Related papers: Scaling Laws from Sequential Feature Recovery: A S…
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…
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…
Scaling laws for large language models (LLMs) have provided useful guidance in training ever larger models for predictable performance gains. Time series forecasting shares a similar sequential structure to language, and is amenable to…
Symbolic regression (SR) aims to discover the underlying mathematical expressions that explain observed data. This holds promise for both gaining scientific insight and for producing inherently interpretable and generalizable models for…
Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…
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…
Sparse autoencoders (SAEs) model the activations of a neural network as linear combinations of sparsely occurring directions of variation (latents). The ability of SAEs to reconstruct activations follows scaling laws w.r.t. the number of…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
Scaling laws have played a major role in the modern AI revolution, providing practitioners predictive power over how the model performance will improve with increasing data, compute, and number of model parameters. This has spurred an…
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of…
Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…
The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…
Deep neural networks trained end-to-end to map a measurement of a (noisy) image to a clean image perform excellent for a variety of linear inverse problems. Current methods are only trained on a few hundreds or thousands of images as…
We develop a solvable model of neural scaling laws beyond the kernel limit. Theoretical analysis of this model shows how performance scales with model size, training time, and the total amount of available data. We identify three scaling…
The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all…
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…
We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…
Neural scaling laws suggest that the test error of large language models trained online decreases polynomially as the model size and data size increase. However, such scaling can be unsustainable when running out of new data. In this work,…
Scaling laws have emerged as a unifying lens for understanding and guiding the training of large language models (LLMs). However, existing studies predominantly focus on the final-step loss, leaving open whether the entire loss dynamics…
Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language…