Related papers: Renormalizable Spectral-Shell Dynamics as the Orig…
Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…
A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting from the high-dimensional interactions between the large number of network parameters. Such non-trivial…
Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
Empirical power--law scaling has been widely observed across modern deep learning systems, yet its theoretical origins and scope of validity remain incompletely understood. The Generalized Resolution--Shell Dynamics (GRSD) framework models…
Training large neural networks exposes neural scaling laws for the generalization error, which points to a universal behavior across network architectures of learning in high dimensions. It was also shown that this effect persists in the…
The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of…
Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and…
This paper explores the intricate behavior of deep neural networks (DNNs) through the lens of neuron activation dynamics. We propose a probabilistic framework that can analyze models' neuron activation patterns as a stochastic process,…
When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…
Scaling laws in deep learning -- empirical power-law relationships linking model performance to resource growth -- have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly…
Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…
We introduce a model for neural scaling laws under sparse activations. In the model, test loss is often dominated by rare coordinates that are never observed in the training input. This mechanism induces a novel bottleneck absent from dense…
Empirical scaling laws describe how test loss and other performance metrics depend on model size, dataset size, and compute. While such laws are consistent within specific regimes, apparently distinct scaling behaviors have been reported…
When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…
As neural networks continue to grow in size but datasets might not, it is vital to understand how much performance improvement can be expected: is it more important to scale network size or data volume? Thus, neural network scaling laws,…
What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists…
Neural scaling laws aim to characterize how out-of-sample error behaves as a function of model and training dataset size. Such scaling laws guide allocation of a computational resources between model and data processing to minimize error.…