Increasing neural network robustness improves match to macaque V1 eigenspectrum, spatial frequency preference and predictivity

Abstract

Task-optimized convolutional neural networks (CNNs) show striking similarities to the ventral visual stream. However, human-imperceptible image perturbations can cause a CNN to make incorrect predictions. Here we provide insight into this brittleness by investigating the representations of models that are either robust or not robust to image perturbations. Theory suggests that the robustness of a system to these perturbations could be related to the power law exponent of the eigenspectrum of its set of neural responses, where power law exponents closer to and larger than one would indicate a system that is less susceptible to input perturbations. We show that neural responses in mouse and macaque primary visual cortex (V1) obey the predictions of this theory, where their eigenspectra have power law exponents of at least one. We also find that the eigenspectra of model representations decay slowly relative to those observed in neurophysiology and that robust models have eigenspectra that decay slightly faster and have higher power law exponents than those of non-robust models. The slow decay of the eigenspectra suggests that substantial variance in the model responses is related to the encoding of fine stimulus features. We therefore investigated the spatial frequency tuning of artificial neurons and found that a large proportion of them preferred high spatial frequencies and that robust models had preferred spatial frequency distributions more aligned with the measured spatial frequency distribution of macaque V1 cells. Furthermore, robust models were quantitatively better models of V1 than non-robust models. Our results are consistent with other findings that there is a misalignment between human and machine perception. They also suggest that it may be useful to penalize slow-decaying eigenspectra or to bias models to extract features of lower spatial frequencies during task-optimization in order to improve robustness and V1 neural response predictivity.

Robust deep learning object recognition models rely on low frequency information in natural images

“…One recent research [ 33 ] measured the preferred spatial frequency of individual model units via in-silico electrophysiology experiments, and showed that representation of robust models are more aligned with macaque V1 neurons in terms of the distribution of preferred spatial frequencies compared with non-robust models. Based on the eigenspectrum analysis, they suggested that the robustness is due to smaller portion of high-frequency tuning units in the robust models.…”

Model metamers illuminate divergences between biological and artificial neural networks

“…Such regularizers are common in neural network visualizations, and although we view them as side-stepping the goal of human-model comparison, it was nonetheless of interest to assess their effect. We implemented the regularizer used in a well-known visualization paper (64) which biases the solution to the metamer optimization to have low total pixel variation (encouraging smoothness). As shown in Figure 4e, adding smoothness regularization to the metamer generation procedure for the standard-trained AlexNet model improved the recognizability of its metamers, but not as much as did adversarial training (and did not come close to generating metamers as recognizable as natural images; see Supplementary Figure 8 for examples generated with different regularization coefficients).…”

“…The methods we use to synthesize model metamers are not new. Previous neural network visualizations have also used gradient descent on the input to visualize representations (76), in some cases matching the activations at individual stages as we do here (64). However, the significance of these visualizations for evaluating neural network models of biological sensory systems has received relatively little attention.…”

“…Model metamers are generated via iterative gradient-based optimization of a non-convex loss function, and only approximately reproduce the activations of the natural stimulus to which they are matched. We attempted to improve on previous neural network visualization work (64, 76) by setting explicit criteria for the optimization success. For models that perform classification tasks, we verified that the model metamer produced the same class label as the reference stimulus to which it was matched.…”

“…To investigate the effects of regularization on metamer recognizability, in one experiment we generated metamers with additional constraints on the optimization procedure. We followed the procedures of an earlier paper by Mahendran and Vedaldi (64). Two regularization terms were included: (1) a total variation (TV) regularizer, and (2) an ɑ-norm regularizer.…”