Abstract
Automatic differentiation through digital signal processing algorithms for virtual analogue modelling has recently gained popularity. These algorithms are typically more computationally efficient than black-box neural networks that rely on dense matrix multiplications. Due to their differentiable nature, they can be integrated with neural networks and jointly trained using gradient descent algorithms, resulting in more efficient systems. Furthermore, signal processing algorithms have significantly fewer parameters than neural networks, allowing the application of the Newton-Raphson method. This method offers faster and more robust convergence than gradient descent at the cost of quadratic storage. This paper presents a method to emulate analogue levelling amplifiers using a feed-forward digital compressor with parameters optimised via the Newton-Raphson method. We demonstrate that a digital compressor can successfully approximate the behaviour of our target unit, the Teletronix LA-2A. Different strategies for computing the Hessian matrix are benchmarked. We leverage parallel algorithms for recursive filters to achieve efficient training on modern GPUs. The resulting model is made into a VST plugin and is open-sourced at this https URL.
Abstract (translated)
最近，通过数字信号处理算法进行自动微分以实现虚拟模拟建模的方法变得越来越受欢迎。这些算法通常比依赖密集矩阵乘法的黑盒神经网络更具有计算效率。由于它们是可微的，因此可以与神经网络集成，并使用梯度下降算法联合训练，从而生成更为高效的系统。此外，信号处理算法相较于神经网络拥有较少的参数量，这使得能够应用牛顿-拉夫森方法。此方法虽然以二次存储为代价，但比梯度下降法提供更快且更稳健的收敛速度。 本文提出了一种使用前馈数字压缩器来模拟类比电平放大器的方法，并利用牛顿-拉夫森方法优化参数。我们展示了通过这种方式，一个数字压缩器可以成功地近似目标单元——Teletronix LA-2A的行为表现。文章还对计算海森矩阵的不同策略进行了基准测试。我们利用递归滤波器的并行算法来实现在现代GPU上的高效训练。最终模型被制作成VST插件，并在以下网址开源：[此链接](https://这个URL需要你根据实际情况提供)。 请注意，上述翻译中的最后一句话提到的链接应当由原文作者或发布者提供一个具体的、可访问的实际地址。
URL
https://arxiv.org/abs/2509.10706
