Incorruptible Neural Networks: Training Models that can Generalize to Large Internal Perturbations

Flat regions of the neural network loss landscape have long been hypothesized to correlate with better generalization properties. A closely related but distinct problem is training models that are robust to internal perturbations to their weights, which may be an important need for future low-power hardware platforms. In this paper, we explore the usage of two methods, sharpness-aware minimization (SAM) and random-weight perturbation (RWP), to find minima robust to a variety of random corruptions to weights. We consider the problem from two angles: generalization (how do we reduce the noise-robust generalization gap) and optimization (how do we maximize performance from optimizers when subject to strong perturbations). First, we establish, both theoretically and empirically, that an over-regularized RWP training objective is optimal for noise-robust generalization. For small-magnitude noise, we find that SAM's adversarial objective further improves performance over any RWP configuration, but performs poorly for large-magnitude noise. We link the cause of this to a vanishing-gradient effect, caused by unevenness in the loss landscape, affecting both SAM and RWP. Lastly, we demonstrate that dynamically adjusting the perturbation strength to match the evolution of the loss landscape improves optimizing for these perturbed objectives.

Analog Bayesian neural networks are insensitive to the shape of the weight distribution

Recent work has demonstrated that Bayesian neural networks (BNN's) trained with mean field variational inference (MFVI) can be implemented in analog hardware, promising orders of magnitude energy savings compared to the standard digital implementations. However, while Gaussians are typically used as the variational distribution in MFVI, it is difficult to precisely control the shape of the noise distributions produced by sampling analog devices. This paper introduces a method for MFVI training using real device noise as the variational distribution. Furthermore, we demonstrate empirically that the predictive distributions from BNN's with the same weight means and variances converge to the same distribution, regardless of the shape of the variational distribution. This result suggests that analog device designers do not need to consider the shape of the device noise distribution when hardware-implementing BNNs performing MFVI.

An out-of-distribution discriminator based on Bayesian neural network epistemic uncertainty

Neural networks have revolutionized the field of machine learning with increased predictive capability. In addition to improving the predictions of neural networks, there is a simultaneous demand for reliable uncertainty quantification on estimates made by machine learning methods such as neural networks. Bayesian neural networks (BNNs) are an important type of neural network with built-in capability for quantifying uncertainty. This paper discusses aleatoric and epistemic uncertainty in BNNs and how they can be calculated. With an example dataset of images where the goal is to identify the amplitude of an event in the image, it is shown that epistemic uncertainty tends to be lower in images which are well-represented in the training dataset and tends to be high in images which are not well-represented. An algorithm for out-of-distribution (OoD) detection with BNN epistemic uncertainty is introduced along with various experiments demonstrating factors influencing the OoD detection capability in a BNN. The OoD detection capability with epistemic uncertainty is shown to be comparable to the OoD detection in the discriminator network of a generative adversarial network (GAN) with comparable network architecture.