This paper explains why ResNets generalize better than FFNets using neural tangent kernels.
problem Understanding why deep ResNets generalize better than deep FFNets.
method Using neural tangent kernels to compare the learnability of functions induced by the kernels of ResNets and FFNets.
result The kernel of ResNets does not exhibit degeneracy as depth increases, unlike FFNets.
Characterizes homology types of neural networks, revealing non-trivial path homology.
problem Understanding homological differences in neural network architectures.
method Characterizes two types of directed homology for fully-connected feedforward networks, showing reductions and dependencies.
result Path homology of deep networks is non-trivial in higher dimensions and depends on network architecture.
Random projections of labels enable feedforward training of deep neural networks without feedback.
problem Biological plausibility and low-cost adaptive smart sensors constrained by backpropagation.
method Fixed random projections of targets for feedforward training of hidden layers.
result DRTP algorithm provides a tradeoff between accuracy and computational cost suitable for edge computing.
This paper improves deep neural network approximation for fully connected networks, achieving optimal convergence rates.
problem Improving approximation of fully connected deep neural networks for optimal convergence rates.
method Deriving approximation bounds specifically for a narrower fully connected deep neural network.
result Achieves an optimal rate (up to a logarithmic factor) for fully connected deep neural networks.
Deep RNNs compute American option prices and deltas efficiently.
problem Computing prices and deltas of high-dimensional American options.
method Two deep RNNs, one for price and one for delta, learn over spacetime.
result Linear time and constant memory cost compared to feedforward networks.
Deep neural network detects anomalies in time series data.
problem Detecting anomalies in diverse time series data.
method End-to-end deep feedforward neural network without feature engineering.
result Effective anomaly detection for various time series types.
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the network output with respect to the space variables which is needed to approxima…
In this study, we propose a novel deep neural network and its supervised learning method that uses a feedforward supervisory signal. The method is inspired by the human visual system and performs human-like association-based learning without any backward error propagation. The feedforward supervisory signal that produc…
A new neural network model for sentiment analysis.
problem Accurate and transferable sentiment analysis models.
method A computationally-efficient feedforward neural network.
result Highly accurate models with low losses.
We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among other things, we deduce that feedforward ReLU neural networks with one hidden laye…
Residual neural networks don't help overcome sampling complexity issues.
problem Learning invertible residual neural networks from samples is hard due to the curse of dimensionality.
method Investigated invertible residual neural networks and their sampling complexity.
result Invertible residual neural networks still suffer from the curse of dimensionality in sampling complexity.
Review of neural network expressivity and architectures.
problem Understanding neural network expressivity across different architectures.
method Comprehensive overview of approximation results for various neural network types.
result Deep neural networks offer advantages over shallow ones for specific function classes.
Predicts trainability of deep neural networks using reconstruction entropy.
problem Predicting the initial conditions for trainability of deep neural networks.
method Cascade of auxiliary networks to reconstruct input from activation layers, computing relative entropy.
result Predicts trainability of deep feedforward networks on various datasets with a single epoch.
PILAE learns DNNs without gradient descent, achieving better performance.
problem Training deep feedforward neural networks efficiently and accurately.
method PILAE uses a pseudoinverse learning algorithm for autoencoder building blocks of MLP DNNs.
result PILAE achieves better performance on tradeoff between training efficiency and accuracy.
Deep neural nets improve inference in semiparametric models.
problem Improving inference in semiparametric models.
method Established novel rates of convergence for deep feedforward neural nets and applied them to semiparametric inference.
result Valid second-step inference after first-step estimation with deep learning is possible.
Stochastic neural networks can approximate any function, even with correlated outputs.
problem Approximating functions with stochastic outputs and correlations.
method Investigating deep sigmoid belief networks to approximate any stochastic mapping.
result Minimal number of layers and units needed for approximation.
Conditions for uniquely identifying parameters of deep ReLU networks.
problem Characterizing networks whose parameters can be uniquely identified.
method Conditions on deep fully-connected feedforward ReLU neural networks.
result Parameters of the network are uniquely identified under certain conditions.
AWDO trains neural networks for digit classification.
problem Training feedforward neural networks.
method Adaptive Wind Driven Optimization (AWDO).
result AWDO outperforms steepest descent method in digit classification.
New method uses mutual info and network science to explain deep learning models.
problem Interpreting deep neural networks for understanding their decision-making process.
method Coupling mutual information with network science to quantify information flow in deep learning models.
result Proposed NIF technique for codifying information flow in deep learning models.
Study on deep neural networks using concentration inequalities and optimal stopping.
problem Understanding the performance and structure of stochastic deep neural networks.
method Introduced concentration inequalities for SDNN outputs and an EC classifier. Determined the optimal number of layers via an optimal stopping procedure.
result Optimal number of layers for SDNNs determined via an optimal stopping procedure.
Spiking neural networks perform similarly to deep networks on occluded images.
problem Robust object recognition in partially occluded images.
method Developed a two-layer spiking neural network trained on natural scenes with a biologically plausible learning rule, compared to deep convolutional networks.
result Spiking neural networks achieve good accuracy and robustness on stepwise pixel erasement tasks.
TVS-FNNs can approximate any continuous function on expanded input spaces.
problem Processing a broader range of inputs like sequences and matrices.
method Proving a universal approximation theorem for TVS-FNNs.
result TVS-FNNs can approximate any continuous function on expanded input spaces.
We simplify neural networks to 3D to study their topological changes.
problem Understanding how neural network layers affect low-dimensional topological invariants.
method Limiting each layer to a width of 3D space, tracking changes in linking numbers.
result ResNets and transformers are equally powerful in changing linking numbers.
Hybrid model predicts stock prices more accurately.
problem Efficient stock price prediction.
method Symbiotic organisms search algorithm trained feedforward neural networks.
result Outstanding predictive performance compared to other models.
This note presents in a technical though hopefully pedagogical way the three most common forms of neural network architectures: Feedforward, Convolutional and Recurrent. For each network, their fundamental building blocks are detailed. The forward pass and the update rules for the backpropagation algorithm are then der…
Neural networks can approximate functions uniformly across various measures.
problem Universal approximation of functions across different probability measures.
method Proving neural networks are dense in Orlicz spaces, extending classical theorems.
result Neural networks uniformly approximate functions for weakly compact families of measures.
Study uses neural networks to improve option pricing accuracy.
problem Reducing variance in Monte Carlo estimators for option pricing.
method Characterizes neural networks' universal approximation property and applies it to sampling measures.
result Sampling measures generated by neural networks can approximate optimal measures arbitrarily well.
This paper proposes a novel approach to train deep neural networks by unlocking the layer-wise dependency of backpropagation training. The approach employs additional modules called local critic networks besides the main network model to be trained, which are used to obtain error gradients without complete feedforward …
Negative results for neural network approximations on multi-dimensional spaces.
problem Approximating functions on compact subsets of R^d (d≥2) using neural networks.
method Proof of negative results for single and multi-layer feedforward neural networks with various activation functions.
result Existence of target functions difficult to approximate by these neural networks.
Neuromorphic hardware tends to pose limits on the connectivity of deep networks that one can run on them. But also generic hardware and software implementations of deep learning run more efficiently for sparse networks. Several methods exist for pruning connections of a neural network after it was trained without conne…
The paper applies Information Bottleneck theory to CNNs and finds compression phase not always present.
problem Understanding the behavior of convolutional neural networks.
method Employed Information Bottleneck theory to analyze CNNs.
result Compression phase not observed in all CNN cases.
Deep learning rules simplified with implicit methods.
problem Complexity and interpretability in deep learning models.
method Simplified notation through fixed-point equations and implicit features.
result Simplified deep learning models with enhanced interpretability.
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the Lipschitz properties of neural network family, we achieve significantly tighter g…
The paper analyzes deep neural networks using rectified linear units.
problem Understanding the individual affine linear representations of deep neural networks.
method Signal processing perspective, atomic decompositions, Lipschitz regularity estimation.
result Conditions for stabilizing learning in deep neural networks without network depth constraints.
Novel approach characterizes deep neural networks at initialization.
problem Characterizing the behavior of deep neural networks at initialization.
method A novel approach considering the evolution of statistical moments of signal and noise.
result Established that skip-connections in residual networks lead to well-behaved moments and no pathology.
LCW reduces activation shift in neural networks, improving training efficiency and generalization.
problem Activation shift in neural networks leading to non-zero mean preactivation values.
method Linearly constrained weights (LCW) to reduce activation shift in fully connected and convolutional layers.
result LCW resolves the vanishing gradient problem and improves generalization of neural networks.
Neural networks' feature geometry evolves like discrete Ricci flow.
problem Understanding neural feature representations and their geometric transformations.
method Approximating input manifold with geometric graphs and analyzing their evolution during training.
result Neural feature geometry evolves like discrete Ricci flow, with nonlinear activations playing a crucial role.
This paper examines properties of feedforward graphs to improve neural network performance.
problem The choice of computational graph can significantly impact neural network performance.
method The paper introduces two measures: fidelity and mixing time, and evaluates popular graphs using these measures.
result Popular graphs are evaluated based on fidelity and mixing time, revealing their performance implications.
Backdoors in deep neural networks are undetectable and enable invariance-based adversarial examples.
problem Statistically undetectable backdoors in deep neural networks.
method Adversarial model trainer method to plant backdoors, showing invariance-based adversarial examples.
result Backdoors are statistically undetectable and enable generation of adversarial examples for every input.
New insights into neural network training efficiency.
problem Understanding the optimal initialization for deep neural networks.
method Exploring the edge of chaos and saturation of tanh activation function.
result The line of uniformity in phase space intersects the edge of chaos, indicating saturation begins to hinder training efficiency.
Gene expression data represents a unique challenge in predictive model building, because of the small number of samples (n) compared to the huge amount of features (p). This "n<<p" property has hampered application of deep learning techniques for disease outcome classification. Sparse learning by incorporating ex…
Math theory explains how neural networks learn abstract representations.
problem Understanding how neural networks learn abstract representations.
method Mathematical theory reformulating network optimization into mean field optimization over neural preactivations.
result Abstract representations of latent variables are guaranteed to appear in neural networks trained on tasks that depend on these variables.
PCGs encompass a broader range of neural networks.
problem Understanding the broader scope of neural network models.
method Proving PCGs as a superset of feedforward neural networks.
result PCGs represent a wider class of neural network models.
We show that there is a simple (approximately radial) function on Rd, expressible by a small 3-layer feedforward neural networks, which cannot be approximated by any 2-layer network, to more than a certain constant accuracy, unless its width is exponential in the dimension. The result holds for virtually all kn…
Deep neural network improves Heston model calibration accuracy and speed.
problem Calibrating the Heston model with numerical stability issues.
method Gradient-based deep learning framework (DDN) to learn Heston model and its derivatives.
result DDN significantly outperforms non-differential neural networks in calibration accuracy and speed.
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling. We approximate the time-dependent controls as feedforward neural networ…
We propose a novel learning method for multilayered neural networks which uses feedforward supervisory signal and associates classification of a new input with that of pre-trained input. The proposed method effectively uses rich input information in the earlier layer for robust leaning and revising internal representat…
Deep learning improves portfolio optimization efficiency.
problem Efficient frontier calculation in high-dimensional finance problems.
method Deep neural networks for portfolio optimization with added constraints.
result A new projected feedforward network outperforms classical methods.