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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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48 results for Small Networks

Early training of deep neural networks leads to small, directionally converging weights.

problem Training dynamics of deep homogeneous neural networks with small initializations.
method Gradient flow analysis and study of KKT points for neural correlation function.
result Weights converge in direction to KKT points during early training stages.

The paper studies neural networks' convergence near origin and saddle points.

problem Directional convergence of neural networks near small initializations and saddle points.
method Gradient flow dynamics analysis of two-homogeneous neural networks.
result Neural networks' weights approximately converge in direction to KKT points for small initializations.

A new test optimizes detecting small communities in large networks.

problem Detecting small communities in large networks.
method Using Sinkhorn's theorem and a degree-corrected block model (DCBM), the study optimizes the SgnQ test for this challenging setting.
result The SgnQ test is optimal for detecting communities larger than √n, achieving the computational lower bound (CLB).

Learning with noisy labels is one of the hottest problems in weakly-supervised learning. Based on memorization effects of deep neural networks, training on small-loss instances becomes very promising for handling noisy labels. This fosters the state-of-the-art approach "Co-teaching" that cross-trains two deep neural ne…

2019-01-14abs ↗pdf ↗

Generative model initializes 2-layer network weights for small datasets.

problem Approximating functions with 2-layer networks using small datasets and gradient-based training.
method Initialize hidden weights with a learned proposal distribution parameterized as a deep generative model. Refine with gradient-based post-processing and regularization.
result Demonstrates effectiveness of the approach with numerical examples.

Deep Neural Networks (DNNs) are usually over-parameterized, causing excessive memory and interconnection cost on the hardware platform. Existing pruning approaches remove secondary parameters at the end of training to reduce the model size; but without exploiting the intrinsic network property, they still require the f…

2019-11-11abs ↗pdf ↗

Training large and highly accurate deep learning (DL) models is computationally costly. This cost is in great part due to the excessive number of trained parameters, which are well-known to be redundant and compressible for the execution phase. This paper proposes a novel transformation which changes the topology of th…

2019-04-09abs ↗pdf ↗

Knowledge distillation is effective for producing small, high-performance neural networks for classification, but these small networks are vulnerable to adversarial attacks. This paper studies how adversarial robustness transfers from teacher to student during knowledge distillation. We find that a large amount of robu…

2019-05-23abs ↗pdf ↗

EASIER-net uses sparse networks to improve prediction accuracy for high-dimensional data.

problem Limited use of neural networks in high-dimensional data with small samples.
method Ensemble by Averaging Sparse-Input Hierarchical networks (EASIER-net) with small modifications to neural network architecture and training procedure.
result EASIER-net achieves higher prediction accuracy than off-the-shelf methods on average.

We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We conduct an extensive study of intrinsic scale for several networks, ranging fro…

2019-01-15abs ↗pdf ↗

Deep neural network solves portfolio optimization with MGARCH and small transaction costs.

problem Optimizing portfolios with MGARCH and small transaction costs.
method Fixed-point RL algorithm using neural networks.
result NN algorithm shows positive testing performance.

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.

This comment reexamines Simard et al.'s work in [D. Simard, L. Nadeau, H. Kroger, Phys. Lett. A 336 (2005) 8-15]. We found that Simard et al. calculated mistakenly the local connectivity lengths Dlocal of networks. The right results of Dlocal are presented and the supervised learning performance of feedforward neural n…

2010-02-27abs ↗pdf ↗

Deep Neural Network (DNN) acoustic models have yielded many state-of-the-art results in Automatic Speech Recognition (ASR) tasks. More recently, Recurrent Neural Network (RNN) models have been shown to outperform DNNs counterparts. However, state-of-the-art DNN and RNN models tend to be impractical to deploy on embedde…

2015-04-07abs ↗pdf ↗

Conventional deep learning classifiers are static in the sense that they are trained on a predefined set of classes and learning to classify a novel class typically requires re-training. In this work, we address the problem of Low-Shot network expansion learning. We introduce a learning framework which enables expandin…

2018-10-19abs ↗pdf ↗

In this paper, we propose a method for training neural networks when we have a large set of data with weak labels and a small amount of data with true labels. In our proposed model, we train two neural networks: a target network, the learner and a confidence network, the meta-learner. The target network is optimized to…

2017-11-30abs ↗pdf ↗

This study investigates how gradient-based methods bias neural networks trained on high-dimensional data.

problem The implicit biases of gradient-based optimization algorithms in neural networks trained on high-dimensional data.
method Investigation of gradient flow and gradient descent in two-layer fully-connected neural networks with leaky ReLU activations.
result Gradient flow and gradient descent lead to neural networks with low-rank solutions and linear decision boundaries.

Most random ReLU networks are vulnerable to small, Euclidean adversarial perturbations.

problem Vulnerability of ReLU networks to adversarial attacks.
method Analysis of random ReLU networks with decreasing dimensions, using gradient flow and descent.
result Most examples can be perturbed by small Euclidean distances via gradient methods.

Deep networks can approximate functions with fewer learnable parameters than previously thought.

problem High computational costs due to large number of parameters in deep neural networks.
method Theoretical design of ReLU networks with a few intrinsic parameters and numerical experiments.
result ReLU networks with a small number of intrinsic parameters can achieve good approximations of functions.

The paper investigates why GNNs struggle to generalize from small to large graphs.

problem Challenges in graph neural networks' ability to generalize across different graph sizes.
method Identified and studied the effect of local structure on size generalization; proposed a novel SSL task.
result GNNs can converge to non-generalizing solutions when there is a discrepancy in local structure.

We propose to study neural networks' loss surfaces by methods of topological data analysis. We suggest to apply barcodes of Morse complexes to explore topology of loss surfaces. An algorithm for calculations of the loss function's barcodes of local minima is described. We have conducted experiments for calculating barc…

2019-11-29abs ↗pdf ↗

New method finds smaller networks with similar performance to large models in fewer epochs.

problem Training large neural networks is computationally expensive and energy-intensive.
method Use PCA to identify a basis of hidden layer activations and reduce network parameters.
result Principal Component Networks (PCNs) can train faster and use less energy than overparameterized models without accuracy loss.

This work finds a point with small test error in polynomial time for mildly overparameterized neural nets.

problem Achieving small test error in mildly overparameterized neural networks.
method The work shows that the landscape of loss functions with explicit regularization has a property that all local minima and certain stationary points achieve small test error. It also proves the existence of polynomial time algorithms for finding such points in convolutional and fully connected neural nets.
result Polynomial time algorithms exist for finding points with small test error in mildly overparameterized neural nets.

The paper analyzes neural network dynamics after weights escape the origin.

problem Understanding gradient flow dynamics of neural networks after the origin.
method Analyzes gradient flow of homogeneous neural networks with locally Lipschitz gradients.
result Characterizes the first saddle point encountered after escaping the origin.

The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international …

2011-07-28abs ↗pdf ↗

Propagation of balance-sheet or cash-flow insolvency across financial institutions may be modeled as a cascade process on a network representing their mutual exposures. We derive rigorous asymptotic results for the magnitude of contagion in a large financial network and give an analytical expression for the asymptotic …

2011-12-24abs ↗pdf ↗

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The…

2011-07-18abs ↗pdf ↗

Paper proposes a method to evaluate SME credit risk using meta paths.

problem Evaluate credit risk of small and medium-sized enterprises with limited data.
method Exploits the representative power of information networks and meta paths to infer SME financial status.
result Meta path feature effectively identifies SMEs with credit risks.