Groups satisfy linear surface isoperimetric functions.
problem Isoperimetric functions for surface diagrams in hyperbolic groups.
method Analyzing word-hyperbolic groups and their surface diagrams.
result Linear isoperimetric functions for all surface types in hyperbolic groups.
Paper introduces non-linear process convolutions for multi-output Gaussian processes.
problem Building accurate covariance functions for multi-output Gaussian processes.
method Volterra series for non-linearity, closed-form expressions for mean and covariance.
result Non-linear model outperforms classical process convolution in synthetic and real datasets.
Study one-dimensional topological theories with linear generating functions.
problem Understanding one-dimensional topological theories with defects.
method Construct bases of hom spaces for decorated unoriented one-dimensional cobordisms.
result Gram determinant and linear generating functions constructed.
Simpler GNNs perform well on graph classification tasks.
problem Understanding what Graph Neural Networks (GNNs) learn and their complexity.
method Dissected GNNs into graph filtering and set function, linearizing them separately.
result Linear graph filtering with non-linear set function is efficient and powerful.
We analyze concave idleness functions of graph curvature.
problem Understanding curvature functions of graphs.
method We study the concavity and piecewise linearity of Ollivier-Ricci idleness functions of graphs.
result Idleness functions are concave and piecewise linear with at most 3 linear parts.
A new complexity measure for neural networks improves upon classical methods.
problem Lack of a refined complexity measure for comparing different neural network architectures, especially permutation-invariant ones.
method Introduced an equivalence relation among linear functions and counted them relative to this relation.
result The new complexity measure clearly distinguishes between different models and increases exponentially with depth.
Study on distributional TD learning with linear approximations for better return estimation.
problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.
Logarithmic regret achieved in RL with linear function approximation.
problem Achieving logarithmic regret in reinforcement learning with linear function approximation.
method LSVI-UCB for linear MDP assumption, UCRL-VTR for linear mixture MDP assumption.
result Logarithmic regret bounds established for RL with linear function approximation.
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.
Papers learn from data to make decisions without interacting, improving on previous methods.
problem Achieving optimal decision-making from offline data with non-linear function approximation.
method Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI) with three innovative components.
result Achieves minimax optimal instance-dependent regret for non-linear function approximation.
DNNs can approximate fractal functions with exponential linear regions.
problem Understanding neural network approximations of complex functions.
method Using Iterated Function Systems (IFS) and neural networks to generate fractal functions.
result DNNs can generate fractal functions with a number of linear regions exponential in the number of parameters.
New algorithms improve distributional TD learning with linear approximations.
problem Estimating return distributions in reinforcement learning.
method Fine-grained analysis of linear-categorical Bellman equation, variance reduction techniques.
result Tight sample complexity bounds for distributional TD learning with linear approximations.
Paper presents efficient RL algorithm for linear dynamics without simulator assumptions.
problem Designing efficient RL algorithms with function approximation for linear settings.
method Optimistic modification of Least-Squares Value Iteration (LSVI).
result Achieves i l d e O ( d 3 H 3 T ) ilde{\mathcal{O}}(\sqrt{d^3H^3T}) i l d e O ( d 3 H 3 T ) regret, independent of states and actions. New neural network models for functional data.
problem Handling non-linear functional data.
method Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN) with gradient-based optimization.
result Demonstrated effectiveness in complex functional models.
New RL algorithm achieves nearly optimal performance for linear MDPs.
problem Optimal reinforcement learning for episodic linear MDPs.
method Weighted linear regression with variance estimator and rare-switching policy.
result Achieves nearly minimax optimal regret i l d e O ( d H 3 K ) ilde O(d\sqrt{H^3K}) i l d e O ( d H 3 K ) . We study Jacobi structures on the dual bundle A ∗ A^\ast A ∗ to a vector bundle A A A such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on A A A and a 1-cocycle φ ∈ Γ ( A ∗ ) φ\in Γ(A^\ast) φ ∈ Γ ( A ∗ ) indu…
Paper proposes a new activation function to reduce overfitting and large weight update issues.
problem Overfitting and large weight update problems in neural networks.
method Introduces a new activation function called Thresholded Exponential Rectified Linear Units (TERELU).
result TERELU shows better performance in reducing overfitting and large weight update issues compared to other activation functions.
Geometric study of linear neural networks identifies pure and spurious critical points.
problem Understanding the landscape of loss functions in linear neural networks.
method Geometric properties of functional spaces and parameterization analysis.
result Different phenomena cause the absence of bad local minima in linear networks, depending on the architecture and loss function.
New algorithm reduces reinforcement learning regret to sqrt(d^3T).
problem Efficient reinforcement learning with generalized linear function approximation.
method Optimistic closure assumption for generalized linear functions.
result Proved regret bound of O(sqrt(d^3T)).
This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.
problem Functional linear regression without target function in RKHS.
method Integral operator approach to establish upper bounds and prove asymptotic optimality.
result Sharp finite sample upper bounds and asymptotic optimality of divide-and-conquer estimators.
Enhances Cox model for survival analysis with symbolic non-linear log-risk functions.
problem Limited interpretability and non-linearity in traditional Cox models.
method Introduces GCPH model using Kolmogorov-Arnold Networks for symbolic non-linear log-risk functions.
result GCPH achieves competitive performance and superior interpretability.
Generative classifiers' properties are linked to linear constraints.
problem Understanding the Markov property in generative classifiers.
method Characterization of discrimination functions using linear constraints and a second order finite difference operator.
result Discrimination functions of undirected Markov network classifiers are characterized by sets of linear constraints.
UCRL2-VTR achieves nearly optimal regret for learning MDPs with linear function approximation.
problem Learning infinite-horizon average-reward MDPs with linear function approximation.
method UCRL2-VTR algorithm with Bernstein-type bonus.
result Achieves a regret of i l d e O ( d D T ) ilde{O}(d\sqrt{DT}) i l d e O ( d D T ) with matching lower bound. Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
Global approximation for piecewise linear paths via signatures.
problem Global approximation theorems for piecewise linear paths.
method Using signatures of piecewise linear paths and their density in L p L^p L p -norms. result Linear functionals of signatures are dense in L p L^p L p -norms under an integrability condition. Gaussian processes with linear constraints ensure function adherence.
problem Ensuring function adherence to known constraints in Gaussian processes.
method Modification of covariance function and explicit incorporation of linear constraints through a transformation operator.
result Guaranteed fulfillment of constraints in predictions and samples.
The paper splits manifolds using infinity harmonic functions with linear growth.
problem Splitting manifolds with specific harmonic functions.
method Analyzes manifolds with non-negative Ricci or sectional curvature, focusing on infinity harmonic functions with linear growth.
result Extends Savin's theorem to surfaces with non-negative sectional curvature.
ENIAC method optimizes and explores complex RL problems with non-linear policies.
problem Theoretical understanding of non-linear policies in RL with strategic exploration.
method ENIAC, an actor-critic method for non-linear function approximation.
result ENIAC finds near-optimal policies in polynomial exploration rounds under bounded eluder dimension.
IKA approximates kernels with linear combinations of chosen functions, outperforming Nyström method.
problem Efficient kernel approximation for large datasets.
method IKA method approximates kernels as a linear combination of user-defined functions.
result IKA consistently outperformed Nyström method on the STL-10 dataset.
The paper provides risk bounds for learning many response functions using linear regression.
problem Learning many response functions from a single dataset.
method Ordinary least squares regression in a high-dimensional feature space.
result Convergence guarantees on worst-case excess prediction risk for infinite response functions with finite VC dimension.
The paper tackles linear regression without knowing the correspondence between variables.
problem Linear regression without known correspondence between variables.
method The paper provides a fully polynomial-time approximation scheme and an efficient algorithm based on lattice basis reduction.
result The efficient algorithm can exactly recover the unknown linear function in arbitrary dimension.
New methods achieve linear convergence on broader convex functions.
problem Optimization on broader convex functions with singular or unbounded second derivatives.
method Discretizations of conformal Hamiltonian dynamics.
result Linear convergence on convex functions with singular or unbounded second derivatives.
Paper presents a machine learning method to improve significance tests for misspecified linear models.
problem Misspecification of linear assumptions in social science models leads to inaccurate significance levels.
method Apply machine learning to fit ground truth function, calculate linear approximation, and adjust the estimator.
result The method significantly outperforms linear regression for non-linear ground truth functions.
Diffusion Maps improves on Functional PCA for non-linear functional data.
problem Functional PCA's linear manifold assumption fails for non-linear functional data.
method Extends Diffusion Maps to functional data and compares it to Functional PCA.
result Diffusion Maps outperforms Functional PCA in non-linear functional data analysis.
Study on the complexity of deep neural networks and their linear regions.
problem Understanding the complexity and structure of deep neural networks.
method Leveraging the dimension of the space defining each linear region, the study presents bounds and methods for counting linear regions.
result Tighter upper and lower bounds for the maximum number of linear regions on rectifier networks, and a method for exact enumeration.
Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.
problem The trade-off between smoothness and margin-based losses in classification and structured prediction.
method Linear-Core (LC) Surrogates, a family of convex loss functions that stitch a linear core to a smooth tail.
result LC Surrogates achieve fast linear consistency rates while maintaining differentiability and strict H H H -consistency bounds. New algorithm for offline RL with linear approx in MDPs and MGs, nearly optimal.
problem Offline RL with linear function approximation in MDPs and MGs.
method Pessimism-based algorithm with uncertainty decomposition via reference function.
result Nearly minimax optimal performance in offline RL for MDPs and MGs.
Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.
problem Adversarial combinatorial bandits with general non-linear reward functions.
method Extending existing work on adversarial linear combinatorial bandits, analyzing minimax optimal regret for polynomial and non-polynomial reward functions.
result Minimax optimal regret bounds for adversarial combinatorial bandits with general non-linear reward functions.
New method uses DC functions for piecewise linear regression.
problem Regression with piecewise linear constraints.
method Estimates piecewise linear convex functions using a difference of convex functions.
result Method achieves close to minimax statistical risk and comparable performance to existing methods.
Uniqueness of asymptotic limits for Ricci-flat manifolds with linear volume growth is proven.
problem Proving uniqueness of asymptotic limits for noncollapsed Ricci flat manifolds with linear volume growth.
method Relating uniqueness to the existence of a harmonic function asymptotic to a Busemann function, proving uniqueness via a monotone quantity.
result Proves uniqueness of the asymptotic limit and establishes a polynomial convergence rate.
Paper proposes robust regression methods using depth functions.
problem Robust regression in Huber's ε ε ε -contamination models. method Maximizers of multivariate regression depth functions.
result Achieves minimax rates in various regression problems.
New proof shows efficient ReLU networks for piecewise linear functions.
problem Existence of efficient ReLU neural networks for piecewise linear functions.
method Degree 1 triangulations of the relative homology class bounded by polyhedra.
result Existence of efficient ReLU neural networks for functions with compact support.
New algorithm for reward-free RL with linear function approximation, reducing sample complexity.
problem Efficiently learning optimal policies without prior reward information in complex environments.
method Developed an algorithm for reward-free RL in linear Markov decision processes, proving sample complexity bounds.
result Polynomial sample complexity in feature dimension and planning horizon, independent of states and actions.
Develops a method to forecast non-linear time series.
problem Inability of traditional methods to handle non-linear dependencies in non-Gaussian series.
method Learning vector-valued functions in reproducing kernel Hilbert space, learning multiple matrix-valued kernels.
result Superior predictive performance and recovery of dynamic relationships.
Researchers combined linear classifiers using score functions and found simple and trimmed averages to be the best combination strategies.
problem Combining linear classifiers using their score functions.
method Two score functions tested; four combination strategies investigated; comparison with majority voting and model averaging.
result Simple and trimmed average combination strategies were the best.
New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.
Notes on linear classifiers and outliers, improving decision boundaries.
problem Negative impact of outliers on linear classifier decision boundaries.
method Use of least-squares cost function, scaling to reduce outlier significance.
result Improved decision boundaries through scaling outliers.
New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.
problem RL with linear function approximation lacks uniform-PAC guarantees.
method FLUTE algorithm with minimax value function estimator and multi-level partition scheme.
result Uniform-PAC convergence to optimal policy with high probability.