We say that a classifier is adversarially robust to perturbations of norm r if, with high probability over a point xdrawn from the input distribution, there is no point within distance rfrom xthat is classified differently. The boundary volume is the probability that a point falls within distance r of a point with a different label. This work studies the task of computationally efficient learning of hypotheses with small boundary volume, where the input is distributed as a subgaussian isotropic log-concave distribution over Rd. Linear threshold functions are adversarially robust; they have boundary volume proportional to r. Such concept classes are efficiently learnable by polynomial regression, which produces a polynomial threshold function (PTF), but PTFs in general may have boundary volume Ω(1), even for r 1. We give an algorithm that agnostically learns linear threshold functions and returns a classifier with boundary volume O(r+ε)at radius of perturbation r.

Figure 1 shows screenshots from our online psychophysical critical band masking experiment. Accuracy heatmaps computed for different observers in our experiment showed little individual difference (Figure 1) and an even smaller difference in terms of threshold noise SD for 50% accuracy. Table 1 shows the value of each channel property computed from Gaussian fits to the averaged human data versus those found by summarizing Gaussian fits to individual human data. Given that they are similar for all channel properties, we use the former for all reported human data in the main paper. Our existing method for computing thresholds and fitting the Gaussian function to them is difficult to apply to observers that have very high noise sensitivity (low efficiency) since it relies on good performance for the baseline (zero-noise) condition.

What spatial frequency information do humans and neural networks use to recognize objects? In neuroscience, critical band masking is an established tool that can reveal the frequency-selective filters used for object recognition. Critical band masking measures the sensitivity of recognition performance to noise added at each spatial frequency. Existing critical band masking studies show that humans recognize periodic patterns (gratings) and letters by means of a spatial-frequency filter (or "channel") that has a frequency bandwidth of one octave (doubling of frequency). Here, we introduce critical band masking as a task for network-human comparison and test 14 humans and 76 neural networks on 16-way ImageNet categorization in the presence of narrowband noise.

What spatial frequency information do humans and neural networks use to recognize objects?

Spiking neural networks (SNNs) are a promising paradigm for energy-efficient computation, yet their theoretical foundations-especially regarding stability and robustness-remain limited compared to artificial neural networks. In this work, we study discrete-time leaky integrate-and-fire (LIF) SNNs through the lens of Boolean function analysis. We focus on noise sensitivity and stability in classification tasks, quantifying how input perturbations affect outputs. Our main result shows that wide LIF-SNN classifiers are stable on average, a property explained by the concentration of their Fourier spectrum on low-frequency components. Motivated by this, we introduce the notion of spectral simplicity, which formalizes simplicity in terms of Fourier spectrum concentration and connects our analysis to the simplicity bias observed in deep networks. Within this framework, we show that random LIF-SNNs are biased toward simple functions. Experiments on trained networks confirm that these stability properties persist in practice. Together, these results provide new insights into the stability and robustness properties of SNNs.