Exploring mechanisms of Neural Robustness: probing the bridge between geometry and spectrum
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Keywords: Latent Geometry, Latent Spectrum, Adversarial Robustness, Mechanistic Model, Unsupervised Learning, Local Learning, Jacobian Regularization, Spectral Regularization
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Abstract: Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety.
In cancer detection, for example, slight image alterations can misclassify benign moles as malignant.
Biological neural systems do not have such issues.
Thus, understanding the biological mechanisms of robustness is an important step towards building trustworthy and safe systems.
Unlike artificial models, biological neurons adjust connectivity based on neighboring cell activity.
Robustness in neural representations is hypothesized to correlate with the smoothness of the encoding manifold.
Recent work suggests power law covariance spectra, which were observed studying the primary visual cortex of mice, to be indicative of a balanced trade-off between accuracy and robustness in representations.
Here, we show that unsupervised local learning models with winner takes all dynamics learn such power law representations, providing upcoming studies a mechanistic model with that characteristic.
Our research aims to understand the interplay between geometry, spectral properties, robustness, and expressivity in neural representations.
Hence, we study the link between representation smoothness and spectrum by using weight, Jacobian and spectral regularization while assessing performance and adversarial robustness.
Our work serves as a foundation for future research into the mechanisms underlying power law spectra and optimally smooth encodings in both biological and artificial systems.
The insights gained may elucidate the mechanisms that realize robust neural networks in mammalian brains and inform the development of more stable and reliable artificial systems.
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Submission Number: 9331
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