This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating bac…
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48 results for “gradient propagation”
Symmetries in shrinking Ricci solitons spread outward.
problem Understanding symmetries in shrinking Ricci solitons.
method Propagating approximate symmetries to larger scales.
result Symmetries in shrinking Ricci solitons spread outward.
NES optimizes discrete structured VAEs effectively without gradient propagation.
problem Learning high-dimensional discrete latent spaces in generative models.
method Natural Evolution Strategies (NES) for gradient-free optimization of discrete structures.
result NES effectively optimizes discrete structured VAEs, comparable to gradient-based methods.
This paper proposes the Mesh Neural Network (MNN), a novel architecture which allows neurons to be connected in any topology, to efficiently route information. In MNNs, information is propagated between neurons throughout a state transition function. State and error gradients are then directly computed from state updat…
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
As traditional neural network consumes a significant amount of computing resources during back propagation, \citet{Sun2017mePropSB} propose a simple yet effective technique to alleviate this problem. In this technique, only a small subset of the full gradients are computed to update the model parameters. In this paper …
Stochastic gradient descent (SGD) has achieved great success in training deep neural network, where the gradient is computed through back-propagation. However, the back-propagated values of different layers vary dramatically. This inconsistence of gradient magnitude across different layers renders optimization of deep …
Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.
problem Understanding long-term behavior of finite-particle systems in relation to their mean-field limits.
method Developed uniform-in-time propagation-of-chaos results for continuous-time SVGD using cutoff strategies and finite-dimensional theories.
result Uniform-in-time propagation-of-chaos bounds in various metrics, including Langevin kernel Stein discrepancy, Wasserstein-1, and Wasserstein-2 distances.
Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is computationally challenging. One heuristic to circumvent this difficulty is to use t…
A new method for target propagation using iterative approximations converges fast and is more biologically plausible.
problem Improving target propagation methods for neural networks.
method Iterative approximate inverses and local auto-encoders.
result The method converges exponentially fast under certain conditions.
In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to train. Nowadays, most of the deep learning model training still relies on the back…
Defines a calculus for integrating Moreau envelopes in differentiable programming.
problem Lack of a mathematical framework for applying Moreau envelopes to deep networks and machine learning systems.
method Develops a compositional calculus adapted to Moreau envelopes and integrates it into differentiable programming.
result Integrates Moreau envelopes into differentiable programming, enabling new gradient back-propagation methods.
Recent breakthroughs in defenses against adversarial examples, like adversarial training, make the neural networks robust against various classes of attackers (e.g., first-order gradient-based attacks). However, it is an open question whether the adversarially trained networks are truly robust under unknown attacks. In…
Neural network has attracted great attention for a long time and many researchers are devoted to improve the effectiveness of neural network training algorithms. Though stochastic gradient descent (SGD) and other explicit gradient-based methods are widely adopted, there are still many challenges such as gradient vanish…
Beyond Signal Propagation: Is Feature Diversity Necessary in Deep Neural Network Initialization?cs.LG
New method shows random, diverse initializations are not essential for deep neural networks.
problem The necessity of random, diverse initializations in deep neural networks.
method Constructed a deep convolutional network with identical features by initializing weights to 0, enabling signal propagation and stable gradients.
result Random, diverse initializations are not necessary for training neural networks.
A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the probabilities of each variable being zero, or Gaussian-distributed. Using the p…
This work develops a particle system to approximate Fisher-Rao gradient flows in mean-field optimization.
problem Optimizing probability measures in neural network contexts.
method Constructing an interacting particle system approximating Fisher-Rao gradient flows.
result Propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimization.
Sparsification is an efficient approach to accelerate CNN inference, but it is challenging to take advantage of sparsity in training procedure because the involved gradients are dynamically changed. Actually, an important observation shows that most of the activation gradients in back-propagation are very close to zero…
New algorithm optimizes nonlinear SDEs online with convergence guarantees.
problem Optimizing nonlinear stochastic differential equations (SDEs) is computationally challenging.
method Forward propagation algorithm that solves an SDE derived using forward differentiation.
result Convergence theorem for nonlinear dissipative SDEs with bounds on stochastic fluctuations.
Backward propagation rules for warped products under Ricci flow.
problem Understanding how warped product structures behave under Ricci flow.
method Establishing sufficient conditions for backward propagation of warped product structures.
result Asymptotically conical shrinkers are multiply-warped products over Einstein manifolds.
EXODUS improves training of SNNs by stabilizing gradients and reducing complexity.
problem Training SNNs using BPTT is time-consuming and numerically unstable.
method EXODUS modifies SLAYER to account for neuron reset and uses IFT for correct gradient calculation, eliminating manual scaling.
result EXODUS achieves comparable or better performance than SLAYER, especially in tasks with temporal features.
Unified framework for training SNNs using EP, faster convergence.
problem Training spiking neural networks with Expectation-Propagation.
method Message-passing framework for learning marginal distributions of SNN parameters.
result Faster convergence compared to gradient-based methods.
Within many machine learning algorithms, a fundamental problem concerns efficient calculation of an unbiased gradient wrt parameters $\gammav$ for expectation-based objectives $\Ebb_{q_{\gammav} (\yv)} [f(\yv)]$. Most existing methods either (i) suffer from high variance, seeking help from (often) complicated variance-…
The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the …
The back-propagation algorithm is widely used for learning in artificial neural networks. A challenge in machine learning is to create models that generalize to new data samples not seen in the training data. Recently, a common flaw in several machine learning algorithms was discovered: small perturbations added to the…
Analyzes self-attention in recurrent networks, proving it mitigates vanishing gradients.
problem Vanishing gradients in recurrent networks when capturing long-term dependencies.
method Formal analysis of self-attention's effect on gradient propagation, proposing a relevancy screening mechanism.
result Self-attention mitigates vanishing gradients in recurrent networks, providing guarantees.
This paper makes two contributions to Bayesian machine learning algorithms. Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not requi…
Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models. In this paper, we propose \emph{block belief propagation learning} (BBPL), whic…
Using back-propagation and its variants to train deep networks is often problematic for new users. Issues such as exploding gradients, vanishing gradients, and high sensitivity to weight initialization strategies often make networks difficult to train, especially when users are experimenting with new architectures. Her…
To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the straight-through gradient method, which enables back-propagation through the quantization ma…
Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagat…
Improved convergence rates for MFLD in various gradient estimators.
problem Proving convergence rates for mean-field Langevin dynamics with stochastic gradient updates.
method General framework for propagation of chaos, including finite-particle approximation, time-discretization, and stochastic gradient approximation.
result Improved convergence rates for SGD and SVRG settings.
Multi-layered representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are the dominant methods for modeling discrete or tabular data, they are hard to incorporate with…
Optimization-based pruning eliminates backpropagation for large language models.
problem Suboptimal pruning performance due to heuristic metrics.
method Optimization of Bernoulli distribution to learn pruning masks without backpropagation.
result Efficient pruning of large language models with improved performance.
We propose a simple yet effective technique to simplify the training and the resulting model of neural networks. In back propagation, only a small subset of the full gradient is computed to update the model parameters. The gradient vectors are sparsified in such a way that only the top-k elements (in terms of magnitude…
New EP variants improve inference stability and efficiency.
problem Inference stability and efficiency issues in EP.
method Motivated by natural-gradient optimization, new EP variants are introduced that are robust to Monte Carlo noise and efficient with single samples.
result Improved stability and efficiency in inference tasks.
A simple gating mechanism improves deep learning convergence.
problem Vanishing or exploding gradients in deep networks.
method Introducing a zero-initialized parameter to each residual connection.
result Training deep networks (up to 120 layers) with fast convergence and better performance.
New theory explains signal propagation in normalization-free transformers.
problem Understanding signal propagation in normalization-free transformers.
method Deriving recurrence relations for activation statistics and APJNs across layers.
result Transformers with elementwise tanh-like nonlinearities exhibit subcritical signal propagation.
These notes aim to shed light on the recently proposed structured projected intermediate gradient optimization technique (SPIGOT, Peng et al., 2018). SPIGOT is a variant of the straight-through estimator (Bengio et al., 2013) which bypasses gradients of the argmax function by back-propagating a surrogate "gradient." We…
EP learns like BPTT but with local weight updates.
problem Existing EP lacks a local time learning rule.
method C-EP updates weights simultaneously with neuron dynamics.
result C-EP follows BPTT gradients and performs well.
New algorithms improve binary neural network configurations.
problem Training binary neural networks efficiently.
method Stochastic message passing algorithms (BP and SP) for discrete inference.
result Stochastic BP and SP find better BNN configurations.
Theoretical framework for target propagation shows differences from backpropagation.
problem Understanding and improving target propagation for neural networks.
method Mathematical optimization analysis and novel reconstruction loss.
result A novel reconstruction loss improves feedback weight training and introduces architectural flexibility.
Training very deep networks is an important open problem in machine learning. One of many difficulties is that the norm of the back-propagated error gradient can grow or decay exponentially. Here we show that training very deep feed-forward networks (FFNs) is not as difficult as previously thought. Unlike when back-pro…
We conduct mathematical analysis on the effect of batch normalization (BN) on gradient backpropogation in residual network training, which is believed to play a critical role in addressing the gradient vanishing/explosion problem, in this work. By analyzing the mean and variance behavior of the input and the gradient i…
Generative Adversarial Networks (GANs) have experienced a recent surge in popularity, performing competitively in a variety of tasks, especially in computer vision. However, GAN training has shown limited success in natural language processing. This is largely because sequences of text are discrete, and thus gradients …
NoProp learns neural networks without full back-propagation or forward-propagation.
problem Learning hierarchical representations in neural networks.
method NoProp independently learns each block to denoise a noisy target using local targets and back-propagation within the block.
result NoProp is a viable learning algorithm that is easy to use and computationally efficient.
The Resilient Propagation (Rprop) algorithm has been very popular for backpropagation training of multilayer feed-forward neural networks in various applications. The standard Rprop however encounters difficulties in the context of deep neural networks as typically happens with gradient-based learning algorithms. In th…
In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model the update rules of the incremental proximal gradient method and develop a syst…