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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.

168,695 papers · 148 categories

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64128191255 · Jun 202019922001200920172026
48 results for shallow exploration

New algorithms reduce dueling bandits' regret with neural networks and efficient exploration.

problem Optimizing dueling bandits with neural networks for better performance.
method Combines shallow exploration strategies with neural networks for utility approximation, using iterative self-improvement and spectral analysis to reduce network width.
result Achieves sublinear regret of O~(dt=1Tσt2+dT)\widetilde{\mathcal{O}}(d\sqrt{\sum_{t=1}^{T} σ_t^2} + \sqrt{dT}).

Study shows shallow ReLU networks struggle with high-dimensional Lipschitz functions.

problem Expressing high-dimensional Lipschitz functions with shallow ReLU networks.
method Established lower bounds on shallow network complexity for polynomial approximation.
result Shallow ReLU networks suffer from the curse of dimensionality for Lipschitz functions.

Shallow Art presents, implements, and tests the use of simple single-output classification and regression models for the purpose of art generation. Various machine learning algorithms are trained on collections of computer generated images, artworks from Vincent van Gogh, and artworks from Rembrandt van Rijn. These mod…

2019-10-21abs ↗pdf ↗

GD-trained shallow ReLU nets learn Lipschitz functions with noise.

problem Learning Lipschitz functions with additive noise in overparameterized neural networks.
method Gradient Descent (GD) with early stopping, focusing on the Neural Tangent Kernel (NTK).
result Early-stopped GD achieves minimax optimal rates for learning Lipschitz functions.

ManifoldMind uses adaptive-curvature probabilistic spheres for trustworthy recommendations in semantic hierarchies.

problem Sparse and abstract recommendation domains where users explore diverse conceptual paths.
method Adaptive-curvature probabilistic spheres, soft multi-hop inference, and curvature-aware semantic kernel.
result Superior NDCG, calibration, and diversity compared to baselines on public benchmarks.

GD with early stopping trains shallow neural nets for nonparametric regression robustly.

problem Learning Lipschitz regression functions with noisy labels.
method Overparameterized shallow neural networks trained by GD with early stopping.
result Optimal rates of convergence for nonparametric regression.

Understanding the power of depth in feed-forward neural networks is an ongoing challenge in the field of deep learning theory. While current works account for the importance of depth for the expressive power of neural-networks, it remains an open question whether these benefits are exploited during a gradient-based opt…

2019-03-08abs ↗pdf ↗

This paper explores how kernel methods can explain data effects on neural collapse.

problem Understanding how data affects neural collapse in neural networks.
method Formulating NC1 as a function of kernel, specializing to NNGP and NTK, and exploring a data-aware Gaussian Process kernel.
result The NTK does not represent more collapsed features than the NNGP for Gaussian data, highlighting the limitations of data-independent kernels.

Deep neural networks can grok better than shallow ones, showing multi-stage generalization.

problem Understanding the generalization behavior of deep neural networks.
method Empirical replication and analysis of grokking phenomenon in deep MLP models.
result Deep neural networks exhibit multi-stage generalization, with a secondary surge in test accuracy.

Shallow neural networks can represent polynomials efficiently.

problem Representing polynomials using shallow neural networks.
method Using shallow neural networks of width 2(R+d)d2(R+d)^d to represent dd-variate polynomials of degree RR.
result Derives minimax optimal convergence rate for shallow networks to unknown univariate regression functions.

The study explores deep and shallow slice knots in 4-manifolds, linking them to conjectures and proving existence and nonexistence results.

problem Understanding slice knots in 4-manifolds and their properties.
method Using Wall self-intersection invariant and Rohlin's result, the study examines various 4-manifolds and their boundaries to find deep slice knots and prove nonexistence results.
result Every 4-manifold with one 0-handle and any number of 2-handles has a deep slice knot in its boundary.

Optimal rates for shallow ReLU networks in nonparametric regression.

problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLUk^k neural networks, using variation norms and deep learning theory.
result Optimal approximation rates for shallow ReLU networks in nonparametric regression.

Hierarchical reinforcement learning has demonstrated significant success at solving difficult reinforcement learning (RL) tasks. Previous works have motivated the use of hierarchy by appealing to a number of intuitive benefits, including learning over temporally extended transitions, exploring over temporally extended …

2019-09-23abs ↗pdf ↗

Theory explains why DARTS favors deep architectures over shallow ones.

problem DARTS selects architectures with dominated skip connections, leading to performance degradation.
method Theoretical analysis of operations' effects on network optimization; introduces sparse binary gates and path-depth-wise regularization.
result Theoretical proof that architectures with more skip connections converge faster.

We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of practical interest can frequently be approximated through "cheap learning" with …

2016-08-29abs ↗pdf ↗

Deep neural networks can learn smooth functions without parameters.

problem Learning smooth functions from shallow ReLU neural networks.
method Using over-parameterized shallow ReLU neural networks with norm constraints.
result Least squares estimators based on shallow neural networks are minimax optimal.

Sharp lower bounds on shallow neural networks' approximation rates are derived.

problem The efficiency of shallow neural networks in approximating functions.
method Lower bounding the L2L^2-metric entropy and Kolmogorov nn-widths of the convex hull of neural network basis functions.
result Sharp lower bounds on the approximation rates for shallow neural networks are provided.

Proves existence of optimal shallow neural networks with ReLU activation.

problem Proving the existence of optimal shallow feedforward networks with ReLU activation.
method Proves existence of global minima in the loss landscape for continuous target functions using shallow feedforward neural networks with ReLU activation.
result Existence of global minima in the loss landscape for shallow feedforward networks with ReLU activation.

Gradient-trained shallow networks can generalize well but are vulnerable to small-radius adversarial attacks.

problem Adversarial robustness of gradient-trained shallow networks.
method Analysis of neuron alignment and polynomial ReLU activation.
result Gradient-trained shallow networks with polynomial ReLU activation are robust to small-radius adversarial attacks.

In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …

2017-03-30abs ↗pdf ↗

Study shows limits on deep and shallow neural networks for approximating compact sets.

problem Understanding the limitations of deep and shallow neural networks in approximating compact sets.
method Proved Carl's type inequalities for approximation error, using Lipschitz widths.
result Lower bounds on approximation error for neural network outputs.

Paper studies shallow ReLU networks' approximation rates for Hölder functions.

problem Understanding shallow ReLU networks' efficiency in approximating Hölder functions.
method Analyzes rates of uniform approximation by ReLU shallow neural networks with mm hidden neurons.
result Shows ReLU shallow neural networks can uniformly approximate Hölder functions with rates close to optimal.

This paper focuses on a comparative evaluation of the most common and modern methods for text classification, including the recent deep learning strategies and ensemble methods. The study is motivated by a challenging real data problem, characterized by high-dimensional and extremely sparse data, deriving from incoming…

2019-02-18abs ↗pdf ↗

Deep ReLU networks approximate as well as shallow ones in kernel regimes.

problem Understanding the limitations of kernel methods for deep ReLU networks.
method Characterizing eigenvalue decays of kernels derived from deep ReLU networks.
result Deep ReLU networks and shallow two-layer networks have equivalent approximation properties in kernel regimes.

Develops vector-valued RKBS for neural networks and operators.

problem Understanding function spaces of Rd\mathbb{R}^d-valued neural networks and neural operators.
method Defines and constructs vector-valued RKBS (vv-RKBS) without restrictive assumptions.
result Establishes Representer Theorem for neural architectures.

It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with generative modelling, the focus has been on shallow neural networks. A natural ques…

2017-08-15abs ↗pdf ↗

New method for efficient proximal mapping of 1-path-norm in shallow networks.

problem Efficiently handling the 1-path-norm of shallow neural networks.
method Closed-form proximal operator for efficient computation and upper bound on Lipschitz constant.
result Proximal mapping allows robust training against adversarial perturbations.

Study shows overparameterization helps shallow neural networks recover signals in high dimensions.

problem Signal recovery in shallow neural networks with overparameterization.
method Gradient flow on population risk, Gaussian distribution assumption, high-dimensional limit analysis.
result Minimal overparameterization is sufficient for strong recovery of signals.

Deep networks learn hierarchical functions more efficiently than shallow ones.

problem Understanding the advantage of deep neural networks over shallow models.
method Analytical study of learning dynamics and generalization performance of deep networks compared to shallow ones.
result Deep networks reduce effective dimensionality, enabling learning with fewer samples.

Combines machine learning and convex limiting for accurate subgrid flux modeling in shallow-water equations.

problem Accurate subgrid flux modeling in shallow-water equations.
method Machine learning and flux limiting for property-preserving subgrid scale modeling.
result The proposed method produces meaningful closures even in untrained scenarios.

This paper considers the power of deep neural networks (deep nets for short) in realizing data features. Based on refined covering number estimates, we find that, to realize some complex data features, deep nets can improve the performances of shallow neural networks (shallow nets for short) without requiring additiona…

2019-01-01abs ↗pdf ↗

This paper analyzes shallow ReLU networks in L^p and Sobolev spaces, focusing on approximation and generalization.

problem Approximation and generalization of shallow ReLU networks in L^p and Sobolev spaces.
method Spherical harmonic analysis and embeddings into spectral Barron spaces for L^p spaces, path-norm control for Sobolev spaces.
result Minimax-optimal rates for nonparametric regression with shallow ReLU networks under path-norm control.

Gradient descent trains shallow neural networks to approximate functions in 1D.

problem Approximating functions in 1D with shallow neural networks trained by gradient descent.
method Gradient descent optimization of non-convex weight space for finite width networks in 1D.
result Gradient descent can approximate functions in 1D with a minimal number of weights, balancing practical performance and theoretical capabilities.

Generative model improves noise estimation in stochastic rotating shallow water models.

problem Improving noise estimation in stochastic partial differential equations for fluid dynamics.
method Replaced PCA with a generative model to avoid constraints on stochastic increments.
result Generative model produces better RMSE, CRPS score, and forecast rank histograms.