Study on neural networks with regularisation and its impact on training dynamics.
problem Understanding the dynamics of neural networks with regularization.
method Established explicit dynamics for neural networks with a regularizing term, linearizing around initialisation.
result The regularisation term modifies the standard NTK dynamics, leading to new insights into network training.
The paper analyzes the training dynamics of neural networks using kernel methods.
problem Understanding the training dynamics of neural networks in high-dimensional settings.
method High-dimensional asymptotics and gradient flow on kernel least-squares objectives.
result The training dynamics of neural networks undergo three stages, characterized by behaviors in the Oracle and Empirical worlds.
Dynamic Sparse Training finds efficient sparse networks from scratch.
problem Finding efficient sparse neural networks.
method Jointly optimizes network parameters and sparsity with trainable thresholds.
result Achieves state-of-the-art performance with minimal performance loss.
Neural ODEs provide a framework for studying the training dynamics of neural networks.
problem Training dynamics of neural networks
method Dynamical mean field theory
result Derive learning curves in the high-dimensional limit
Panda predicts chaotic systems without retraining, showing emergent properties.
problem Predicting chaotic systems with small errors.
method Trained on a synthetic dataset of chaotic dynamical systems using evolutionary algorithms.
result Panda predicts unseen chaotic systems with zero-shot learning.
Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present …
We analyze training dynamics in Gaussian mixture models using a comparison theorem.
problem Analyzing training algorithms with Gaussian mixture data.
method Applying a Gaussian comparison theorem to a specific family of training algorithms.
result Validated dynamic mean-field expressions and provided iterative refinement schemes.
EBMs trained with ML are shown to behave like GANs with a self-adversarial loss.
problem Training EBMs with ML is intractable due to intractable unnormalized distributions.
method Replaced MCMC with deterministic gradient descent ODE solutions to study density induced by dynamics.
result EBM training is effectively a self-adversarial procedure rather than ML estimation.
Parallel neural network training yields better long-term prediction accuracy.
problem Choosing the right training strategy for neural networks in dynamical systems.
method Comparison of parallel and series-parallel training strategies on five neural network architectures and two examples.
result Parallel training consistently outperforms series-parallel training in long-term prediction accuracy.
This study explains RL training dynamics in LLMs, focusing on token-level optimization and reasoning pattern reshaping.
problem Understanding the training dynamics of RL in LLMs to improve their reasoning capabilities.
method Empirical analysis and theoretical modeling of RL training process, focusing on reasoning patterns and token optimization.
result RL primarily optimizes a sparse subset of critical tokens, reshaping reasoning pattern distributions and affecting model performance.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
problem Training large neural networks with low precision is unstable.
method Derive a Bayesian learning rule with log-normal posterior distributions and multiplicative updates.
result LMD achieves stable and accurate training for Vision Transformer and GPT-2.
We introduce a scalable measure of curvature for analyzing training dynamics of large language models.
problem Analyzing the training dynamics of large language models due to high computational cost of measuring Hessian sharpness.
method We introduce critical sharpness and relative critical sharpness as computationally efficient measures capturing Hessian sharpness phenomena.
result We provide the first demonstration of sharpness phenomena at scale up to 7B parameters.
GFM models neural network training as a dynamical system to forecast final weights.
problem Computational intensity and inefficiency in training deep neural networks.
method Gradient Flow Matching (GFM) treats training as a dynamical system with learned vector fields.
result GFM achieves forecasting accuracy competitive with Transformer-based models and significantly outperforms classical baselines.
This paper improves volatility forecasting using dynamic subset selection in genetic programming.
problem Improving accuracy of implied volatility forecasting.
method Dynamic training-subset selection methods applied to genetic programming.
result Dynamic subset selection improves predictive accuracy of genetic programming models.
Proposes dynamic channel pruning during neural network training.
problem Pruning neural networks during training to reduce computational cost and improve efficiency.
method Dynamic channel propagation to update channel utility values and selectively prune channels.
result Our scheme trains and prunes neural networks simultaneously, achieving superior performance.
Aims to describe neural network training dynamics using two-time-scale models.
problem Lack of a general mathematical description of neural network training.
method Introduces a theoretical framework based on two-time-scale population dynamics.
result Derives selection-mutation equations and effective fitness for hyperparameters.
The paper analyzes the dynamics of a simple neural network using a mean-field approach.
problem Understanding the training dynamics of neural networks, especially in classification tasks.
method Developed an analytic theory using a mean-field limit for a simple neural network.
result Explicitly solved the dynamics of a linearly separable dataset with a linear hinge loss.
Dynamic sample pruning speeds up spatio-temporal forecasting models.
problem Training deep learning models on large, redundant datasets is computationally expensive.
method Dynamic sample pruning based on real-time learning state.
result Significant acceleration of training speed with improved performance.
Dynamic Influence Tracker measures changing sample importance during model training.
problem Static influence measurements during training overlook how sample importance varies over time.
method Dynamic Influence Tracker (DIT) captures time-varying sample influence across arbitrary time windows.
result DIT reveals distinct learning phases with shifting priorities and detects corrupted samples more efficiently.
Improved latent dynamics identification framework reduces training time and improves accuracy.
problem Accurate numerical solutions of partial differential equations require computationally expensive solvers.
method Sequential decoder training (mLaSDI) to correct residual errors from previous stages.
result mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time.
Survey on statistical theories of neural networks, focusing on approximation, training dynamics, and generative models.
problem Understanding the statistical properties and training dynamics of neural networks.
method Review of existing literature on neural networks from three perspectives: approximation, training dynamics, and generative models.
result Theoretical insights into neural network training dynamics and generative models.
This paper analyzes the training dynamics of binary neural networks using information bottleneck.
problem Training binary neural networks is challenging due to discontinuity in activation functions.
method The approach uses the Information Bottleneck principle to analyze BNN training dynamics.
result Training dynamics of BNNs are different from DNNs, with both phases occurring simultaneously.
This paper improves dynamic hedging accuracy using genetic programming to forecast implied volatilities.
problem Improving the accuracy of dynamic hedging using implied volatilities.
method The paper uses genetic programming to forecast implied volatilities and tests the performance of these forecasts in dynamic hedging strategies.
result Genetic programming-generated implied volatilities improve hedging accuracy compared to static training methods.
The study analyzes a three-layer neural network's training dynamics using a functional-space mean-field theory.
problem Understanding the training dynamics of partially-trained three-layer neural networks.
method Generalized mean-field theory to functional spaces, proving convergence and feature learning.
result The training loss of the model decays to zero at a linear rate in the L2 regression setting. Orthogonal initialization does not speed up training in ultra-wide neural networks.
problem Exploring the effect of orthogonal initialization on training speed in deep neural networks.
method Study of neural tangent kernel dynamics in FCNs and CNNs with orthogonal initialization.
result The NTK of orthogonally-initialized networks remains constant during training, suggesting no speedup in the NTK regime.
Paper analyzes convergence of dynamic policy gradient for MDPs, improving performance in finite-time problems.
problem Optimal policies in finite-time MDPs are not stationary and require epoch-specific training.
method Introduces dynamic policy gradient combining dynamic programming and policy gradient, analyzes convergence for softmax parametrisation.
result Dynamic policy gradient training exploits finite-time structure, leading to better convergence bounds.
ES improves training efficiency by dynamically selecting data samples.
problem Efficiently selecting informative data samples for faster learning.
method Evolved Sampling (ES) dynamically selects data samples based on loss dynamics and differences.
result ES achieves significant training acceleration without compromising model performance.
Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In practice this leads to dynamics equivalent to many hundreds or even thousands of layers. In this paper, we overcome this apparent difficulty b…
Diffusion models generalize well until a threshold is reached, preventing memorization.
problem Understanding why diffusion models don't memorize training data.
method Investigation of training dynamics and two timescales: τgen and τmem. result The threshold τmem increases linearly with training set size n, preventing memorization. The study analyzes deep linear networks from random initialization, capturing dynamics and hyperparameter effects.
problem Understanding training dynamics in deep linear networks from random initialization.
method Theoretical analysis of gradient descent dynamics in deep linear networks with random initialization and large data.
result Captures the 'wider is better' effect and hyperparameter transfer effects, contrasting with neural-tangent parameterization.
New metric measures dynamical richness without relying on accuracy.
problem Lack of a reliable metric for measuring dynamical richness.
method Developed a computationally efficient, performance-independent metric based on low-rank bias.
result Metric recovers neural collapse as a special case and captures known transitions without accuracy.
FedDST trains sparse sub-networks to improve efficiency in federated learning.
problem Efficiently train large models on resource-limited edge devices with limited network bandwidth.
method Dynamic sparse training to reduce model size and communication.
result FedDST outperforms existing methods in federated learning, especially in non-i.i.d. settings.
In this paper, we explore the effectiveness of dynamic analysis techniques for identifying malware, using Hidden Markov Models (HMMs) and Profile Hidden Markov Models (PHMMs), both trained on sequences of API calls. We contrast our results to static analysis using HMMs trained on sequences of opcodes, and show that dyn…
New pruning methods improve dynamic sparse training performance.
problem Improving dynamic sparse training performance.
method Design and empirical analysis of pruning criteria.
result Most pruning methods yield similar results, but magnitude-based pruning performs best in low-density regimes.
Modern deep neural networks are typically highly overparameterized. Pruning techniques are able to remove a significant fraction of network parameters with little loss in accuracy. Recently, techniques based on dynamic reallocation of non-zero parameters have emerged, allowing direct training of sparse networks without…
Superposition accelerates training to a universal power-law exponent.
problem Training dynamics in neural networks.
method Teacher-student framework and analytic theory.
result Superposition leads to a universal power-law exponent of ~1, independent of data and channel statistics.
RLVR training dynamics reveal an implicit curriculum that shapes learning progression.
problem Understanding how RLVR overcomes the long-horizon barrier.
method Developed a theory of training dynamics for RLVR on transformers, using Fourier analysis on finite groups.
result Mixed-difficulty training naturally follows an implicit curriculum, shaping the learning progression from easy to hard.
Gradient descent dynamics in wide neural networks are analyzed using a dynamical CLT.
problem Understanding the fluctuations in wide shallow neural networks trained via gradient descent.
method Dynamical Central Limit Theorem (CLT) applied to neural network dynamics.
result Asymptotic fluctuations remain bounded in mean square throughout training.
New model explains GAN training dynamics and mode collapse.
problem Mode collapse in GANs, where generators fail to reproduce diversity.
method Simplified model using particles in output space, coupled by universal kernel.
result Gradient regularizers can optimally yield convergence through critical damping.
Study on how optimal representations emerge during deep learning training, focusing on the role of implicit regularization.
problem Understanding how optimal representations for tasks are learned during training.
method Investigates the role of implicit regularization in learning minimal sufficient representations, analyzing changes in representation content during training.
result Semantically meaningful but ultimately irrelevant information is encoded in early transient dynamics of training, which is later discarded.
Study models deep learning training dynamics using locally elastic SDEs to reveal feature separability.
problem Understanding how deep learning models separate features from different classes during training.
method Modeling deep learning training using locally elastic SDEs with a drift term reflecting backpropagation impact.
result Local elasticity in SDEs leads to linear separability of features, resulting in vanishing training loss.
Letter analyzes training dynamics of a nonlinear contrastive learning model in high dimensions.
problem Understanding training dynamics of nonlinear contrastive learning models in high-dimensional settings.
method High-dimensional analysis using McKean-Vlasov PDEs and low-dimensional ODEs.
result The model's performance evolves according to specific ODEs, revealing features like feature learnability and noise effects.
Optimizes neural network training by dynamically updating Tucker decomposition ranks.
problem Redundant parameters in neural network architectures.
method Geometry-aware training of factorized layers in tensor Tucker format.
result Optimal locally approximating the original dynamics without initial rank knowledge.
Adversarial training leads to clean data generalization with significant robust overfitting gap.
problem Significant robust generalization gap in adversarial training.
method Two theoretical views: representation complexity and training dynamics.
result ReLU nets with O(ND) extra parameters can achieve CGRO. We propose and systematically evaluate three strategies for training dynamically-routed artificial neural networks: graphs of learned transformations through which different input signals may take different paths. Though some approaches have advantages over others, the resulting networks are often qualitatively similar…
Study L2 regularization in deep networks, uncovering performance relations and proposing a training schedule.
problem Understanding and optimizing L2 regularization in deep learning models. method Empirical observations and theoretical analysis of gradient flow dynamics in infinitely wide networks.
result Empirical relations between model performance, L2 coefficient, learning rate, and training steps; optimal regularization parameter prediction; improved training schedule. The learning rate is one of the most important hyper-parameters for model training and generalization. However, current hand-designed parametric learning rate schedules offer limited flexibility and the predefined schedule may not match the training dynamics of high dimensional and non-convex optimization problems. In …
New model explains deep learning performance at large learning rates.
problem Understanding deep learning performance at different learning rates.
method Developed neural networks with solvable training dynamics.
result Large learning rates lead to convergence to flatter minima.