Semantic segmentation neural networks (SSNs) are increasingly essential in highstakes fields such as medical imaging, autonomous driving, and environmental monitoring, where robustness to input uncertainties and adversarial examples is crucial for ensuring safety and reliability. However, traditional probabilistic verification methods struggle to scale effectively with the size and depth of modern SSNs, especially when dealing with their high-dimensional, structured inputs/outputs. As the output dimension increases, these methods tend to become overly conservative, resulting in unnecessarily restrictive safety guarantees. In this work, we propose a probabilistic, data-driven verification algorithm that is architecture-agnostic and scalable, capable of handling the high-dimensional outputs of SSNs without introducing conservative and loose guarantees. We leverage efficient sampling-based reachability analysis to explore the space of possible outputs while maintaining computational feasibility.

Semantic segmentation neural networks (SSNs) are increasingly essential in high-stakes fields such as medical imaging, autonomous driving, and environmental monitoring, where robustness to input uncertainties and adversarial examples is crucial for ensuring safety and reliability. However, traditional probabilistic verification methods struggle to scale effectively with the size and depth of modern SSNs, especially when dealing with their high-dimensional, structured inputs/outputs. As the output dimension increases, these methods tend to become overly conservative, resulting in unnecessarily restrictive safety guarantees. In this work, we propose a probabilistic, data-driven verification algorithm that is architecture-agnostic and scalable, capable of handling the high-dimensional outputs of SSNs without introducing conservative and loose guarantees. We leverage efficient sampling-based reachability analysis to explore the space of possible outputs while maintaining computational feasibility.

We consider the regime where nd. We propose randomized Newton-type algorithms that exploit non-uniform sub-sampling of { 2fi(w)}ni=1, as well as inexact updates, as means to reduce the computational complexity, and are applicable to a wide range of problems in machine learning. Two non-uniform sampling distributions based on block norm squares and block partial leverage scores are considered. Under certain assumptions, we show that our algorithms inherit a linear-quadratic convergence rate in w and achieve a lower computational complexity compared to similar existing methods. In addition, we show that our algorithms exhibit more robustness and better dependence on problem specific quantities, such as the condition number. We empirically demonstrate that our methods are at least twice as fast as Newton's methods on several real datasets.

Here, we narrow this gap by developing aneffectivemethod fortraining acanonical model ofcortical neural circuits, the stabilized supralinear network (SSN), that in previous work had to beconstructed manually ortrainedwithundueconstraints.

Our solution to this task is simple: we split the latent codez into many independent blocks, and regularize the generator so that each block affects only a particular part of the image.

There continues to be a trade-off between the biological realism and performance of neural networks. Contemporary deep learning techniques allow neural networks to be trained to perform challenging computations at (near) human-level, but these networks typically violate key biological constraints. More detailed models of biological neural networks can incorporate many of these constraints but typically suffer from subpar performance and trainability. Here, we narrow this gap by developing an effective method for training a canonical model of cortical neural circuits, the stabilized supralinear network (SSN), that in previous work had to be constructed manually or trained with undue constraints. SSNs are particularly challenging to train for the same reasons that make them biologically realistic: they are characterized by strongly-connected excitatory cells and expansive firing rate non-linearities that together make them prone to dynamical instabilities unless stabilized by appropriately tuned recurrent inhibition. Our method avoids such instabilities by initializing a small network and gradually increasing network size via the dynamics-neutral addition of neurons during training. We first show how SSNs can be trained to perform typical machine learning tasks by training an SSN on MNIST classification. We then demonstrate the effectiveness of our method by training an SSN on the challenging task of performing amortized Markov chain Monte Carlo-based inference under a Gaussian scale mixture generative model of natural image patches with a rich and diverse set of basis functions -- something that was not possible with previous methods. These results open the way to training realistic cortical-like neural networks on challenging tasks at scale.

Many computer vision problems can be phrased as conditional or unconditional image generation. This includes super-resolution, colorization, and semantic image synthesis among others.

However, these models were not capable of actually achieving the brain's performance on its wide range of complex computations.