Related papers: Is Grokking Worthwhile? Functional Analysis and Tr…

We investigate grokking in transformers through the lens of inductive bias: dispositions arising from architecture or optimization that let the network prefer one solution over another. We first show that architectural choices such as the…

Mechanistic interpretability typically relies on post-hoc analysis of trained networks. We instead adopt an interventional approach: testing hypotheses a priori by modifying architectural topology to observe training dynamics. We study…

Neural networks readily learn a subset of the modular arithmetic tasks, while failing to generalize on the rest. This limitation remains unmoved by the choice of architecture and training strategies. On the other hand, an analytical…

Grokking is proposed and widely studied as an intricate phenomenon in which generalization is achieved after a long-lasting period of overfitting. In this work, we propose NeuralGrok, a novel gradient-based approach that learns an optimal…

Transformer-based language models have achieved significant success; however, their internal mechanisms remain largely opaque due to the complexity of non-linear interactions and high-dimensional operations. While previous studies have…

Recent research on the grokking phenomenon has illuminated the intricacies of neural networks' training dynamics and their generalization behaviors. Grokking refers to a sharp rise of the network's generalization accuracy on the test set,…

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…

Grokking, the sudden transition from memorization to generalization, is characterized by the emergence of low-dimensional representations, yet the mechanism underlying this organization remains elusive. We propose that intrinsic task…

Humans exhibit remarkable compositional reasoning by integrating knowledge from various sources. For example, if someone learns ( B = f(A) ) from one source and ( C = g(B) ) from another, they can deduce ( C=g(B)=g(f(A)) ) even without…

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…

Delayed generalization, termed grokking, in a machine learning calculation occurs when the increase in test accuracy is delayed relative to the training accuracy. This paper examines grokking in the context of a dense neural network trained…

Grokking -- the delayed transition from memorization to generalization in small algorithmic tasks -- remains poorly understood. We present a geometric analysis of optimization dynamics in transformers trained on modular arithmetic. PCA of…

Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to…

Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…

A major challenge for transformers is generalizing to sequences longer than those observed during training. While previous works have empirically shown that transformers can either succeed or fail at length generalization depending on the…

Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic…

Grokking -- the sudden generalisation that appears long after a model has perfectly memorised its training data -- has been widely observed but lacks a quantitative theory explaining the length of the delay. We show that grokking is a…

To process novel sentences, language models (LMs) must generalize compositionally -- combine familiar elements in new ways. What aspects of a model's structure promote compositional generalization? Focusing on transformers, we test the…

Despite exceptional capabilities in knowledge-intensive tasks, Large Language Models (LLMs) face a critical gap in understanding how they internalize new knowledge, particularly how to structurally embed acquired knowledge in their neural…

Neural collapse, i.e., the emergence of highly symmetric, class-wise clustered representations, is frequently observed in deep networks and is often assumed to reflect or enable generalization. In parallel, flatness of the loss landscape…