are stratified naturally.
problem Describing the monster tower's spaces.
method Natural stratification of parameter spaces.
result A natural stratification of the monster tower's spaces.
This work formalizes and extends parameter sharing in multi-agent reinforcement learning.
problem Parameter sharing limits multi-agent learning to a single policy, preventing different tasks or action spaces.
method Introduces agent indication and extends parameter sharing to heterogeneous observation and action spaces.
result Proves convergence to optimal policies for parameter sharing in heterogeneous environments.
Parameter noise enhances RL exploration efficiency.
problem Enhancing RL exploration efficiency through parameter noise.
method Combining parameter noise with traditional RL methods.
result RL with parameter noise learns more efficiently than traditional RL methods.
Generatability in metric spaces studied with novel novelty parameters.
problem Understanding generatability in metric spaces with asymmetric novelty parameters.
method Introducing (ε,ε′)-closure dimension to characterize uniform and non-uniform generatability. result Generatability is stable across novelty scales in doubling spaces but can be highly scale-sensitive in general metric spaces.
Minimal surfaces in 4D space characterized with specific parameters and Weierstrass formulas.
problem Characterizing minimal surfaces in Euclidean 4-space.
method Characterization with canonical parameters and derivation of Weierstrass representations.
result Minimal surfaces in 4D space correspond to pairs of minimal surfaces in 3D space.
This Ph.D. thesis is devoted to the constructions of Lagrangian formulation on Finsler and Kawaguchi manifolds. While Finsler geometry is a natural extension of Riemannian geometry, Kawaguchi geometry is the extension of Finsler geometry to higher order derivatives and to k-dimensional parameter space. The latter exten…
Teichmüller space and hyperelliptic surfaces parametrized by angles.
problem Parametrizing Teichmüller space and hyperelliptic surfaces using angles.
method Proved parametrization using 6g-5 and 4g-2 angle parameters for Teichmüller space and hyperelliptic surfaces respectively.
result Proved parametrization of Teichmüller space and hyperelliptic surfaces by angle parameters.
New method encodes function preferences into neural nets for better generalization.
problem Challenges in encoding explicit function preferences in neural network training.
method Function-space empirical Bayes (FSEB) regularization.
result FSEB leads to near-perfect semantic shift detection and improved generalization.
Study surfaces with parallel mean curvature in 4D spaces.
problem Characterize surfaces with parallel normalized mean curvature in Euclidean or Minkowski 4-space.
method Introduced special isothermal parameters and described surfaces using invariant functions.
result Surfaces with parallel normalized mean curvature are uniquely determined by three invariant functions.
Noise added to deep Q-networks reduces adversarial attacks.
problem Vulnerability of deep reinforcement learning to policy manipulation attacks.
method Addition of noise to the parameter space of deep reinforcement learners during training.
result Noise reduces the transferability of adversarial examples.
Improved likelihood-free inference for high-dimensional models.
problem Challenges in likelihood-free inference for high-dimensional parameter spaces.
method Bayesian optimization-based approach with misspecification-robust characterisation.
result Efficient inference in 100-dimensional space with real data application.
Sliced Inverse Regression reduces parameter space for estimating complex financial models.
problem High-dimensional parameter space in stochastic differential equations.
method Sliced Inverse Regression for dimension reduction.
result Reduced computational costs in estimating parameters.
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
New Riemannian radial distributions help estimate parameters on symmetric spaces.
problem Challenges in manifold data analysis due to lack of parametric distributions.
method Introduced Riemannian radial distributions on symmetric spaces, utilized symmetry, and developed M-estimators.
result MLE achieves root-n convergence rate up to logarithmic terms, demonstrating optimality.
New black-box reductions simplify online learning algorithms.
problem Designing adaptive and parameter-free online learning algorithms.
method Introducing black-box reductions to simplify analysis and improve regret guarantees.
result Improved regret bounds for parameter-free learning.
Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. We derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these paramete…
A projective parameter of a geodesic on a Finsler space is defined to be solution of a certain ODE. Using projective parameter and Funk metric, one can construct a projectively invariant intrinsic pseudo-distance on a Finsler space. In the present work, solutions of the projective parameter's ODE are characterized with…
Function-space MAP estimation leads to better generalization and robustness.
problem The mismatch between parameter posterior and function posterior in model training.
method Directly estimating the most likely function implied by the model and data.
result Function-space MAP estimation can lead to flatter minima, better generalization, and improved robustness.
A non-elementary Möbius group generated by two-parabolics is determined up to conjugation by one complex parameter and the parameter space has been extensively studied. In this paper, we use the results of \cite{GW} to obtain an additional structure for the parameter space, which we term the {\sl two-parabolic space}. …
Study geodesics in homogeneous spaces and find conditions for their existence.
problem Characterize geodesics in homogeneous spaces.
method Analyze geodesics of the form γ(t)=π(exp(tX)exp(tY)) in G/K. result Existence of geodesics for specific conditions in homogeneous spaces.
Global conformal parameters found for complex and hyperbolic curves.
problem Finding global conformal parameters for analytic curves.
method Analytic curves in complex and hyperbolic planes, and their generalizations.
result Spherical and hyperbolic arc-lengths are global conformal parameters for analytic curves.
Using the navigation data (h,W) of a Kropina space, we characterize weakly-Berwald Kropina spaces and Berwald Kropina spaces by means of the Killing vector field W and the parallel vector field W, respectively. Moreover, the local 1-parameter group of Finslerian local isometries of the Kropina space coincides with the …
Develops methods to measure and set function-space learning rates in neural networks.
problem Measuring and optimizing changes in neural network output functions.
method Efficient methods to measure and set function-space learning rates, requiring minimal computational overhead.
result Demonstrates FLeRM (Function-space Learning Rate Matching) for hyperparameter transfer across model scales.
In this paper we construct a compactification for the parameter space of convex projective structures on a fixed n-manifold M. This parameter space is a closed semi-algebraic subset of the variety of characters of representations of the fundamental group of M in SL_{n+1}(R). The boundary is the inverse limit of an inve…
Trains neural networks to efficiently solve Navier-Stokes equations across parameter space.
problem Efficiently solving Navier-Stokes equations in parameter space.
method Physics-informed neural networks, active learning algorithm.
result Neural networks can accurately interpolate and aggregate solutions to physical problems.
INNs solve ambiguous inverse problems by learning forward and inverse processes together.
problem Determining hidden system parameters from ambiguous measurements.
method Invertible Neural Networks (INNs) learn both forward and inverse processes.
result INNs provide a full distribution over parameter space given a measurement and latent variables.
The paper examines geometric curvatures in generalized Riemannian spaces.
problem Understanding the physical meaning of scalar curvatures in generalized Riemannian spaces.
method Developed Madsen's formulae for pressures and energy-densities, analyzed with different concepts of generalized Riemannian spaces.
result Linearities of energy-momentum tensor, pressure, energy-density, and state-parameter are examined.