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Training Transformers on algorithmic tasks frequently demonstrates an intriguing abrupt learning phenomenon: an extended performance plateau followed by a sudden, sharp improvement. This work investigates the underlying mechanisms for such…

We study the approximation capabilities, convergence speeds and on-convergence behaviors of transformers trained on in-context recall tasks -- which requires to recognize the \emph{positional} association between a pair of tokens from…

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for…

Recent analysis on the training dynamics of Transformers has unveiled an interesting characteristic: the training loss plateaus for a significant number of training steps, and then suddenly (and sharply) drops to near--optimal values. To…

Do reasoning models have "Aha!" moments? Prior work suggests that models like DeepSeek-R1-Zero undergo sudden mid-trace realizations that lead to accurate outputs, implying an intrinsic capacity for self-correction. Yet, it remains unclear…

Pre-trained transformers exhibit the capability of adapting to new tasks through in-context learning (ICL), where they efficiently utilize a limited set of prompts without explicit model optimization. The canonical communication problem of…

Transformers have demonstrated remarkable in-context learning (ICL) capabilities. The strong ICL performance of transformers is commonly believed to arise from their ability to implicitly execute certain algorithms on the context, thereby…

Transformers have recently revolutionized many domains in modern machine learning and one salient discovery is their remarkable in-context learning capability, where models can solve an unseen task by utilizing task-specific prompts without…

Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of…

In this paper, I introduce the retrieval problem, a simple yet common reasoning task that can be solved only by transformers with a minimum number of layers, which grows logarithmically with the input size. I empirically show that large…

Transformer-based large language models have achieved remarkable performance across various natural language processing tasks. However, they often struggle with seemingly easy tasks like arithmetic despite their vast capabilities. This…

Transformers have transformed the field of natural language processing. This performance is largely attributed to the use of stacked self-attention layers, each of which consists of matrix multiplies as well as softmax operations. As a…

While transformer models exhibit strong in-context learning (ICL) abilities, they often fail to generalize under simple distribution shifts. We analyze these failures and identify Softmax, the scoring function in the attention mechanism, as…

This paper introduces a high-order Markov chain task to investigate how transformers learn to integrate information from multiple past positions with varying statistical significance. We demonstrate that transformers learn this task…

The remarkable ability of transformers to learn new concepts solely by reading examples within the input prompt, termed in-context learning (ICL), is a crucial aspect of intelligent behavior. Here, we focus on understanding the learning…

Intermediate task fine-tuning has been shown to culminate in large transfer gains across many NLP tasks. With an abundance of candidate datasets as well as pre-trained language models, it has become infeasible to run the cross-product of…

The pretrained large language models (LLMs) are finetuned with labeled data for better instruction following ability and alignment with human values. In this paper, we study the learning dynamics of LLM finetuning on reasoning tasks and…

Transformers have transformed modern machine learning, driving breakthroughs in computer vision, natural language processing, and robotics. At the core of their success lies the attention mechanism, which enables the modeling of global…

Models need appropriate inductive biases to effectively learn from small amounts of data and generalize systematically outside of the training distribution. While Transformers are highly versatile and powerful, they can still benefit from…

We train Transformer-based language models on ten foundational algorithmic tasks and observe pronounced phase transitions in their loss curves that deviate from established power-law scaling trends. Over large ranges of compute, the…