Recurrent neural networks are extremely powerful yet hard to train. One of
their issues is the vanishing gradient problem, whereby propagation of training
signals may be exponentially attenuated, freezing training. Use of orthogonal
or unitary matrices, whose powers neither explode nor decay, has been proposed
to mitigate this issue, but their computational expense has hindered their use.
Here we show that in the specific case of convolutional RNNs, we can define a
convolutional exponential and that this operation transforms antisymmetric or
anti-Hermitian convolution kernels into orthogonal or unitary convolution
kernels. We explicitly derive FFT-based algorithms to compute the kernels and
their derivatives. The computational complexity of parametrizing this subspace
of orthogonal transformations is thus the same as the networks' iteration.

该研究使用卷积指数函数，将反对称或反 - 厄米卷积核变换为正交或幺正卷积核，用于解决递归神经网络中的梯度消失问题，并通过提出 FFT 算法来优化计算。

卷积幺正或正交循环神经网络

Convolutional unitary or orthogonal recurrent neural networks

This paper studies the problem of predicting the distribution over multiple
possible future paths of people as they move through various visual scenes. We
make two main contributions. The first contribution is a new dataset, created
in a realistic 3D simulator, which is based on real world trajectory data, and
then extrapolated by human annotators to achieve different latent goals. This
provides the first benchmark for quantitative evaluation of the models to
predict multi-future trajectories. The second contribution is a new model to
generate multiple plausible future trajectories, which contains novel designs
of using multi-scale location encodings and convolutional RNNs over graphs. We
refer to our model as Multiverse. We show that our model achieves the best
results on our dataset, as well as on the real-world VIRAT/ActEV dataset (which
just contains one possible future).

本文提出了一个名为 Multiverse 的新模型来生成多个合理的未来人物运动路径，并使用 3D 模拟器创建了一个名为 VIRAT/ActEV 的数据集用以对该模型进行测试。通过使用多尺度位置编码和图卷积神经网络，该模型达到了最佳效果。

多重未来轨迹预测之分岔路径园

The Garden of Forking Paths: Towards Multi-Future Trajectory Prediction

The encoder-decoder networks are commonly used in medical image segmentation
due to their remarkable performance in hierarchical feature fusion. However,
the expanding path for feature decoding and spatial recovery does not consider
the long-term dependency when fusing feature maps from different layers, and
the universal encoder-decoder network does not make full use of the
multi-modality information to improve the network robustness especially for
segmenting medical MRI. In this paper, we propose a novel feature fusion unit
called Recurrent Decoding Cell (RDC) which leverages convolutional RNNs to
memorize the long-term context information from the previous layers in the
decoding phase. An encoder-decoder network, named Convolutional Recurrent
Decoding Network (CRDN), is also proposed based on RDC for segmenting
multi-modality medical MRI. CRDN adopts CNN backbone to encode image features
and decode them hierarchically through a chain of RDCs to obtain the final
high-resolution score map. The evaluation experiments on BrainWeb, MRBrainS and
HVSMR datasets demonstrate that the introduction of RDC effectively improves
the segmentation accuracy as well as reduces the model size, and the proposed
CRDN owns its robustness to image noise and intensity non-uniformity in medical
MRI.

本文提出了一种名为 Recurrent Decoding Cell（RDC）的新型特征融合单元，利用卷积 RNN 从前面的层中记忆长期上下文信息，同时基于 RDC 提出了 Convolutional Recurrent Decoding Network（CRDN）用于分割多模态医学 MRI，实验证明引入 RDC 能有效提高分割准确性并减少模型大小，并且所提出的 CRDN 具有在医学 MRI 中对抗图像噪声和强度不均匀性的鲁棒性。