Uncovering which feature combinations are encoded by visual units is critical to understanding how images are transformed into representations that support recognition. While existing feature visualization approaches typically infer a unit's most exciting images, this is insufficient to reveal the manifold of transformations under which responses remain invariant, which is critical to generalization in vision. Here we introduce Stretch-and-Squeeze (SnS), a model-agnostic, gradient-free framework to systematically characterize a unit's maximally invariant stimuli, and its vulnerability to adversarial perturbations, in both biological and artificial visual systems. SnS frames these transformations as bi-objective optimization problems. To probe invariance, SnS seeks image perturbations that maximally alter (stretch) the representation of a reference stimulus in a given processing stage while preserving unit activation downstream (squeeze). To probe adversarial sensitivity, stretching and squeezing are reversed to maximally perturb unit activation while minimizing changes to the upstream representation. Applied to CNNs, SnS revealed invariant transformations that were farther from a reference image in pixel-space than those produced by affine transformations, while more strongly preserving the target unit's response. The discovered invariant images differed depending on the stage of the image representation used for optimization: pixel-level changes primarily affected luminance and contrast, while stretching mid- and late-layer representations mainly altered texture and pose. By measuring how well the hierarchical invariant images obtained for L2 robust networks were classified by humans and other observer networks, we discovered a substantial drop in their interpretability when the representation was stretched in deep layers, while the opposite trend was found for standard models.

翻译：揭示视觉单元编码了哪些特征组合对于理解图像如何转化为支持识别的表征至关重要。虽然现有的特征可视化方法通常推断一个单元最兴奋的图像，但这不足以揭示响应保持不变的变换流形，而这对于视觉泛化至关重要。本文介绍拉伸与压缩（Stretch-and-Squeeze, SnS），这是一种模型无关、无梯度的框架，用于系统性地表征生物和人工视觉系统中单元的最大不变刺激及其对对抗扰动的脆弱性。SnS将这些变换构建为双目标优化问题。为探究不变性，SnS寻求在给定处理阶段最大程度改变（拉伸）参考刺激的表征，同时保持下游单元激活（压缩）的图像扰动。为探究对抗敏感性，拉伸与压缩的目标反转，即最大程度扰动单元激活，同时最小化上游表征的变化。应用于CNN时，SnS揭示的不变变换在像素空间中比仿射变换产生的变换距离参考图像更远，同时更有效地保留了目标单元的响应。所发现的不变图像因优化所用图像表征的阶段而异：像素级变化主要影响亮度和对比度，而拉伸中层和深层表征主要改变纹理和姿态。通过测量人类和其他观察者网络对L2鲁棒网络获得的层次不变图像的分类准确度，我们发现当表征在深层被拉伸时，其可解释性显著下降，而标准模型则呈现相反趋势。