Testing Deep Neural Networks on the
Nicola Messina, Giuseppe Amato, Fabio Carrara, Fabrizio Falchi, Claudio Gennaro
Institute of Information Science and Technologies
National Research Council
Abstract—Developing abstract reasoning abilities in neural
networks is an important goal towards the achievement of
human-like performances on many tasks. As of now, some works
have tackled this problem, developing ad-hoc architectures and
reaching overall good generalization performances. In this work
we try to understand to what extent state-of-the-art convolutional
neural networks for image classiﬁcation are able to deal with a
challenging abstract problem, the so-called same-different task.
This problem consists in understanding if two random shapes
inside the same image are the same or not. A recent work
demonstrated that simple convolutional neural networks are
almost unable to solve this problem. We extend their work,
showing that ResNet-inspired architectures are able to learn,
while VGG cannot converge. In light of this, we suppose that
residual connections have some important role in the learning
process, while the depth of the network seems not so relevant.
In addition, we carry out some targeted tests on the converged
architectures to ﬁgure out to what extent they are able to
generalize to never seen patterns. However, further investigation
is needed in order to understand what are the architectural
peculiarities and limits as far as abstract reasoning is concerned.
Index Terms—AI, Deep Learning, Abstract Reasoning, Rela-
tional Reasoning, Convolutional Neural Networks
Artiﬁcial intelligence and in particular deep neural networks
have recently shown impressive results in key domains such
as vision, language, control, and decision-making. In partic-
ular, with the work carried out on the ImageNet challenge,
Krizhevsky et al.  demonstrated major capabilities of deep
neural networks in the ﬁeld of image processing. Deep learning
architectures, and in particular Convolutional Neural Networks
(CNNs) , constitute now de-facto standard approaches to
image processing and understanding.
Recently, deep convolutional architectures have deﬁned the
state-of-the-art on multiple computer vision tasks, such as
image classiﬁcation , , , object detection and seg-
mentation , , multimedia and cross-media information
retrieval , , and detection of adversarial examples .
Despite their success, there are still many open problems
with current deep architectures. In fact, it is known that they
cannot generalize well to unseen objects and they lack human-
like reasoning capabilities.
Humans, as well as animals, are able to abstract visual
perception in order to recognize some shape patterns never
seen before. Unlike humans, convolutional networks are able
to learn very precise representations, usually very difﬁcult to
generalize to abstract concepts.
For this reason, in this work, we concentrate on a very
speciﬁc task designed to test abstract reasoning capabilities of
neural networks. This task is called same-different and consists
in predicting if two shapes inside the same image are the same
or not. It is a challenging task for convolutional architectures
since it is required not to learn speciﬁc shape patterns in order
to solve the problem.
A clear understanding of the same-different concept, and the
ability to actuate complex relational reasoning are considered
key features in many tasks. For example, these concepts may
have a great impact in classiﬁcation problems, in the research
of particular patterns in cultural heritage, and in the detection
of patterns deﬁning aesthetic beauty in images and even music.
In fact, the world is often perceived by humans as a set of
recurrent structures composited together, such as the human
eyes in a face or the repeating chorus in a song.
In this work we employ a carefully designed dataset, called
SVRT , containing multiple visual problems pertaining to
the same-different category. We study the behavior of modern
standard visual deep-learning architectures by training and
validating them on the SVRT dataset.
More in detail, we extend the study carried out by Kim
et al. , by testing a variety of state-of-the-art deep con-
volutional architectures, originally designed for image classi-
ﬁcation, on some challenging same-different problems in the
SVRT dataset. In particular, we show that residual networks
are able to correctly solve the problem, with a remarkable
We also discovered that different image interpolation al-
gorithms used during the data augmentation process have
an important effect on the ﬁnal performance. This ﬁnding
remarks the overall vulnerability of neural networks to subtle
perturbations of the input image.
Our contribution is two-fold: ﬁrst, we train state-of-the-
art deep image classiﬁcation networks on the same-different
task, treating it as a binary classiﬁcation problem; second, we
perform an extensive study upon the generalization capabilities
of the probed networks, in order to understand to what978-1-7281-4673-7/19/$31.00 ©2019 IEEE
extent current models are able to deal with higher-level visual
The rest of the paper is organized as follows: in Section
II we review some of the related work concerning abstract
reasoning capabilities of deep neural networks; in Section III
we go into details with the SVRT dataset and we recall the
models that will be probed against the same-different problem;
in Section IV we will present our experimental setup and we
will discuss the obtained results; ﬁnally, in Section V we will
remark on the importance of these studies and we will propose
future directions for this work.
II. RE LATE D WOR K
It has been proven that deep neural networks can obtain
remarkable performance on different computer vision ﬁelds.
However, relatively few works have tackled the cognitive and
abstract reasoning capabilities of state-of-the-art deep neural
Recently, the introduction of on-purpose generated bench-
marks such as CLEVR and Sort-of-CLEVR  has paved
the way towards ﬁne-grained studies on relational capabilities
of neural networks. In particular,  developed a relational
reasoning module able to solve the CLEVR visual-question-
answering task, by augmenting a standard convolutional net-
work with a reasoning module able to process couples of
objects. A slight variation of this network, the 2S-RN ,
has been used for relational content-based image retrieval (R-
CBIR), in order to extract relationship-aware visual features
for indexing purposes.
Transparency and explainability have been considered key
objectives for understanding what kind of reasoning neural net-
works are internally performing. To this aim, on the CLEVR
dataset,  used explicit module composition in order to
build an explicit reasoning pipeline, while  proposed a set
of primitives which, when composed, manifest as a model ca-
pable of performing complex reasoning tasks in an explicitly-
interpretable manner. In particular,  reached more than
99% accuracy on the CLEVR test set.
Other than CLEVR, other difﬁcult tasks, such as Raven’s
Progressive Matrices (RPM), have been proposed to test in
great detail, and under fully-controlled environments, reason-
ing capabilities of a given architecture.
In particular,  worked on RPMs and tried to establish
a semantic link between vision and reasoning by providing
structured representation. Similarly,  used an on-purpose
created dataset similar to RPM, called Procedurally Generated
Matrices (PGM). They demonstrated that popular models such
as ResNets perform poorly on this benchmark, and they
presented a novel architecture demonstrating quite effective
reasoning capabilities. Differently from , our work con-
centrates on a very simple yet challenging problem, the same-
The work by  introduced a synthetic dataset composed
of sequences of 2D images in order to test memorization
capabilities of neural networks.
 introduced SVRT, a simple dataset composed of 2D
shapes in order to test comparison and relational capabilities
of neural networks.  ﬁrst showed that problems involv-
ing comparisons between SVRT shapes were difﬁcult for
convolutional architectures like LeNet and GoogLeNet .
By contrast, instead, the traditional boosting method used by
 was able to reach very good results even on comparison
Even , in their recent work, found that the same-different
problem strains simple feed-forward convolutional networks.
In this paper we extend their work, giving some insights about
the behavior of very-deep convolutional networks on the same-
III. MET HO D
This work takes into consideration state-of-the-art deep
convolutional neural networks originally developed for image
classiﬁcation tasks. Our aim consists in studying their perfor-
mance when dealing with higher-level abstraction problems.
First of all, we give some insights into the SVRT bench-
mark; then, we will discuss the architectures that we will
employ to tackle this problem.
A. SVRT Dataset
SVRT  is an extensive benchmark designed to test
abstract reasoning capabilities of machine learning algorithms.
SVRT requires more than trivial local descriptors in order to
be solved correctly. It consists of simple 2D images containing
simple closed curves. It is clear that brute-force memorization
cannot solve the task since the shape of curves is always
SVRT collects 23 different sub-problems, that can be further
divided into two clusters: problems related to the spatial
arrangement of shapes, and problems regarding comparisons
between shapes. The latter set of sub-problems pertain to
the same-different challenge, and this is the set that we are
Kim et al.  probed simple CNNs upon all the problems
in the SVRT dataset, and they found some of them particularly
straining for their simple setup. In particular, following the
ﬁndings by Kim et al., problems 1, 5, 20, 21, are among the
most difﬁcult to solve for a convolutional neural network.
In particular, these problems pose the following challenges:
•Problem 1 (P.1): Detecting the very same shapes, ran-
domly placed in the image, but having the same rotation
•Problem 5 (P.5): Detecting two couples of identical
shapes, randomly placed in the image. The two images
inside every couple have the same rotation and scale.
•Problem 20 (P.20): Detecting the same shape, translated
and ﬂipped along a randomly chosen axis.
•Problem 21 (P.21): Detecting the same shape, randomly
translated, rotated and scaled.
All the images from the proposed problems contain two
shapes except problem 5, where images contain two couples
#1 #5 #20 #21
Fig. 1: Positive and negative examples from the four considered SVRT problems.
of shapes. Figure 1 shows some positive and negative examples
from each one of the above-listed problems.
In none of these benchmarks are shapes overlapping. They
are always well separated. Despite being a quite straightfor-
ward dataset, built of simple shapes and with no color infor-
mation, SVRT can help to highlight some intrinsic limitations
of current neural network models.
In this work we take into consideration the following state-
of-the-art architectures for image classiﬁcation: AlexNet ;
VGG19 ; three variants of the Resnet , in order of
increasing complexity ResNet-18, ResNet-34 and ResNet-101;
a recently introduced biologically inspired network called
CorNet-S , and its simpler version, Cornet-Z, a simple
feed-forward convolutional network used as baseline.
AlexNet and CorNet-Z are intended to be our baselines.
In fact, they are straightforward convolutional networks, with
relative few layers with respect to VGG and ResNets. In
particular, CorNet-Z is a lightweight version of the AlexNet.
It consists of only four convolutional layers, with ReLU
activations and MaxPooling, with a single fully-connected
layer as a classiﬁer, outputting probabilities for the two target
VGG19 still contains a simple convolutional architecture
comparable with the AlexNet structure, but it is signiﬁcantly
deeper. ResNets, on the other hand, introduce residual connec-
tions. These skip connections force the architecture to learn
incremental differences in the stored representations, reﬁning
the information multiple times until it can be used for the
Following the work by Kar et al. , it seems that ResNets
can be considered, from a functional point of view, biologi-
cally inspired networks. In fact, they continuously reﬁne the
information coming from pixels, just like the visual cortex
processes the information ﬂow coming from the eyes. In
particular,  found some experimental evidence on primates
brain claiming that visual cortex could be comprised of
recurrent connections. In light of this, they developed CorNet-
S . CorNet-S is composed of four blocks, mimicking
different brain cortical areas involved with vision; each one of
these four blocks contains a recurrent connection together with
a skip connection, taking inspiration from ResNets. Basically,
ResNets are unrolled versions of CorNet-S. Compared to
ResNet101, that has a comparable number of weights with
CorNet-S, this model is also lighter to train since, differently
from ResNets, recurrent connections make most of neurons
weights shared among different timesteps.
IV. EXP ER IM EN TAL SETUP
We train the networks discussed in Section III on all the four
same-different problems from the SVRT dataset. Concerning
AlexNet, ResNets, and VGG19, we use the models provided
by the PyTorch framework. Instead, for CorNet-S and CorNet-
Z, we employ the public available implementation provided by
For each of the benchmarks, we use 400k training examples
and 100k images for testing. All the positive and negative
examples are perfectly balanced in both sets. For all the
probed models, we use SGD as optimization algorithm, with a
momentum of 0.9, weight decay of 1e-4 and an initial learning
rate of 0.1. We use an exponential decay schedule for the
learning rate, that halves it every 20 epochs. We do not use
pre-trained weights if they are available.
A. Experiment 1
a) Description: Our primary objective consists in trying
to correctly learn an SVRT problem, measuring the accuracy
on the test set of the same problem.
Together with the obtained accuracies, in this experiment we
are also interested in understanding what is the convergence
speed of the model, as a measure of the strain perceived by the
network during the training phase. For this reason, we keep
track of the epoch in which the test accuracy reaches 90%.
From this moment on, we will refer to this particular point
as the convergence epoch (CE). For performance reasons we
validate the model every half epoch, so we are able to provide
the CE with a resolution of 0.5 epochs. This resolution is
enough to capture substantial differences in the training curves.
Problem 1 Problem 5 Problem 20 Problem 21
Model Acc. (%) CE Acc. (%) CE Acc. (%) CE Acc. (%) CE
LeNet  57.0 n.a. 54.0 n.a. 55.0 n.a. 51.0 n.a.
GoogLeNet  50.0 n.a. 50.0 n.a. 50.0 n.a. 51.0 n.a.
AdaBoost  98.0 n.a. 87.0 n.a. 70.0 n.a. 50.0 n.a.
Human  98.0 n.a. 90.0 n.a. 98.0 n.a. 83.0 n.a.
AlexNet 50.0 - 50.0 - 50.0 - 50.0 -
CorNet-Z 50.0 - 50.0 - 50.0 - 50.0 -
VGG-19 50.0 - 50.0 - 50.0 - 50.0 -
ResNet-18 99.0 2.0 99.8 2.5 95.8 2.0 96.1 17.5
ResNet-34 99.4 0.5 98.7 1.5 94.6 6.5 96.9 13.0
ResNet-101 99.1 3.5 97.8 3.5 95.9 4.0 91.1 20.5
CorNet-S 99.5 2.0 96.8 2.0 95.3 2.0 95.9 13.0
TABLE I: Accuracy values measured on the probed architectures, for each of the four SVRT problems. The values from the
ﬁrst experiments are reported as they are from , . They did not report any convergence information (CE is n.a.).
Together with our measurements on deep convolutional
networks, we also report the values as measured by , 
on LeNet, GoogLeNet and AdaBoost (using feature group 3).
Table I summarizes the accuracies reached from all the
architectures, over the test sets of the respective problems. For
the architectures trained by us, we report also the measured
CEs, only when the architecture converged.
Learning rotation invariance is known to be one of the major
sources of strain in convolutional networks. For this reason, we
also validate ResNet18, ResNet101, and Cornet-S on different
instances of the test set, where all the images from the same
instance are rotated by the same amount. For these trials, we
take as reference the models trained on P.21.
Rotation is inherently lossy for digital images, especially if
images do not have high resolution, as in our case. For this
reason, we try to rotate images with and without interpolation,
in order to appreciate how much the model is robust to the
noise added during the transform.
Figure 2 collects accuracy values measured on a particular
rotated instance of the test set, with and without pixel inter-
b) Discussion: Table I shows that, among all the probed
architectures, only ResNets and Cornet-S are able to learn all
the four problems correctly, perhaps with a very few error rate,
defeating all the state-of-the-art results previously reached with
AlexNet, CorNet-Z, and VGG19 are unable to learn. On
the validation set, they remain on the chance level accuracy
of 50%. AlexNet and CorNet-Z are not very deep and they are
quite straightforward. Hence, the performance obtained with
these models seems to be in line with results shown by Kim
et al.  on their simple convolutional architectures.
One interesting ﬁnding is the fact that a very-deep convo-
lutional network, VGG19, is unable to learn. Speciﬁcally, it
always outputs same for all the test samples of all the four
problems. This particular outcome conﬁrms the inability of
the VGG architecture to discern discriminant data from the
By contrast, residual networks (ResNet-18, ResNet-34,
ResNet-101 and CorNet-S) are able to obtain best perfor-
mances on all the problems. Even the small ResNet-18 behaves
well, both in terms of reached accuracies and CEs. Considering
P.1, all the ResNets reach almost perfect performance on
the validation set, approaching more than 99% accuracy with
pretty fast convergence. Only P.21 seems to cause some strain
in the training process since more epochs are required in order
for the models to converge.
Overall, ResNets and Cornet-S are able to defeat humans
on three of the four tasks.
These pieces of evidence on the probed models suggest that
the cause of the convergence is not related to the depth of the
network, but to its architecture instead. Given that also the
very-deep inception architecture of GoogLeNet seems unable
to converge , the results obtained with ResNets make us
realize that their residual architecture may have an important
role in the convergence when addressing the same-different
Looking at Figure 2, it seems that converged models are also
able to correctly handle rotated test set images. The peaks at
0, 90, 180 and 270 degrees tell us that the models are robust
to rotation, and they are able to generalize to a brand new set
of rotated ﬁgures never seen before.
On the other hand, the ﬂuctuations in the accuracy at inter-
mediate angles are a clear signal that the noise added while
rotating images strains these models. In particular, ResNet18
and ResNet101 show more sensitivity to this noise. ResNet101
is the most vulnerable to this disturbance. Its accuracy falls
to full chance when the image is rotated by 45 degrees and
no interpolation is used. Resnet18 and Resnet101 suffer in the
same way from the padding and center-crop transforms needed
in order to preserve shapes during the rotation (see Figure 2
caption for details), meaning that ResNets have also stronger
scale-dependent problems with respect to Cornet-S.
By contrast, CorNet-S seems very stable, both to rotation
(a) ResNet101 (b) ResNet18 (c) CorNet-S
Fig. 2: Accuracy values when the test set is rotated by the given angle. Ideal refers to the accuracy value as measured on the
original validation-set, without the re-scaling operations used for rotating the images. No interp is measured by removing the
interpolation during the rotation; the shape acquires at most 1-pixel wide distortion; Bilinear interp. uses bilinear interpolation
during rotation; in this case, rotation artifacts are strongly attenuated. At zero degrees, Ideal can diverge from No interp. and
Bilinear Interp.. In fact, in order to be rotated, the image has been ﬁrst padded and then center-cropped, in order to avoid
cutting the shapes during the rotation. These preliminary transforms are responsible for the gap in the case of zero rotation. A
gap at zero degrees is a clear signal indicating that the model is strained by this simple pre-scaling procedure.
noise and to image re-scaling.
B. Experiment 2
a) Description: In this scenario, we test generalization
capabilities of the converged models by measuring their per-
formance on the test set of other problems. In particular, we
set up the following trials:
1) Train on P.21, test on P.20: we test the capability of the
model to generalize to mirroring transformations, never
seen when training on P.20.
2) Train on P.21, test on P.5: we test the capability of the
model to generalize to multiple instances of the same-
3) Train on P.1, test on P.20: we test the capability of the
model to generalize to mirroring transformations. It is
more challenging with respect to point 1), since P.1
does not even give the possibility to learn the notion
of rotation and scale invariance.
4) Train on P.1, test on P.21: we test the capability of the
model to generalize to arbitrary rotations and scales.
Table II summarizes the accuracies of all the converged
models in the above-proposed conﬁgurations.
b) Discussion: Looking at Table II it turns out that
almost all the architectures trained on P.21 are also able to
correctly solve P.20. This means that P.21 gave the ResNets
the ability to correctly understand shape ﬂips, starting from
the notion of scale and rotation.
By contrast, there is no notion of rotation or ﬂip invariance
in the architectures trained on the simple P.1. This is an
expected result since convolutional architectures are not able
to natively deal with invariance to afﬁne transformations, with
the exception of the plain translation.
Also, tests on P.5 reveal that discerning multiple instances
of the same-different problem is a difﬁcult task when the
Model Train P.21
ResNet-18 95.9 57.5 67.8 51.8
ResNet-34 96.5 66.1 60.1 51.5
ResNet-101 90.5 56.2 57.3 51.3
CorNet-S 95.7 54.7 55.4 51.6
TABLE II: Accuracy values measured on the probed archi-
tectures, by training and testing them on different SVRT
architectures have been trained to detect only one instance.
This problem requires the models to understand that objects
should be clustered into two couples of possibly identical
shapes. Instead, an architecture trained on P.1 most likely
learned to output a positive result only if all the shapes are
In this study we tackled the problem of understanding
to what extent very-deep convolutional neural networks are
able to deal with the same-different challenging task. We
think that developing abstract and relational abilities of neural
networks is an important step towards the achievement of
some interesting new tasks, such as the discovery of particular
patterns in cultural heritage, or the search for aesthetic beauty
patterns in images and even music.
In particular, we stuck to the work by Kim et al. .
They showed how the same-different problem strain simple
feed-forward convolutional neural networks. We extended their
study to very-deep state-of-the-art neural networks for image
Considering the SVRT visual challenge, our results show
that, despite some difﬁculties, ResNets and CorNet-S (a
biologically-inspired architecture similar to ResNet architec-
ture) are able to correctly understand and generalize to never
seen shapes. We also found that Cornet-S is able to reach
strong stability with respect to 1-pixel wide noise, in the case
of shapes rotation without interpolation.
By contrast, not very-deep models such as AlexNet and
CorNet-Z are not able to learn any of the proposed problems.
This evidence is aligned with Kim et al. ﬁndings.
However, with the evidence that also deep neural networks
such as VGG19 and GoogLeNet are not able to converge, we
hypothesized that the residual connections in the ResNet archi-
tecture are important key points for the successful convergence
of these models.
There are still many open problems in this research di-
rection. As of now, abstract reasoning capabilities of neural
networks are tested on very simple and low distribution
variability datasets, such as SVRT or Sort-of-CLEVR. One
of the important steps to enhance this research would be to
consider more complex images collecting real-world shapes,
possibly seen from different perspective angles.
In our work, we tested CorNet-S, a model that directly
draws inspiration from neuroscientiﬁc evidence on the pri-
mates brain. We think that it would be interesting to access
more neuroscience research, in order to understand what are
the functional components of the human brain that contribute
to complex abstract reasoning.
ACK NOW LE DG ME NT S
This work was partially supported by the AI4EU project,
funded by the EC (H2020 - Contract n. 825619), and Auto-
matic Data and documents Analysis to enhance human-based
processes (ADA), CUP CIPE D55F17000290009.
We also gratefully acknowledge the support of NVIDIA
Corporation with the donation of the Tesla K40 GPU used
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