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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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143286429572 · Jun 202019922001200920172026
48 results for active complexity

Complexity measures for neural nets with general activations using path-based norms.

problem Control complexity of neural networks with arbitrary activation functions.
method Approximate general activations with ReLU networks and derive path-based norms for complexity control.
result Preliminary analyses of function spaces and regularized estimators.

This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise model of Tsybakov (2004), the minimax label complexity of active …

2014-10-03abs ↗pdf ↗

Paper proposes LANN to measure model complexity of neural networks with curve activation functions.

problem Measuring model complexity of neural networks with curve activation functions.
method Proposes LANN, a piecewise linear framework to approximate curve activation functions, and derives complexity measure based on the number of linear regions.
result Demonstrates positive correlation between overfitting and model complexity during training.

Optimal noise excitation for linear system identification reduces sample complexity.

problem Efficiently identifying linear systems with minimal data.
method Active learning algorithm using ordinary least squares and semidefinite programming.
result The proposed algorithm matches lower bounds on sample complexity for any active learning method.

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization.…

2011-02-22abs ↗pdf ↗

Active learning improves GP regression on complex, high-dimensional data.

problem Improving Gaussian Process regression in high-dimensional spaces with discontinuous functions.
method Combines manifold learning with active learning to optimize data selection and reduce dimensionality.
result Superior performance over random learning in synthetic data experiments.

Maxout networks show similar complexity issues as ReLU networks.

problem Understanding the complexity of maxout networks and decision boundaries.
method Analyzing the parameter space and decision boundaries, obtaining lower bounds, and investigating initialization procedures.
result Maxout networks exhibit a wide range of complexity, similar to ReLU networks.

Complex-valued neural networks can approximate any continuous function with bounded widths and depths.

problem Approximating continuous functions with complex-valued neural networks of bounded widths and depths.
method Analyzing activation functions and proving universality for complex-valued networks.
result Deep narrow complex-valued networks are universal if and only if their activation function is neither holomorphic, nor antiholomorphic, nor R\mathbb{R}-affine.

Mixtures of neural operators reduce active complexity in operator learning.

problem Reduction of active complexity in operator learning models.
method Constructive comparison between routed mixtures of neural operators (MoNOs) and a fixed single-neural-operator construction.
result Every scalar uniformly continuous nonlinear operator can be approximated by a MoNO whose active expert has smaller depth, width, and rank scaling.

The paper proves deep neural networks with analytic activation can approximate any function.

problem Approximating functions with neural networks using analytic activation functions.
method Elementary proofs for real and complex networks, Stone-Weierstrass theorem, Mergelyan's theorem.
result Closure of neural network classes equals space of polynomials for analytic activation.

CVNNs improve performance in tasks with complex-valued inputs.

problem Improving performance in tasks with complex-valued inputs.
method Analyze the approximation properties of complex-valued neural networks (CVNNs).
result Quantitative approximation bounds for CVNNs, showing error scales as mk/(2n)m^{-k/(2n)}.

Improved generalization bounds for CNNs using Rademacher complexity.

problem Establishing non-vacuous generalization bounds for deep learning models.
method Rademacher complexity framework with novel contraction lemmas for high-dimensional mappings.
result Enhanced generalization bounds for a broader class of activation functions.

New algorithm trains deep neural networks without global optimization.

problem Training deep neural networks efficiently and without global optimization.
method Uses random complex exponential activation functions and Markov Chain Monte Carlo sampling.
result Consistently attains theoretical approximation rate for residual networks.

Counterfactual learning from observational data involves learning a classifier on an entire population based on data that is observed conditioned on a selection policy. This work considers this problem in an active setting, where the learner additionally has access to unlabeled examples and can choose to get a subset o…

2019-05-29abs ↗pdf ↗

We derive and analyze a new, efficient, pool-based active learning algorithm for halfspaces, called ALuMA. Most previous algorithms show exponential improvement in the label complexity assuming that the distribution over the instance space is close to uniform. This assumption rarely holds in practical applications. Ins…

2011-12-07abs ↗pdf ↗

BLADE uses Bayesian methods to discover complex systems from scarce data.

problem Efficiently discovering governing equations of complex dynamical systems from limited data.
method Combines replica-exchange stochastic gradient Langevin Monte Carlo with active learning.
result Reduces measurement requirements by 60% for Lotka-Volterra and 40% for Burgers' equation.

New algorithm improves active learning in agnostic pool-based classification.

problem Efficient active learning in the agnostic setting with minimized sample complexity.
method Solves an experimental design problem to determine a distribution over examples for label requests.
result Achieves sample complexity bounds never worse than best disagreement coefficient-based bounds, sometimes significantly smaller.

INP accelerates stochastic simulations using deep Bayesian active learning.

problem Computational expense of stochastic simulations at fine-grained resolution.
method Interactive Neural Process (INP) framework combining spatiotemporal surrogate model and active learning acquisition function.
result STNP outperforms baselines in accelerating stochastic simulations and LIG achieves state-of-the-art for Bayesian active learning.

Active learning methods, like uncertainty sampling, combined with probabilistic prediction techniques have achieved success in various problems like image classification and text classification. For more complex multivariate prediction tasks, the relationships between labels play an important role in designing structur…

2019-12-29abs ↗pdf ↗

Study efficient active learning for halfspaces with Tsybakov noise using non-convex optimization.

problem Efficiently learn halfspaces with Tsybakov noise under structured unlabeled data.
method Non-convex optimization approach to find approximate first-order stationary points.
result Designs an algorithm with improved label complexity compared to previous methods.

Deep active inference agents learn complex environments using Monte-Carlo methods.

problem Understanding and modeling biological intelligence in complex, continuous state-spaces.
method Neural architecture for deep active inference agents using multiple forms of Monte-Carlo sampling.
result Deep active inference agents can learn environmental dynamics and plan future actions.

Unified theory of deep neural networks with diverse activations.

problem Understanding the relationship between depth and complexity in deep neural networks.
method Developed a unified function space theory for deep networks with various activations.
result Unified theory provides meaningful complexity for deep networks with diverse activations.

Complex-valued neural networks can approximate any continuous function.

problem Generalizing the universal approximation theorem to complex-valued networks.
method Characterizing activation functions for complex networks to approximate any continuous function.
result Different activation functions are required for deep vs shallow complex networks to achieve universal approximation.

Study of urban lifestyles from mobility data of 1.2M people in 11 U.S. cities.

problem Lack of interpretability in digital mobility data for understanding urban lifestyles.
method Privacy-enhanced dataset of mobility visitation patterns, latent activity behavior decomposition.
result Detected 12 latent activity behaviors that describe urban lifestyles, not single lifestyles.

We extend neural networks with fractional and mixed activation functions for better function approximation.

problem Limitations in approximating higher-order smooth functions in complex spaces.
method Incorporating fractional exponents in activation functions and defining new density functions.
result Improved accuracy and broader applicability of neural network approximation theory.

In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to local strong convexity\mathit{local~strong~convexity} in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation function…

2017-06-10abs ↗pdf ↗

New algorithms improve label complexity for active multi-distribution learning.

problem Active multi-distribution learning with improved label complexity.
method Developed new algorithms for active multi-distribution learning and established improved label complexity upper and lower bounds.
result Improved label complexity upper and lower bounds for active multi-distribution learning.

We present a new active learning algorithm that adaptively partitions the input space into a finite number of regions, and subsequently seeks a distinct predictor for each region, both phases actively requesting labels. We prove theoretical guarantees for both the generalization error and the label complexity of our al…

2020-02-18abs ↗pdf ↗

Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while 1\ell_1 optimization-based SSC algorithms suffer from high computational complexity, other variants of SSC, such as Orthogonal Matching Pursuit-based S…

2017-08-16abs ↗pdf ↗

We study active learning of homogeneous ss-sparse halfspaces in Rd\mathbb{R}^d under the setting where the unlabeled data distribution is isotropic log-concave and each label is flipped with probability at most ηη for a parameter η[0,12)η\in \big[0, \frac12\big), known as the bounded noise. Even in the presence of mild la…

2020-02-12abs ↗pdf ↗