On-device research index

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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11 results for “underparametrized”

On non-approximability of zero loss global

{\mathcal L}^2

minimizers by gradient descent in Deep Learningcs.LG

Gradient descent struggles to achieve zero loss in deep learning models due to non-generic data distributions.

problem Achieving zero loss minimizers in deep learning networks.

method Analysis of gradient descent algorithm in deep learning, focusing on underparametrized networks.

result Zero loss minimization cannot be achieved generically in deep learning networks.

deep learning gradient descent zero loss non-approximability underparametrized networks

2023-11-13abs ↗pdf ↗

Geometric structure of Deep Learning networks and construction of global

{\mathcal L}^2

minimizerscs.LG

The paper constructs minimizers for deep learning networks and analyzes their geometric structure.

problem Underparametrized deep learning networks and their minimizers.

method Direct construction of minimizers without gradient descent, considering specific settings.

result Explicit family of minimizers for the global minimum and a set of degenerate local minima.

Deep Learning Minimizers Geometric Structure Underparametrized Networks Truncation Map

2023-09-19abs ↗pdf ↗

Geometric structure of shallow neural networks and constructive

{\mathcal L}^2

cost minimizationcs.LG

The paper constructs upper bounds for cost minimization in shallow neural networks.

problem Cost minimization in underparametrized shallow ReLU networks.

method Explicit construction of upper bounds based on the geometric structure of classification data.

result An upper bound on the minimum of the cost function of order

O(δ_P)

, with exact degenerate local minimum in the special case

M=Q

shallow neural networks ReLU networks cost minimization geometric structure underparametrized

2023-09-19abs ↗pdf ↗

Zero loss guarantees and explicit minimizers for generic overparametrized Deep Learning networkscs.LG

Zero loss is achievable in overparametrized DL networks under specific conditions.

problem Achieving zero loss in overparametrized deep learning networks.

method Determine sufficient conditions for zero loss attainability and present an explicit construction of zero loss minimizers.

result Explicit minimizers for zero loss in overparametrized DL networks are constructed without gradient descent.

Deep Learning Overparametrization Zero Loss Explicit Minimizer Gradient Descent

2025-02-19abs ↗pdf ↗

Continual Learning with Distributed Optimization: Does CoCoA Forget?stat.ML

COCOA can learn new tasks without forgetting previously learned ones in a distributed setting.

problem Continual learning with tasks arriving sequentially.

method Distributed optimization with COCOA algorithm.

result COCOA can perform continual learning without forgetting.

Continual Learning Distributed Optimization COCOA Overparametrization Underparametrization

2022-11-30abs ↗pdf ↗

Nonasymptotic theory for two-layer neural networks: Beyond the bias-variance trade-offcs.LG

New theory explains how overparametrized neural networks generalize well without bias-variance trade-off.

problem Overparametrized neural networks generalize well despite classical bias-variance trade-off.

method Nonasymptotic generalization theory for two-layer neural networks with ReLU activation, incorporating scaled variation regularization.

result Prediction bounds for all network widths reproduce the double descent phenomenon, and overparametrized models are nearly minimax optimal.

neural networks two-layer ReLU activation generalization ridge regression

2021-06-09abs ↗pdf ↗

Theory of overparametrization in quantum neural networksquant-ph

Overparametrization improves QNN trainability by reducing spurious local minima.

problem Understanding how overparametrization affects the loss landscape of QNNs.

method Rigorous analysis of overparametrization in QNNs with periodic structure.

result Overparametrization corresponds to a computational phase transition improving QNN trainability.

quantum neural networks overparametrization loss landscape Lie algebra quantum Fisher information

2021-09-23abs ↗pdf ↗

Effects of noise on the overparametrization of quantum neural networksquant-ph

Noise can affect the overparametrization of QNNs, enabling new directions but also suppressing sensitivity.

problem The overparametrization of QNNs in the presence of noise.

method Analyzing the Quantum Fisher Information Matrix (QFIM) to understand how noise affects the rank of QFIM.

result Noise can turn previously-zero eigenvalues of the QFIM to non-zero, enabling exploration of new directions.

Quantum Neural Networks Overparametrization Noise Quantum Fisher Information Matrix Eigenvalues

2023-02-10abs ↗pdf ↗

Regularization properties of adversarially-trained linear regressionstat.ML

Adversarial training improves linear regression solutions, offering robustness against small perturbations.

problem Vulnerability of linear models to adversarial perturbations.

method Formulated as a min-max problem, adversarial training minimizes the best solution under worst-case attacks.

result Adversarial training yields the minimum-norm interpolating solution in overparameterized models, equivalent to parameter shrinking methods in underparameterized models.

adversarial training linear regression min-max optimization robustness interpolating solution

2023-10-16abs ↗pdf ↗

Global