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We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces…

Distribution shifts on graphs -- the discrepancies in data distribution between training and employing a graph machine learning model -- are ubiquitous and often unavoidable in real-world scenarios. These shifts may severely deteriorate…

At present, the mechanisms of in-context learning in Transformers are not well understood and remain mostly an intuition. In this paper, we suggest that training Transformers on auto-regressive objectives is closely related to…

Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks…

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Predicting simple function classes has been widely used as a testbed for developing theory and understanding of the trained Transformer's in-context learning (ICL) ability. In this paper, we revisit the training of Transformers on linear…

Transformers have the capacity to act as supervised learning algorithms: by properly encoding a set of labeled training ("in-context") examples and an unlabeled test example into an input sequence of vectors of the same dimension, the…

What computational structure are we building into large language models when we train them on next-token prediction? Here, we present evidence that this structure is given by the meta-dynamics of belief updating over hidden states of the…

Out-of-distribution (OOD) detection is essential for reliably deploying machine learning models in the wild. Yet, most methods treat large pre-trained models as monolithic encoders and rely solely on their final-layer representations for…

It is crucial to detect when an instance lies downright too far from the training samples for the machine learning model to be trusted, a challenge known as out-of-distribution (OOD) detection. For neural networks, one approach to this task…

Reasoning capability is essential to ensure the factual correctness of the responses of transformer-based Large Language Models (LLMs), and robust reasoning about transitive relations is instrumental in many settings, such as causal…

Modern deep neural networks display striking examples of rich internal computational structure. Uncovering principles governing the development of such structure is a priority for the science of deep learning. In this paper, we explore the…

Transformer language models have demonstrated impressive generalization capabilities in natural language domains, yet we lack a fine-grained understanding of how such generalization arises. In this paper, we investigate length…

Autoregressive transformers exhibit adaptive learning through in-context learning (ICL), which begs the question of how. Prior works have shown that transformers represent the ICL tasks as vectors in their representations. In this paper, we…

In the field of computer vision, fine-tuning pre-trained models has become a prevalent strategy for out-of-distribution (OOD) generalization tasks. Different from most prior work that has focused on advancing learning algorithms, we…

Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile…

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…

Traditional machine learning paradigms are based on the assumption that both training and test data follow the same statistical pattern, which is mathematically referred to as Independent and Identically Distributed ($i.i.d.$). However, in…

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…

Recent studies in interpretability have explored the inner workings of transformer models trained on tasks across various domains, often discovering that these networks naturally develop highly structured representations. When such…