Related papers: Grokking Explained: A Statistical Phenomenon

Existing accounts of grokking explain the phenomena in terms of mechanistic frameworks such as circuit efficiency or lazy-to-rich transitions. However, despite a known dependence between grokking and model size, how model capacity shapes…

We propose that learning in deep neural networks proceeds in two phases: a rapid curve fitting phase followed by a slower compression or coarse graining phase. This view is supported by the shared temporal structure of three phenomena:…

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…

We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

It has been observed by Belkin et al.\ that over-parametrized neural networks exhibit a `double descent' phenomenon. That is, as the model complexity (as reflected in the number of features) increases, the test error initially decreases,…

Distribution shifts introduce uncertainty that undermines the robustness and generalization capabilities of machine learning models. While conventional wisdom suggests that learning causal-invariant representations enhances robustness to…

Critical-data-size accounts of grokking suggest a natural post-threshold intuition: once training data is sufficient to identify the underlying rule, additional data should accelerate validation convergence. We show that this intuition can…

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been…

Grokking describes a delayed generalization phenomenon in which a neural network achieves perfect training accuracy long before validation accuracy improves, followed by an abrupt transition to strong generalization. Existing detection…

Why do neural networks trained with large learning rates for a longer time often lead to better generalization? In this paper, we delve into this question by examining the relation between training and testing loss in neural networks.…

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of…

Deep neural networks exhibit periodic loss spikes during unregularized long-term training, a phenomenon known as the "Slingshot Mechanism." Existing work usually attributes this to intrinsic optimization dynamics, but its triggering…

We study whether transformers can learn to implicitly reason over parametric knowledge, a skill that even the most capable language models struggle with. Focusing on two representative reasoning types, composition and comparison, we…

Work on continual learning (CL) has thus far largely focused on the problems arising from shifts in the data distribution. However, CL can be decomposed into two sub-problems: (a) shifts in the data distribution, and (b) dealing with the…

Neural networks trained by gradient descent (GD) have exhibited a number of surprising generalization behaviors. First, they can achieve a perfect fit to noisy training data and still generalize near-optimally, showing that overfitting can…

Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…

Dropout is a simple but efficient regularization technique for achieving better generalization of deep neural networks (DNNs); hence it is widely used in tasks based on DNNs. During training, dropout randomly discards a portion of the…

The study of Deep Network (DN) training dynamics has largely focused on the evolution of the loss function, evaluated on or around train and test set data points. In fact, many DN phenomenon were first introduced in literature with that…

For humans, language production and comprehension is sensitive to the hierarchical structure of sentences. In natural language processing, past work has questioned how effectively neural sequence models like transformers capture this…