The self-attention mechanism prevails in modern machine learning. It has an
interesting functionality of adaptively selecting tokens from an input sequence
by modulating the degree of attention localization, which many researchers
speculate is the basis of the powerful model performance but complicates the
underlying mechanism of the learning dynamics. In recent years, mainly two
arguments have connected attention localization to the model performances. One
is the rank collapse, where the embedded tokens by a self-attention block
become very similar across different tokens, leading to a less expressive
network. The other is the entropy collapse, where the attention probability
approaches non-uniform and entails low entropy, making the learning dynamics
more likely to be trapped in plateaus. These two failure modes may apparently
contradict each other because the rank and entropy collapses are relevant to
uniform and non-uniform attention, respectively. To this end, we characterize
the notion of attention localization by the eigenspectrum of query-key
parameter matrices and reveal that a small eigenspectrum variance leads
attention to be localized. Interestingly, the small eigenspectrum variance
prevents both rank and entropy collapse, leading to better model expressivity
and trainability.

自我注意机制在现代机器学习中盛行，通过调节注意定位的程度，它有能力自适应地从输入序列中选择标记，被许多研究人员认为是强大模型性能的基础之一，但也使学习动态的基本机制复杂化。近年来，主要有两个论点将注意定位与模型性能联系起来，即秩坍缩和熵崩溃，它们似乎互相矛盾，但通过特征化查询 - 键参数矩阵的特征谱，我们揭示出小特征谱方差会防止秩和熵的崩溃，从而提高模型的表达能力和可训练性。

自注意力网络当 QK 特征向量集中时的局部化

Self-attention Networks Localize When QK-eigenspectrum Concentrates

Training stability is of great importance to Transformers. In this work, we
investigate the training dynamics of Transformers by examining the evolution of
the attention layers. In particular, we track the attention entropy for each
attention head during the course of training, which is a proxy for model
sharpness. We identify a common pattern across different architectures and
tasks, where low attention entropy is accompanied by high training instability,
which can take the form of oscillating loss or divergence. We denote the
pathologically low attention entropy, corresponding to highly concentrated
attention scores, as $\textit{entropy collapse}$. As a remedy, we propose
$\sigma$Reparam, a simple and efficient solution where we reparametrize all
linear layers with spectral normalization and an additional learned scalar. We
demonstrate that the proposed reparameterization successfully prevents entropy
collapse in the attention layers, promoting more stable training. Additionally,
we prove a tight lower bound of the attention entropy, which decreases
exponentially fast with the spectral norm of the attention logits, providing
additional motivation for our approach. We conduct experiments with
$\sigma$Reparam on image classification, image self-supervised learning,
machine translation, automatic speech recognition, and language modeling tasks,
across Transformer architectures. We show that $\sigma$Reparam provides
stability and robustness with respect to the choice of hyperparameters, going
so far as enabling training (a) a Vision Transformer to competitive performance
without warmup, weight decay, layer normalization or adaptive optimizers; (b)
deep architectures in machine translation and (c) speech recognition to
competitive performance without warmup and adaptive optimizers.

本文通过追踪每层 Transformer 中 attention head 的注意熵来检验其训练动态。作者提出了一个名为 entropy collapse 的现象，即低的注意熵伴随着高的训练不稳定性，提出了一种简单高效的解决方案 sigma Reparam 可以避免这种现象，并进一步证明了注意熵的下限。作者在图像分类、自监督学习、机器翻译、自动语音识别和语言建模任务中测试了 sigma Reparam，在各种 Transformer 结构中均能提供更稳定和鲁棒的训练，甚至不需要预热、重量衰减、层归一化或自适应优化器。