Automated creation of synthetic traffic scenarios is a key part of validating
the safety of autonomous vehicles (AVs). In this paper, we propose Scenario
Diffusion, a novel diffusion-based architecture for generating traffic
scenarios that enables controllable scenario generation. We combine latent
diffusion, object detection and trajectory regression to generate distributions
of synthetic agent poses, orientations and trajectories simultaneously. To
provide additional control over the generated scenario, this distribution is
conditioned on a map and sets of tokens describing the desired scenario. We
show that our approach has sufficient expressive capacity to model diverse
traffic patterns and generalizes to different geographical regions.

自动驾驶车辆的安全验证方面，合成交通场景的自动创建是关键部分。本文提出了一种新颖的基于扩散的场景生成架构 ——Scenario Diffusion，可实现可控的场景生成。我们结合了潜在扩散、目标检测和轨迹回归，同时生成合成代理人的姿势、方向和轨迹的分布。为了对生成的场景进行额外控制，此分布以描述所需场景的地图和令牌组为条件。我们证明我们的方法具有足够的表达能力，能够建模多样的交通模式，并且适用于不同的地理区域。

情景扩散：可控驾驶情景生成与扩散

Scenario Diffusion: Controllable Driving Scenario Generation With  Diffusion

Existing analyses of the expressive capacity of Transformer models have
required excessively deep layers for data memorization, leading to a
discrepancy with the Transformers actually used in practice. This is primarily
due to the interpretation of the softmax function as an approximation of the
hardmax function. By clarifying the connection between the softmax function and
the Boltzmann operator, we prove that a single layer of self-attention with
low-rank weight matrices possesses the capability to perfectly capture the
context of an entire input sequence. As a consequence, we show that
single-layer Transformer has a memorization capacity for finite samples, and
that Transformers consisting of one self-attention layer with two feed-forward
neural networks are universal approximators for continuous functions on a
compact domain.

通过澄清 softmax 函数与 Boltzmann 算子之间的联系，我们证明具有低秩权重矩阵的自注意力单层具备完美捕获整个输入序列上下文的能力，从而表明单层 Transformer 具有有限样本的记忆能力，并且由一个自注意力层和两个前馈神经网络组成的 Transformer 是紧致域上连续函数的通用逼近器。

一层自注意力变压器使用低秩权重矩阵是通用逼近器吗？

Are Transformers with One Layer Self-Attention Using Low-Rank Weight  Matrices Universal Approximators?

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a
natural generalization of convolutional neural networks that reduces sample
complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of
layer that enjoys a substantially higher degree of weight sharing than regular
convolution layers. G-convolutions increase the expressive capacity of the
network without increasing the number of parameters. Group convolution layers
are easy to use and can be implemented with negligible computational overhead
for discrete groups generated by translations, reflections and rotations.
G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST.

介绍了一种新型卷积神经网络，称为 Group equivariant Convolutional Neural Networks (G-CNNs)，它通过利用对称性降低样本复杂度，使用新型层 G-convolutions，增加网络的表达能力，且易于使用和实现。 G-CNNs 在 CIFAR10 和旋转的 MNIST 上实现了最先进的结果。