Related papers: The Bayesian Geometry of Transformer Attention

Transformers empirically perform precise probabilistic reasoning in carefully constructed ``Bayesian wind tunnels'' and in large-scale language models, yet the mechanisms by which gradient-based learning creates the required internal…

Recent work has shown that small transformers trained in controlled "wind-tunnel'' settings can implement exact Bayesian inference, and that their training dynamics produce a geometric substrate -- low-dimensional value manifolds and…

Transformers are the dominant architecture in AI, yet why they work remains poorly understood. This paper offers a precise answer: a transformer is a Bayesian network. We establish this in five ways. First, we prove that every sigmoid…

What computational structures emerge in transformers trained on next-token prediction? In this work, we provide evidence that transformers implement constrained Bayesian belief updating -- a parallelized version of partial Bayesian…

Transformers have significantly advanced the field of natural language processing, but comprehending their internal mechanisms remains a challenge. In this paper, we introduce a novel geometric perspective that elucidates the inner…

In recent years, the transformer has established itself as a workhorse in many applications ranging from natural language processing to reinforcement learning. Similarly, Bayesian deep learning has become the gold-standard for uncertainty…

Despite its long history, Bayesian neural networks (BNNs) and variational training remain underused in practice: standard Gaussian posteriors misalign with network geometry, KL terms can be brittle in high dimensions, and implementations…

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.…

Prior-data fitted networks (PFNs) have recently emerged as a powerful approach for Bayesian prediction tasks, approximating the posterior predictive distribution (PPD) through in-context learning. Despite their strong empirical performance…

Transformers serve as the foundational architecture for large language and video generation models, such as GPT, BERT, SORA and their successors. Empirical studies have demonstrated that real-world data and learning tasks exhibit…

Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs…

We study the capabilities of the transformer architecture with varying depth. Specifically, we designed a novel set of sequence learning tasks to systematically evaluate and comprehend how the depth of transformer affects its ability to…

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…

The rapid progress seen in terms of large-scale generative AI is largely based on the attention mechanism. It is conversely non-trivial to conceive small-scale applications for which attention-based architectures outperform traditional…

The transformer architecture is central to the success of modern Large Language Models (LLMs), in part due to its surprising ability to perform a wide range of tasks - including mathematical reasoning, memorization, and retrieval - using…

Transformers have reshaped machine learning by utilizing attention mechanisms to capture complex patterns in large datasets, leading to significant improvements in performance. This success has contributed to the belief that "bigger means…

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…

The self-attention mechanism, a cornerstone of Transformer-based state-of-the-art deep learning architectures, is largely heuristic-driven and fundamentally challenging to interpret. Establishing a robust theoretical foundation to explain…

When do transformers commit to a decision, and what prevents them from correcting it? We introduce \textbf{prolepsis}: a transformer commits early, task-specific attention heads sustain the commitment, and no layer corrects it. Replicating…

Transformers are extremely successful machine learning models whose mathematical properties remain poorly understood. Here, we rigorously characterize the behavior of transformers with hardmax self-attention and normalization sublayers as…