Comparative Study of State-based Neural Networks for Virtual Analog Audio Effects Modeling (2405.04124v5)

Abstract: Analog electronic circuits are at the core of an important category of musical devices, which includes a broad range of sound synthesizers and audio effects. The development of software that simulates analog musical devices, known as virtual analog modeling, is a significant sub-field in audio signal processing. Artificial neural networks are a promising technique for virtual analog modeling. While neural approaches have successfully accurately modeled distortion circuits, they require architectural improvements that account for parameter conditioning and low-latency response. This article explores the application of recent machine learning advancements for virtual analog modeling. In particular, we compare State-Space models and Linear Recurrent Units against the more common Long Short-Term Memory networks. Our comparative study uses these black-box neural modeling techniques with various audio effects. We evaluate the performance and limitations of these models using multiple metrics, providing insights for future research and development. Our metrics aim to assess the models' ability to accurately replicate energy envelopes and frequency contents, with a particular focus on transients in the audio signal. To incorporate control parameters into the models, we employ the Feature-wise Linear Modulation method. Long Short-Term Memory networks exhibit better accuracy in emulating distortions and equalizers, while the State-Space model, followed by Long Short-Term Memory networks when integrated in an encoder-decoder structure, and Linear Recurrent Unit outperforms others in emulating saturation and compression. When considering long time-variant characteristics, the State-Space model demonstrates the greatest capability to track history. Long Short-Term Memory networks tend to introduce audio artifacts.

• The paper compares RNN architectures including LSTM, L-ED, LRU, and S4D to evaluate their efficiency in digital analog effects emulation.
• It demonstrates S4D's superior ability to capture long-term dependencies for accurate modeling of saturation and compression effects.
• Findings emphasize real-time applicability and highlight challenges such as artifact production in LRU models.

A Comparative Study of Recurrent Neural Networks for Virtual Analog Audio Effects Modeling

The paper titled "Comparative Study of Recurrent Neural Networks for Virtual Analog Audio Effects Modeling" by Riccardo Simionato and Stefano Fasciani explores the potential of machine learning techniques, particularly recurrent neural network (RNN) architectures, in simulating the behavior of analog audio effects. Analog audio effects are essential in music production due to their distinctive sound qualities, attributed to the nonlinear characteristics of their electronic components. Emulating these effects digitally—known as virtual analog (VA) modeling—poses significant challenges and opportunities for AI-driven solutions.

Study Objectives and Methodology

The primary objective of this research is a comparative analysis of different recurrent neural network (RNN) architectures in modeling various analog audio effects. Specifically, the paper compares Long Short-Term Memory (LSTM), an LSTM-based Encoder-Decoder (L-ED), Linear Recurrent Unit (LRU), and State-Space models (SSM), with a focus on the recently proposed S4D model variant.

The authors designed models with the following constraints:

• Real-time applicability with low computational complexity and minimal input-output latency.
• All models incorporate parameter conditioning using the Feature-wise Linear Modulation (FiLM) method, allowing user control over the audio effect parameters.

The models were assessed using various common and novel metrics, including the Mean Squared Error (MSE), Mean Absolute Error (MAE), Root-Mean-Square Energy (RMSE) error, spectral flux, multi-resolution STFT, and Mel-Frequency Cepstral Coefficients (MFCC) to determine their accuracy in replicating energy envelopes, transients, and frequency contents. These metrics provide a comprehensive evaluation of the models across different dimensions of the audio signal.

Datasets and Audio Effects

The paper encompasses several types of analog audio effects:

• Overdrive: Examined through the Behringer OD300 pedal and Neutron’s Overdrive module.
• Saturation: Analyzed via Helper Saturator software and the TC Electronic Bucket Brigade Analog Delay pedal.
• Equalization: Measured using the Universal Audio Pultec Passive EQ plugin.
• Compression: Investigated using CL 1B and Teletronix LA2A optical compressors.
• Low-pass Filter: Considered with the Neutron synthesizer’s filter module.

The datasets were collected or sourced, reflecting various configurations and control parameter settings. These configurations provided a robust testbed for training and evaluating the different RNN architectures.

Results and Findings

1. Overall Performance:
   • LSTM Models: The paper finds LSTM models to perform well in modeling distortion and equalizer effects due to their effective encoding of short-term audio dependencies. However, they exhibit limitations in effects requiring extended temporal dependencies.
   • L-ED Architectures: These models outperform basic LSTM in scenarios requiring prolonged temporal tracking (e.g., optical compression) due to their enhanced capability to encode long-term dependencies.
   • SSM (S4D): The S4D model consistently demonstrates superior performance across most metrics, especially in effects with substantial temporal variances like saturation and compression. This model’s ability to encode extended signal history explains its higher accuracy.
   • LRU Models: LRU architectures, while offering stable training, tend to introduce significant audio artifacts, making them less suitable for accurate VA modeling.
2. Specific Observations:
   • Distortion Effects: LSTM and SSM models show notable success, particularly evident in replicating variable distortion amounts and tonal shifts.
   • Saturation and Compression: S4D models emerge as the most effective due to their proficiency in handling long-term dependencies and accurately modeling the temporal dynamics inherent in these effects.
   • Low-pass Filters and Equalizers: LSTM-based models perform adequately, benefiting from their capability to manage relatively simpler time-dependencies inherent in these effects.
3. Model Limitations and Artifacts:
   • LRU Models: Despite theoretical benefits, LRU implementations produce noticeable artifacts, questioning their practical viability for VA modeling.
   • Training Challenges: The paper highlights the rapid convergence of models in training epochs, suggestive of potential training instabilities or the need for more nuanced hyperparameter tuning.

Implications and Future Work

This paper contributes valuable insights into the applicability of advanced recurrent neural network architectures in virtual analog modeling. The findings suggest that state-space models, specifically the S4D variant, present a promising technique for accurate and real-time emulation of analog audio effects. The comparative analysis underlines the importance of selecting appropriate architecture based on the specific characteristics of the audio effect to be emulated.

Future research should explore:

• Enhanced conditioning techniques that accommodate more complex parameter interactions.
• Hybrid models combining the strengths of different architectures.
• Finely-tuned hyperparameter schedules tailored to specific audio effects.

Ultimately, this paper signifies a step forward in leveraging AI for high-fidelity, real-time VA modeling, underscoring the potential for further advancements in the domain.