使用牛頓-拉弗森法進行模擬電平放大器的聲音匹配

摘要

透過數位信號處理算法實現的自動微分技術在虛擬類比建模領域近期備受關注。這些算法通常比依賴密集矩陣乘法的黑箱神經網絡更具計算效率。由於其可微分的特性，它們能夠與神經網絡整合，並利用梯度下降算法進行聯合訓練，從而構建出更高效的系統。此外，信號處理算法的參數量遠少於神經網絡，這使得牛頓-拉夫森方法的應用成為可能。該方法以二次存儲為代價，提供了比梯度下降更快且更穩健的收斂性能。本文提出了一種方法，利用前饋數位壓縮器模擬類比電平放大器，並通過牛頓-拉夫森方法優化其參數。我們展示了數位壓縮器能夠成功近似目標設備Teletronix LA-2A的行為。文中對計算海森矩陣的不同策略進行了基準測試。我們利用遞歸濾波器的並行算法，在現代GPU上實現了高效的訓練。最終模型被製作成VST插件，並在https://github.com/aim-qmul/4a2a開源。

English

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 https://github.com/aim-qmul/4a2a.

使用牛頓-拉弗森法進行模擬電平放大器的聲音匹配

Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method

摘要

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