Related papers: Grokking From Abstraction to Intelligence

Training loss and accuracy are the standard signals used to monitor generalization during deep neural network training. Two well-documented phenomena complicate this picture: in grokking, train loss falls rapidly while test performance…

The widespread use of diffusion models has led to an abundance of AI-generated data, raising concerns about model collapse -- a phenomenon in which recursive iterations of training on synthetic data lead to performance degradation. Prior…

Why does a Transformer that has memorized its training set wait thousands of steps before it generalizes? Existing accounts locate this delay in norm minimization, feature emergence, or the late discovery of sparse subnetworks. These…

Grokking -- the delayed onset of generalization after early memorization -- is often described with phase-transition language, but that claim has lacked falsifiable finite-size inputs. Here we supply those inputs by treating the group order…

Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or…

A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a…

Classical statistical inference and learning theory often fail to explain the success of modern neural networks. A key reason is that these models are non-identifiable (singular), violating core assumptions behind PAC bounds and asymptotic…

We study the dynamics of gradient flow with small weight decay on general training losses $F: \mathbb{R}^d \to \mathbb{R}$. Under mild regularity assumptions and assuming convergence of the unregularised gradient flow, we show that the…

Supervised Fine-Tuning (SFT) is widely used for task-specific adaptation, yet recent work shows it systematically undermines reasoning generalization. We argue the root cause is not memorization itself, but its target: vanilla SFT drives…

Transformers trained on modular arithmetic exhibit sharp transitions between memorization, generalization, and collapse. We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap…

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…

Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of…

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…

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…

The manifold hypothesis (MH) is often used to explain how machine learning can overcome the curse of dimensionality. However, the MH is only applicable in regimes where the training data provides a sufficiently dense sample of the…

We study implicit reasoning, i.e. the ability to combine knowledge or rules within a single forward pass. While transformer-based large language models store substantial factual knowledge and rules, they often fail to compose this knowledge…

We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions…

Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by…

Traditional machine learning relies on explicit models and domain assumptions, limiting flexibility and interpretability. We introduce a model-free framework using surprisal (information theoretic uncertainty) to directly analyze and…

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training…