# The developmental trajectory of object recognition
robustness: children are like small adults but unlike big deep neural networks

Lukas S. Huber1,2, §
0000-0002-7755-6926 Robert Geirhos2
0000-0001-7698-3187 Felix A. Wichmann2
0000-0002-2592-634X

###### Abstract

In laboratory object recognition tasks based on undistorted photographs, both
adult humans and Deep Neural Networks (DNNs) perform close to ceiling. Unlike
adults’, whose object recognition performance is robust against a wide range
of image distortions, DNNs trained on standard ImageNet (1.3M images) perform
poorly on distorted images. However, the last two years have seen impressive
gains in DNN distortion robustness, predominantly achieved through ever-
increasing large-scale datasets—orders of magnitude larger than ImageNet.
While this simple brute-force approach is very effective in achieving human-
level robustness in DNNs, it raises the question of whether human robustness,
too, is simply due to extensive experience with (distorted) visual input
during childhood and beyond. Here we investigate this question by comparing
the core object recognition performance of 146 children (aged 4–15) against
adults and against DNNs. We find, first, that already 4–6 year-olds showed
remarkable robustness to image distortions and outperform DNNs trained on
ImageNet. Second, we estimated the number of “images” children have been
exposed to during their lifetime. Compared to various DNNs, children’s high
robustness requires relatively little data. Third, when recognizing objects
children—like adults but unlike DNNs—rely heavily on shape but not on texture
cues. Together our results suggest that the remarkable robustness to
distortions emerges early in the developmental trajectory of human object
recognition and is unlikely the result of a mere accumulation of experience
with distorted visual input. Even though current DNNs match human performance
regarding robustness they seem to rely on different and more data-hungry
strategies to do so.

Keywords: bject recognition, robustness, out-of-distribution, deep learning,
development, generalization, children, deep neural networks, machine vision

1Department of Psychology, University of Bern, Switzerland
2Neural Information Processing Group, University of Tübingen, Germany
§To whom correspondence should be addressed<EMAIL_ADDRESS>
## Introduction

_At a functional level, visual object recognition is at the center of
understanding how we think about what we see_ ([57], p. 76). Subjectively,
visual object recognition typically appears effortless and intuitively easy to
us; it is, however, an extremely difficult computational achievement:
Arbitrary “nuisance” variables like object distance (size), pose and lightning
potentially exert a massive influence on the proximal (retinal) stimulus,
sometimes resulting in the very same distal stimulus (3-D object in a scene)
to have a very different proximal stimuli. Conversely, for any given 2-D image
on the retina—the proximal stimulus—there are an infinite number of
potentially very different 3-D scenes—distal stimuli—whose projections would
have resulted in the very same image (e.g., see [60, 13]).111At least if
similarity is measured using standard image processing metrics like the
Euclidean distance between, or correlation of, the images. The human ability
to recognise objects rapidly and effortlessly across a wide range of identity
preserving transformations has been termed _core object recognition_ (see [14]
for a review). The computational difficulty notwithstanding, human object
recognition ability is not only subjective effortless but objectively often
impressive (e.g., [8] or see [44, 57, 20] for reviews).

This computational complexity of (core) visual object recognition is also
reflected in the long time it took computational models to reach human-level
object classification accuracy—despite considerable, decade-long research
efforts in vision science. It was not until 2012, when [39] trained “brain
inspired” deep neural networks (DNNs) on 1.3M natural images that
computational models began to compete with humans in object recognition tasks.
Today, DNNs are the state-of-the-art models in computer vision and surpass
human performance on standard object recognition tasks such as image
classification on the ImageNet dataset (e.g., see [32]). It took even longer
to obtain models that are not only performing well on natural, undistorted
images similar to the training data but also, crucially, on more challenging
datasets, so-called out-of-distribution (OOD) datasets containing for example
image distortions that the models had never seen during training. This is
precisely what humans excel on: robustly recognising objects even under
hitherto unseen “viewing conditions” and distortions; in machine learning
lingo humans show a high degree of OOD robustness. Even though some of these
models have an innovative architecture and/or training procedure—such as CLIP
[61] or other variants of vision transformers [15]—the most crucial feature to
achieve human-like OOD robustness appears to be training on large-scale
datasets [22]. While standard training on ImageNet includes 1.3M images, most
models showing human-like OOD robustness are trained on much larger
datasets—ranging from 14M (Big Transfer models; [38]) to 940M images (semi-
weakly supervised models; [80]) and even to a staggering 3.6B images [70].
However, both architecture and data matter—vision transformers, e.g., trained
on ImageNet are more robust than standard DNNs trained on ImageNet—but even
standard DNNs trained on large-scale datasets (such as Big Transfer models)
achieve remarkable robustness. This indicates that large-scale training may be
sufficient for OOD robustness in computational models.

It remains an open question, however, whether large-scale experience is also
neccessary for robust core object recognition. This is precisely the question
that we intend to answer with the present study: If large-scale exposure to
visual input is indeed necessary to achieve a robust visual representation of
objects, then we would expect human OOD robustness to be low in early
childhood, and to increase with age due to continued exposure during lifetime.
Alternatively, human OOD robustness might instead result from clever
information processing and representation as well as suitable inductive bias
[50, 28], achieving OOD robustness with comparatively little data. In this
case, we would expect human OOD robustness to be already high in early
childhood. Both hypotheses can be evaluated with developmental data.

Here we present a detailed investigation of the developmental trajectory of
object recognition and its robustness in humans from age four to adolescence
and beyond. We believe that resolving the competing hypotheses presented above
may be relevant for understanding important aspects of both machine and human
object recognition: in terms of machine vision, it is unclear whether large-
scale training is the only way to achieve robustness—if children were able to
achieve high robustness with little data, this would indicate that the limit
of data-efficient robustness has not yet been reached. In terms of human
vision, on the other hand, the developmental trajectory of object recognition
robustness is still a puzzle with many missing pieces, limiting our
understanding of the underlying processes and how they develop, as we will
describe in the following section.

### Development of object recognition

Many cognitive abilities, like language or logical reasoning, mature with
time; motor skills, too, take years to develop and be refined. What about our
impressive object recognition abilities, particularly robustness to image
degradations? Behavioral research investigating the _development_ of object
recognition (robustness) in children (after 2 years of age) and adolescents is
comparatively sparse, however. A number of reviews have pointed out the lack
of such studies [52, 72, 63]. Clearly, the ventral visual cortex is subject to
structural and functional changes from childhood, through adolescence and into
adulthood (see [29, 62] or [36] for a review). It has been shown that young
children (5–12 years of age) already show adult-like category-selectivity for
objects in the ventral visual cortex [67, 26] and that the magnitude of
retinotopic signals in V1, V2, V3, V3a and V4 are approximately the same in
children as in adults [11]. In addition, contrast sensitivity in V1 and V3a
also appears to reach adult-level by the age of seven [6]. These findings
indicate that at least neural prerequisites for visual object recognition are
in place at a comparatively early age.222Note that this is not the case for
face-selective regions, which continue to develop well into adolescence [29].

Most available behavioral data stems from children younger than two years. In
those first two years of development, there are two major developmental
changes. First, children start to use abstract representations of global shape
rather than local features to recognise objects [1, 58, 71]. This change
enables adult-like performance in simple object recognition tasks and is
thought to facilitate generalization and increase the robustness of object
recognition [74]. Second, children start to use object shape as the crucial
property to generalize names to never before seen objects—a tendency termed
shape bias (e.g., see [41]). An empirical study suggests that these two
changes are developmentally connected, so that the ability to form abstract
representations of global object shape precedes the shape bias [81]. To our
knowledge, only one study has systematically investigated the development of
object recognition after the age of two. [9] have shown a progressive
improvement of visual object recognition abilities in children from 6 to 11
years of age as measured by a battery of neuropsychological tests.333Tests
used included the Efron Test, Warrington’s Figure-Ground Test, the Street
Completion Test, the Poppelreuter-Ghent Test, a selection of stimuli from the
Birmingham Object Recognition Battery, and a series of color photographs of
objects presented from unusual perspectives or illuminated in unusual ways.
They report that simple visual abilities (such as shape discrimination) were
already mature at the age of six whereas more complex abilities (such as the
recognition of objects presented in a hard-to-decode way) tended to improve
with age.444Note that most tests were very different from the psychophysical
task we employed in this study. The tests most similar to the task used here
are those administered to asses the ability to recognise the structural
identity of an object even when its projection on the retina is
altered—perceptual categorisation as meassured by the Street Completion Test,
the Poppelreuter-Ghent Test, and the identification of color photographs of
objects viewed from unusual perspectives and presented under unusual lighting
conditions. However, all of these test only consist of a small number of
stimuli (11, 13 or 44 respectively), did not apply parameterised distortions
to real photographs and did not implement a limited stimulus-presentation
duration—and thus are not suitable as a rigorous psychophysical assessment of
core object recognition. However, this study did not use stimuli typically
used to assess object recognition in adults or DNNs, preventing any
quantitative comparisons to be made—something we attempt to remedy with the
present study (but see footnote 14). In the present study, we investigate how
well children of different age groups (4–6, 7–9, 10–12, 13–15) are able to
recognise objects in 2D images at different levels of difficulty (degree of
distortions) in order to trace the developmental trajectory of human object
recognition robustness.

## Method

### General

The methods used in this study are adapted from a series of psychophysical
experiments conducted by Geirhos and colleagues (geirhos2018generalisation,
geirhos2019imagenet). The paradigm is an image-category identification task to
compare human observers and DNNs as fairly as possible. Images are presented
on a computer screen and for each image observers are asked to choose the
corresponding category as quickly and accurately as possible. Concerning the
fairness of the comparison between humans and DNNs one aspect needs to be
highlighted: Standard DNNs are typically trained on the ImageNet (ILSVRC)
database [66], which contains about 1.3 million images grouped into 1,000
fine-grained categories (e.g., over a hundred different dog breeds). However,
human observers categorise objects most quickly and naturally at the entry-
level, which is very often the basic-level e.g., dog rather than German
shepherd [64, 65]. In order to account for this discrepancy and to provide a
fair comparison, Geirhos et al. used a mapping from 16 human-friendly entry-
level categories to their corresponding ImageNet categories based on the
WordNet hierarchy [49].

We adapted the following aspects of the original Geirhos et al. studies to
make the paradigm more suitable to test young children: We introduced a
certain degree of gamification, added more breaks, and did not force the
children to respond within 1500 msec after stimulus offset to avoid undue
stress. After each block of 20 trials children were free to either quit the
experiment or continue with another block. Compared to Geirhos et al., we
slightly increased the stimulus presentation duration from 200 ms to 300 ms
and only used stimuli which were correctly recognised by at least two adults
in the previous studies. We employed a between-subject design to test
participants on two different types of distortions: binary salt-and-pepper
noise and so-called “eidolon” distortions [37]. In an additional experiment we
also used texture-shape cue-conflict stimuli as in [23]. In what follows we
first provide a description of the procedure, the introduced gamification and
the employed stimuli. We then proceed by giving details on the tested
participants (children, adolescents, adults), the experimental setup, and the
evaluated DNNs.

### Procedure

Each trial consisted of several phases. First, we presented an attention
grabber inspired by an expiring clock (solid white circle which empties itself
within 600 ms) in the center of the screen. We chose a moving stimulus instead
of a more commonly used fixation cross in order to compensate for possible
weaker attention in children. Second, the target image was shown in the center
of the screen for 300 ms, followed by a full-contrast pink noise mask (1/$f$
spectral shape) of the same size and duration to prevent after-images and
limit internal processing time. Next, the screen turned blank and participants
were required to indicate their answers. They did this by physically pointing
to one of 16 icons corresponding to the 16 entry-level categories on a
laminated DIN A4 sheet arranged in a $4\times 4$ grid (icon size: $3\times 3$
cm). We chose this physical response surface mainly for time efficacy (having
4-year-olds handle a computer mouse by themselves can be a lengthy and
somewhat unreliable undertaking). Next, the 16 icons appeared on screen, and
the experimenter recorded the response provided by the child using a wireless
computer mouse. As in the experiments conducted by Geirhos et al., our icons
were a modified version of the ones from the MS COCO website
(https://cocodataset.org/#explore). Figure 1 shows the schematic of a trial.

Figure 1:  Schematic of a trial. After the attention grabber clock had expired
(600 ms), the target image was presented for 300 ms, followed immediately by a
full-contrast pink noise mask (1/$f$ spectral shape) of the same size and
duration. Following the mask, participants had unlimited time to make their
choice employing the physical response surface. Note, however, that
participants were instructed to respond as quickly and accurately as possible.
After the participant responded, the response surface was shown on screen and
the experimenter clicked on the icon corresponding with the participant’s
response. Icons on the response screen represented the 16 entry-level
categories—row-wise from top to bottom: knife, bicycle, bear, truck, airplane,
clock, boat, car, keyboard, oven, cat, bird, elephant, chair, bottle, dog.
Below the response surface there is a gamified progress-bar indicating the
degree to which the current block has been completed.

All participants were tested in a separate, quiet room—either in their school
(children, adolescents) or at home (adults). The experimental session started
with the presentation of example images. For each category we showed a
prototypical example image in the center of the screen and asked participants
to name the depicted object. The correct category was indicated by the
subsequent presentation of the corresponding category icon. After completing
all 16 examples, participants completed ten practice trials on undistorted
color images (no overlap with stimuli from experimental trials). Extremely
rarely some of the youngest children failed on two or more images and had to
complete another round of ten practice trials. Before the experimental trials
started, a single distorted image (matched for the given experimental
distortion) was shown and a short story-like explanation was given to justify
why some of the subsequent images would be distorted.555Eidolon: Someone left
the images in the rain; that is why some of them are blurry. Noise: Somebody
spilled salt and pepper; that is why some of them look a bit strange. Cue-
Conflict: Someone left the images in the beating sun; that is why some of them
stuck together. Experimental trials were arranged in blocks containing 20
trials each. After each block, participants received feedback and were asked
whether they would like to continue, have a break or terminate the session.
Adults were not explicitly asked if they want to terminate the session—but of
course all participants were informed at the outset that they could abort the
experiment at any given time. Participants could complete a maximum of 16
blocks (320 images) in the eidolon and salt-and-pepper experiments and 20
blocks (400 images) in the cue-conflict experiment.

### Gamification

In order to increase motivation and make the experiment more appealing to
children, we gamified several aspects of the experiment. In the beginning,
participants could choose one of four characters (matched for gender)
corresponding to four different roles: spy, detective, scientist or safari
guide. The chosen character had to undergo a training session designed to
improve her or his crucial skill. What the participants did not know was that
the crucial skill—identifying objects as quickly and accurately as
possible—was the same for all characters. After each trial, the chosen
character was displayed at the foremost position of a progress bar indicating
how far the participant had progressed in the current block (level). After
each block, participants were provided with feedback designed to be
perceptually similar to the display of a game score in an arcade game. There
were three different types of scores. Participants received 10 coins as a
reward for a finished block (not performance related). Additionally, for every
two correctly recognised images, they received a star (performance-related).
If they scored more than eight stars, they earned a special emblem matched for
the chosen story character.666The emblems were sunglasses for the spy, a
magnifying glass for the detective, a microscope for the scientist, and a
camera for the safari guide. Figure 9 in the Appendix A.1 visualises different
gamified elements.

### Stimuli

#### Salt-and-pepper noise and eidolon distortion

As mentioned above we used images from 16-class-ImageNet [24]. A subset of 521
stimuli—stimuli that were correctly classified by at least two adults in prior
experiments—served as a starting point for the present study. We chose this
subset because we feared that children’s motivation might be weaker compared
to that of adults and wanted to avoid frustrating children with stimuli that
even adults are unable to recognize. We then randomly sampled 320 images (20
for each of the 16 categories) to be manipulated in the next step. For both
experiments (eidolon and noise), we manipulated the images to four different
degrees, resulting in 4 different difficulty levels per experiment. For the
eidolon experiment, we used the eidolon toolbox [37] with the following
settings: $grain=10$, $coherence=1$ and four different $reach$ $levels$
corresponding to the four difficulty levels ($0,4,8,16$). The higher the reach
level, the more distorted the images are and the more difficult it is to
recognise them. In the noise experiment, a certain proportion of pixels were
either set to a gray value of 1 (white) or 0 (black). This manipulation is
often referred to as _salt and pepper noise_. The four difficulty levels in
this experiment corresponded to 4 different proportions of flipped pixels (0,
0.1, 0.2 or 0.35). For example, 0.2 means that 20% of the pixels are switched
while 80% of the pixels remain untouched. For simplicity, we use the term
“difficulty level” to refer to both: the different reach levels of the eidolon
experiment and the different noise levels of the salt-and-pepper noise
experiment. It is important to note, however, that the difficulty levels were
not precisely matched between conditions as can be seen in the results. Figure
2 displays an example image to which both distortions were applied.

(a) Noise level = 0

(b) Noise level = 0.1

(c) Noise level = 0.2

(d) Noise level = 0.35

(e) Reach level = 0

(f) Reach level = 4

(g) Reach level = 8

(h) Reach level = 16

Figure 2: Systematic degradation of images in the salt-and-pepper noise (a-d)
and the eidolon (e-h) experiments. Note that even though different degradation
levels are shown for the same image, participants never encountered the same
initial image multiple times.

For each difficulty level we randomly selected five images per category to be
distorted. Note that in both experiments the lowest difficulty level (either
reach level or proportion of switched pixels equals 0) can be interpreted as
only a gray scale transformation of the original color images.777This is true
for the noise images, however, this was not fully true for the eidolon
transformations: As can be seen in sub-figure 3a, the sharpness decreased a
little bit compared to the original images—an unforseen result of the eidolon
toolbox. Next, we divided the 320 images into four chunks of 80 images each.
Such a chunk features five images per category and 20 images per difficulty
level. From each chunk, we created four blocks of 20 images each, resulting in
16 blocks that we later used in the experiment. To minimize predictability,
individual blocks of 20 images were not balanced for categories (i.e. a block
could contain a variable number of images from a given category). However,
each block was balanced for difficulty levels (five images per difficulty
level). To keep the participant’s motivation as high as possible, we pseudo-
randomized the order of image presentation within each block during the
experiment given the following constraint: The first and last three images of
a block had to be easy to recognise (difficulty level one or two).

#### Cue-conflict

In the cue-conflict experiment we used a subset of images as used in [23].
These 224$\times$224 pixel cue-conflict images are designed to have a conflict
between two cues, namely, object shape and object texture, for example, the
shape of a cat combined with the texture of elephant skin (see Figure 3). The
stimuli were created using the style transfer method [19], whereby the content
of an image (shape) is combined with the appearance of another image (texture)
using a DNN-based approach. From the 1280 cue-conflict images created by [23]
we sampled 240 images (15 per category) to use in this experiment. We included
160 original colour images (10 per category) as a baseline and to help keep
the task intuitive for the children (sampled from the 521-image subset of
16-class-ImageNet as described above). The whole sample of 400 images was
split into five chunks of 80 images each—32 original images (2 per category)
and 48 cue-conflict images (3 per category). As in the other two experiments,
we created four blocks (20 stimuli each) from each chunk, resulting in 20
blocks that we later used in the experiment. The selection of the images was
again not balanced regarding categories but for difficulty levels (i.e., each
block contained eight original and 12 cue-conflict images). Again, the order
of image presentation in the experiment was pseudo-random with the following
constraint: The first and last three images had to be original but not cue-
conflict images.

(a) Texture image

(b) Content image

(c) Texture-shape cue conflict

Figure 3: Stimuli generation for cue-conflict images. Initial images (a, b)
used for style transfer [19] in order to create texture-shape cue conflict
stimuli (c) employed in the cue-conflict experiment. Note that participants
never encountered texture or content images. They only encountered texture-
shape cue conflict images and original images that were similar to content
images but featured natural backgrounds. Figure adapted from [23].

### Participants

In total we collected 23,474 trials from a sample of 146 children and
adolescents (4–15 years) and nine adults. Participants were assigned to one of
three experiments: Noise (48 children and three adults, 60% female), Eidolon
(46 children and three adults, 45% female) and Cue-Conflict (52 children and
three adults, 45% female). Further descriptive information about the sample
and observations is presented in Table LABEL:tab:demo in the Appendix A.2. We
recruited children from 17 different schools in Bern (Switzerland). The adult
sample was recruited through private contacts. All participants reported
normal or corrected to normal vision, provided (parental) written consent, and
were tested in accordance with national and international norms that govern
research with human participants. The study was approved by the institutional
ethical review board of the University of Bern (no. 2020-08-00003). As a token
of appreciation for their participation, children received a book of their
choice. Only one child decided to cancel the study right after completing
practice trials.

### Apparatus

Programming and stimulus presentation were realized with Python (version
3.8.2) on a Lenovo Thinkpad T490s (Quad core CPU i5-8365U, Intel UHD 620
graphic card) running Linux Mint 20 Ulyana. We programmed the experiment’s
interface with the Psychopy library ([56]; version 2020.2.4). The 14” screen
(356 mm diagonal) had a spatial resolution of $1920\times 1200$ pixels at a
refresh rate of 120 Hz. Measured luminance of the display was 361.4 cd/m2 and
gamma set to 2.2. Images were presented at the center of the screen with a
size of $256\times 256$ pixels, corresponding, at a viewing distance of
approximately 60 cm, to $4\times 4$ degrees of visual angle.888This is only
true for the eidolon and noise experiment. Due to an unnoticed cropping error
image size in the cue-conflict experiment was $224\times 224$ pixels,
corresponding, at a viewing distance of approximately 60 cm, to only
$3.5\times 3.5$ degrees of visual angle. We do not think that this small
change in absolute size had any influence on the data or results we report.
Note that viewing distance varied somewhat between participants due to
children’s agitation. For the whole experiment the background color was set to
a gray value in the [0,1] range corresponding to the mean grayscale value of
all images in the dataset of the particular experiment (eidolon: 0.452, noise:
0.459, and cue-conflict: 0.478).999To evaluate the mean grayscale value,
images in the cue-conflict data set were converted to grayscale using
skimage.color.rgb2gray. All responses were recorded with a standard wireless
computer mouse.

### Models

In order to investigate the effect of dataset size on model robustness, we
selected four representative models from the modelvshuman Python-toolbox [22].
The models were chosen according to the following criteria: (1.) in terms of
training dataset size, they are separated by an approximate log unit each;
(2.) to a certain degree, they are all derivatives of ResNet building blocks
[32]; and (3.) within the class of models that satisfies the first two
constraints, each of them is the _very best performing model_ in terms of OOD
accuracy as evaluated on the modelvshuman benchmark—thus they are, as of now,
some of the most robust DNNs and therefore the strongest DNN competitors for
our human to DNN robustness comparison. According to these criteria, the
following four models were chosen:

  * $>1$M:

ResNeXt: a ResNeXt-101_32x8d model by [79] trained on 1.3M images;

  * $>10$M:

BiT-M: a BiT-M model by [38] based on a ResNetV2-152x2 trained on 14M images;

  * $>100$M:

SWSL: a SWSL model by [80] based on a ResNeXt-101_32x16d trained on 940M
images;

  * $>1,000$M:

SWAG: a SWAG model by [70] based on a RegNetY-128GF trained on 3.6B images.

Additionally, we decided to include one widely known DNN, VGG-19 by [69], for
comparison purposes since it is based on a very simple architecture and it has
been studied extensively in the past.

We used a single feed-forward pass with $224\times 224$ px RGB images except
for the SWAG model which requires $384\times 384$ px input. In this case, the
images were scaled up to $384\times 384$ px using PIL.Image.BICUBIC
interpolation. For grayscale images (noise and eidolon experiment) all three
channels were set to be equal to the grayscale image’s single channel.

## Results

Recent machine learning models have seen tremendous gains in object
recognition robustness, predominantly achieved through ever-increasing large-
scale datasets. Here we ask whether human robustness, too, may simply be the
result of extensive visual experience acquired during lifetime. If so, we
would expect human robustness to be low in young children, and to increase
over the years. To this end, we perform three comparisons between children of
different age groups vs. adults and vs. DNNs. We first investigate the
developmental trajectory of object recognition robustness (section
developmental trajectory). Having found essentially adult-level robustness
already in young children, we then perform a back-of-the-envelope calculation
to estimate bounds on the amount of “images” that children can possibly have
been exposed to (section back-of-the-envelope calculation). Finally, we
investigate whether object recognition _strategies_ change over the course of
development (section strategy development).

### Developmental trajectory: human object recognition robustness develops
early

Accuracy Normalized accuracy

(a) (b) Salt-and-pepper noise

(b)

(c) (a) Eidolon

(d)

Figure 4: Classification accuracy (top 1) and normalized classification
accuracy for different age groups and models. (a) shows the results for the
salt-and-pepper noise and (b) for the eidolon experiment. The dotted line
represents chance level performance of 6.25 % (100 % divided by the number of
categories, which was 16). Normalized accuracy shows the change in accuracy
relative to the initial accuracy at difficulty level zero of each age group or
DNN, respectively.

In order to assess the developmental trajectory of object recognition
robustness, we measure classification accuracy depending on the amount of
image degradation for two different experiments: salt-and-pepper noise and
eidolons (visualised in Figure 2). The results are shown in the left column of
Figure 4. In addition to classification accuracy, we plot normalized accuracy
with respect to the initial accuracy at difficulty level zero since this makes
it easier to disentangle the effects of initial accuracy and of a change in
robustness (right column in Figure 4).

First, looking at classification accuracy it can be seen that while the
adults’ performance is close to ceiling at difficulty level zero, there is a
moderate decrease in accuracy as the difficulty level increases (circles, dark
red). However, even at difficulty level three, adults still demonstrate a
fairly high accuracy, which is far above chance level. The robustness
trajectories for DNNs differ dramatically (shades of blue and violet): older
models trained on ImageNet ($>$1M images) are typically far below the human
level (VGG-19; ResNeXt), while modern models trained on large-scale datasets
($>$10, $>$100 or even $>$1,000M images) are sometimes even above the human
level, a finding consistent with [22] who reported that the model-to-human gap
in out-of-distribution distortion robustness has essentially closed. However,
the developmental trajectory of robustness during childhood and adolescence
has not been studied so far: Across both experiments (salt-and-pepper noise as
well as eidolons), overall performance increases as a function of age. The
biggest gain in performance is achieved between the groups of 4–6 year-olds
(circles,  light orange) and 7–9 year-olds (circles, darker orange). That
being said, across all age groups, there appears to be only a linear offset
when compared to adults (who have a similar slope): relative to their
performance level at zero noise or distortion, even 4–6 year-olds appear to
have acquired essentially adult-like robustness—i.e., their relative
(normalized) performance under noise is similar to that of adults (top right
panel) or very nearly so (bottom right panel).

As shown above, already 4–6 year-olds display remarkable levels of object
recognition robustness. However, their overall accuracies, even in the noise-
free case, are substantially lower than those of older children and adults.
Therefore, we ask: Is this difference either due to a general weaker ability
to recognise objects—which indicates a qualitative change in object processing
and robustness—or could it be due to a weak performance on a subset of
categories, which in turn would indicate only a quantitative change in terms
of the number of categories they have already acquired? In Figure 5(a), we
take a closer look at accuracies across different classes. We observe highly
non-uniform accuracies: for some classes like “airplane”, “car” etc., 4–6
year-olds have nearly adult-level accuracies. On the other hand, there are
also a number classes where young children perform substantially worse, such
as “clock” or “knive”. This overall pattern is confirmed when looking at
confusion matrices (Figure 5(b)), which shows that 4–6 year-olds maintain high
performance on a number of classes even for severe levels of noise (as
indicated by high accuracies (red-ish entries) on the
diagonal).101010Additional confusion matrices can be found in the Appendix
A.3. This may indicate that young children’s weaker overall performance is not
due to to a generally weaker ability to recognise objects but rather to weak
performance on a subset of categories. Even though 4–6 year-olds have not yet
acquired robust representations for the same number of categories as adults,
they appear almost adult-like regarding some age-appropriate categories they
have already acquired. This suggests that the change in robustness along the
developmental trajectory is rather quantitative (incremental) and not
qualitative in nature.

(a) Class-conditional accuracy difference (adults minus 4-6-year-olds)

(b) Confusion matrices

Figure 5: Classification accuracy as a function of different classes. Panel
(a) shows the difference ($Delta$) of class-wise accuracy between 4–6 year-
olds and adults on undistorted images (averaged over the salt-and-pepper noise
and eidolon experiment). For example while adults recognised 96.66% of all
undistorted clock images, 4–6 year-olds only recognised 36.36%
correctly—resulting in a $Delta$ of 60.30%. Panel (b) shows confusion matrices
for 4–6 year-olds and adults for undistorted images (Noise-level = 0.0) and
heavily distorted images (noise level = 0.35) in the salt-and-pepper noise
experiment. Rows show classification decision of observers and columns show
the ground truth label of the presented category. Transparency of single
squares within a matrix represent response probabilities (fully transparent =
0%, solid red = 100%). Entries along the negative diagonal represent correct
responses; entries which are off the negative diagonal indicate errors.

### Back-of-the-envelope calculation: human robustness doesn’t require seeing
billions of images during lifetime

So far we have seen that robust object recognition emerges early in
development and is largely in place by the age of five. After the age of nine,
OOD robustness does not seem to increase substantially. This indirectly
indicates that for humans—quite different than for DNNS—more “data” (or
experience) does not necessarily imply better robustness. As an attempt to
quantify this more directly, we estimate the number of “images” that young
children are exposed to during their lifetime and compare different age groups
with different models.

We estimated the amount of external visual input by calculating the total
number of fixations during lifetime for each age group. In order to do so we
made two assumptions: (a) accumulated wake time for any given age group and
(b) fixations per second for any given age group. Calculating the former is
straightforward: During development, wake time gradually increases as a
function of age. For example 0–1 year-olds are, on average, awake for 11.5
hours a day, whereas adults are awake for 16.5 hours [77]. We took the mean
age of each tested age group and calculated the total accumulated wake time
for this particular age in seconds. Estimating the number of fixations per
second is more difficult: Fixation duration varies to a great extent (100–2000
ms; e.g., see [82, 35]) and is heavily dependent on age and the given visual
task [18]. Thus, as a reference, we chose a task which is close to an everyday
natural setting (a picture inspection task) and for which developmental data
is available [18]. We then calculated fixations per second for each age group
based on the fixation duration measured for the mean age of this particular
age group. Because there is no available data for adults in the picture
inspection task, we estimated the fixation duration of adults by fitting a
linear regression line. Fixations per second calculated in this way ranged
from 2.56 for 4–6 year-olds to 3.42 for adults (mean adult fixation time of
292 msec; see Table Table 2 in the Appendix A.4 for details).

(a)

(b)

Figure 6: Mean OOD robustness for different age groups and models as a
function of (a) sample size and (b) dataset size on semi-logarithmic
coordinates. For human observers four different estimates of the amount of
visual input are given (indicated by different line types) which results in
four different trajectories. We suggest that for the comparison regarding
sample size the two most right trajectories, and regarding dataset size the
two most left trajectories should be considered (bold lines). Circle area for
models reflect number of parameters optimised during training.

However, given that for extended periods of time in everyday life visual input
does not change significantly, one may not want to count each fixation as a
new input image. Furthermore, using head-mounted cameras it has been shown
that frequency distributions of objects in toddlers’ input data are extremely
right skewed [73]: Toddlers have only experience with very few objects of a
certain category but see those objects (images) very often. It is not clear
whether this is just a non-optimal consequence of the natural learning
environment of humans or whether the existence of many similar views of the
same object plays an important role in object name learning and thus in
learning robust visual representations [10]. To account for these ambiguities,
we provide four different estimates regarding the amount of human visual
input. As a minimum we assume a new image every minute, whereas as maximum we
assume a new image every single fixation. Additionally, and less extreme, we
propose a lower (new image every eight seconds) and an upper (new image every
single second) estimate between the bounds set by every minute and every
fixation.111111Whereas we argue that the maximum—given by a new image every
single fixation—constitutes a naturally occurring constraint, the other three
estimates can be considered as “reasonable” guesses. Furthermore, there are
different choices for counting input images for DNNs. Should every encountered
image (_sample size_ $=$ training dataset size $\times$ number of epochs, i.e.
iterations over the entire training dataset) or the _dataset size_ (number of
images in training dataset) be considered as visual input? It is unlikely that
training on a smaller datasets for an increased number of epochs yields the
same increase in robustness as training on a larger datasets. In fact, the
evaluated models vary substantially regarding dataset size (1.28M to 3.6B) and
epochs (2 to 90). Thus, we decided to plot human data against both metrics,
sample size as well as dataset size (see Table 3 in the Appendix A.4 for
details on the calculation of input images for DNNs). Figure 6 shows the
comparison between different age groups and models regarding OOD robustness
and number of input images for DNNs’ sample size (Subfigure 6(a)) and dataset
size (Subfigure 6(b)). As a unified measurement of classification robustness
we calculated the mean classification accuracy over all moderately and heavily
distorted images (salt-and-pepper noise: noise level 0.2 and 0.35, eidolon:
reach level 8 and 16) for each age group and all models.

Overall, human object recognition robustness is more data-efficient compared
to DNN robustness, irrespective of the choice of metric. For example, focusing
on sample size, we find that the two least data-hungry models (ResNeXt and
VGG-19) have been exposed to about as much input as 4–6 year-olds (notably
only looking at the two highest of our image number estimates) but are 15–30%
less robust. The only model which is comparable to 13–15 year-olds in terms of
OOD robustness as a function of sample size is SWAG (0.642 vs. 0.659).
However, even when counting all fixations as input images—most likely an
overestimation of the human external visual input—SWAG needs about ten times
more data to achieve human-like OOD robustness (779M vs. 7.2B). Probably a
more plausible comparison is accomplished by looking at the two more moderate
estimates—a new image every single second (dashdotted line) or every eight
seconds (dashed line)—and comparing them with sample size or dataset size,
respectively. Regarding sample size we find that all three models achieving
high OOD robustness (BiT-M, SWSL, and SWAG) need substantially more data than
humans to do so. The same is true if we consider datset size, except for BiT-M
which aligns with the human OOD trajectory (similar OOD robustness of a 6–7
year-old and similar dataset size of a 6–7 year-old if every awake second is
equated with a new image).

It may be important to recall that except for VGG-19, all of the investigated
models were chosen since they were the _most robust_ ResNet-based models for a
given training dataset size according to the model-vs-human bechmark [22].
Thus these models represent some of the current best models in terms of data-
efficient robustness—comparisons with the many other DNNs would have resulted
in even larger discrepancies between humans and DNNs.

Looking only at the different DNNs we find that BiT-M achieves similar
robustness to SWSL with a much smaller dataset (14M vs. 940M). However, this
gap almost vanishes when looking at sample size. This indicates that the total
number of images exposed to during training (sample size) seems to matter more
in terms of OOD robustness than plain dataset size. This may be the case since
due to data augmentation, images are not exactly the same for every epoch. It
has been shown that common data augmentations (such as random crop with flip
and resize, colour distortion, and Gaussian blur) lead to higher OOD
robustness [59, 68, 48]. Regarding the number of parameters optimised during
training—the area of the circles in the figure—we do not find any direct link
to OOD robustness.

### Different strategies: big models aren’t like children, but children are
like small adults

In the sections above we have seen comparisons of overall accuracy and
robustness and how this is related to the amount of visual input. While
accuracy increases with age (i.e., older children successively categorise more
and more images correctly), it is still unclear whether children just
gradually acquire more categories, or whether they go through a more radical
change of perceptual strategy at some point (at least in terms of overall
behaviour, teenagers clearly change a lot). To this end we performed two
analyses aimed at understanding how object recognition _strategies_ change (if
at all) during childhood and adolescence. The first analysis is related to the
image cues used for object recognition (shape or texture), and the second
related to image-level errors (error consistency).

#### Texture-shape cue-conflict: no evidence of a strategy change

Figure 7: Shape vs. texture biases of different models and age groups. Box
plots show category-dependent distribution of shape/texture biases (shape
bias: high values, texture bias: low values). For example, 4–6 year-olds show
a shape bias of 0.88, meaning that of all correct responses they decided in
88% of cases based on shape- and in 12% of cases based on texture-cues. The
dotted line indicates the maximum possible shape bias (100% shape based
decisions). Shape vs. texture biases for individual categories are shown in
Figure 11 in the Appendix.

[23] and [3] have shown that adults and ImageNet-trained DNNs have a clear
discrepancy in object recognition strategy. While human adults base their
classification decisions on object shape, DNNs are much more prone to using
texture cues instead. In order to determine whether children are more similar
to adults or to DNNs in this regard, we evaluated performance on texture-shape
cue-conflict images. These images contain conflicting shape and texture
information (e.g., the shape of a cat combined with the texture of an
elephant; example stimuli shown in Figure 3). It may be worth pointing out
that there is no right or wrong answer in those cases—both the correct texture
category or the correct shape category is considered as a correct response.
Instead, we are interested in understanding whether decisions are consistent
with the shape or the texture category. The results are visualised in Figure
7. The exact fractions of shape vs. texture biases and the category wise
proportions of texture vs. shape decisions are shown in the Appendix A.5.
Those results clearly show that irrespective of age, humans have a very strong
shape bias (between approximately 0.88 and 0.97), and there is no evidence to
suggest any change of strategy during human development in this
regard.121212Note that we use the term “shape bias” for the tendency to use
object shape as the crucial feature to identify an object. However, in the
developmental literature the term “shape bias” is used to describe the
tendency of young children to use object shape as the crucial property to
generalize names to objects that were not seen before. Even models trained on
extremely large datasets, however, still don’t have a shape bias comparable to
humans. In other words, when it comes to using texture or using shape, big
models are not like children, but children are like small adults.

#### Error consistency: distorted input serves as a magnifying glass for
object recognition strategies

Figure 8: Distorted input serves as a magnifying glass for object recognition
strategies—irrespective of age, children make errors on the same noisy images
as adults; at the same time, models make errors on different images as humans.
The plot shows error consistency as measured by Cohen’s kappa ($\kappa$) for
different distortion levels split by different within- and between-group
comparisons (4–6, 7–9, adults, and DNNs) for the salt-and-pepper noise
experiment. $\kappa=0$ indicates chance level consistency (i.e., both systems
are using independently different strategies), $\kappa>0$ means consistency
above chance level (i.e., both systems are using similar strategies) and
$\kappa<0$ means inconsistency beyond chance level (i.e., both systems use
inverse strategies). Plots are horizontally divided in three subsection*s:
Upper subsection* (within-group comparisons), middle subsection* (between-
group comparisons humans only), and lower subsection* (between-group
comparison humans and DNNs). Colored dots represent error consistency between
two single observers (one from each group featured in the comparison). Box
plots represent the distribution of error consistencies from observers of the
two given groups. Boxes indicate the interquartile range ($IQR$) from the
first ($Q1$) to the third quartile ($Q3$). Whiskers represent the range from
$Q1-IQR$ to $Q3+IQR$. While vertical black markers indicate distribution
medians, faint vertical green markers indicate distribution means.

In the previous section, we have seen that there does not appear to be a
radical change of perceptual strategy during childhood when it comes to using
texture or shape cues to identify object categories. Nonetheless, all of the
previously analysed measures are fairly coarse. Both accuracy and shape bias
analyses could potentially overlook more subtle changes of strategy—if, for
example, adults struggle with certain images that children find easy, and vice
versa, then we would end up with very similar aggregated decisions (as
measured by accuracy) despite highly different image-level decisions.
Therefore, we here looked at image-level decision patterns through the lens of
error consistency [21]. Error consistency is a quantitative analysis for
measuring whether two decision-makers systematically make errors on the exact
same stimuli. Error consistency between two individual observers is calculated
in three steps: First, observed error overlap is calculated by dividing the
total number of equal responses—in which both observers either classified an
image correctly or incorrectly—by the total number of images both observers
have evaluated. Second, since even two completely independent observers with
high accuracy will necessarily agree on many trials by chance alone, error
overlap expected by chance is calculated (based on the assumption of binomial
observers). Third, the empirically observed error overlap is compared against
the error overlap expected by chance via Cohen’s $\kappa$, which quantifies
the agreement of two observers considering the possibility of the agreement
occurring by chance.

Here, we compared four different decision-makers (4–6 year-olds, 7–9 year-
olds, adults and DNNs) using error consistency. We performed all possible
within-group (e.g., 4–6 year-olds with 4–6 year-olds) and between-group (e.g.,
4–6 year-olds and DNNs) comparisons.131313Since not all children responded to
all stimuli (see method section), error consistency sometimes was only
calculated on a subset of stimuli. In those cases, we set a minimum constraint
of 20 individual stimuli, which had to be evaluated by both observers.
Otherwise error consistency was not calculated. In Figure 8 error consistency
is visualised for all difficulty levels of the salt-and-pepper-noise
experiment split by different within- and between-group comparisons; the
(similar) error consistency plot for the eidolon experiment can be found in
Figure 12 in the Appendix A.6.

It may be worth pointing out the central patterns: First of all, in line with
[21, 22] human-to-human consistency is generally high, and while it is highest
within the same age group it is also well beyond chance in all between-age-
group comparisons. Second, human-to-human error consistency _increases_ as the
tasks becomes harder (i.e. with increasing noise level). Third, regarding
comparisons involving DNN models, a very different pattern emerged. Model-to-
model consistency starts at chance level and does not increase substantially
beyond chance as a function of noise level (highest at noise level 0.1; mean
$=$ 0.18). Furthermore, regardless of age, model-to-human consistency is at
chance level for noise level zero. And also for distorted images, model-to-
human consistency (mean over all model-to-human comparisons for distorted
images $=$ 0.127) is far below human-to-human consistency (mean over all
human-to-human between-age-group comparisons for distorted images $=$ 0.361).
Thus, it almost appears as though distorted input serves as a magnifying glass
for object recognition strategies—irrespective of age, children make errors on
the same noisy images as adults; at the same time, models make errors on
different images as humans.

## Discussion

We investigated the developmental trajectory of core object recognition
robustness to asses whether human OOD robustness is a result of training
(experience) on a very large amount of visual input–similar as in currently
OOD-robust DNNs. To this end we collected 23,474 psychophysical trials from
146 children and nine adults and compared their OOD performance against five
DNNs trained on datasets of different sizes. To our knowledge this is the
first study to directly compare children, adolescents, and different DNNs in a
psychophysical core object recognition task using an experimental protocol
also employed for adults and in machine learning.141414There is one
unpublished investigation comparing children and DNNs that was presented at
the 20th Annual Meeting of the Vision Sciences Society [2]. They find that
young children (4–5 year-olds) display remarkable object recognition abilities
and outperform a VGG-19 and a ResNet-101 model on perturbed images. Thus,
their findings fit our results regarding classification accuracy. However, the
current study extends their findings by covering a larger age range, using
naturalistic images with parameterized distortions and more response
categories. Furthermore, we provide a range of additional analysis such as
accuracy delta between children and adults, confusion matrices, human-model
comparison regarding OOD robustness and input images, texture-shape cue-
conflict analysis, and error consistency. Additionally, we compare human data
with some of the most powerful models to date.

We find that, first, human OOD robustness develops very early and is
essentially in place by the age of five. While there may be a small increase
in robustness as function of age, by the time children reach middle childhood
they have approximately obtained adult-level robustness (see Figure 4, right
column, normalized accuracy). This finding fits with neuroscience data showing
that brain maturation relevant for object recognition reaches adult-level at
this point of development [26, 67, 11, 6]. Furthermore, we find that young
children did not perform uniformly weaker on all categories (see Figure 5),
indicating that the observed overall improvement in accuracy is due to
acquisition of new categories rather than to a global change in representation
and information processing (see Figure 4, left column, accuracy). This allows
even 4–6 year-olds to outperform DNNs trained on standard ImageNet. Second, by
estimating the visual input for human observers at different points during
development, we find that—in contrast to current DNNs—human OOD robubstness
requires relatively little external visual input (see Figure 6). This
indicates that in humans, OOD robustness may not be achieved solely by sheer
quantity of training data alone. Third, the former two findings are supported
by our observations that all tested age groups employ similar object
recognition strategies as indicated by a similar shape-bias (see Figure 7) and
high error consistency across different age groups and difficulty levels (see
Figure 8).

Taken together, these findings suggest that for both humans and DNNs, robust
visual object recognition is possible, but achieved by different means. While
human robustness seems fairly data-efficient, machine robustness, at least
today, is data-hungry.151515Assuming that (a) from a evolutionary point of
view robustness is a crucial feature of our visual system (e.g., food
detection and predator avoidance under difficult conditions such as in the
dark or during snow, rain or fog), and that (b) it is not feasible to gather
enough visual input during development (even when counting all fixations as
new images humans are not gathering as much images as robust DNNs are trained
on) to achieve robustness by the same means as modern DNNs (large-scale
training), there is a high selection pressure for highly data-efficient
learning. In other words, from an evolutionary point of view, our back-of-the-
envelope calculation shows that human data-efficient robustness should not be
surprising. In other words, there are two different systems with the same
property which came about in different ways—a phenomenon which in biology is
called _convergence_ [47]. As an example, consider the ability to fly, which
emerged at least three different times during evolution: in mammals (e.g.,
bats), in sauropsida (e.g., birds) and in insects (e.g., dragonflies). [45]
recently argued that considering DNNs and humans as different visual species,
and adopting an approach of comparative biology by focusing on the differences
rather than the similarities, is a promising way to understand visual object
recognition. Accordingly, in what follows, we elaborate on possible
differences between human and DNN vision, which might explain the difference
in data-efficiency to solve robust object recognition.161616This elaboration
is not thought to be exhaustive, but rather to address aspects in which the
present study is limited and which we suggest are promising for future
research.

First, there might be a difference in _data-quality_ , which allows humans to
form more robust robust representation from limited data. While human data is
continuous and egocentric [5], this is not the case for standard image
databases. Recent advances in data collection using head-mounted cameras allow
for developmentally realistic first-person video datasets [75, 17, 34, 4].
While studies have shown that models trained with such biologically plausible
datastreams form powerful, high-level representations [55] and achieve good
neural predictivity on different areas across the ventral visual stream [84],
others find that in order to match human performance in object recognition
tasks models would need millions of years of natural visual experience [54]. A
further difference regarding the data-quality of humans vs. machines lies in
the modality of the data; while model input is most often unimodal, human
input is multi-modal. It has been shown that the availability of information
across different sensory systems is linked to the robustness of human
perception (e.g., see [16, 25, 78, 76]). Regarding vision, [7] famously argued
that “touch educates vision”. Affirmatively, a recent study demonstrated that
neural networks trained in a visual-haptic environment (compared to networks
trained on visual data only) form representation that are less sensitive to
identity-preserving transformation such as variations in view-point and
orientation [33]. Taken together, the continuous, egocentric and multi-modal
nature of human training data might explain why current DNNs are not as data-
efficient as humans. Accordingly, a limitation of our study is the lack of
systematic variation in the quality of training data. Perhaps providing DNNs
with high quality training data even current DNN architectures could achieve
OOD robustness with as little data as humans. Thus, future research should
systematically acquire multi-modal datasets of varying quality and evaluate
the trained models on OOD datasets.

Second, humans may rely on different _inductive biases_ —i.e. constraints or
assumption prior to training (learning)—allowing for more data-efficient
learning. Especially intuitive theories, e.g., intuitive physics, theory of
mind or implicit knowledge about the causal structure of the world, might lead
to efficient processing of the available data (e.g., see [40, 46] or [27]) for
the role of inductive biases in OOD robustness in general). For example, once
learned that the representation of a certain object does change based on
certain physical conditions (such as lighting or distance), intuitively
knowing that all objects obey the laws of physics and behave in a causally
predictable way, should facilitate object recognition for other objects which
are affected in similar ways. Human inductive biases are the product of
million years of evolution and are built in right from the start (birth). Thus
in order to further disentangle the influence of evolution vs. lifetime
experience it would be interesting to investigate the developmental trajectory
during infancy. In this regard, the present study is limited, however, because
the employed experimental set-up does not allow to test children younger than
four years of age.

Third, an exciting possibility is that humans enlarge their initial dataset
provided through external input by creatively using already encountered
instances to create new instances during _offline states_ —a concept similar
to what in reinforcement learning is called _experience replay_ (e.g., see
[53, 42, 43, 51]). The idea is that during imagination and dreaming, stored
memories are combined to generate new training data (e.g., see [12]). Thus,
additionally to the external input provided by the sensory system, an internal
generative model provides the visual system with additional training data.
Putting this into context, one could argue that humans and DNNs might be
similar to the extent that they both rely on large-scale datasets to solve
object recognition robustness, but are, however, very different in how they
attain such large datasets: While DNNs are entirely dependent on external
input, humans are somewhat self-sufficient by producing their own training
data from limited external input. Assuming that this hypothesis about the
emergence of human OOD robustness is true, the question is whether learning
during offline states could make DNNs as data-efficient as humans. In the
present study, we only compare how much _external_ input is required to
achieve high OOD robustness. Our results are thus not suited to answer this
question. However, recently, [12] proposed a model based on generative
adversarial networks (GANs), which captures the idea of learning offline
states by distinguishing between wake-states where external input is
processed, and offline states where the model is trained by a generative model
either by reconstructing perturbed images based on latent representations
(similar to simple memory recall as during non-REM sleep) or by generating new
visual sensory input based on convex combinations of multiple randomly chosen
stored latent representations (similar to the rearranging of stored episodic
patterns during REM sleep). Experiments with these models show that
introducing such offline states increases robustness and the near separability
of latent representations. Further evidence for the benefit of learning during
offline states comes from world-model-based reinforcement learning. It has
been shown that reinforcement learning agents are able to solve different task
only being trained in a latent space which could be conceptually associated
with the model’s dreams, imagination or hallucinations (e.g., see [83, 31,
30]).

The three above described differences between humans and DNNs might explain
the difference in data-efficiency found in the present study. However, they
are arguably only a small subset of all differences which might account for
the differences in data-efficiency. What is clear, however, is that object
recognition robustness is not only solvable by a single approach. In
evolution, there are often many paths to the same feature. Why a certain path
was taken by a given system can only be understood by looking at the
environmental constraints present during phylogenesis. Not being biological
systems, DNNs were not exposed to similar evolutionary pressure as humans and
thus data-efficiency seems not to be as important as for humans. Accordingly,
it comes as no surprise that DNNs are less data-efficient than humans.
However, the data-efficiency of humans seems to be a crucial feature of the
human visual system. Thus, in order to truly understand the robustness of
human vision, we need not only to model the behaviour (OOD robustness) but
also the means by which it is achieved.

## Conclusion

Recent improvements in OOD robustness in machine learning are primarily driven
by ever-increasing large datasets, with models trained on several billions of
images. However, humans achieve remarkable OOD robustness at a very early
point in life. Our investigations and calculations suggest that children learn
a lot from relatively little data. Children benefit from experience, but they
do not require the same amount of experience as state-of-the-art neural
network models, indicating that they are achieving OOD robustness by different
means as DNNs. It seems to be the case that even the entire time children have
already lived is not long enough to gather as much input as current data-rich
DNNs. The human visual system appears highly data-efficient, which may be an
evolutionary advantage. It remains an open question what the sources of this
data-efficiency are: Is it due to the accumulation of high-quality data alone?
High-quality data combined with suitable inductive biases and mechanisms to
“upcycle” data in order to enlarge the training dataset during offline states
such as dreaming? We believe that comparing children with adults and DNNs is a
fruitful approach to understand data-efficiency in humans and to perhaps
inspire a healthy diet for current data-hungry models, without sacrificing
their robustness.

## Acknowledgements

We would like to thank the members of the Wichmann-lab for their support and
insightful discussions. Special thanks goes to Uli Wannek for excellent
technical advice and Silke Gramer for extremely kind and patient
administrative support. Additionally, we would like to express our gratitude
to Gert Westermann and Hannes Rakoczy for their advice and help with designing
the children’s study and to all children and teachers who participated in our
study. Felix Wichmann is a member of the Machine Learning Cluster of
Excellence, funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) under Germany’s Excellence Strategy – EXC number 2064/1 –
Project number 390727645. Some preliminary parts of this work have been
presented as an oral at the Annual Meeting of the Vision Sciences Society 2021
and at the 3rd Workshop on Shared Visual Representations in Human and Machine
Intelligence (SVRHM 2021) of the Neural Information Processing Systems
(NeurIPS) conference.

## Author contributions

The project was initiated and lead by L.S.H. All authors planed and designed
the experiments and data analysis. L.S.H. collected the psychophysical data,
evaluated the models and analysed the data. The first draft was written by
L.S.H. with significant input from R.G. and F.A.W. All authors contributed to
the final version of the manuscript.

## Competing interests

The authors declare no competing interests.

## Data and Code

All code and data are available from this repository:
https://github.com/wichmann-lab/robustness-development

## Appendix

In this Appendix we provide further experimental details as well as
supplementary plots and details about the data analysis. Appendix A.1 provides
some exemplary screenshots of the visual details of the user interface.
Details and characteristics of the tested sample of children and adults are
reported in Appendix A.2. A full set of confusion matrices for 4–6 year-olds
and adults for both experiments can be found in Appendix A.3. Supplementary
details regarding the estimation of human input images and dataset and sample
size of evaluated models are given in Appendix A.4. Further, we provide
additional details about the results of the cue-conflict experiment in
Appendix A.5. Finally, the error consistency plot of the eidolon experiment
can be found in Appendix A.6.

### A.1 Gamification

(a) Character selection at the beginning of each session.

(b) Response screen with gamified progress-bar.

(c) Score display with star- and coin-scores and emblem.

Figure 9: Screenshots at different time-points during the experiment.

### A.2 Demographic characteristics of participants and observations

Table 1: Descriptive statistics of participants and observations split by experiments. Sample size and quantity of observations (n), as well as mean (M) and standard deviation (SD) for age and trials within observer groups. Gender distribution (♂/♀) is given in percentages. Note that for adults, trial M equals the total number of trials in the respective experiment and trial SD is zero because they completed all trials of that particular experiment. |  |  | Age within group |  |  | Trials
---|---|---|---|---|---|---
Age group | Experiment | n | M | SD | ♂/♀ |  | n | M | SD
4–6 year-olds | Noise | 15 | 5.13 | 0.64 | 33/67 |  | 1240 | 62.66 | 54.96
| Eidolon | 11 | 5.27 | 0.65 | 64/36 |  | 1234 | 102.83 | 92.06
| Cue-conflict | 21 | 5.29 | 0.64 | 62/38 |  | 1292 | 61.52 | 36.12
7–9 year-olds | Noise | 9 | 8.11 | 0.78 | 47/53 |  | 1840 | 204.44 | 112.60
| Eidolon | 14 | 8.36 | 0.93 | 43/57 |  | 1708 | 127.14 | 61.57
| Cue-conflict | 11 | 8.09 | 0.94 | 55/45 |  | 2020 | 183.63 | 118.60
10–12 years-olds | Noise | 15 | 11 | 0.85 | 47/53 |  | 1880 | 125.33 | 71.9
| Eidolon | 14 | 11.14 | 0.77 | 43/57 |  | 1820 | 130.00 | 72.64
| Cue-conflict | 12 | 11.08 | 0.90 | 50/50 |  | 2080 | 173.33 | 126.01
13–15 years-olds | Noise | 9 | 14.22 | 0.97 | 44/56 |  | 1280 | 142.22 | 82.12
| Eidolon | 7 | 14.00 | 1.00 | 71/29 |  | 1700 | 242.86 | 76.10
| Cue-conflict | 8 | 14.38 | 0.74 | 50/50 |  | 2260 | 282.50 | 107.14
Adults | Noise | 3 | 28.33 | 5.51 | 33/67 |  | 960 | 320.00 | 0.00
| Eidolon | 3 | 26.00 | 2.65 | 67/33 |  | 960 | 320.00 | 0.00
| Cue-conflict | 3 | 29.33 | 2.89 | 33/67 |  | 1200 | 400.00 | 0.00

### A.3 Confusion matrices

(a) Salt-and-pepper noise

(b) Eidolon

Figure 10: Confusion matrices for 4–6 year-olds and adults across all
difficulty levels in the salt-and-pepper noise (a) and the eidolon (b)
experiment. Rows show classification decision of observers and DNNs and
columns show the ground truth label of the presented category. Transparency of
single squares within a matrix represent response probabilities (fully
transparent = 0%, solid red = 100%). Entries along the negative diagonal
represent correct responses; entries which are off the negative diagonal
indicate errors.

### A.4 Back-of-the-envelope calculation

Table 2: Details regarding the estimation of the number of input images for human observers. The estimate of accumulated Wake time (in millions of seconds) is based on [77]. Fixation Duration (in milliseconds) refers to the fixation duration in a picture inspection task [18] and is used to calculate Fixations per second. Because there was no available data regarding the fixation duration of adults in this task we assumed a linear relationship between age and fixation duration and used the children’s data to fit a simple regression model to estimate the fixation duration of adults ($\hat{y}=-4.33X+413.66$). Plugging in the mean age of adults (M = 28) yields a predicted fixation duration of 292.42 for adults. Min (in millions) refers to the minimal assumed number of input images—a new image every minute. Max (in millions) refers to the maximal possible number of input images—a new image every single fixation. Lower and Upper (in millions) refers to a—what we believe—reasonable estimate of the lower and upper bound of input images encountered during lifetime. The lower bound is calculated by scaling the total number of fixations by 24 (new images approximately every eight seconds) and the upper bound by 3 (new images approximately every single seconds). E.g., at the age of five a child has been awake for approximately 99.41 million seconds; it has made about 254.5 million fixations during this time (99.41 $\times$ 2.56). Based on these numbers we estimate that a five year old child has most likely not seen less than 10.6 and not more than 84.83 million images (total number of fixations during lifetime either scaled down by a factor of 24 or 3). Age group |  M age | Wake time | Fixation duration | Fixations per second | Min | Lower | Upper | Max
---|---|---|---|---|---|---|---|---
4–6 year-olds | 5.13 | 99.41 | 390.00 | 2.56 | 4.24 | 10.60 | 84.83 | 254.49
7–9 year-olds | 8.11 | 154.16 | 380.00 | 2.63 | 6.76 | 16.90 | 135.15 | 405.44
10–12 year-olds | 11.00 | 211.54 | 370.00 | 2.70 | 9.52 | 23.80 | 190.39 | 571.16
13–15 year-olds | 14.22 | 272.42 | 350.00 | 2.86 | 12.99 | 32.43 | 259.43 | 779.12
Adults | 28.33 | 591.71 | 292.42 | 3.42 | 33.73 | 84.32 | 674.55 | 2023.65
Table 3: Model details regarding all employed models. _Dataset size_ refers to the number of images in the training set and is plotted on the x-axis in Subfigure 6(b). _Sample size_ is equal to the number of total encountered images during training (dataset size $\times$ epochs) and is plotted on the x-axis in Subfigure 6(a). *Note that the SWSL model was trained one epoch on 940M images and then 30 epochs on standard ImageNet (1.28M images)—thus sample size equals $940M+30\times 1.28M$. _Parameters_ refer to the total number of parameters optimised during training and is represented by the area of the circles throughout Figure 6. Model | Dataset size | Epochs | Sample size | Parameters
---|---|---|---|---
VGG-19 | 1.28M | 74 | 94.72M | 144.00M
ResNeXt | 1.28M | 90 | 115.20M | 44.00M
BiT-M | 14.00M | 30 | 420.00M | 928.00M
SWSL | 940.00M | 1+30* | 978.40M | 829.00M
SWAG | 3.60B | 2 | 7.2B | 644.80M

### A.5 Shape-bias

Table 4: Exact fractions of texture vs. shape decisions of different age groups and DNNs in percent. Observer | Shape bias | Texture bias
---|---|---
4–6 year-olds | 87.55 | 12.45
7–9 year-olds | 90.86 | 9.14
10–12 year-olds | 93.52 | 6.48
13–15 year-olds | 93.18 | 6.82
Adults | 96.72 | 3.28
VGG-19 ($>$1M) | 7.96 | 92.04
ResNeXt ($>$1M) | 25.52 | 74.48
BiT-M ($>$10M) | 57.24 | 42.76
SWSL ($>$100M) | 55.88 | 44.12
SWAG ($>$1,000M) | 45.00 | 65.00
Figure 11: Category wise proportions of texture vs. shape decisions for
different age groups (4–6, 7–9, 10–12, 13–15, and Adults) and DNNs (VGG-19,
ResNext, BiT-M, SWSL, and SWAG). Only responses that corresponded to either
the correct texture or correct shape category are taken into account. Vertical
lines indicate averages over all categories.

### A.6 Error consistency

Figure 12: Error consistency as measured by Cohen’s kappa ($\kappa$) for
different distortion levels split by different within- and between-group
comparisons (4–6, 7–9, adults, and DNNs) for the eidolon experiment.
$\kappa=0$ indicates chance level consistency (i.e., both systems are using
independently different strategies), $\kappa>0$ means consistency above chance
level (i.e., both systems are using similar strategies) and $\kappa<0$ means
inconsistency beyond chance level (i.e., both systems use inverse strategies).
Grid line at $\kappa=0$ is highlighted. Plots are horizontally divided in
three subsection*s: Upper subsection* (within-group comparisons), middle
subsection* (between-group comparisons humans only), and lower subsection*
(between-group comparison humans and DNNs). Colored dots represent error
consistency between two single observers (one from each group featured in the
comparison). Box plots represent the distribution of error consistencies from
observers of the two given groups. Boxes indicate the interquartile range
($IQR$) from the first ($Q1$) to the third quartile ($Q3$). While vertical
black markers indicate distribution medians, vertical green markers indicate
distribution means. Whiskers represent the range from $Q1-IQR$ to $Q3+IQR$.
Compared groups are indicated by the color of dots and boxes, respectively.

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