Despite the remarkable success of transformer-based models in various real-world tasks, their underlying mechanisms remain poorly understood. Recent studies have suggested that transformers can implement gradient descent as an in-context learner for linear regression problems and have developed various theoretical analyses accordingly. However, these works mostly focus on the expressive power of transformers by designing specific parameter constructions, lacking a comprehensive understanding of their inherent working mechanisms post-training. In this study, we consider a sparse linear regression problem and investigate how a trained multi-head transformer performs in-context learning. We experimentally discover that the utilization of multi-heads exhibits different patterns across layers: multiple heads are utilized and essential in the first layer, while usually only a single head is sufficient for subsequent layers. We provide a theoretical explanation for this observation: the first layer preprocesses the context data, and the following layers execute simple optimization steps based on the preprocessed context. Moreover, we demonstrate that such a preprocess-then-optimize algorithm can significantly outperform naive gradient descent and ridge regression algorithms. Further experimental results support our explanations. Our findings offer insights into the benefits of multi-head attention and contribute to understanding the more intricate mechanisms hidden within trained transformers.
Learning with Fredholm kernel has attracted increasing attention recently since it can effectively utilize the data information to improve the prediction performance. Despite rapid progress on theoretical and experimental evaluations, its generalization analysis has not been explored in learning theory literature. In this paper, we establish the generalization bound of least square regularized regression with Fredholm kernel, which implies that the fast learning rate O(l^{-1}) can be reached under mild capacity conditions. Simulated examples show that this Fredholm regression algorithm can ach…
Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on methodically evaluating the predictive uncertainties of these models. In this work, we demonstrate that traditional training procedures for NLMs drastically underestimate uncertainty on out-of-distribution inputs, and that they therefore cannot be naively deployed in risk-sensitive applications. We identify the underlying reasons for this behavior and p…
Accurate estimates of rotation are crucial to vision-based motion estimation in augmented reality and robotics. In this work, we present a method to extract probabilistic estimates of rotation from deep regression models. First, we build on prior work and argue that a multi-headed network structure we name HydraNet provides better calibrated uncertainty estimates than methods that rely on stochastic forward passes. Second, we extend HydraNet to targets that belong to the rotation group, SO(3), by regressing unit quaternions and using the tools of rotation averaging and uncertainty injection on…
Where Computation Lives Inside TabPFN: Causal Localisation of Attention Head Function
Department of Computer Science, Birla Institute of Technology（比拉理工学院计算机科学系）；School of Computer Engineering, Kalinga Institute of Industrial Technology（凯林加工业技术学院计算机工程系）；Birla AI Labs, Office of Ananya Birla, Aditya Birla Group（比拉人工智能实验室，阿尼娅·比拉办公室，阿迪塔亚比拉集团）
Regression problems with time-series predictors are common in banking and many other areas of application. In this paper, we use multi-head attention networks to develop interpretable features and use them to achieve good predictive performance. The customized attention layer explicitly uses multiplicative interactions and builds feature-engineering heads that capture temporal dynamics in a parsimonious manner. Convolutional layers are used to combine multivariate time series. We also discuss methods for handling static covariates in the modeling process. Visualization and explanation tools ar…
Can input reconstruction be used to directly estimate uncertainty of a regression U-Net model? -- Application to proton therapy dose prediction for head and neck cancer patients
Institut de Recherche Expérimentale et Clinique (IREC), UCLouvain（比利时鲁汶大学实验与临床研究所（IREC））；UT Southwestern Medical Center（德克萨斯大学西南医学中心）
本文提出一种基于输入重建误差的直接不确定性估计方法，用于回归 U-Net 模型，并在头颈癌质子治疗剂量预测中验证其比 MCDO 和 DE 具有更高相关性、更强 OOD 检测能力和更低计算开销。
University of Denver（丹佛大学）；Department of Electrical and Computer Engineering, University of Denver（丹佛大学电气与计算机工程系）
Understanding emotions and responding accordingly is one of the biggest challenges of dialog systems. This paper presents EmpTransfo, a multi-head Transformer architecture for creating an empathetic dialog system. EmpTransfo utilizes state-of-the-art pre-trained models (e.g., OpenAI-GPT) for language generation, though models with different sizes can be used. We show that utilizing the history of emotions and other metadata can improve the quality of generated conversations by the dialog system. Our experimental results using a challenging language corpus show that the proposed approach outper…
HeadRouter: A Training-free Image Editing Framework for MM-DiTs by Adaptively Routing Attention Heads
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Beihang University（北京航空航天大学）；National Cheng-Kung University（国立成功大学）
Sharif University of Technology（谢里夫理工大学）；Electronics Research Institute, Sharif University of Technology（谢里夫理工大学电子研究所）；McGill University（麦吉尔大学）
In this paper, a novel multi-head multi-layer perceptron (MLP) structure is presented for implicit neural representation (INR). Since conventional rectified linear unit (ReLU) networks are shown to exhibit spectral bias towards learning low-frequency features of the signal, we aim at mitigating this defect by taking advantage of the local structure of the signals. To be more specific, an MLP is used to capture the global features of the underlying generator function of the desired signal. Then, several heads are utilized to reconstruct disjoint local features of the signal, and to reduce the c…
Recently, convolutional neural networks (CNNs) and attention mechanisms have been widely used in image denoising and achieved satisfactory performance. However, the previous works mostly use a single head to receive the noisy image, limiting the richness of extracted features. Therefore, a novel CNN with multiple heads (MH) named MHCNN is proposed in this paper, whose heads will receive the input images rotated by different rotation angles. MH makes MHCNN simultaneously utilize features of rotated images to remove noise. To integrate these features effectively, we present a novel multi-path at…
