An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance ba…
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48 results for “Neural nets”
Despite the phenomenal success of deep learning in recent years, there remains a gap in understanding the fundamental mechanics of neural nets. More research is focussed on handcrafting complex and larger networks, and the design decisions are often ad-hoc and based on intuition. Some recent research has aimed to demys…
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 …
GIT-Net uses neural networks to approximate PDE operators efficiently.
problem Approximating PDE operators for complex geometries.
method Parametrizes adaptive generalized integral transforms with deep neural networks.
result GIT-Net outperforms existing neural network operators in multiple areas.
DP-Net uses dynamic programming for efficient deep neural network compression.
problem Efficiently compressing deep neural networks while maintaining accuracy.
method Dynamic Programming for optimal weight quantization and clustering-friendly training.
result Achieves up to 77X compression ratio on Wide ResNet with minimal accuracy loss.
Study measures impact of data and neural net similarity on transferability in restaurant sales data.
problem Identify indicators for successful transferability of neural nets across different data sets.
method Empirical study on sales data from six restaurants, calculating indicators based on data and neural net similarities.
result Negative correlations between transferability and indicators, allowing better model performance and fewer transfers.
Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional stochastic optimization problems present interesting challenges for existing reinf…
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…
DNF-Net tackles tabular data challenges with neural architecture.
problem Handling tabular data efficiently using neural networks.
method DNF-Net uses a neural architecture with inductive bias corresponding to logical Boolean formulas in disjunctive normal form over affine soft-threshold decision terms.
result DNF-Net significantly outperforms fully connected networks on tabular data.
SDE-Net quantifies uncertainty in deep nets using stochastic dynamics.
problem Uncertainty quantification in deep neural networks.
method Viewing DNN transformations as state evolution of a stochastic dynamical system, introducing a Brownian motion term for epistemic uncertainty.
result SDE-Net outperforms existing methods in uncertainty estimation across various tasks.
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural nets and by using the technique of chaining mutual information introduced in Asadi…
fSDE-Net generates time series with long-term memory using neural networks.
problem Generating time series with long-term memory from irregularly sampled data.
method fSDE-Net: neural fractional Stochastic Differential Equation Network using fractional Brownian motion.
result fSDE-Net can replicate distributional properties of real time-series data.
New algorithm reduces neural net error in contextual bandits.
problem Neural contextual bandits with general activation functions.
method Proposed an efficient algorithm with sublinear regret bound.
result Demonstrated provably sublinear regret bound in finite regime.
Proposes -Nets, polynomial neural networks, for improved representation power.
problem Improving representation power in deep learning models.
method Introduces -Nets, a new class of deep polynomial neural networks.
result Demonstrates -Nets outperform standard DCNNs and achieve state-of-the-art results.
Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernelstat.ML
Recent works have shown that on sufficiently over-parametrized neural nets, gradient descent with relatively large initialization optimizes a prediction function in the RKHS of the Neural Tangent Kernel (NTK). This analysis leads to global convergence results but does not work when there is a standard regulari…
Study on how reparametrization affects neural nets' parameter spaces from a geometric perspective.
problem Inconsistencies in flatness measures, optimization, and probability densities under reparametrization.
method Riemannian geometry to study invariance of neural nets under reparametrization.
result Invariance of neural nets is an inherent property if the metric is explicitly represented and transformation rules are correct.
Unified framework for U-Net design and analysis.
problem Understudied design and architecture of U-Nets.
method Theoretical results, Multi-ResNets, function constraints encoding.
result Competitive and superior performance in various tasks.
Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal function approximation in an arbitrarily high dimensional Euclidian space. It is show…
G-Net constructs binary neural networks with high accuracy using randomized binary embeddings.
problem Creating high-accuracy binary neural networks with theoretical guarantees.
method Proposes a novel floating-point G-Net family with randomized binary embeddings and theoretical accuracy guarantees.
result Empirically, G-Net achieves almost 30% higher accuracy on CIFAR-10 compared to prior HDC models.
Proposes EE-Net for neural exploration in contextual bandits.
problem Exploitation-Exploration tradeoff in contextual bandits.
method Uses two neural networks: Exploitation and Exploration, to learn reward function and adaptively explore.
result Achieves regret and outperforms existing methods.
Electronic phenotyping is the task of ascertaining whether an individual has a medical condition of interest by analyzing their medical record and is foundational in clinical informatics. Increasingly, electronic phenotyping is performed via supervised learning. We investigate the effectiveness of multitask learning fo…
Catapult phase in neural nets shows exponential loss growth before quick decrease.
problem Understanding phase transitions in neural networks during training.
method Analyzing weight norm and loss behavior for super-critical learning rates.
result Proven existence of catapult phase in quadratic models and two-layer nets.
Reconstructing the local density field with combined convolutional and point cloud architectureastro-ph.CO
Neural net reconstructs dark matter density from halo velocities.
problem Reconstructing local dark matter density from halo velocities.
method Hybrid architecture combining U-Net and DeepSets.
result Hybrid network recovers density amplitudes and phases better than U-Net.
Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains ignorant to its prediction confidence. Orthogonally to Bayesian neural nets that indi…
The sizes of deep neural networks (DNNs) are rapidly outgrowing the capacity of hardware to store and train them. Research over the past few decades has explored the prospect of sparsifying DNNs before, during, and after training by pruning edges from the underlying topology. The resulting neural network is known as a …
The digital revolution of the banking system with evolving European regulations have pushed the major banking actors to innovate by a newly use of their clients' digital information. Given highly sparse client activities, we propose CPOPT-Net, an algorithm that combines the CP canonical tensor decomposition, a multidim…
Global convergence of SGD proven for two-layer neural nets with regularization.
problem Proving global convergence of SGD for two-layer neural nets.
method Regularized empirical risk, SGD iterates, Villani functions.
result Global convergence of SGD for a special class of initializations.
Oracle inequality for sparse neural nets adapts to unknown structure.
problem Sparse deep neural nets in nonparametric regression.
method Gibbs posterior distribution with Metropolis-adjusted Langevin algorithms and mixture of uniform priors.
result Oracle inequality showing adaptation to unknown regularity and structure, achieving minimax-optimal rate of convergence.
Computational Fluid Dynamics (CFD) is a hugely important subject with applications in almost every engineering field, however, fluid simulations are extremely computationally and memory demanding. Towards this end, we present Lat-Net, a method for compressing both the computation time and memory usage of Lattice Boltzm…
NANSDE-Net models time series with memory using neural ARMA-type noise.
problem Modeling time series with long- or short-memory characteristics.
method Developed NANSDE-Net, a generative model that incorporates Neural Network-kernel ARMA-type noise.
result NANSDE-Net matches or outperforms existing models in reproducing long- and short-memory features of data.
Meta-learning is a promising method to achieve efficient training method towards deep neural net and has been attracting increases interests in recent years. But most of the current methods are still not capable to train complex neuron net model with long-time training process. In this paper, a novel second-order meta-…
NeurISE uses neural nets to learn graphical models efficiently.
problem Efficiently learning graphical models with high-order terms.
method NeurISE, a neural net-based algorithm that approximates interaction screening objective function.
result NeurISE can find parsimonious representations without prior information.
Parameter reduction has been an important topic in deep learning due to the ever-increasing size of deep neural network models and the need to train and run them on resource limited machines. Despite many efforts in this area, there were no rigorous theoretical guarantees on why existing neural net compression methods …
This study shows neural nets can approximate Turing machines with meaningful statistical properties.
problem Theoretical limitations in approximating Turing machines with neural networks.
method Formal definition of statistically meaningful approximation, analysis of boolean circuits and Turing machines using neural nets.
result Transformers can statistically meaningfully approximate Turing machines with polynomial sample complexity.
This article concerns the expressive power of depth in neural nets with ReLU activations and bounded width. We are particularly interested in the following questions: what is the minimal width so that ReLU nets of width (and arbitrary depth) can approximate any continuous functio…
Bonsai-Net efficiently discovers state-of-the-art models with fewer parameters.
problem Efficiently discovering state-of-the-art neural architectures with minimal computational expense.
method Bonsai-Net uses a modified differential pruner to explore a relaxed search space.
result Bonsai-Net consistently discovers better architectures than random search with fewer parameters.
Tensoring volatility calibrationq-fin.RM
Efficiently calibrates volatility models using Chebyshev Tensors.
problem Calibrating pricing models efficiently.
method Used Chebyshev Tensors to speed up calibration of the rough Bergomi volatility model.
result Chebyshev Tensors can calibrate the rough Bergomi volatility model 40,000 times more efficiently than brute-force methods.
MEP-Net uses MEP to generate solutions from limited data.
problem Generating solutions to scientific problems with incomplete information.
method Combines MEP with neural networks to learn complex distributions from moment constraints.
result Demonstrates MEP-Net's effectiveness in modeling biochemical reaction networks and generating complex distributions.
We consider the problem of deep neural net compression by quantization: given a large, reference net, we want to quantize its real-valued weights using a codebook with entries so that the training loss of the quantized net is minimal. The codebook can be optimally learned jointly with the net, or fixed, as for bina…
SGD converges globally to logistic loss minima for two-layer nets.
problem Global convergence of SGD for logistic loss on two-layer neural nets.
method Demonstrates existence of Frobenius norm regularized logistic loss functions as Villani functions, proving convergence and exponential rate.
result SGD converges globally to the global minima of appropriately regularized logistic empirical risk of depth 2 nets.
New method uses neural nets in Hilbert space for option pricing on flow forwards.
problem Pricing options on flow forwards with neural networks in Hilbert space.
method Optimization problem in Hilbert space solved by a novel feedforward neural network architecture.
result Excellent numerical efficiency and superior performance over classical methods.
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.
RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forestscs.LG
Automatic debiasing for causal and policy effects using Neural Nets and Random Forests.
problem Estimating causal and policy effects from high-dimensional or non-parametric regression functions.
method Automatic learning of Riesz representation using Neural Nets and Random Forests.
result Automatic debiasing method performs well compared to state-of-the-art algorithms.
MoreauGrad interprets neural nets robustly and sparsely.
problem Lack of robustness and sparsity in gradient-based interpretation methods.
method Moreau envelope for smooth and robust interpretation, combined with L1 regularization for sparsity.
result MoreauGrad provides a smooth, robust, and sparse explanation of neural nets.
We replace the output layer of deep neural nets, typically the softmax function, by a novel interpolating function. And we propose end-to-end training and testing algorithms for this new architecture. Compared to classical neural nets with softmax function as output activation, the surrogate with interpolating function…
Delay-SDE-net models time series with memory and uncertainty, outperforming other models.
problem Accurately modeling time series with memory and uncertainty.
method Stochastic delay differential equations (SDDEs) neural network model with aleatoric and epistemic uncertainty.
result The Delay-SDE-net consistently outperforms other models in predicting time series values and uncertainties.
Proposes polynomial neural networks for improved function approximation in various tasks.
problem Improving function approximation in various tasks like image generation, face verification, and 3D mesh representation learning.
method Introduces polynomial neural networks (-Nets) and three tensor decompositions to reduce parameter count and enhance expressiveness.
result Demonstrates that -Nets can produce state-of-the-art results in challenging tasks without non-linear activation functions.
PCA-Net combines PCA and neural networks for operator approximation, with new bounds on complexity.
problem Developing approximation theory for PCA-Net architecture.
method Combines PCA and neural networks, derives universal approximation results and lower bounds on complexity.
result PCA-Net can overcome the curse of parametric complexity for specific operators.