Instabilities in Convolutional Neural Networks for Raw Audio Signals

Core Concepts

Convolutional neural networks (convnets) with random initialization often fail to outperform hand-crafted filterbank baselines for audio processing tasks, due to instabilities in the energy response of the randomly initialized filters.

Abstract

The article investigates the instabilities in convolutional neural networks (convnets) when used for processing raw audio signals. The key insights are:

The variance of the energy response of a randomly initialized convnet filterbank (Φx) depends on the autocorrelation of the input signal (x). Highly autocorrelated signals like speech and music are more prone to large deviations in the energy response compared to less autocorrelated signals.

The authors derive explicit formulas for the expected value and variance of the energy response (∥Φx∥²) and provide upper bounds on the probability of large deviations using Cantelli's and Chernoff's inequalities.

The authors analyze the extreme value statistics of the optimal frame bounds (A and B) of the random filterbank Φ. They show that the expected values of A and B are related to the order statistics of chi-squared random variables, and provide bounds on their variances.

An asymptotic analysis reveals that the condition number κ = B/A of Φ follows a logarithmic scaling law between the number and length of the filters, reminiscent of discrete wavelet bases. This suggests that convnets are most stable when using many short filters, rather than few long filters.

The theoretical findings are supported by extensive numerical simulations, which demonstrate the instabilities of convnets with random initialization, especially for highly autocorrelated audio signals.

The insights from this work can guide the design of more stable and robust convolutional architectures for raw audio processing tasks.

Stats

The following sentences contain key metrics or figures:
∥Φx∥² = σ²T∥x∥²
V[∥Φx∥²] = 2σ⁴∑ᵀ⁻¹ᵀ⁻|τ| (T-|τ|)Rₓₓ(τ)²

Quotes

"What makes waveform-based deep learning so hard?"
"Filterbanks are linear time-invariant systems which decompose a signal x into J > 1 subbands."
"Arguably, such a careful initialization procedure defeats the purpose of deep learning; i.e., sparing the effort of feature engineering."

Key Insights Distilled From

Instabilities in Convnets for Raw Audio

by Daniel Haide... at arxiv.org 04-17-2024

https://arxiv.org/pdf/2309.05855.pdf

Deeper Inquiries

How can the insights from this work be leveraged to design more stable and robust convolutional architectures for raw audio processing tasks

The insights from this work can be instrumental in designing more stable and robust convolutional architectures for raw audio processing tasks. By understanding the impact of initialization on the stability of convnets, researchers and practitioners can implement strategies to mitigate instabilities during training. For instance, incorporating regularization techniques that account for the high autocorrelation of audio signals can help stabilize the learning process. Additionally, adjusting the architecture to include a larger number of shorter filters, as suggested by the scaling law identified in the study, can enhance stability and performance. Moreover, leveraging the theoretical framework developed in this work to optimize the initialization process of convnets for audio processing tasks can lead to more reliable and efficient models.

What are the implications of the identified scaling law between the number and length of filters on the overall architecture design and performance of convnets for audio processing

The identified scaling law between the number and length of filters in convolutional architectures for audio processing has significant implications for overall architecture design and performance. By understanding that convnets are most stable with many short filters, designers can tailor the architecture to align with this principle. This may involve adjusting the architecture to include a higher number of filters with shorter lengths, optimizing the trade-off between complexity and stability. Furthermore, the scaling law provides a guideline for balancing the architectural components to achieve optimal stability and robustness in audio processing tasks. Implementing architectures that adhere to this scaling law can lead to improved performance and reliability in raw audio processing applications.

Could the theoretical framework developed in this work be extended to analyze the stability of other types of neural network layers or architectures beyond convnets and audio processing

The theoretical framework developed in this work can be extended to analyze the stability of other types of neural network layers or architectures beyond convnets and audio processing. By adapting the concepts of large deviations, frame theory, and condition numbers to different neural network structures, researchers can assess the stability and robustness of various architectures. For instance, the framework could be applied to recurrent neural networks (RNNs), transformers, or graph neural networks to evaluate their stability characteristics. By exploring the stability properties of diverse neural network architectures, researchers can gain insights into the factors influencing their performance and reliability. This extension of the theoretical framework can contribute to the development of more stable and efficient neural network models across different domains and applications.