Degraded Polygons Raise Fundamental Questions of Neural Network Perception
Authors: Leonard Tang
Dan Ley
Venue: NeurIPS 2023 Datasets and Benchmarks Poster (2023)
Keywords: Geometry
Cognitive Science
Psychology
Vision
Robustness
Safety
TL;DR: We introduce an extremely simple shape detection task that elicits fundamental, inconsistent phenomenon between humans and widely used neural network models

Abstract: It is well-known that modern computer vision systems often exhibit behaviors misaligned with those of humans: from adversarial attacks to image corruptions, deep
learning vision models suffer in a variety of settings that humans capably handle. In
light of these phenomena, here we introduce another, orthogonal perspective studying the human-machine vision gap. We revisit the task of recovering images under
degradation, first introduced over 30 years ago in the Recognition-by-Components
theory of human vision. Specifically, we study the performance and behavior of
neural networks on the seemingly simple task of classifying regular polygons at
varying orders of degradation along their perimeters. To this end, we implement the
Automated Shape Recoverability Test
for rapidly generating large-scale datasets
of perimeter-degraded regular polygons, modernizing the historically manual creation of image recoverability experiments. We then investigate the capacity of
neural networks to recognize and recover such degraded shapes when initialized
with different priors. Ultimately, we find that neural networks’ behavior on this
simple task conflicts with human behavior, raising a fundamental question of the
robustness and learning capabilities of modern computer vision models

Degraded Polygons Raise Fundamental Questions of Neural Network Perception
Leonard Tang
Dan Ley
Department of Mathematics
School of Engineering and Applied Sciences Harvard University Cambridge, MA 02134 dleyêg harvard. edu
Harvard University Cambridge, MA 02138
Leonardtang@college haw.:eeaaannollllleeeaaarrrrrrr hww.arrd
Abstract
It is well-known that modern computer vision systems often exhibit behaviors mis- aligned with those of humans: from adversarial attacks to image corruptions, deep learning vision models suffer a variety of settings that humans capably handle. light of these phenomena, here introduce another, orthogonal perspective study- ing the human-machine vision gap. We revisit the task recovering images under degradation, first introduced over 30 years ago in the Sesoggnttion-y-Coooooeeeee theory of human vision. Specifically, we study the performance and behavior of neural networks the seemingly simple task of classifying regular polygons varying orders of degradation along their perimeters. To this end, we implement the Automated Shape Recoverability Test! for rapidly generating large-scale datasets of prrimeter-degrader regular polygons, modernizing the historically manual cre- ation of image recoverability experiments. We then investigate the capacity of neural networks to recognize and recover such degraded shapes when initialized with different priors. Ultimately, we find that neural networks' behavior on this simple task conflicts with human behavior, raising fundamental question of the robustness and learning capabilities of modern computer vision models.
Introduction
Since the advent of adversarial attacks (Goodfellow al., 2015), researchers have grown increasingly wary of machine learning models' susceptibility to learning irrelevant patterns (Yuan et al., 2019). Oftentimes, neural networks rely on spurious features that humans know avoid (Khani and Liang, 2021). A poignant example of such unorthodox behavior comes in the form of machine vision's 's over-dependency on object textures rather than object shapes (Geirhos et al., 2019). This often leads to dangerous consequences in practice (Hendrycks et al., 2021a). Similarly, the fragility of vision models in response to minor image transformations such as shifts or rotations (Azulay and Weiss, 2019), raises concerns how well these models truly learn, especially when considering these small geometric transformations are commonplace in natural vision scenarios. The specifics when or how vision models might be expected generalize well remains mystery (Zhang et al., 2017).
Beyond being unreliable in real-world settings, current vision models are decidely unhuman in nature. They tend to learn undesirable features that are fundamentally misaligned with how humans perceive the world. Given unexpected nature of such models, we study if models are also capable of correctly identifying recoverable images, concept first presented in the Recognition-by by-opooo------tttt theory of human vision (Biederman, 1987). Similarly, we investigate whether or not these models' performance is marred by non-recoverable images.
http://ttthbbcommmmoodddgggggggd Polg RBC
37th Conference on Neural Information Processing Systems (NeurIPS 2023) Track on Datasets and Benchmarks.

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Figure I: Specific instance of the Automated Shape Recoverablility Test generation pipeline for an example pentagon with 50% degradation proportion. Whole shapes are generated and subsequently edited with corner degradation (top), and edge degradation (bottom). Our experiments indicate that, unlike constrontr humans performing sketch recovery (Biederman, 1987). neural networks rely heavily on edges rather than corners to recover degraded shapes.
To make progress in understanding the behavior of computer vision models, we introduce the Automated Shape Recoverablility Test pipeline for evaluating vision models across spectrum of image degradation in regular polygons. The intrinsic difficulty in classifying a generated image is directly controlled by the proportion of the image we delete, subject the constraint of where the image deletion is allowed to occur. We operate on the domain of black-and-whhe sketches, since they most closely resemble the distribution of images presented in Biederman (1987), which consist of simple sketches of common objects. Moreover, our ultimate results on this simple task setting suggest fundamental misalignment the way humans and machine approach image classification.
Using our pipeline, we produce 1, 1,260,000 sketches regular polygons evenly distributed across 7 shape categories, 9 levels of image degradation, and 2 forms of degradation (corner and edge degradation). Though seemingly simple, these images measure model performance against a canonical human vision task, yielding surprising discrepancies. We release the editing pipeline and final dataset of 1, 1,260,000 images in the hopes of encouraging further research in this direction.
In image classification experiments tectures poorly recover (i.c. correctly classify) heavily edge-degraded and corner-degraded shapes, both of which humans are capable of recognizing. Surprisingly, neural networks also rely primarily on edges rather than corners for shape recovery the exact opposite of human behavior. Moreover, results also indicate that models pretrained entirely on non-accidental properties generated by Iterated Function Systems (Barnsley and Vince, 2010) display much stronger performance patterns on the corner-removed class. Overall, our contributions are summarized follows:
subset of the data, observe that common vision archi-
We introduce the Automated Shape Recoverability Test, pipeline for generating datasets with parameterized degradation of regular polygons. We publicly release the pipeline and the accompanying dataset of 1.260,000 images, which span across seven categories and include varying degrees and forms of image degradation.
Through a comprehensive analysis of various neural network architectures on the task shape recovery across varying levels of image degradation, we demonstrate striking discrepancy in how machine learning models and humans perceive images. Unlike humans, neural networks consistently rely more on edges than corners for image recovery, pointing to a fundamental difference in image processing between machines and humans.
Our exploration of pretraining dataset choice reveals that models pretrained on fractals, unlike those pretrained on ImageNet, retain greater accuracy on edge-degraded shapes, while continuing to perform poorly on corner-degraded shapes, further misaligning human and machine vision. Through Grad-CAM visualizations, we reveal differences how ImageNet and fractal pretrained models leam features and process degraded shapes.

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2 Related Work
2.1 Sketch Classification
Though sketch classification is not as common a task as natural image classification, much existing research attempts tackle the problem. The TUBerlin Sketch Benchmark the first large-scale sketch classification dataset for machine learning, consisting of 20,000 unique sketches distributed over 250 object categories that exhaustively cover most objects that commonly encountered in everyday life Eitz et al. (2012). 1,350 unique Amazon Mechanical Turk (MTurk) workers were recruited sketch these images, with each worker only being able to sketch a limited number of sketches per category so as to preserve diversity within each sketch class. Eitz et al. (2012) also develop bag-of-features sketch representation alongside multi-class support vector machines trained on the dataset, which classifies unseen sketches with 56% accuracy.
Since the introduction of this dataset, significant work has been done to build more accurate models of sketch classification using deep-learning architectures, particularly Convolutional Neural Networks and Recurrent Neural Networks, well as solving challenges including partial sketch classification and sketch progression incorporation (Tran, 2017; Seddati et al., 2015, 2016; Yang and Hospedales, 2015; Ha and Eck, 2018). As result of these efforts, the competitive accuracy the TÜBerlin Sketch Benchmark is now 77.69% a significant improvement over the original paper.
2.2 Image Recovery from a Cognitive Science Perspective
The task of image recovery was first introduced in the landmark theory from cognitive science, which explains how humans recognize and categorize objects based on their basic geometric structures, called geons, and their spatial relationships (Biederman, 1987; Cooper and Biederman, 1993). A critical component of Recognition- by- Sy-Components theory states that object recognition of two-dimensional black-and- sketches is impaired when feature-relation information - the information about the relationships between geons- is degraded. In the limit of feature-relation information degradation, it is ambiguous what the original object was supposed to be: contextual inference of the original object is no longer possible. We define such degraded image to be non-recoverable. Otherwise, degraded image that can still be recognized is recoverable.
Recognition-by-Compoeeee
Recognition-by: Sirtlion-------oeeeeee also posits that parsing of an object into components is performed vertex regions of sharp concavity, with multiple curves terminating verify this claim, Biederman (1987) tested humans' ability to classify sketches of objects in timed setting after object contours had undergone heavy degradation. Expectedly, heavier degradation - greater proportions of the sketch being deleted led to lower classification accuracy. Additionally, corroborating the original claim, degradation centered at object corners induced much lower accuracy in subjects compared to degradation along curves between corners (Biederman, 1987; Guez et al., 1994).
common point. To
While our proposed dataset and task do not exactly match the setting of Biederman's 's (1987) experi- ments in the sense that we focus on distinct set of sketch shapes and do not consider time-constrained recognition, our results indicate that this task is sufficiently challenging for modern deep learning models. Moreover, the simple structure of our data, being merely regular polygons, indicates fundamental misalignment of deep learning vision models with respect human vision. We view our dataset as a minimum viable task that highlights this misalignment: the fact that deep learning models exhibit pathologies even on this simple shape classification task suggests that neural network perception may be even less robust than we know. To contextualize our findings, we compare Biederman's 's (1987) human subject performance to those of common vision architectures in $4.1.
Gollin Figures Test Closely related to image recovery is the Gollin figures test for assessing human visual perception. Subjects are shown variations of a common object in quick secession, with five consecutive incomplete line drawings of a picture, from least most complete, displayed to each subject (Gollin, 1960). The subject needs to mentally complete the underlying drawing in order to identify the original object drawn, similar to testing for Gestalt closure phenomena (Rock and Palmer, 1990; Kim et al., 2021). Notably, unlike in Recognition-by Seaiitioonby--oooeeettttt theory, the Gollin figures test makes no distinction between image degradations that yield recoverable images and degradations that yield non recoverceea images.
3

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Non-Accidental Property
Examples
Collinearity
Curvilinearity
Symmetry
Parallel Curves
Vertices
Figure 2:
The five classes of nonaccidental properties (NAPs) for object recognition in the visual cortex are 1) collinearity, the presence of straight lines; 2) carvilinearity. the presence of smoothly curved elements: 3) symmetry across arbitrary axes; 4) parallel curves; and 5) vertices, junctions of two or more contours (Lowe. 1985). Critically, cognitive scientists suggest that NAPs form perceptual basis for the set of components that enable object recognition.
Historically, the Gollin figures test has been automated in order to provide more fine- fine-graing meee-graind control over the proportion of an image that is degraded. That is, rather than having five discrete variants of degradation as in the original test, software was introduced to construct infinitely many variants of degradation continuous spectrum (Foreman and Hemmings, 1987). Motivated by this precedent, we automate the generation of recoverable and non-recoverable image degradations at scale.
Non-Accidental Properties Non-accidental properties (NAPs) are image properties that are in- variant over orientation and depth (Amir et al., 2012). The human visual system processes NAPs in two-dimensional drawing as feasibly occurring in three dimensions (Witkin and Tenenbaum, 1983). For example, if there is straight line, a manifesation of collinearity, in a wwo-dimensional drawing, the visual system infers that the edge producing that line in the three-dimensional world is also straight. In other words, NAPs are dimension-invariant. Another perspective understanding NAPs is the non-accidentalness principle, which states that spatiotemporal coherence and regularity so unlikely to arise by the random interaction of independent components, that such structure, when observed, almost certainly denotes an underlying unified process (Blusseau et al., 2016). NAPs precisely capture these unlikely coherences, providing useful cues for human object recognition. Figure 2 displays the five canonical NAPs and examples of each property (Lowe, 1985).
NAPs and image recoverability are intimately related notions. Specifically, NAP location and type directly parameterizes regions of necvvecceee image degradations. If NAPs are removed from any image region, becomes more difficult to recover the object component that the deleted NAP belongs too. Under certain NAP removals, it becomes more difficult to recover the relationship between object components, and thus the overall image. For instance, Biederman (1987) demonstrated that deletion of vertices adversely affected object recognition more than deletion of midsegments. Inspired

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by this result, here we focus on producing degradation of regions surrounding vertices as well as midsegments order to generate non-recoverable and recoverable images, respectively.
Fractals as Partial Non-Accidental Properties While there are not any known ways of specifying the generation of NAPs directly, we draw inspiration from Barnsley and Vince (2010) automatically generate fractals. Due to their intrinsic collinearity, curvilinearity, symmetry, parallel nature, multi- tude of junctions, and occurrence in natural objects and scenes, fractals may be regarded form of NAPs. To that end, we investigate the performance of models pretrained via fractal -utiee Formula-driven Supervised Learning (FSDL) on our benchmark. In FSDL, fractals are generated by mathematical formulae, then binned into categories based on the range of formula parameters. The learning task is thus to classify fractals within the correct parameter range (Kataoka et al., 2020).
proxy
Recent results in the deep learning literature also motivate the use of fractal pretraining. In particular, Hendrycks et al. (2021b) showed that simple data augmentation technique mixing fractals with natural images comprehensively improves model robustness and safety metrics. Contemporaneously, Kataoka al. (2020) also demonstrate that pretraining neural networks entirely on synthetically generated fractals achieves the same level of performance on downstream tasks as pretraining on natural images. For our experiments, we use models pretrained on synthetic fractals with 10,000 fractal classes, which we refer to as FractalDB models.
3 Automating Shape Recoverability Experiments
We implement the Automated Shape Recoverablility Test, an automatic image editing pipeline for creating degraded regular polygons at varying severities. Figure I displays an example of our generation pipeline. In total, our pipeline requires less than 30 seconds of compute time to serially generate 6,000 diverse images across 7 shape categories - triangles, squares, pentagons, hexagons, heptagons, and octagons with 1,000 images each². Moreover, this procedure can be trivially scaled up to any arbitrary number of polygon classes and images per class. Our approach broadly consists of generating regular polygons, then degrading their perimeters to produce recoverable (edge degradation) and non-recoverable (corner degradation) images.
Regular Polygon Generation Our shape generation pipeline begins by constructing regular poly- gons. We generate polygons by first implicitly defining a circle, then placing an appropriate number of points, matching the desired number of sides, on its circumference. For example, to draw a pentagon, we place five points equally spaced on the circumference of the circle, then use line segments to connect them. To promote image diversity, the center of the circle is chosen randomly within a 224 x 224 grid, subject to a minimum acceptable radius size m'in- Subsequently, the circle's radius is chosen uniformly random between the minimum accepted radius size and the maximum radius size allowed by the sampled circle center. Furthermore, shapes are rotated uniformly at random by an angle between 0 and 360". The border of each polygon is fixed to be two pixels thick. All generated shapes have black borders overlaid on top of white background.
Producing Degraded Shapes In order to produce recoverable and non-recoverable versions of our shapes, we parametrically and evenly degrade the perimeter of each polygon. To do so, we first specify the proportion pa of the shape's 's perimeter to degrade. Naturally, a larger degradation proportion yields more occluded shapes that are more difficult to recognize, and a smaller degradation proportion yields shapes closer to the original polygon, which are more easily recognized. To produce non-recoverable shapes, we degrade perimeter regions surrounding each corner, and to produce recoverable shapes, we degrade perimeter regions from the midsegment of each edge.
Corner Degradation To degrade corners from an initial regular polygon generation, we overlay white circles at each corner, effectively erasing the perimeter of the corresponding local neighborhood around the corner. Given a desired global degradation proportion pa, each individual white circle is then defined with the following radius, where N, is the number of sides of the regular polygon and P is the total perimeter:
Pd 2 N₂
P
Benchmarked on 8-core Apple MI Pro chip.
5

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ImageNet-Pretrained Models
ResNet-18
Re
100
Tisst Accurary (%)
Top-1 Teat Accuraty (%)
80
60
40
40
20
Fdge Degradation Degradation
20
Edge Negraditton Comer Degradatior
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Degradation Proportion,
Degradation Proportion, Pa
ML P-Mixer
VIT
100
100
Tap-1 Test Accuratcy (96)
80
80
Top-1 Test Accurary
60
60
40-
Edge Degr Degtionatoon Corner Degradation
Edge Degratation Comer Degradation
0.1
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Degradation Prosortion,
Degradation Proportion,
Figure 3: Top-1 test accuracy (%) within #1 SD (across 10 training trials) of ImageNet-prettie pretrained and whole-polygon finetuned models on the shape recovery task. Accuracy decreases as degradation proportion, Pa. increases. Moreover, ResNet-15, ResNet-50, and MLP-Mixer all exhibit worse performance on edge-degraded compared to comer-degraded shapes, the opposite of human behavior.
Under this construction, the circle each corner will erase 2r (P pa)/N, pixels from the shape's ' perimeter, and in aggregate N, circles will erase P-Pa pixels, thus precisely degrading (P pa)/ = Pa proportion of the original image, as desired.
Edge Degrading We adopt similar procedure for edge degradation. However, instead of overlay- ing circles at shape corners, we overlay circles at midpoints between corners. Critically. defining exactly as above, observe that no circle drawn at midpoint can erase a corner so long as Pa < which is true for all of our experiments and in all meaningful degradation cases. In the limiting cases, pr- erases the entire perimeter of the shape, and p, retains the shape in full. Notably, this procedure performs single removal at the middle of each edge, not dashed-line edit.
Experiments
Our experiments evaluate neural networks' ability to classify degraded shapes at 10%, 15%, 20%, 25%, 30%, 40%, 50%, 60%, and 70% perimeter degradation proportions. our architectures. we benchmark ResNet- ResNet-50 (He et al., 2016), MI.-Mixer (Tolstikhin et al., 2021), and ViT (Dosovitskiy et al., 2021). We consider the ResNet family due to its universality in vision experiments and relative simplicity. We also test MLP-Mixer and ViT due to their qualitatively different learning procedure and behavior. MLP-Mixer uses simple multi-layer perceptrons (MLPs) to mix features locally and globally, contrasting the explicit weight sharing seen in convolutional and transformer models. ViT adapts the transformer architecture from natural language processing to handle images, learning global dependencies by treating image patches sequence.
initialize our models using pretrained weights derived from ImageNet (Deng et al., 2009) and FractaIDB-11 database without any natural images (Kataoka et al., 2020). All models are then fine- tuned on whole, non-degraded regular polygons according to 60% /20%% traininngvaliddationnest split. Subsequently, they directly tested on corner-degraded and edge-degraded polygons vary-

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Confuston Matrices Edge Degraded Shapes
ResNet-
ReshNet
30%
50%
35%
1462
100
Pikkial Clzo
Prefited Cape
FREE CENE CINTE
Fref Pred-ceed Class
000
600
MLF-Mixer
VI
PHOMEIO CAERA
PHOR Clzar
Tredithet Cayss
FRESERNO CAYS
Fredieed Cays
600
Toe
Toe Clas
Claaa
Clasa
C103
Confusion Matrices for Corner Degraded Shapes
ResNet
ResiNet: 30
30%
50%
70%
32%
92%
70%
Puskito Capo
Fredd Ctter Care
Fred STNNE CINOS
Fred stee Cless
400
448
Thee Class
Thee Class
True Closs
Thus Class
Thus Class
Thae Cans
Mix-M
30%
50%
10%
30%
90%
70%
1030
PROPEOO CARO
Pesktdd Clas
Tredicted Cays
PROErre CIVS
Fredicted Clvss
Protited
The
Toe
Tre
Thus Class
Claaa
Cuaa
Figure Confusion matrices 30%, 50%, and 70% removal proportions for corner-degraded shapes (top) and edge-degraded shapes (bottom) using ImageNet-pretrainee ResNet-18 18, ResNet-50, MI.-Mixer, and ViT. As removal proportion increases, models default to predicting single class.
ing degradation strengths. While our models obtain high accuracy on whole shape classification, we are chiefly interested in their performance on degraded shapes.
Training Setup We finetune ResNet- 18 and ResNet-50 on whole polgyons for 20 epochs using SGD with a learning rate of 0.01, a momentum term of 0.9, no weight decay, and batch size of 64. Sate-on-Pllateuu scheduler with patience of 3 epochs
The learning rate follows a Reduce-Learning and learning rate reduction factor of 0.1. For ViT, we use SGD with learning rate of 0.001, weight decay of 0.001, momentum of 0.9, and batch size of 32. Across all experiments, standard data augmentation and preprocessing techniques are used, namely random cropping, random rotations, random horizontal flipping, and normalization over the whole-polygon dataset.
At every epoch, we compute top-1 and top-5 validation accuracy on the whole-polygen dataset, and the weights of the network are saved. After training, the set of weights with the highest top-1 validation accuracy is used compute model on corner-degraded and edge-degre degredee shapes. Critically, our models achieve 100% validation accuracy within epochs, and also consistently achieve greater than 99.7% accuracy on randomly held out test sets of whole shapes. More interestingly, they perform much worse on degraded shapes.
accuracy on whole polygons. We then evaluate this best
Comparison Across Architectures The top-1 test accuracies on corner-degraded and edge- degraded shapes for mmageNet-pretrained models are shown in Figure 3. Unsurprisingly, as degra- dation proportion increases, all architectures perform worse, both in the corner-degraded and edge- degraded settings. While ViT performs similarly on all degraded shapes at each degradation propor- tion, ResNet-18 18, ResNet-50, and MLP-Mixer consistently perform worse edge-degraded shapes

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BoactalDB-Pretrainee Models
ResNet-18
ResNet-50
Top-1 Text Accuracy (50
80
Top-3 Test Accuracy (86)
80
60
60
20
20
Edga Degradatton Comer Degradation
Edge Degrodation Corner Degrodation
0.3
0.5
0.7
0.3
0.5
0.7
Degradation Praportian, Pr
Degradation Proportion, Pr
Figure 5: Top-1 test accuracy (%) within 11 SD (across 10 training trials) of FractalDB-pretrraine and whole-polygon finetuned models on the shape recovery task. Again, accuracy decreases across the board as degradation proportion, Pa. increases. Compared their SraageNet-pretraiing however, ResNet-18 18 and ResNet-50 both retain better performance on corner- degerdde shapes. We also note the discrepancy compared edge-degraded shapes, the opposite of human behavior.
counterparts.
versus comerrdeegraded shapes. Notably, this is the opposite of how time-constrained humans perform on Biederman's 's (1987) degraded sketch recognition task.
Figure 4 also presents confusion matrices for pergeNee--rettaineed ResNet-18, ResNet-50, MLP- Mixer, and ViT 30%, 50%, and 70% degradation. As degradation proportion increases, we note that models tend to default to predicting single class, for example to defaulting to triangles for ResNet- 18 and hexagons for Resnet-50 at 70% degradation.
4.1 Results
Human Comparison To contextualize the behav- ior 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 degra- dation at corners and edges was performed for 18 objects at degradation proportions of 25%, 45%, and 65%. Degraded objects were then exposed subjects for 100msec, 200msec, and 750msec. Figure 6 com- pares MLP-Mixer performance against these human subjects in the 100msec setting. Specifically, we com-
MLP-Mixer Comparison with Biederman's Human Subjects
Edge-Comer Accuracy Gap (%g
20
Human Subjects
-20
-40
pute the percentage difference in accuracy on edge- degraded shapes relative corner-degraeed shapes for both humans and MLP-Mixer. As degradation proportion increases, human subjects show greater accuracy preservation on edge-degraded shapes com- pared to corner-degraded shapes. Conversely, MLP. Mixer retains increasingly higher accuracy on corner- degraded shapes relative to edge-degraded shapes.
0.2
0.3
0.4
0.6
Deg Degraioioon Proportion, Pa
Figure 6: Differential (Edge - Corner) in edge-degradation accuracy relative corner- degradation accuracy on the shape and im- age recovery tasks. As pa increases, humans retain high accuracy on edge-degraded im- ages but perform worse on degnerdde images. On the other hand, MLP-Mixe quickly experiences decreasing accuracy on edge-degraded images, while retaining high accuracy on corner-degraded images. Over- all, MLP-Mixen and human subjects exhibit starkly contrasting behavior.
Dataset Priors We also investigate the effect of pre- training 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 and 2 show the analogous per class performance ResNet-18. While the general trend counterparts, these models retain greater accuracy corner-degraded shapes and fail more rapidly
these models the same as their ImageNet

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Pa 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
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--reetrinee ResNet-18 at varying degradation proportions.
Pa 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
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 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 those in FractalDBB, the resulting images primarily exhibit the NAPs of collinearity and symmetry, and not much structurally complex vertices. Therefore, it not surprising that these fractal-pretrained models 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 suitable substitute for natural image pretraining. However, we 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.
more
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-pretrainee ResNet- and FractalDB-pretralne pretrained ResNet-18 18. On two randomly selected pentagons from our dataset and their corresponding 50% adge-degrader and 50% corner-degraded variants, the highlighted regions of the ImageNet model are less concentrated within the shape's 's radius than the highlighted regions of the FractalDB model, suggesting that fractal pretraining endowed ResNet-18 with somewhat more robust ability to classify degraded shapes. Though not a full explanation for model behavior, we see such discrepancies as potential indication that fractal pretraining enables models to learn and leverage more robust geometric features, though not necessarily buman-like vertex features.

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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 mmageNet-pretrainne with an SmageNet-pretraiing model, (c) 50% comnerdeerraed pentagon with a BractalDB-preerrann model, and (d) 50% edge-degraded pentagon with FractalDB FractalDD--rretaanned model.
model, (b) 50% edge-degraded pentagon
5 Conclusion
Inspired by cognitive science and the theory of recognitionbby-Cooommmee we introduce 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 Recoverablility 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 this fundamental conflict between human and machine vision.
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Reviews:
[{"review_id": "Z1lJ2H5rDb", "reviewer": "Reviewer_d9g1", "summary": "", "questions": "", "limitations": "Potential impact of the results is not very clear (see opportunities for improvement).\n\n**Irrelevance to the datasets and benchmark track (?)** Overall, I do not dot understand why this paper is submitted to the benchmark and datasets track. To be precise, the dataset created here is rather simple (and, in my opinion, this dataset is not a significant contribution) and it seems to me that the main contribution is their empirical findings about neural networks. Hence the current paper may better suit the main conference track or, even better, some other conference or journal, possibly related to human/AI perception etc.", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "The paper is well written, the presentation is quite logical and easy to follow. The experiments are convincing and support the claims about neural networks' perception. The obtained experimental result is interesting.", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "tgy2qanNKY", "reviewer": "Reviewer_Q8xH", "summary": "", "questions": "", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "1.\tStudies like this comparing network properties to characteristic properties of humans (found in perception or cognitive science literature) are important to keep track of the similarities and differences between human and network behavior.\n2.\tExperiments use standard networks and training settings.\n3.\tCode and dataset are public.\n", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "8EAtZ6bzBF", "reviewer": "Reviewer_fh2w", "summary": "", "questions": "", "limitations": "The presented data (and problem) are interesting, but very basic. It remains largely unclear how the proposed setup will translate to real world classification problems, whereas the existing dimensions like robustness and texture bias have effect that  can be observed in real world applications. Here the paper somewhat fails to at least show a perspective... ", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "The paper presents a very simply but also very intriguing property of CNNs, which has not been described before but also enriches the broughter current discussion on model biases. The experimental setup is well motivated from prior work in other research communities and has the potential to introduce new perspectives and methods into the ML comunity.  ", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "t9iMSSnwYM", "reviewer": "Reviewer_5Kr2", "summary": "", "questions": "", "limitations": "The authors have sufficiently addressed the limitations of their work in my opinion.", "rating": 9, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "The striking difference in human- and machine-learned perceptions of such simple images is one of the most interesting aspects of this work. The authors have come up with an intuitive benchmark dataset that seems very promising to help improve our understanding of how image-based models make their decisions.", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}]

Author rebuttal:

Meta-review: A well crafted benchmark that raises an interesting question and addresses an important gap in the ML literature. The authors make the observation that, in contrast to studies of human perception, ML models seem to use edges to classify occluded shapes, while humans tend to use corners. To this end, they provide a dataset specifically designed to expose this behaviour in trained models. This misalignment, while documented thoroughly in the work, remains a mystery. While some reviewers raised concerns that this contribution, while interesting, is not useful for the development of high-performance ML systems, it is an exceptional example of a systematic analysis of existing systems on a novel dataset that yields an important new insight. Many reviewers believed that a more thorough study of this problem in follow-up works will yields important insight into the differences between human and machine perception, and all but one reviewer revised their review to accept after the discussion period (the final reviewer did not reply to any rebuttals or follow-up queries).
Decision: Accept (Poster)