We propose a categorical semantics for machine learning algorithms in terms
of lenses, parametric maps, and reverse derivative categories. This foundation
provides a powerful explanatory and unifying framework: it encompasses a
variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov
momentum, as well as a variety of loss functions such as MSE and Softmax
cross-entropy, and different architectures, shedding new light on their
similarities and differences. Furthermore, our approach to learning has
examples generalising beyond the familiar continuous domains (modelled in
categories of smooth maps) and can be realised in the discrete setting of
Boolean and polynomial circuits. We demonstrate the practical significance of
our framework with an implementation in Python.

我们提出了一种基于镜头、参数化映射和反向导数范畴的机器学习算法的分类语义学。这一基础提供了一个强大的解释性和统一性框架：它包括了各种梯度下降算法，如 ADAM、AdaGrad 和 Nesterov 动量，以及各种损失函数，如 MSE 和 Softmax 交叉熵，以及不同的架构，揭示了它们的相似性和差异。此外，我们的学习方法超越了熟悉的连续领域的示例（在光滑映射范畴中建模），并且可以应用于布尔电路和多项式电路的离散环境。我们通过 Python 实现展示了我们框架的实际意义。

参数化透镜的深度学习

Deep Learning with Parametric Lenses

Deep learning has shown great potential in accelerating diffusion tensor
imaging (DTI). Nevertheless, existing methods tend to suffer from Rician noise
and detail loss in reconstructing the DTI-derived parametric maps especially
when sparsely sampled q-space data are used. This paper proposes a novel
method, AID-DTI (Accelerating hIgh fiDelity Diffusion Tensor Imaging), to
facilitate fast and accurate DTI with only six measurements. AID-DTI is
equipped with a newly designed Singular Value Decomposition (SVD)-based
regularizer, which can effectively capture fine details while suppressing noise
during network training. Experimental results on Human Connectome Project (HCP)
data consistently demonstrate that the proposed method estimates DTI parameter
maps with fine-grained details and outperforms three state-of-the-art methods
both quantitatively and qualitatively.

本文提出了一种名为 AID-DTI（加速高保真扩散张量成像）的新方法，通过基于奇异值分解的正则化器在网络训练期间有效地捕获细节和抑制噪声，以实现仅使用六个测量的快速并准确的扩散张量成像。对人体连通性项目（HCP）数据的实验证明，所提出的方法在定量和定性上优于三种最先进的方法，并能够估计出具有细粒度细节的扩散张量成像参数图。

AID-DTI: 基于细节保留模型的深度学习加速高保真扩散张量成像

AID-DTI: Accelerating High-fidelity Diffusion Tensor Imaging with  Detail-Preserving Model-based Deep Learning

Magnetic Resonance Fingerprinting (MRF) is a new approach to quantitative
magnetic resonance imaging that allows simultaneous measurement of multiple
tissue properties in a single, time-efficient acquisition. Standard MRF
reconstructs parametric maps using dictionary matching and lacks scalability
due to computational inefficiency. We propose to perform MRF map reconstruction
using a recurrent neural network, which exploits the time-dependent information
of the MRF signal evolution. We evaluate our method on multiparametric
synthetic signals and compare it to existing MRF map reconstruction approaches,
including those based on neural networks. Our method achieves state-of-the-art
estimates of T1 and T2 values. In addition, the reconstruction time is
significantly reduced compared to dictionary-matching based approaches.

本文提出使用循环神经网络进行磁共振指纹重建方法，比传统字典匹配法具有更高的可扩展性和更短的重建时间，能够同时测量多种组织属性的定量成像方法。