Deep learning still has drawbacks in terms of trustworthiness, which
describes a comprehensible, fair, safe, and reliable method. To mitigate the
potential risk of AI, clear obligations associated to trustworthiness have been
proposed via regulatory guidelines, e.g., in the European AI Act. Therefore, a
central question is to what extent trustworthy deep learning can be realized.
Establishing the described properties constituting trustworthiness requires
that the factors influencing an algorithmic computation can be retraced, i.e.,
the algorithmic implementation is transparent. Motivated by the observation
that the current evolution of deep learning models necessitates a change in
computing technology, we derive a mathematical framework which enables us to
analyze whether a transparent implementation in a computing model is feasible.
We exemplarily apply our trustworthiness framework to analyze deep learning
approaches for inverse problems in digital and analog computing models
represented by Turing and Blum-Shub-Smale Machines, respectively. Based on
previous results, we find that Blum-Shub-Smale Machines have the potential to
establish trustworthy solvers for inverse problems under fairly general
conditions, whereas Turing machines cannot guarantee trustworthiness to the
same degree.

通过建立透明的算法模型，研究论文探讨了深度学习的可靠性和信任度，使用数学框架分析了不同计算模型下逆问题的可信解决方案，发现 Blum-Shub-Smale Machines 具有潜力在广泛条件下建立可信的解决方案。

社会与法律约束下的深度学习数学算法设计：算法透明性要求

Mathematical Algorithm Design for Deep Learning under Societal and  Judicial Constraints: The Algorithmic Transparency Requirement

Neural Algorithmic Reasoning is an emerging area of machine learning which
seeks to infuse algorithmic computation in neural networks, typically by
training neural models to approximate steps of classical algorithms. In this
context, much of the current work has focused on learning reachability and
shortest path graph algorithms, showing that joint learning on similar
algorithms is beneficial for generalisation. However, when targeting more
complex problems, such similar algorithms become more difficult to find. Here,
we propose to learn algorithms by exploiting duality of the underlying
algorithmic problem. Many algorithms solve optimisation problems. We
demonstrate that simultaneously learning the dual definition of these
optimisation problems in algorithmic learning allows for better learning and
qualitatively better solutions. Specifically, we exploit the max-flow min-cut
theorem to simultaneously learn these two algorithms over synthetically
generated graphs, demonstrating the effectiveness of the proposed approach. We
then validate the real-world utility of our dual algorithmic reasoner by
deploying it on a challenging brain vessel classification task, which likely
depends on the vessels' flow properties. We demonstrate a clear performance
gain when using our model within such a context, and empirically show that
learning the max-flow and min-cut algorithms together is critical for achieving
such a result.

该研究主要探讨利用神经算法推理来解决复杂问题，通过优化算法学习和同时学习最大流和最小割算法，可以在神经网络中进行更好的学习，并且在实际应用中产生了显著的性能提升。

双算法推理

Dual Algorithmic Reasoning

Deep learning has excelled on complex pattern recognition tasks such as image
classification and object recognition. However, it struggles with tasks
requiring nontrivial reasoning, such as algorithmic computation. Humans are
able to solve such tasks through iterative reasoning -- spending more time
thinking about harder tasks. Most existing neural networks, however, exhibit a
fixed computational budget controlled by the neural network architecture,
preventing additional computational processing on harder tasks. In this work,
we present a new framework for iterative reasoning with neural networks. We
train a neural network to parameterize an energy landscape over all outputs,
and implement each step of the iterative reasoning as an energy minimization
step to find a minimal energy solution. By formulating reasoning as an energy
minimization problem, for harder problems that lead to more complex energy
landscapes, we may then adjust our underlying computational budget by running a
more complex optimization procedure. We empirically illustrate that our
iterative reasoning approach can solve more accurate and generalizable
algorithmic reasoning tasks in both graph and continuous domains. Finally, we
illustrate that our approach can recursively solve algorithmic problems
requiring nested reasoning

通过建立神经网络的能量模型和迭代计算方法，使得深度学习能够处理算法计算等需要迭代推理的任务，并在离散和连续领域中展现出更准确和可推广的解决方案。

通过能量最小化学习迭代推理

Learning Iterative Reasoning through Energy Minimization

Algorithms have been fundamental to recent global technological advances and,
in particular, they have been the cornerstone of technical advances in one
field rapidly being applied to another. We argue that algorithms possess
fundamentally different qualities to deep learning methods, and this strongly
suggests that, were deep learning methods better able to mimic algorithms,
generalisation of the sort seen with algorithms would become possible with deep
learning -- something far out of the reach of current machine learning methods.
Furthermore, by representing elements in a continuous space of learnt
algorithms, neural networks are able to adapt known algorithms more closely to
real-world problems, potentially finding more efficient and pragmatic solutions
than those proposed by human computer scientists.
Here we present neural algorithmic reasoning -- the art of building neural
networks that are able to execute algorithmic computation -- and provide our
opinion on its transformative potential for running classical algorithms on
inputs previously considered inaccessible to them.

通过构建神经网络来执行算法计算的神经算法推理有可能将经典算法运用于以前被视为不可达的输入，从而有了转化性的潜力。