不变多项式与机器学习
Invariant polynomials and machine learning
摘要：
我们提出了一个应用程序的不变多项式在机器学习。使用在以前的工作中开发的方法，我们得到两种类型的生成器的洛伦兹和置换不变的多项式在粒子动量;最小代数生成器和Hironaka分解。我们讨论并证明了一些近似定理，以便在机器学习算法中使用这些不变生成器，特别是在神经网络中。通过在应用于回归任务的神经网络中实现这些生成器，我们测试了在广泛的超参数选择下性能的改善，并发现训练数据的损失减少，验证数据的损失显着减少。对于量化这些神经网络的性能的不同方法，我们从贝叶斯推断的角度来处理这个问题，并采用嵌套采样技术来执行模型比较。在一定的网络规模之外，我们发现利用Hironaka分解的网络表现最好。
英文摘要：
We present an application of invariant polynomials in machine learning. Using the methods developed in previous work, we obtain two types of generators of the Lorentz- and permutation-invariant polynomials in particle momenta; minimal algebra generators and Hironaka decompositions. We discuss and prove some approximation theorems to make use of these invariant generators in machine learning algorithms in general and in neural networks specifically. By implementing these generators in neural networks applied to regression tasks, we test the improvements in performance under a wide range of hyperparameter choices and find a reduction of the loss on training data and a significant reduction of the loss on validation data. For a different approach on quantifying the performance of these neural networks, we treat the problem from a Bayesian inference perspective and employ nested sampling techniques to perform model comparison. Beyond a certain network size, we find that networks utilising Hironaka decompositions perform the best.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
