We find a normal form for two-input flat discrete-time systems.
problem No comparable normal form exists for flat continuous-time systems.
method State- and input transformations to achieve a triangular structure.
result A systematic parameterization of system variables by the flat output and its shifts.
Training state-of-the-art, deep neural networks is computationally expensive. One way to reduce the training time is to normalize the activities of the neurons. A recently introduced technique called batch normalization uses the distribution of the summed input to a neuron over a mini-batch of training cases to compute…
This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum correntropy criterion (NMCC) is derived from a correntropy based…
Deep gradient boosting normalizes neural network inputs layer by layer.
problem Improving neural network performance on image recognition tasks.
method Introducing deep gradient boosting with layer-wise input normalization.
result Layer-wise input normalization improves image recognition performance.
GraN-GAN normalizes gradients for better GAN performance.
problem Improving image generation in GANs with piecewise linear discriminators.
method Piecewise Gradient Normalization (GraN) for input-dependent normalization.
result Significant performance gains in image generation across various datasets.
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently pro…
Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change o…
ENRNN uses eigenvalue normalization for short-term memory in RNNs.
problem Vanishing/exploding gradient problem and long-term dependency modeling.
method Eigenvalue normalization of recurrent matrix to simulate short-term memory.
result ENRNN outperforms existing RNN variants in experiments.
Batch normalization with regularization turns deterministic autoencoders into generative models.
problem Creating generative models from deterministic autoencoders.
method Using batch normalization as a source of non-determinism and adding entropic regularization.
result Deterministic autoencoders can be transformed into generative models with similar performance to variational autoencoders.
While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- Internal Covariate Shift-- the current solution has certain drawbacks. Specifically, BN depends on batch statistics for layerwise input normalization during training which makes the estimates of …
The article warns against assuming normality in machine learning, especially when feature vectors are not normally distributed.
problem The assumption of normality in machine learning models can be misleading, especially when feature vectors are not normally distributed.
method The article provides a mathematical counterexample and experiments to illustrate the risks of assuming normality.
result Prudence is needed when assuming normality in machine learning models, particularly when feature vectors are not normally distributed.
The cost of wind energy can be reduced by using SCADA data to detect faults in wind turbine components. Normal behavior models are one of the main fault detection approaches, but there is a lack of consensus in how different input features affect the results. In this work, a new taxonomy based on the causal relations b…
Neurons predict future scalar inputs by learning top modes of lag vectors.
problem Predicting future scalar inputs with physiological delays.
method Normal Mode Decomposition to extract independently evolving modes.
result Temporal filters of neurons correspond to left eigenvectors of a generalized eigenvalue problem.
Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when DL is used for financial time series forecasting tasks, where the non-stationary…
While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- \textit{Internal Covariate Shift}-- the current solution has certain drawbacks. For instance, BN depends on batch statistics for layerwise input normalization during training which makes the esti…
EDAIN layer normalizes time series data for neural networks, improving model performance.
problem Irregularities in time series data degrade model performance in neural networks.
method EDAIN layer learns adaptive normalization parameters during end-to-end training.
result EDAIN layer outperforms conventional normalization methods and adaptive layers.
Recently, self-normalizing neural networks (SNNs) have been proposed with the intention to avoid batch or weight normalization. The key step in SNNs is to properly scale the exponential linear unit (referred to as SELU) to inherently incorporate normalization based on central limit theory. SELU is a monotonically incre…
Proposes a new normalization method for deep neural networks in financial forecasting.
problem Deep neural networks are sensitive to input variable range and prone to numerical issues, especially with financial time-series.
method Bilinear input normalization method that handles high-frequency financial time-series without expert knowledge.
result Significant improvements in forecasting future stock price dynamics over other normalization techniques.
Batch normalization (batch norm) is often used in an attempt to stabilize and accelerate training in deep neural networks. In many cases it indeed decreases the number of parameter updates required to achieve low training error. However, it also reduces robustness to small adversarial input perturbations and noise by d…
New normalization method makes neural networks more robust to adversarial attacks.
problem Adversarial vulnerability of BatchNorm in deep neural networks.
method Identified distribution shift caused by adversarial images, proposed RobustNorm to use inference-time statistics.
result RobustNorm makes models more robust to adversarial attacks without sacrificing BatchNorm benefits.
Efficiently computes optimal transport maps and Wasserstein barycenters using conditional normalizing flows.
problem Computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces.
method Uses conditional normalizing flows to approximate distributions and solve the primal problem.
result Shows computational feasibility for hundreds of input distributions and yields accurate results.
The paper studies how grid cell patterns emerge in neural networks.
problem Understanding how grid cells in the brain form hexagonal firing patterns.
method Training recurrent neural networks with conformal normalization of velocity inputs.
result Conformal normalization is crucial for the emergence of hexagonal grid patterns in neural networks.
RMSNorm simplifies LayerNorm, reducing computational cost.
problem Computational overhead of LayerNorm in deep neural networks.
method RMSNorm re-scales inputs using root mean square (RMS) instead of invariance.
result RMSNorm achieves comparable performance to LayerNorm but reduces running time.
This paper explains how batch normalization auto-tunes the regularization parameter based on data statistics.
problem Batch normalization accelerates deep learning training but the exact relationship to regularization is unclear.
method Theoretical analysis and empirical validation of batch normalization's role in auto-tuning the regularization parameter.
result Batch normalization auto-tunes the regularization parameter based on data statistics.
Validates neural networks inputs to protect against adversarial examples.
problem Ensuring neural networks robustness against adversarial attacks.
method Runtime local robustness verification based on normal distribution of robustness radii.
result Improves neural network accuracy and protects against adversarial examples.
Normalizing Flows improve prediction interval efficiency in CP.
problem Inefficient prediction intervals in CP due to non-uniform error distribution.
method Train a Normalizing Flow to optimize the distance metric between errors and inputs.
result Optimized prediction intervals are more efficient and valid.
Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from the viewpoint of Fisher kernels. We show that assuming samples within a mini-ba…
Batch Normalization (BatchNorm) is a widely adopted technique that enables faster and more stable training of deep neural networks (DNNs). Despite its pervasiveness, the exact reasons for BatchNorm's effectiveness are still poorly understood. The popular belief is that this effectiveness stems from controlling the chan…
FF algorithm uses goodness as a measure of input quality, derived from likelihood-ratio tests.
problem Training each layer locally with a goodness measure.
method FF algorithm uses a likelihood-ratio test to define goodness, which is the sum of squared activations normalized between layers.
result The goodness measure is a sufficient statistic for a likelihood-ratio test, explaining the FF algorithm's performance.
Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.
problem Efficiently sampling lattice field theories with computational challenges.
method Integrates locality into autoregressive conditional normalizing flows.
result Autocorrelation times improved by orders of magnitude for φ4 theory on a 2D lattice. We improve neural network explainability by bypassing batch normalization.
problem Lack of transparency in neural networks.
method Layer-wise Relevance Propagation with a method to include normalization layers.
result Heatmaps are more accurate for convolutional layers with our method.
CN normalizes channels for better time series model performance.
problem Improper channel identification in time series models.
method Channel Normalization (CN) and its variants (ACN, PCN) using distinct affine transformations.
result Significant performance gains across various time series models.
This work investigates how gradient-based learning performs with structured data, revealing issues and improvements.
problem Gradient-based learning under structured data, particularly with a spiked covariance structure.
method Investigates the effect of a spiked covariance structure on gradient-based feature learning and proposes weight normalization.
result Gradient-based dynamics may fail to recover the true direction in anisotropic settings, but weight normalization can improve performance.
Finet uses FBN for efficient, lightweight neural networks.
problem Building efficient neural networks with limited computational resources.
method Introduces Fine-grained Batch Normalization (FBN) and a novel light-weight network (Finet) that combines FBN with standard convolution.
result Finet achieves state-of-the-art performance on ImageNet classification with reduced computational complexity.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
Graph Metanetworks process diverse neural architectures efficiently.
problem Processing diverse neural architectures efficiently.
method Builds metanetworks using graph neural networks to process graphs representing input neural networks.
result Proves GMNs are expressive and equivariant to parameter permutation symmetries.
We address the problem of estimating statistics of hidden units in a neural network using a method of analytic moment propagation. These statistics are useful for approximate whitening of the inputs in front of saturating non-linearities such as a sigmoid function. This is important for initialization of training and f…
Gradient control plays an important role in feed-forward networks applied to various computer vision tasks. Previous work has shown that Recurrent Highway Networks minimize the problem of vanishing or exploding gradients. They achieve this by setting the eigenvalues of the temporal Jacobian to 1 across the time steps. …
New Convolutional Unit improves Batch Whitening performance.
problem Improving the efficiency and effectiveness of Batch Whitening.
method Proposes a new Convolutional Unit that aligns with Batch Whitening theory and empirically analyzes the original Convolutional Unit.
result Significantly improved performance on multiple image classification datasets.
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.
Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns. Bittorf, Recht, Ré and Tropp (`Factoring nonnegative matrices with linear programs', …
This paper improves RNN generalization without normalization conditions.
problem Generalization of over-parameterized RNNs without normalization constraints.
method Detailed analysis of neural tangent kernel matrix for improved generalization bounds.
result RNNs can learn functions without normalization conditions and with almost-polynomial scaling in input length.
Layer normalization with activations prevents Gram matrix rank collapse at initialization.
problem Rank collapse in Gram matrices at initialization slows training in deep networks.
method Proved that layer normalization, with activation layers, biases Gram matrix towards identity matrix at exponential rate.
result Layer normalization with activations biases Gram matrix towards identity matrix at exponential rate with depth at initialization.
Recurrent Neural Networks (RNNs) are powerful models for sequential data that have the potential to learn long-term dependencies. However, they are computationally expensive to train and difficult to parallelize. Recent work has shown that normalizing intermediate representations of neural networks can significantly im…
GAS-Norm improves deep learning time series forecasting in non-stationary settings.
problem Deep learning models struggle with non-stationary time series data.
method Combines GAS model for adaptive normalization with deep neural networks.
result Improves deep learning performance in 21 out of 25 settings.
Two new rational formulae for normal implied volatility are presented.
problem Calculating normal implied volatility using iterative methods.
method Two explicit rational formulae that avoid iteration and logarithms.
result Accurate and fast formulae for normal implied volatility.
Normalization techniques such as Batch Normalization have been applied successfully for training deep neural networks. Yet, despite its apparent empirical benefits, the reasons behind the success of Batch Normalization are mostly hypothetical. We here aim to provide a more thorough theoretical understanding from a clas…
ScieNet improves deep learning resilience to input perturbations.
problem Deep learning's poor resilience to input perturbations in real-world scenarios.
method Hybrid architecture combining SNN for contextual info extraction and DNN for classification.
result Significant improvement in accuracy on noisy and rainy images without prior training.