SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Figure 4 also presents confusion matrices for ImageNet-pretrained ResNet-18, ResNet-50, MLP-Mixer, and ViT at  $30\%$ ,  $50\%$ , and  $70\%$  degradation. As degradation proportion increases, we note that models tend to default to predicting a single class, for example to defaulting to triangles for ResNet-18 and hexagons for Resnet-50 at  $70\%$  degradation.
Human Comparison To contextualize the behavior of neural networks on our shape recovery task, we compare the performance of MLP-Mixer against human subjects from Biederman's (1987) original image recovery experiments. There, image degradation at corners and edges was performed for 18 objects at degradation proportions of  $25\%$ ,  $45\%$ , and  $65\%$ . Degraded objects were then exposed to subjects for 100msec, 200msec, and 750msec. Figure 6 compares MLP-Mixer performance against these human subjects in the 100msec setting. Specifically, we compute the percentage difference in accuracy on edge-degraded shapes relative to corner-degraded shapes for both humans and MLP-Mixer. As degradation proportion increases, human subjects show greater accuracy preservation on edge-degraded shapes compared to corner-degraded shapes. Conversely, MLP-Mixer retains increasingly higher accuracy on corner-degraded shapes relative to edge-degraded shapes.
Dataset Priors We also investigate the effect of pretraining dataset choice on our models' performance. Besides ImageNet, we also pretrain ResNet-18 and ResNet-50 on FractalDB before finetuning them on our whole-polygon dataset. Figure 5 displays the performance of these models on the shape recovery task. Tables 1 and 2 show the analogous per class
performance for ResNet-18. While the general trend of these models is the same as their ImageNet counterparts, these models retain greater accuracy on corner-degraded shapes and fail more rapidly
MLP-Mixer Comparison with Biederman's Human Subjects
Figure 6: Differential (Edge - Corner) in edge-degradation accuracy relative to corner-degradation accuracy on the shape and image recovery tasks. As  $p_d$  increases, humans retain high accuracy on edge-degraded images but perform worse on corner-degraded images. On the other hand, MLP-Mixer quickly experiences decreasing accuracy on edge-degraded images, while retaining high accuracy on corner-degraded images. Overall, MLP-Mixer and human subjects exhibit starkly contrasting behavior.
pd and Type	Triangle	Square	Pentagon	Hexagon	Heptagon	Octagon
0.3 Edge Degradation	100.0	67.7	92.2	0.2	0.9	100.0
0.4 Edge Degradation	100.0	27.6	0.0	0.0	0.0	94.7
0.5 Edge Degradation	100.0	39.0	0.0	0.0	0.1	92.9
0.6 Edge Degradation	100.0	32.7	0.0	0.0	0.0	0.1
0.7 Edge Degradation	6.6	98.9	0.0	0.0	0.0	0.0
0.3 Corner Degradation	100.0	96.0	88.9	87.0	93.7	82.3
0.4 Corner Degradation	100.0	79.2	55.9	66.3	42.4	60.5
0.5 Corner Degradation	100.0	69.8	0.1	14.4	16.3	55.6
0.6 Corner Degradation	100.0	16.1	0.0	0.0	0.0	0.0
0.7 Corner Degradation	60.4	95.2	0.0	0.0	0.0	0.0
Table 1: Per-class accuracy of ImageNet-pretrained ResNet-18 at varying degradation proportions.
pd and Type	Triangle	Square	Pentagon	Hexagon	Heptagon	Octagon
0.3 Edge Degradation	100.0	99.3	98.6	30.1	9.4	100.0
0.4 Edge Degradation	97.5	98.3	89.5	1.7	0.0	100.0
0.5 Edge Degradation	58.0	57.0	2.4	0.2	0.2	99.9
0.6 Edge Degradation	2.4	27.0	0.4	0.0	0.1	100.0
0.7 Edge Degradation	0.0	12.0	0.0	0.1	69.7	26.5
0.3 Corner Degradation	100.0	100.0	100.0	100.0	11.4	0.0
0.4 Corner Degradation	100.0	100.0	100.0	100.0	99.1	0.0
0.5 Corner Degradation	100.0	100.0	100.0	100.0	32.3	0.1
0.6 Corner Degradation	100.0	98.5	100.0	62.5	100.0	84.0
0.7 Corner Degradation	99.9	89.9	53.5	99.8	84.6	0.0
Table 2: Per-class accuracy of FractalDB-pretrained ResNet-18 at varying degradation proportions.
on edge-degraded shapes as degradation proportion increases, diverging even further from human behavior.
For fractals generated by linear Iterated Function Systems (IFS), such as those in FractalDB, the resulting images primarily exhibit the NAPs of collinearity and symmetry, and not so much structurally complex vertices. Therefore, it is not surprising that these fractal-pretrained models are more amenable to processing edges, thus performing even better on corner-degraded shapes. In that sense, fractal pretraining further misaligns neural network behavior from humans, raising the question of if standard fractal pretraining can indeed be a suitable substitute for natural image pretraining. However, we note that extensions to the traditional IFS generative process exist that enable emphasis on different NAPs. For example, the Fractal Flame algorithm (Spotworks and Berthoud, 2008) produces curved fractals, thus emphasizing curvilinearity. We leave the investigation of such fractal generation procedures' effects on neural network behavior and alignment for future work.
Visualizing Network Internals To gain further intuition for neural network behavior, we study our learned ResNet-18 models by analyzing their corresponding Grad-CAM visualizations (Selvaraju et al., 2017). Figure 7 shows an illustrative example of the difference in gradients for the true target concept flowing into the final convolutional layer between ImageNet-pretrained ResNet-18 and FractalDB-pretrained ResNet-18. On two randomly selected pentagons from our dataset and their corresponding  $50\%$  edge-degraded and  $50\%$  corner-degraded variants, the highlighted regions of the ImageNet model are less concentrated within the shape's radius than the highlighted regions of the FractalDB model, suggesting that fractal pretraining endowed ResNet-18 with a somewhat more robust ability to classify degraded shapes. Though not a full explanation for model behavior, we see such discrepancies as a potential indication that fractal pretraining enables models to learn and leverage more robust geometric features, though not necessarily human-like vertex features.
(a) ImageNet; Corner-degraded
(b) ImageNet; Edge-degraded
(c) FractalDB; Corner-degraded
(d) FractalDB; Edge-degraded
Figure 7: Grad-CAM visualizations with respect to the true pentagon class for ResNet-18 on (a)  $50\%$  corner-degraded pentagon with an ImageNet-pretrained model, (b)  $50\%$  edge-degraded pentagon with an ImageNet-pretrained model, (c)  $50\%$  corner-degraded pentagon with a FractalDB-pretrained model, and (d)  $50\%$  edge-degraded pentagon with a FractalDB-pretrained model.
Inspired by cognitive science and the theory of Recognition-by-Components, we introduce a new perspective on the human-machine vision gap and investigate the notion of image recovery in degraded regular polygons. To do so, we develop the Automated Shape Recoverability Test pipeline for generating regular polygon sketches at scale with varying orders of degradation, which we open-source to the machine learning community. We then train common deep learning vision models for this simple task and find that their behavior fundamentally conflicts with how humans perceive images. Furthermore, we show that fractal pretraining further misaligns neural network and human behavior. Based on these results, we encourage further investigation into this fundamental conflict between human and machine vision.
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