Method measures weight similarity in neural networks using normalization and statistical inference.
problem Quantifying weight similarity in non-convex neural networks.
method Chain normalization rule and hypothesis-training-testing statistical inference.
result Weights of identical neural networks converge to similar local solutions.
DeepWeightFlow generates diverse neural network weights efficiently.
problem Generating complete neural network weights efficiently and accurately.
method Flow Matching in weight space with Git Re-Basin and TransFusion.
result DeepWeightFlow generates high-accuracy neural networks without fine-tuning.
Formula found for neural network error with fixed weights.
problem Understanding error in neural networks with fixed weights.
method Provided an explicit formula for approximation error.
result Explicit formula for neural network error with fixed weights.
Complex-valued neural networks avoid spurious local minima.
problem Finding spurious local minima in neural networks.
method Proved no spurious local minima for shallow complex neural networks with quadratic activations.
result Complex-valued weights eliminate spurious local minima in neural networks.
Bayesian priors for neural networks are improved by incorporating weight correlations and tail behavior.
problem Improving Bayesian priors for neural networks to better reflect true beliefs and performance.
method Analyzed summary statistics of neural network weights in different architectures and incorporated these observations into new priors.
result Improved performance on image classification datasets by using new priors that account for weight correlations and tail behavior.
Proposes volumization for neural networks to control bias-variance tradeoff.
problem Improving generalization and preventing memorization in neural networks.
method Defines a physical volume for weights, interpolating between L2 and L∞ regularization.
result Volumization interpolates between weight decay and clipping, improving generalization.
Not all neural network architectures are created equal, some perform much better than others for certain tasks. But how important are the weight parameters of a neural network compared to its architecture? In this work, we question to what extent neural network architectures alone, without learning any weight parameter…
Predicting neural network accuracy from weights without testing.
problem Predicting neural network performance based on weights alone.
method Used simple statistics of weights to rank neural networks' performance.
result Simple predictors can rank networks' performance with high accuracy (R2 score > 0.98).
Neural networks with learned biases can approximate any function.
problem Whether neural networks with only learned biases can approximate any continuous function.
method Theoretical and numerical analysis of random weights and learned biases in neural networks.
result Feedforward and recurrent neural networks with random weights can approximate any continuous function and dynamical systems.
Neural networks with integer weights approximate continuous functions efficiently.
problem Approximating continuous functions using neural networks with integer weights.
method Integrates superexpressive activation functions and integer weights.
result Convergence rate of order n2β+d−2βlog2n for neural network regression. The study examines Fisher information matrices and neural tangent kernels for simple ReLU networks with random weights.
problem Understanding the relationship between Fisher information matrices and neural tangent kernels for 2-layer ReLU networks.
method Analyzes Fisher information matrices and neural tangent kernels for 2-layer ReLU networks with random hidden weights, focusing on spectral decomposition and eigenfunctions.
result Obtained an approximation formula for functions represented by 2-layer neural networks.
New bound for neural networks with full-rank weights, independent of network width.
problem Understanding generalization of neural networks with full-rank weight matrices.
method Using Koopman operators to derive a tighter generalization bound for full-rank weight matrices.
result The bound is tighter than existing norm-based bounds when condition numbers are small.
Hardness proven for neural networks with natural weights.
problem Difficulty in learning neural networks with weights from natural distributions.
method Proved hardness for depth-2 networks with natural weights distributions.
result Most networks are hard to learn with natural weights.
SGD and weight decay encourage neural networks to learn low-rank weight matrices.
problem The bias of SGD towards low-rank weight matrices in neural networks.
method The study investigates the effect of SGD and weight decay on the rank of weight matrices in neural networks, both theoretically and empirically.
result Training with SGD and weight decay induces a bias towards rank minimization in weight matrices, which becomes more pronounced with smaller batch sizes and stronger weight decay.
New regularizer improves neural network robustness and generalization.
problem Ineffective weight decay for networks with homogeneous activation functions.
method Proposes an invariant regularizer to penalize intrinsic weight norms.
result Improves generalization and adversarial robustness on various datasets.
Improved neural networks by averaging late-stage weights.
problem Improving the performance of neural networks.
method Ensemble late-stage weights and average them.
result Augmenting standard models with late-phase weights improves generalization.
This study uncovers how neural architectures and weights interact in classification tasks.
problem Understanding the role of neural architecture and weights in classification performance.
method Developed a novel method to find optimal task-specific architectures as binary networks with {0, 1}-valued weights, using approximate gradient descent.
result Well-trained architectures may not require fine-tuning of weights, highlighting the importance of structure over weights.
RSO uses random weight perturbations to train deep networks without gradients.
problem Training deep neural networks efficiently and without gradient information.
method RSO is a gradient-free Markov Chain Monte Carlo approach that updates weights based on mini-batch loss reduction.
result RSO achieves high accuracy (99.1% on MNIST) with significantly fewer updates than traditional methods.
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide networks.
Enhances neural network regression performance by modeling weight and variance uncertainty.
problem Improving predictive performance of neural networks for regression tasks.
method Extended Blundell's framework to include variance uncertainty, using a full posterior distribution over variance parameters.
result Explicitly modeling variance uncertainty improves generalization of Bayesian neural networks.
Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dime…
New neural network rates for unbounded domains with weighted Sobolev spaces.
problem Improving neural network approximation rates for unbounded domains.
method Embedding results for weighted Fourier-Lebesgue spaces in weighted Sobolev spaces, followed by asymptotic approximation rates.
result Asymptotic approximation rates for shallow neural networks without curse of dimensionality for unbounded domains and Muckenhoupt weights.
Neural networks' weights don't converge to stationary points but training loss stabilizes.
problem The disconnect between theoretical analyses and neural network training practice.
method An invariant measure perspective inspired by ergodic theory of dynamical systems.
result The distribution of weights converges to an approximate invariant measure, explaining loss stabilization.
Paper proves multiplicative weight updates can train neural networks without learning rate tuning.
problem Vanishing and exploding gradients in gradient descent for compositional functions.
method Proves descent lemma for compositional functions using multiplicative weight updates and derives Madam optimizer.
result Madam optimizer trains state-of-the-art neural networks without learning rate tuning.
Recently, Neural networks have seen a huge surge in its adoption due to their ability to provide high accuracy on various tasks. On the other hand, the existence of adversarial examples have raised suspicions regarding the generalization capabilities of neural networks. In this work, we focus on the weight matrix learn…
Bayesian weight priors improve neural network learning of identity relations.
problem Neural networks struggle to learn abstract and systematic relations, especially identity relations.
method Extended RBP approach using Bayesian weight priors as a regularization term.
result Bayesian weight priors lead to perfect generalization for identity relations and do not hinder standard neural network learning.
Adaptive weights improve physics-informed neural networks and deep operator networks.
problem Training physics-informed neural networks and deep operator networks can be challenging, leading to unsatisfactory accuracy and efficiency.
method Proposes a pointwise adaptive weighting method that balances the residual decay rate across different training points.
result Our proposed approach of balanced residual decay rates offers advantages including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.
K-FAC speeds up training of modern neural networks with linear weight-sharing.
problem Efficiently training modern neural networks with linear weight-sharing layers.
method Kronecker-Factored Approximate Curvature (K-FAC) applied to linear weight-sharing layers.
result K-FAC-reduce is generally faster than K-FAC-expand for deep linear networks.
Neural networks trained with backpropagation, the standard algorithm of deep learning which uses weight transport, are easily fooled by existing gradient-based adversarial attacks. This class of attacks are based on certain small perturbations of the inputs to make networks misclassify them. We show that less biologica…
Guarantees sparse recovery for neural networks with iterative hard thresholding.
problem Recovering sparse network weights in neural networks.
method Structural properties of sparse network weights and iterative hard thresholding algorithm.
result Simple iterative hard thresholding algorithm recovers sparse network weights exactly using linear memory.
Analyzes minima of deep linear networks with weight decay.
problem Understanding the loss landscape of deep neural networks.
method Analytical solutions for global minima with weight decay and stochastic neurons.
result The origin is a special point with qualitatively different minima in networks with more than 1 hidden layer.
Bayesian neural networks learn weights with closed-form updates.
problem Efficiently learning Bayesian neural networks with closed-form updates.
method Closed-form Bayesian inference for online learning of Gaussian-weighted BNNs.
result Closed-form expressions for sequential/online training of BNNs.
New methods train neural networks without changing weights, achieving similar or higher performance.
problem Training neural networks efficiently with randomly initialized weights.
method Switching connections on and off, flipping weights' signs, minimizing changed connections.
result Achieves similar or higher performance with less computational cost than training all weights.
Paper develops a framework to optimize neural networks using weighted metrics.
problem Discrepancy between maximizing weighted classification scores and minimizing loss function.
method Formalizes weighted classification metrics and constructs corresponding losses.
result Framework includes well-established approaches like cost-sensitive learning and weighted cross entropy.
Infinite CNNs lose spatial correlations, but can be restored by correlated weights.
problem Infinite CNNs lose spatial correlations, which are crucial for their performance.
method Introduced correlated weights to restore spatial correlations in infinite CNNs.
result Optimal performance is achieved with a moderate level of weight correlation.
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.
MLDS dataset reveals hidden model behavior via weight-space analysis.
problem Neural networks' opacity makes them hard to evaluate.
method Presented MLDS dataset of trained neural networks.
result Weight-space analysis reveals meaningful divergence with small changes in training data.
BiTAT improves neural network quantization for edge devices by focusing on weight dependencies and disentangling them.
problem Performance degradation of compact neural networks under extreme quantization.
method Task-dependent Aggregated Transformation (BiTAT) method that orthonormalizes weights and progressively quantizes them.
result BiTAT effectively preserves model performance on ImageNet and CIFAR-100 with compact backbones.
Two retraining techniques outperform fine-tuning in neural network pruning.
problem Improving accuracy and compression in neural network pruning.
method Weight rewinding and learning rate rewinding compared to fine-tuning.
result Rewinding techniques outperform fine-tuning in accuracy and compression.
Characterizes deep neural network weight space for adversarial attacks.
problem Poor performance of deep learning models in adversarial examples.
method Characterizes deep neural network solution space using two paradigms.
result Adversarial attacks are less successful against Associative Memory Models.
Dense neural networks can't approximate all functions.
problem Approximation capabilities of dense neural networks.
method Model compression approach combining weak regularity lemma and graph neural networks.
result Existence of Lipschitz continuous functions not approximable by dense neural networks.
A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these results, we show that under a single mild condition on the weights of the network,…
The paper shows neural networks can approximate functions over non-compact domains with non-polynomial activation.
problem Approximating functions over non-compact domains using neural networks.
method Using single-hidden-layer feedforward neural networks with non-polynomial activation functions over non-compact subsets of Euclidean spaces.
result Neural networks can approximate functions in weighted Ck-spaces and weighted Sobolev spaces over unbounded domains. Constraints improve deep neural network training by stabilizing and enhancing robustness.
problem Vanishing/exploding gradients and poor weight magnitudes in deep neural networks.
method Weight-constrained stochastic dynamics using Langevin dynamics framework.
result Enhanced exploration of the loss landscape and improved generalization.
Proposes learning invariances in neural networks using a weight-space approach.
problem Learning invariances from data in neural networks remains an open problem.
method Minimizes a lower bound on the marginal likelihood in weight space.
result Results in higher performing models with naturally learned invariances.
This paper extends the Gaussian process interpretation of deep networks to more varied weight distributions.
problem Understanding the impact of different weight initialization schemes on deep learning dynamics.
method Extending the Gaussian process interpretation to PSEUDO-IID weight distributions, including sparse and low-rank networks.
result PSEUDO-IID initialized networks are effectively equivalent up to variance, enabling tractable posterior distributions.
EWC helps prevent forgetting in neural networks by adjusting weights dynamically.
problem Preventing forgetting in neural networks during training.
method EWC adjusts weights dynamically to prevent forgetting.
result EWC effectively prevents catastrophic forgetting in neural networks.
A new method to prune neural networks with iterative randomization improves efficiency.
problem Efficiency in pruning randomly initialized neural networks.
method Iteratively randomizing weight values to reduce parameter requirements.
result The method achieves remarkable performance with fewer parameters.