# Performance-optimized deep neural networks are evolving into worse models of
inferotemporal visual cortex

Drew Linsley∗1,2, Iván F. Rodriguez∗1, Thomas Fel3, Michael Arcaro4,
Saloni Sharma5, Margaret Livingstone5, Thomas Serre1,2,3
<EMAIL_ADDRESS>
###### Abstract

One of the most impactful findings in computational neuroscience over the past
decade is that the object recognition accuracy of deep neural networks (DNNs)
correlates with their ability to predict neural responses to natural images in
the inferotemporal (IT) cortex [1, 2]. This discovery supported the long-held
theory that object recognition is a core objective of the visual cortex, and
suggested that more accurate DNNs would serve as better models of IT neuron
responses to images [3, 4, 5]. Since then, deep learning has undergone a
revolution of scale: billion parameter-scale DNNs trained on billions of
images are rivaling or outperforming humans at visual tasks including object
recognition. Have today’s DNNs become more accurate at predicting IT neuron
responses to images as they have grown more accurate at object recognition?

Surprisingly, across three independent experiments, we find that this is not
the case. DNNs have become progressively worse models of IT as their accuracy
has increased on ImageNet. To understand why DNNs experience this trade-off
and evaluate if they are still an appropriate paradigm for modeling the visual
system, we turn to recordings of IT that capture spatially resolved maps of
neuronal activity elicited by natural images [6]. These neuronal activity maps
reveal that DNNs trained on ImageNet learn to rely on different visual
features than those encoded by IT and that this problem worsens as their
accuracy increases. We successfully resolved this issue with the _neural
harmonizer_ , a plug-and-play training routine for DNNs that aligns their
learned representations with humans [7]. Our results suggest that harmonized
DNNs break the trade-off between ImageNet accuracy and neural prediction
accuracy that assails current DNNs and offer a path to more accurate models of
biological vision. Our work indicates that the standard approach for modeling
IT with task-optimized DNNs needs revision, and other biological constraints,
including human psychophysics data, are needed to accurately reverse-engineer
the visual cortex.

##  1 Introduction

11footnotetext: These authors contributed equally.††footnotetext: 1Department
of Cognitive, Linguistic, & Psychological Sciences, Brown University,
Providence, RI††footnotetext: 2Carney Institute for Brain Science, Brown
University, Providence, RI††footnotetext: 3Artificial and Natural Intelligence
Toulouse Institute, Toulouse, France††footnotetext: 4Department of Psychology,
University of Pennsylvania, Philadelphia, PA††footnotetext: 5Harvard Medical
School, Cambridge, MA

The release of AlexNet [8] was significant not only for shifting the paradigm
of computer vision into the era of deep learning, it also heralded a new
approach for “systems identification,” and approximating the transformations
used by neurons in the visual cortex to build robust and invariant object
representations. Over the past decade, deep neural networks (DNNs) like
AlexNet, which are trained for object recognition on ImageNet [9], have been
found to contain units that significantly better fit neural activity in
inferior temporal (IT) cortex in non-human primates compared to classic hand-
tuned models from computational neuroscience [1]. It was later found that DNN
fits with neural data improved as these models grew more accurate at object
recognition and began to rival humans on the task [10, 11]. This surprising
similarity between such task-optimized DNNs and brains supported the extant
theory that object recognition is a core principle shaping the organization of
the visual cortex [12], and raised the question of how important the many
biological details amassed by visual neuroscience actually are for predicting
neural responses in visual cortex. In the years since those findings, deep
learning has undergone a revolution of scale, and current DNNs which rival or
exceed human accuracy in vision and language are significantly larger and
trained with orders of magnitude more data than ever before [13]. Does the
object recognition accuracy of a DNN still correlate with its ability to
predict IT responses to natural objects?

To answer this question, we turned to Brain-Score [3], the standard approach
for benchmarking the accuracy of models at predicting neural activity in
visual cortex of non-human primates. In brief, the Brain-Score evaluation
method involves linearly mapping model unit responses to neural activity and
then evaluating model unit predictions on held-out images. With this approach,
we found a consistent trend across three different IT datasets hosted on the
official Brain-Score website (Brain-score.org), which reflect neural responses
to gray-scale versions of realistic rendered objects and natural images [14,
15, 16]. As DNNs have improved on ImageNet [9] over recent years, they have
become progressively less accurate at predicting IT neuron responses to images
(Fig. 1) ***In [11] it was noted that while there was an overall correlation
of 0.92 between DNN accuracy on ImageNet and predicting IT responses, the
correlation weakened for state-of-the-art models.

In this study, we investigate two potential explanations for why task-
optimized DNNs are turning into poor models of IT. (i) The internet data diets
of DNNs and the routines used to train them to high accuracy on ImageNet leads
them to learn the wrong visual features for explaining primate vision and IT
responses to objects [7, 17, 18, 19]. (ii) Newer DNNs have become less brain-
like, and this problem has been magnified as DNNs have grown larger and
ultimately deeper than the visual cortex [20].

Figure 1: Deep neural networks (DNNs) are becoming progressively worse models
of inferior temporal (IT) cortex as they grow more accurate on ImageNet.
Experimental data shown here is taken from Brain-score.org, and each
experiment utilized different stimuli. The 104 dots in each panel depict the
ImageNet accuracy and neural prediction accuracy of DNNs, and the grey-shaded
region denotes the pareto-front governing the trade-off between these
variables.

### Contributions.

To understand if the trade-off between ImageNet accuracy and IT predictions
tjat we observed (Fig. 1) is due to the training routines and data diets of
DNNs or their architectures, we turned to a new set of experimental recordings
of IT neuronal responses to high-resolution color images [6]. The experimental
images were significantly closer to the statistical distribution of images in
ImageNet (Fig. §1.), unlike prior studies of IT [14]. The recordings also
provided a coarse estimate of which image features drove neuronal activity
(Fig. 2), which helped characterize DNN errors in explaining neural responses.
As we will show, compared to the recordings used in the official Brain-Score
benchmark, such spatially-resolved neural data provide far greater insight
into why DNNs are becoming worse models of IT. We adopted the Brain-Score
evaluation method to measure the prediction accuracy of 135 DNNs on recordings
from medial (ML) and posterior (PL) lateral IT in two different Monkeys. To
summarize our findings:

  * •

We observed the same trade-off we found on Brain-Score.org data (Fig. 1) in
each of our recordings: DNNs are becoming less accurate at predicting IT
responses as they improve on ImageNet (Fig. 3).

  * •

DNNs trained on ImageNet learn different features than those encoded by IT
(Fig. 4), and this mismatch is not helped by training on more internet data,
using newer DNN architectures like Transformers, relying on self-supervision,
or optimizing for adversarial robustness.

  * •

We successfully broke this trade-off by training DNNs with the _neural
harmonizer_ [7] and aligning the representations they learn for object
recognition with those that are diagnostic for humans.

  * •

We further demonstrate that harmonized DNNs (hDNNs) are not only significantly
better at explaining IT responses than any other DNN available, they also
generate interpretable hypotheses on the features driving IT neuron responses.

Figure 2: IT recordings that reveal spatial maps of neuronal responses to
complex natural images offer unprecedented insights into their feature
selectivity [6]. (a) Neurons in posterior (PL) and/or medial (ML) lateral IT
in two animals were localized using functional magnetic resonance imaging
(fMRI), and neural responses to images were recorded using chronically
implanted 32-channel multi-electrode arrays. (b) The monkeys were rapidly
shown each image multiple times for 200ms each time (Monkey 1: $n=256$, Monkey
2: $n=49$). Images were positioned differently each time to measure neural
responses to every part of the image. (c) This procedure yielded spatially
resolved maps of neural activity for an image, revealing the relative
importance of different features for the recorded neurons. (d) DNNs were fit
to these recordings following the Brain-Score evaluation method [11], in which
partial least squares decoders were used to find the units in a DNN that
provided the best match for neuronal responses to images.

##  2 Methods

### Neural recordings.

We leveraged recordings of IT neuronal responses from two monkeys [6], which
were designed to reveal feature preferences of putative face-selective
neurons. The recorded neurons also exhibited selectivity for non-face object
features [6]. Recordings were made using chronically implanted 32-channel
multi-electrode arrays within the fMRI-defined middle lateral (ML) and
posterior lateral (PL) face patches of one monkey (Monkey 1), and ML of
another monkey (Monkey 2, Fig. 2a). The activating regions in these areas were
mapped (1-3o), then each image was shown to the animals after they were cued
to fixate at a specific position in space (Fig. 2b). The same images were
shown multiple times while the monkeys fixated at a red dot in the center of
the screen, which made it possible to derive spatial activity maps of neuronal
responses (Fig. 2c). Fixation positions fell in a 16 $\times$ 16 grid for
Monkey 1 and 7 $\times$ 7 grid for Monkey 2, and the average neuronal activity
at each position was taken to generate spatial activity maps. A total of 14
images were shown to Monkey 1, and a different set of 14 images were shown to
Monkey 2.

The recordings for Monkey 1 resulted in responses from 32 neurons in ML and 31
neurons in PL. For Monkey 2, we obtained responses from 32 neurons (see
Appendix §2 for more details). Following [6], we binned neuronal responses
every 40ms of the recording, from 50ms to 250ms. Within each bin, we
calculated the noise ceiling for every neuron, which represents the maximum
correlation achievable between any two neurons within that time interval.
Noise ceilings for each recording were similar to those reported for standard
IT Brain-Score datasets (Appendix §2). In the main text, we present modeling
results from the time bins that exhibited the highest average noise ceiling
for each Monkey and recording site. Additional results from other time bins,
which are consistent with these findings, can be found in Appendix §2.

### DNNs.

We investigated the neural fits of 135 different DNNs representing a variety
of approaches used in computer vision today: 62 convolutional neural networks
trained on ImageNet [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 34, 39, 40, 41, 42, 43, 44, 45, 46, 47] (CNNs), 23 DNNs
trained on other datasets in addition to ImageNet (which we refer to as “DNN
extra data”) [48, 36, 32], 25 vision transformers [49, 50, 51, 52, 53, 54]
(ViTs), 10 DNNs trained with self-supervision [55, 56], and 15 DNNs trained to
be robust to noise or adversarial examples [57, 58]. Each model was
implemented in PyTorch with the TIMM toolbox
(https://github.com/huggingface/pytorch-image-models) and pre-trained weights.
Inference was executed on one NVIDIA TITAN X GPU. Additional model details,
including the licenses used for each, are detailed in Appendix §3.

### Neural Harmonizer.

It was recently found that DNN representations are becoming less aligned with
human perception as they evolve and improve on ImageNet [7, 59, 60]. A partial
solution to this problem is the _neural harmonizer_ , a training routine that
can be combined with any DNN to align its representations with humans without
sacrificing performance. Here, we test the hypothesis that aligning DNNs with
human visual representations can similarly significantly improve their
accuracy in predicting neural responses to images.

Training DNNs with the _neural harmonizer_ on ImageNet involves an additional
loss to standard cross-entropy for object recognition. This extra loss forces
a model’s gradients to appear as similar as possible to feature importance
maps derived from human behavioral experiments (see [7] for details). To
implement this loss, let $\mathcal{P}_{i}(.)$ be a function that a multi-scale
Gaussian pyramid of a human feature importance map $\bm{\phi}$ to $N$, with
$i\in\\{1,...,N\\}$. During training, we seek to minimize
$\sum_{i}^{N}||\mathcal{P}_{i}(\bm{g}(\bm{f}_{\theta},\bm{x}))-\mathcal{P}_{i}(\bm{\phi})||^{2}$
in order to align feature importance maps between humans and DNNs at every
scale of the pyramid. Before they are compared, feature importance maps from
humans and DNNs are normalized and rectified using $\bm{z}(.)$, a function
that transforms a feature importance map $\bm{\phi}$ from either source to
have 0 mean and unit standard deviation. This procedure yields the complete
neural harmonization loss:

$\displaystyle\mathcal{L}_{\text{Harmonization}}=$
$\displaystyle\lambda_{1}\sum_{i}^{N}||(\bm{z}\circ\mathcal{P}_{i}\circ\bm{g}(\bm{f}_{\theta},\bm{x}))^{+}-(\bm{z}\circ\mathcal{P}_{i}(\bm{\phi}))^{+}||_{2}$
(1)
$\displaystyle+\mathcal{L}_{CCE}(\bm{f}_{\theta},\bm{x},\bm{y})+\lambda_{2}\sum_{i}\theta_{i}^{2}$
(2)

Following the original _neural harmonizer_ implementation [7] and training
recipe, we trained six DNNs on ImageNet and human feature importance maps from
the _ClickMe_ game [61]: VGG16 [25], LeViT [62], ResNetV2-50 [63],
EfficientNet$\\_$b0 [22], ConvNext [32], and MaxViT [64]. Each model was
trained with Tensorflow 2.0 on 8 V4 TPU cores with all of the images in the
ImageNet training set, and ClickMe human feature importance maps for the
200,000 images which were annotated. Images and feature importance maps were
augmented with mixup [65], random left-right flips, and random crops during
training. Only the object recognition loss was computed for images without
human feature importance maps. Model weights were optimized with stochastic
gradient descent and momentum, batches of 512 images, label smoothing [66], a
learning rate of $0.3$, and a learning rate schedule that began with a 5-epoch
warm-up period followed by a cosine decay over 90 epochs at steps 30, 50 and
80.

### Neural fitting.

We evaluated the neural fit of each model by computing their fit separately
for each IT recording, using the Brain-Score evaluation method [11]. This
method involved fitting image-evoked activities from a layer of a deep neural
network (DNN) to the corresponding neural responses using the partial least
squares regression algorithm from Scikit-Learn.

To implement the Brain-Score evaluation method on the spatially-resolved
recordings we investigate here, we first pass the image through the network
and split the resulting feature map into an equal number of patches as there
were fixation locations in the image shown to the animal. Each image patch
captured the receptive field of recorded neurons, and in total, there were
$4,046$ image patches for ML and $4,046$ image patches for PL in Monkey 1, and
$1,134$ image patches for ML in Monkey 2. We measured DNN neuronal fits as the
Spearman correlations between model predictions and true neural responses for
each patch of an image held out of training divided by each neuron’s noise
ceiling. We then stored the median Spearman correlation over neurons and
repeated the training/testing procedure to get the mean correlation across all
images viewed by a monkey. Separate fitting procedures were performed for
every layer of activities in a model, and we report a DNN’s Brain-Score as its
best possible fit across layers.

Figure 3: DNNs trained on ImageNet face a trade-off between achieving high
object recognition accuracy and predicting responses to natural images in IT..
We measured the accuracy of 135 DNNs at predicting image-evoked responses from
neurons in posterior lateral (PL) and medial-lateral (ML) areas of IT [6] by
computing the neural predictivy of each model with the Brain-Score evaluation
method [11]. DNN neural predictivity is progressively worsening as models
improve on ImageNet. This problem can be partially fixed by training DNNs with
the _neural harmonizer_ , which aligns their learned object representations
with humans. Error bars denote 95% bootstrapped confidence intervals.

##  3 Results

### Task Optimization is insufficient for reverse-engineering IT.

Ever since it was found that DNNs optimized for object recognition produce
accurate predictions of IT neural responses to images, it was suggested that
prediction accuracy would continue improve alongside DNN performance on
ImageNet [10, 12, 11]. Is this the case with today’s DNNs that rival or exceed
the performance of human object recognition?

To answer this question, we leverage recordings of neuronal responses to high-
resolution natural images in medial (ML) and posterior lateral (PL) IT (see
Methods and Fig. 2). These images fall within the same statistical
distribution as ImageNet images (Appendix §1), ensuring that our findings are
not influenced by distributional shifts that are a well-known problem faced by
computer vision models [67]. Image-evoked neural responses were spatially
mapped, enabling insights into the visual features driving the responses of IT
neurons and DNNs. Moreover, while these regions were localized according to
their selectivity to face stimuli, they were also noted to respond to non-face
stimuli [6].

Across 135 different DNNs, representing the variety of approaches used today
in computer vision, we found that DNNs pretrained on ImageNet have become
progressively less accurate at predicting ML and PL responses in two separate
Monkeys (Fig. 3). For instance, ConvNext tiny, which achieved 74.3% accuracy
on ImageNet, is as accurate in predicting neural responses to images as the
ResNetv2-152x4, which reached 84.9% accuracy on ImageNet. Moreover, training
routines that have been suggested to be more biologically plausible or yield
representations that are closer to biological vision, such as training with
self-supervision [68] or for adversarial robustness [69], made no difference.
All DNNs trained on internet data faced a pareto-front that bounded their
accuracy in predicting IT responses as a function of their ImageNet accuracy.

### DNNs need biologically-aligned training routines

There are at least two potential reasons why ImageNet-trained DNNs face a
trade-off between object recognition and neural prediction accuracy: (i) DNN
data diets and training routines work well for ImageNet but lead them to learn
features that are misaligned with biological vision [7, 17, 18, 19] or (ii)
their architectures are a poor match to visual cortex [20]. To test this first
possibility, we turned to the _neural harmonizer_. Given prior work
demonstrating that aligning DNNs with human perception using the _neural
harmonizer_ significantly improved their ability to predict human behavior, we
reasoned that harmonization might similarly improve DNN explanations of neural
data by forcing them to rely on human-like visual features. Indeed, we found
that harmonized DNNs (hDNNs) were significantly more accurate at predicting
image-evoked responses in ML ($T(5)=5.30$, $p<0.01$) and PL ($T(5)=6.11$,
$p<0.001$) neurons of Monkey 1 and ML ($T(5)=6.89$, $p<0.001$) neurons of
Monkey 2 (reported as the average of $T$ score from independent samples
$t-$tests comparing the predictivity of each hDNN to the DNN with the highest
neural-predictivty). The success of hDNNs indicates that the architectural
mismatch between DNNs and the visual cortex is far less of a problem for
modeling the visual cortex than the training routines and data diets that are
being used today to achieve high accuracy on ImageNet. Behavior – even from
humans – is an important constraint on DNNs that is needed to build more
accurate models of primate visual cortex.

Figure 4: DNNs optimized for object recognition on ImageNet rely on different
features than those encoded by neurons in primate inferior temporal (IT)
cortex.. The activity of PL IT neurons is plotted next to the predicted
activity of a model representing each class of DNNs: harmonized DNNs (hDNNs),
visual transformers, self-supervised DNNs, convolutional neural networks, DNNs
trained on more data than ImageNet, and adversarially robust DNNs.

### Spatially-mapped neural responses reveal a feature mismatch between IT and
DNNs

The IT recordings used in the Brain-Score benchmark all utilized the same
paradigm, in which hundreds or thousands of images were shown to multiple
animals during passive viewing [14]. In contrast, the recordings we rely on
involve many fewer unique images, but neural responses for each image are
spatially mapped. This spatial mapping reveals what types of features are
driving neural responses and makes it easier to understand the successes and
failures of DNNs in explaining these data [6].

Although the neurons in ML and PL were located based on their selectivity to
faces, the spatial maps of their responses revealed a much more complex
response profile. IT neurons in both animals were strongly driven by faces,
non-face objects, and contextual cues associated with faces [6]. In contrast,
the best-fitting units of DNNs with state-of-the-art accuracy on ImageNet,
like the ResNetv2-152x4 (Fig. 4), responded strongly to background features.
This problem was shared by DNNs trained on internet data but with routines
that have been considered more biologically plausible, like self-supervised
learning (e.g., SSL ResNet-18), or routines that yield perceptual robustness
that is closer to humans, like adversarial training (e.g., Robust
ResNetv2-50). hDNNs like the harmonized MaxViT, on the other hand, were, in
general, reliably predictive of what parts of images elicited the most
activity from IT neurons.

Figure 5: Predictions of the visual features drive neuronal responses in PL of
Monkey 1 from a harmonized ResNet-50 and a standard ResNet-50. Image patches
for each model depict what the important features are across all images shown
to the animal. The relative importance of each feature for predicting the
recordings is color-coded in the bar chart on the right.

### hDNNs generate testable predictions for visual neuroscience

The surprising effectiveness of DNNs pre-trained on object recognition for
predicting IT responses to images was a significant finding in computational
neuroscience, which raised the tantalizing possibility that these models could
form the basis of neuroprosthetics, and reduce the need for animal
experiments. However, a persistent problem with DNNs since their inception is
their lack of interpretability, meaning that using DNNs for systems
identification effectively swaps one black box (the visual system) with
another (a DNN) without getting the field any closer to understanding how
vision works. Recent strides in the field of explainable artificial
intelligence (XAI) have begun to alleviate this problem. For instance, it is
now possible to reliably locate and characterize the features in datasets,
like ImageNet, that drive patterns of model behavior using concept recursive
activation factorization (CRAFT [70]). When paired with accurate models of IT
and recordings that reveal locations in images that elicit neuronal responses,
CRAFT can generate testable predictions of _what_ those features are.

We used CRAFT to extract features from harmonized and regular ResNet-50s
trained on ImageNet that explain their predictions of neural activity in PL of
Monkey 1 (Fig. 5). To do this, we decomposed a DNNs predicted activities for
image patches into the most important and distinct features using non-negative
matrix factorization, then scaned over every single image patch to find those
which most strongly explained each discovered feature. While the harmonized
ResNet-50 predicted that parts of faces, arms, and heads explained the
majority of variance in IT, the less accurate and unharmonized ResNet-50
predicted that the background, oriented-edges, and a feature combining head,
body, arm, and hand parts were most important for IT. Thus, hDNNs not only
break the trade-off between ImageNet and neural prediction accuracy of
ImageNet-trained DNNs, they can also generate testable hypotheses on the
relative importance of different features for visual system neurons.

##  4 Related work

### The scaling laws of deep learning

The immense gains of DNNs in computer vision [13] and natural language
processing [71] over recent years share a common theme: they have relied on
unprecedented computational resources to train models with billions of
parameters on internet-scale datasets. These benefits of scale have been
studied over the past several years across a number of domains and often yield
predictable improvements on standard internet benchmarks [72, 71].
Surprisingly, scale has also caused models to exhibit human-like behavior in
psychophysics experiments [13, 73, 57, 74]. In other words, many aspects of
primate behavior _are_ captured progressively better by DNNs as they scale-up
and improve in accuracy on benchmarks like ImageNet.

### Scale is sufficient for modeling internet benchmarks, but not primate
intelligence

In parallel, there’s a growing body of research suggesting that large-scale
DNNs are becoming less aligned with human perception in multiple ways. For
instance, the representations and visual decision-making behavior of DNNs are
inconsistent with humans, and this problem has worsened as they have improved
on ImageNet [7]. DNNs are also becoming less capable at predicting perceptual
similarity ratings of humans, and they remain vulnerable [75] to so-called
“adversarial attacks.” Our work adds to this body of research, indicating that
current scaling laws are incompatible with modeling primate behavior _and_
poorly suited for explaining the neural computations that shape it.

### Aligning DNNs with primate vision

There have been a number of methods proposed for aligning DNNs with primate
vision beyond the _neural harmonizer_ that we leverage here [7]. It was found
that co-training DNNs for object recognition and minimizing representational
dissimilarity improved the adversarial robustness of a recurrent DNN [76].
Others have shown that similar forms of representational alignment improve
few-shot learning and predictions of human semantic judgments in DNNs [77,
78]. The successes of these behavioral and representational alignment methods
highlight the real limitations of current DNN training routines and data diets
for generating artificially intelligent systems that act like biological ones.

### Biological learning routines

There have been many efforts to align the object functions, learning rules,
and data diets of DNNs more closely with biological systems. It was found that
DNNs trained with self-supervision on ImageNet instead of supervised
recognition achieve similar accuracy in predicting V1, V4, and IT responses to
images [68]. DNNs trained with self-supervised learning on head-mounted camera
video from infants instead of ImageNet were approximately as accurate at
predicting neural data as DNNs trained on Imagenet but needed far less data to
do this [68]. Others have found that adversarial training of DNNs yields
models that are more accurate at predicting neural responses to images [79]
and have similar tolerance to adversarial attacks as neurons in IT [69].

##  5 Discussion

### A revised approach for reverse engineering visual cortex

Biological data is expensive to gather and often noisy. This makes the
prospect of accurately modeling the responses of IT to complex stimuli
especially daunting. DNNs optimized for object recognition represented a
potential solution for this problem: pretraining on internet datasets
alleviated training issues associated with small-scale neural data, and the
architectures and training routines of accurate DNNs could offer insights into
the circuits that underlie visual perception as well as the developmental
principles that shape those circuits. Our findings suggest that while DNNs
still hold great potential for predicting image-evoked responses from IT
neurons, new training routines and data diets are necessary for continued
improvement.

The _neural harmonizer_ is a partial solution to the problems that DNNs face
in modeling primate IT. The success of hDNNs in breaking the pareto-front
faced by 135 different DNNs indicates that significant aspects of primate
perception and the neural circuits that shape it cannot be divined from
internet data alone. We believe that the _neural harmonizer_ and learning
constraints provided by large-scale human behavior data is only a short-term
solution to this problem, and that if DNNs were able to learn about the visual
world more like primates do, they would be even better at predicting neural
data. In support of this goal, we release our code and data at https://serre-
lab.github.io/neural_harmonizer.

### Limitations.

One limitation of our work is that we use the responses of neurons with face-
selectivity to replicate and understand the trade-off between ImageNet
accuracy and neural predictivity faced by DNNs. As faces (and even humans) are
not a category in ImageNet, it is possible that this dataset [6] could bias
our results in ways that are difficult to predict†††Note, however, that there
are many animal and human faces in Imagenet images, giving DNNs ample
opportunity to learn about them.. However, we find the same ImageNet accuracy
and neural predictivity trade-off on this dataset (Fig. 3) as we did on the
three recordings of object selective neurons hosted on the Brain-Score website
(Fig. 1), indicating that DNNs face similar issues in predicting each set of
recordings. Moreover, the neural harmonizer was successful in breaking this
trade-off, even though it involves ImageNet training using human feature
importance maps for objects. Finally, it was noted in the original paper where
our recordings came from that the neurons, while localized based on their
face-selectivity, responded to non-face stimuli as well [6]. In summary, our
work reliably demonstrates that new paradigms are needed to advance DNNs as
models of IT, and spatially-resolved recordings such as those used in this
work support this goal.

Another limitation of our work is that while we found that hDNNs are
significantly more predictive of IT neuron responses than any other DNN, they
still explain only 50-60% of the variance in neuronal activity. One
straightforward way of doing better is by expanding the dataset of human
feature importance maps we used for harmonization from annotations for
approximately 200,000 images to the entire 1.2M ImageNet dataset.

### Broader impacts.

By building better models of primate IT, we are taking significant steps
toward the reducing the reliance of visual neuroscience on animal models for
experimentation, supporting the development of neuroprosthetic devices that
resolve visual dysfunctions, and providing vision scientists with a richer
understanding of how IT works. Our findings also highlight a main limitation
of the scaling laws that are guiding progress throughout artificial
intelligence today: scale is not sufficient for explaining biological
intelligence.

## Acknowledgments and Disclosure of Funding

This work was supported by ONR (N00014-19-1-2029), NSF (IIS-1912280 and
EAR-1925481), DARPA (D19AC00015), NIH/NINDS (R21 NS 112743), and the ANR-3IA
Artificial and Natural Intelligence Toulouse Institute (ANR-19-PI3A-0004).
Additional support provided by the Carney Institute for Brain Science and the
Center for Computation and Visualization (CCV). We acknowledge the Cloud TPU
hardware resources that Google made available via the TensorFlow Research
Cloud (TFRC) program as well as computing hardware supported by NIH Office of
the Director grant S10OD025181.

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##  Appendix A Datasets

### Distribution shifts

One possible explanation for the trade-off we observed between DNN accuracy on
ImageNet vs. predictions of neural data is that there was a distributional
shift between the images used in the two evaluations. To test this
possibility, we extracted activity vectors for a large sample of images from
ImageNet and all images from the standard Brain-Score benchmark dataset for IT
[14] and the images we used in our experiments [6]. For ImageNet, we used all
images in the validation set that also had human annotations from _ClickMe_.

We measured distribution shifts by measuring the accuracy of a linear
classifier in discriminating between ImageNet and either the standard Brain-
Score benchmark dataset for IT [14] or the images we used in our experiments
[6]. We began by taking equal-sized random samples of ImageNet image encodings
and encodings from either the Brain-Score dataset (28 of 191 images) or our
dataset (all 28 images). We then trained a linear SVM using Sklearn and
performed leave-one-out cross-validation on either set of samples. Finally, we
repeated this procedure 1,000 times, using a new random sample of ImageNet
encodings each time, and measured the average accuracy for discriminating
between ImageNet and either neural data image set. We found that images used
in the standard Brain-Score benchmark for IT [14] are significantly further
out-of-distribution from ImageNet than the images that we used in the main
text [6] ($T(999)=98.12$, $p<0.001$, Fig. S1).

Figure S1: Stimuli from [14], but not [6], are out-of-distribution from
ImageNet. Penultimate-layer activities from a ResNetv2-50 trained on ImageNet
were extracted for 1916 images from the validation set of ImageNet, 191 images
from [14], and 28 images from [6]. A principle components analysis decomposed
those activities into a 2-Dimensional projection, which demonstrated a
distribution shift for stimuli from [14], but not [6]. Indeed, while stimuli
from [14] could be reliably discriminated from ImageNet (98.7 acc,
$T(999)=98.12$, $p<0.001$), images from [6] were not discriminable from
ImageNet (56.5 acc, $T(999)=98.12$, $n.s$

.

##  Appendix B Neural data analysis

We measured the maximum explainable variance, or noise ceiling, in our neural
data recordings in every 40ms bin of activity from 0ms - 250ms. We binned
every 40ms by following the original procedure for processing this data [6].
Because images were not repeatedly shown to the same population receptive
field, we computed each neuron’s noise ceiling for an image as the highest
correlation between it and another neuron for that image. We then focused our
analyses in the main text on the time bin where each neurons in each
animal/brain area achieved the highest average noise ceiling (Fig. S2).

Figure S2: Noise ceilings at every 40ms bin of activity from 0ms - 250ms. We
binned every 40ms of neural responses following the original procedure for
processing this data [6]

##  Appendix C Models

### DNN Model Zoo

We comprehensively evaluated the ability of a myriad of DNNs from the TIMM
toolbox. These DNNs, available under the Apache 2.0 license, are intended for
non-commercial research purposes. The complete list of DNNs we evaluated can
be found in Table S1.

Architecture | Model | Versions
---|---|---
CNN | VGG | 4
ResNet | 24
EfficientNet | 8
ConvNext | 10
MobileNet | 6
Inception | 7
DenseNet | 4
RegNet | 3
Xception | 4
MixNet | 4
DarkNet | 2
NFNet | 2
TinyNet | 4
LCNet | 2
DLA | 2
MnasNet | 2
Resnext101 | 6
GhostNet | 2
ViT | General ViT | 21
leViT | 4
MaxViT | 7
DeiT | 4
Hybrid | CoAtNet | 5
Table S1:  Our DNN model zoo, taken from the TIMM library.

##  Appendix D Neural Harmonizer Training

We relied on the original neural harmonizer recipe [7] to train and harmonize
14 DNNs for object recognition on the ImageNet [9] dataset. For each model, we
searched for settings of the regularization terms $\lambda_{1}$ and
$\lambda_{2}$, which control the relative importance of losses for object
recognition and human feature alignment during training, that maximized
accuracy on the ImageNet validation set. In total, we trained a VGG16,
ResNet50_v2, ViT_b16, EfficientNet_b0, ConvNext Tiny, and MaxViT Tiny (Table.
S2). We did not attempt to apply the neural harmonizer to models which relied
on pretraining with datasets other than ImageNet because the _ClickMe_ feature
importance dataset we used only contained annotations on a subset of images in
ImageNet. Thus, we expect that more work is needed for expanding _ClickMe_ to
larger-than-ImageNet scale data before these DNNs can be harmonized.

Model | Accuracy | Human Alignment | Note
---|---|---|---
VGG | 69.3 | 61.5 |  $\lambda$ = 2
ResNet 50 | 77.17 | 45.0 |  $\lambda$ = 2
EfficientNet B0 | 77.51 | 52.3 |  $\lambda$ = 20
ViT B16 | 75.7 | 72.6 |  $\lambda$ = 5
ConvNext Tiny | 75.9 | 73.2 |  $\lambda$ = 1
MaxViT Tiny | 78.6 | 45.3 |  $\lambda$ = 1
Table S2:  DNNs trained with the neural harmonizer.

##  Appendix E Extended results

Here, we present the results on other time bins (with lower noise ceilings)
than those considered in the main text (Figs. S3\- S5). For ML IT in monkey 1
and monkey 2, we present 90ms-130ms, 130ms-170ms, and 210ms-250ms. For PL IT
of Monkey 1, we present 130ms-170ms, 170ms-210ms, and 210ms-250ms, windows. In
each case, we found a similar trade-off in these data as we did in those
highlighted in the main text, as well as a significant improvement for
harmonized vs. unharmonized DNNs. This similarity extends to the qualitative
predictions made by each model on ML IT neurons (recall that we show the
image-evoked activities of PL IT neurons in the main text, S5).

Figure S3: Results using different time bins than in the main text for the
same region (ML) for both monkeys. The pattern of results for each time-bin
are consistent with the main text, despite these data having lower noise
ceilings. Figure S4: Results using different time bins than in the main text
for the IT PL in Monkey 1.. The pattern of results for each time-bin are
consistent with the main text, despite these data having lower noise ceilings.
Figure S5: DNNs optimized for object recognition on ImageNet rely on different
features than those encoded by neurons in primate inferior temporal (IT)
cortex. The activity of ML IT neurons of Money 1 is plotted next to the
predicted activity of a model representing each class of DNNs: harmonized DNNs
(hDNNs), visual transformers, self-supervised DNNs, convolutional neural
networks, DNNs trained on more data than ImageNet, and adversarially robust
DNNs.


# Agreement or Disagreement in Noise-tolerant Mutual Learning?

Jiarun Liu, Daguang Jiang, Yukun Yang, Ruirui Li1 1 Corresponding author.
Information Science and Technical Institute
Beijing University of Chemical Technology
Beijing, China
<EMAIL_ADDRESS>
###### Abstract

Deep learning has made many remarkable achievements in many fields but suffers
from noisy labels in datasets. The state-of-the-art learning with noisy label
method Co-teaching and Co-teaching+ confronts the noisy label by mutual-
information between dual-network. However, the dual network always tends to
convergent which would weaken the dual-network mechanism to resist the noisy
labels. In this paper, we proposed a noise-tolerant framework named MLC in an
end-to-end manner. It adjusts the dual-network with divergent regularization
to ensure the effectiveness of the mechanism. In addition, we correct the
label distribution according to the agreement between dual-networks. The
proposed method can utilize the noisy data to improve the accuracy,
generalization, and robustness of the network. We test the proposed method on
the simulate noisy dataset MNIST, CIFAR-10, and the real-world noisy dataset
Clothing1M. The experimental result shows that our method outperforms the
previous state-of-the-art method. Besides, our method is network-free thus it
is applicable to many tasks. Our code can be found at
https://github.com/JiarunLiu/MLC.

##  I Introduction

Deep Neural Networks (DNN) have achieved remarkable success on many tasks.
Most applied algorithms rely on accurate labels to supervise model learning.
However, collecting extensive data and accurate labels is a daunting and
laborious task. Many researchers turn to costless methods to acquire labels,
such as online queries or crowdsourcing, which inevitably introduces label
noise in the dataset and leads to a significant degeneration in the
generalization of DNN models.

Research on learning with noisy labels (LNL) has become a hot topic and
strategies such as noise transition matrix[1], redesigning loss functions[2,
3, 4], or re-weighting samples[5, 6] et.al. are often combined with to obtain
robust models. Recently, methods derived from co-training have achieved state-
of-the-art results on the LNL tasks due to their ability to reduce error
accumulation. Specifically, Co-teaching[7] maintains two networks
simultaneously. Each network views its small-loss instances as useful
knowledge and teaches such useful instances to its peer network for updating
parameters. Researchers later found that mutual updates could cause the
parameters of the two networks to converge, resulting in premature stopping of
learning. To solve this problem, inspired by Decoupling[8], Co-teaching+[9]
selects small-loss samples with inconsistent predictions between the two
networks to mutually update the gradients. However, Co-teaching+ probably
fails without sufficient qualified instances, especially when there is a large
proportion of noisy labels. We have observed that Co-teaching+ performs worse
than Co-teaching in some LNL tasks, such as medical image classification[10].
On the contrary, JoCoR[11] believes that there is no need to ensure the
inconsistency of the two networks. It uses a regularization term in the loss
function to enhance the consistency of the predictions against the label
noise. Therefore, there arises a question to be answered: Is “Disagreement”
necessary for training two networks to deal with noisy labels?

Figure 1: Comparison of different error flow. First Panel: MentorNet[12]
(M-Net) maintains only one network; Second Panel: Co-teaching[7] maintains two
networks A and B. In each mini-batch, each network samples its small-loss
instances and teaches these instances to its peer network; Third Panel: Co-
teaching+[9] adopts the idea of update by disagreement when selects useful
instances; Fourth Panel: JoCoR[11] narrows the distance between A and B
through a co-regularization on instances; Fifth Panel: MLC follows Co-
teaching’s strategies but adds a co-regularization directly on network
parameters to maintain a certain degree divergence.

To address this question, we conducted a series of exploration experiments and
have observed that:

  1. 1.

Mutual learning tends to maximize prediction consistency.

  2. 2.

A certain disagreement is required for mutually training two networks to
handle noisy labels.

Based on the observations, there is an urgent need for us to come up with a
mechanism capable of self-adjusting to maintain the optimal divergence between
two networks. Regularization is a technique widely used in co-training, e.g.,
co-regularization in JoCoR. Unlike JoCoR, which updates gradients respectively
and increases agreement by co-regularization, we design a new co-
regularization from the perspective of maintaining disagreement between the
two networks and propose a noise-tolerant learning framework named Mutual
Label Correction (MLC). To this end, we introduce a new way to measure the
distance between the two networks. We also present a label probability
distribution model based on mutual learning, which can be used in correcting
the noisy labels along with the model training. As far as we can observe, MLC
not only prevents premature agreement (like Co-teaching in Fig. 2) but also
avoids performing poorly on extremely noisy data (like Co-teaching+ in Table
II and III). Compared with JoCoR, MLC inherits the merits of mutual gradient
updates which can ensure consistency and meanwhile better prevent error
accumulation. Below, we summarize the key contributions of this work:

  * •

We discovered that mutual learning-based LNL methods need to maintain a
certain degree of inconsistency while pursuing the consistency of predictions.

  * •

A new co-regularization term for constraining the network divergence is
designed to solve the problem of network convergence.

  * •

A novel noise-tolerant learning framework with a new co-regularization is
introduced, which adopts a label probability model and corrects the noisy
labels during training.

##  II Related Work

###  II-A Learning with noisy labels

Many approaches have been proposed to the learning-with-noisy-labels (LNL)
problem based on supervised learning[13] including designing new robust loss
functions[2, 3], estimating transition matrix[1] and etc. DNNs have been
proved to have a certain degree of generalization and have been leveraged to
promote classification robustness[14]. Some methods [15] require a small clean
sample set for training, which is not suitable for many practical problems.
[16] has shown that DNNs tend to learn simple patterns first before fitting
noises, resulting in a general rule that samples with lower loss are more
likely to be clean samples. Based on this, [17] fits a two-component Beta
Mixture Model (BMM) to distinguish the distribution of clean and noisy
samples, which tends to produce undesirable flat distributions under
asymmetric noises. MentorNet[12] leverages curriculum learning to screen
correct labels for student network training. Inspired by Co-training, Co-
teaching[7] and Co-teaching+[9] train two neural networks simultaneously and
learn each other’s small loss samples to update together. JoCoR[11] does not
uses cross-updating. Instead, it calculates a joint loss with Co-
Regularization and uses small-loss instances in updating gradients to
explicitly reduce the diversity of two networks. DivideMix[18] combines two
networks in implicit and explicit two ways. It models samples loss
distribution with a Gaussian Mixture Model (GMM) to divide the dataset into a
labeled set (mostly clean) and an unlabeled set (mostly noisy), then uses an
improved MixMatch[19] method to perform semi-supervised training. Unlike
previous work, MoPro[20] combined self-supervised learning and supervised
learning together to release the unscalability in webly-supervised
representation learning.

###  II-B Co-training

As an extension of self-training, co-training[21] lets multiple individual
models iteratively learn from each other[22, 23]. It requires the “sufficiency
and independence” assumptions hold. That is to say two classifiers should keep
diverged to achieve the better ensemble effects. Recently, Deep Co-
training[24] maintains disagreement through a view difference constraint. For
example, to prevent consensus, TriNet[25] designs different head structures
and samples different sub-datasets for learners. [26] applies a graph-based
regularization and also integrates supervised contrastive learning. However,
in the tasks of learning with noisy labels, without the distinct views of
data, co-training has to promote diversity in some other ways.

##  III Preliminary

Inspired by co-training in semi-supervised learning, Co-teaching, Co-
teaching+, and JoCoR all adopt the scheme of training two networks
simultaneously. But they follow different error flow strategies to combat
label noise, just as Fig. 1 illustrated. Both Co-teaching and Co-teaching+
adopt cross updates of mutual learning.

In order to further understand the performance of mutual learning on noisy
labels, we conducted exploratory experiments on two noisy datasets, namely
MNIST and CIFAR-10 with 20% pair-flip pollution. We use KL divergence to
measure the degree of inconsistency between the two networks in predicted
probability distributions, and define the divergence as follows:

$Divergence=KL(p_{1},p_{2})+KL(p_{2},p_{1})$ (1)

where $p_{1}$ is the Softmax output of the first network, $p_{2}$ is that of
the second network, and $KL()$ is the operation of KL divergence.

(a) MNIST Co-teaching

(b) CIFAR-10 Co-teaching

(c) MNIST Co-teaching w/o

(d) CIFAR-10 Co-teaching w/o

Figure 2: Accuracy and Divergence of Co-teaching with or without mutual
updates on MNIST and CIFAR-10 datasets with $20\%$ pair-flip noise.

Fig.2 reports the exploratory experiments result of the total variation in
divergence and accuracy on the test sets. The red line represents the overall
accuracy of the current model, and the blue line represents the divergence of
the predictions between the two networks. It could be found that Co-teaching
that uses mutual updates (Fig. 2(a), 2(b)) has better robustness and
generalization than training two networks independently (Fig. 2(c), 2(d)). For
Co-teaching, as the training process progresses, the overall accuracy
increases while the value of divergence decreases. This suggests that mutual
updates will make the two networks increasingly consistent. In essence, noisy
labels exacerbate the complexity of the optimization space, easily causing
gradient-based optimizers to fit noise and get stuck in local optima. Mutual
information updates from the peer network will reduce the likelihood of
getting stuck in local minima, but its ultimate goal is to form consistent
predictions in the global optimum. So we get the observation as follows.

###### Lemma 1

Mutual learning tends to maximize prediction consistency.

(a) CIFAR-10 sn-0.2 (b) CIFAR-10 sn-0.4 (c) CIFAR-10 sn-0.8 (d) MNIST sn-0.2

(e) MNIST sn-0.4 (f) MNIST sn-0.8

Figure 3: The variation of average accuracy under different network
divergences.

However, during mutual training, two networks may converge prematurely due to
the unbalanced sample distribution, which will cause Co-teaching to degenerate
into self-paced learning[9] Co-teaching+ tries to tackle this problem by
adopting an “update by disagreement” strategy, which results in slower and
more volatile optimization. Fig. 3 shows the experimental results of Co-
teaching on MNIST and CIFAR-10 with different random label corruption. It
shows the variation of average accuracy under different network divergences.
There is a clear trend that with the divergences increase they first go up and
then come down within different dataset and noise corruption. It indicates
that a certain degree of variance helps to better judge label accuracy on
noisy datasets, thereby improving generalization. Then we get the second
observation as follows.

###### Lemma 2

A certain disagreement is required for mutually training two networks to
handle noisy labels.

Therefore, there is a need for us to find a better way to update the gradients
and design an effective mechanism to maintain the divergence of different
networks, thus to maintain the robustness via mutually training.

##  IV Proposed Method

###  IV-A Co-Regularization

Many co-training-based methods add regularization to make predictions less
divergent, ensuring that networks will eventually learn a consistent global
optimum. Unfortunately, it will introduce bias locally. Especially in the case
of noisy annotations, the situation becomes complicated and difficult to
quantify. To avoid this kind of bias, we design an adaptive co-regularization
from the perspective of quantifying the distance of network parameters. This
is because network has the ability to remember. Its parameters are more stable
and less irrelevant to label noise. Given two collaborative networks
$f\left(\theta_{1}\right)$ and $f\left(\theta_{2}\right)$ parameterized by
$\theta_{1},\theta_{2}$, we use Euclidean distance to measure the distance of
network parameters as follows:

$dist=\|\theta_{1},\theta_{2}\|_{2}$ (2)

And the co-regularization term $l_{d}$ can be formulate as:

$l_{d}={dist}^{\mu}$ (3)

where $\mu$ is a negative hyper-parameter. A lower $\mu$ forces models to
separate more. As previously mentioned in Section III, MLC adopts mutual
updates which will naturally let models from different networks get closer
during training. Therefore, in this paper, we hope to prevent the consensus
between the two networks by setting this regularization. Specifically, in our
experiment we set $\mu=-1$. It is worth noting that the learner will
degenerate to Co-teaching when $\mu=-\infty$, and it will degenerate to co-
teaching+ when $\mu=0$.

###  IV-B Mutual Label Correction Framework

Based on mutual learning and co-regularization, we proposed a mutual label
correction (MLC) framework for noise-tolerant classification. The key
architect is illustrated in Fig. 4. It contains two kinds of learning at the
same time, namely network update (dotted blue lines) and label update (dotted
orange lines).

Figure 4: Mutual Label Correction (MLC) architecture.

We adopt the label probability distribution model $y^{d}$ that was originally
proposed by PENCIL[27] and adapt it for our collaborative training. To this
end, we define an auxiliary variable $\widetilde{y}$ to assist the label
updating which is initialized by multiplying one-hot encoding of the noisy
labels $\hat{y}$ and a constant hyper-parameter $K$:

$\widetilde{y}=K\hat{y}$ (4)

Then the label probability distribution $y^{d}$ can be obtained through a
softmax function:

$y^{d}=softmax(\widetilde{y})$ (5)

By inputting $p_{1},p_{2}$ and $y^{d}$ into the loss function which is defined
in the following section, we can obtain the losses $l_{1}$ and $l_{2}$
respectively. Then we compute the gradient of them with respect to the network
parameters and label probability distribution through back-propagation. The
No.1 network is updated by the gradient of $\frac{\delta L^{2}}{\theta_{2}}$
and the No.2 network is updated by the gradient of $\frac{\delta
L^{1}}{\theta_{1}}$.

In PENCIL, since it has only a single label distribution, the way to update
the label distribution is as follows:

$\widetilde{y}\leftarrow\widetilde{y}-\lambda\frac{\delta L}{y^{d}}$ (6)

where $\lambda$ is the step size of the label update. To maximize label
consistency, we update the labels using the sum of the two network gradients:

$\widetilde{y}\leftarrow\widetilde{y}-\lambda(\frac{\delta
L^{1}}{y^{d}}+\frac{\delta L^{2}}{y^{d}})$ (7)

###  IV-C Loss Function

The loss function of MLC contains multiple loss terms, which are defined as
follows:

$L=l_{c}\left(p,y^{d}\right)+\alpha l_{o}\left(\hat{y},y^{d}\right)+\beta
l_{e}\left(p\right)+\xi l_{d}\left(\theta_{1},\theta_{2}\right)$ (8)

In which $l_{c}$ is flipped Kullback-Leibler (KL) divergence of prediction and
label distribution. $l_{o}$ is the KL divergence between original noisy labels
$\hat{y}$ and updated label distribution $y^{d}$. $l_{e}$ is the Shannon
entropy of network prediction to avoid over-smooth prediction. $l_{d}$ is co-
regularization. $\alpha,\ \beta,\ \xi$ are their weighted hyper-parameters.
Detailed formulation of $l_{c},l_{o}$ and $l_{e}$ can be found at [27].

##  V Experiment

###  V-A Experiment Setup

####  V-A1 Datasets

We compare MLC with state-of-the-art methods on two classical datasets with
artificial label noise and a real-world noisy dataset, Clothing1M.

(a) symmetric (b) pairflip

Figure 5: Transition matrices of different noise types (using 6 classes as an example with $20\%$ noise) TABLE I: Choice of label update step on MNIST and CIFAR-10. | sn-0.2 | sn-0.4 | sn-0.8 | pair-0.2 | pair-0.45
---|---|---|---|---|---
MNIST | 1000 | 3000 | 3000 | 2000 | 2500
CIFAR-10 | 3000 | 4000 | 4000 | 1500 | 4000

MNIST contains 60k handwriting characters of 0-9 with size 28px*28px. We split
the dataset into a training set of 50k images and a testing set of 10k images.
All images are randomly augmented by image perspective transformation and
color jittering.

CIFAR-10 contains 60k 32px * 32px images of 10 categories with 50k training
data and 10k testing data. We apply random horizontal flips and random
cropping to all training data.

According to the definition provided by [7] (Fig. 5), we use symmetric noise
(sn) and pairflip noise (pair) to randomly corrupt labels on MNIST and
CIFAR-10. We test with symmetric noise of progressively increased noise ratios
on these two datasets, including 0.2, 0.4, and 0.8. For the more challenging
pairflip noise, we test with it in the ratios of 0.2 and 0.45.

Clothing1M contains 1 million training data with real-world label noise and
10526 clean testing data in 14 classes of different clothing types. Following
JoCoR, we scale all images into 256px * 256px and apply 224px *224px centered
crop. After that, we applied the normalization for all images.

Our experiments were carried out on the software platform of Ubuntu 18.04 LTS
and PyTorch 1.4.0, using the hardware of Intel i7-8700k CPU, NVIDIA RTX2080Ti
GPU, and 32GB RAM.

TABLE II: Accuracy on MNIST | sn-0.2 | sn-0.4 | sn-0.8 | pair-0.2 | pair-0.45
---|---|---|---|---|---
| best | last | best | last | best | last | best | last | best | last
Standard | 97.29 | 91.04 | 96.45 | 83.86 | 86.69 | 35.14 | 96.28 | 85.1 | 73.13 | 55.72
Co-teaching | 97.56 | 97.45 | 96.5 | 96.24 | 80.43 | 76.87 | 96.7 | 96.22 | 90.29 | 88.4
Co-teaching+ | 96.82 | 96.64 | 95.84 | 95.7 | 75.13 | 74.49 | 96.73 | 96.44 | 82.21 | 81.61
PENCIL | 97.31 | 93.94 | 96.44 | 85.31 | 86.58 | 33.44 | 96.07 | 85.61 | 74.52 | 55.08
JoCoR | 97.23 | 97.2 | 96.16 | 96.11 | 76.62 | 74.35 | 96.27 | 96.15 | 90.63 | 90.18
MoPro | 97.21 | 96.75 | 96.46 | 96.22 | 83.65 | 82.84 | 97.11 | 96.83 | 66.97 | 64
MLC | 97.92 | 97.85 | 97.52 | 97.43 | 89.86 | 89.58 | 97.95 | 97.85 | 91.56 | 90.28
TABLE III: Accuracy on CIFAR-10 | sn-0.2 | sn-0.4 | sn-0.8 | pair-0.2 | pair-0.45
---|---|---|---|---|---
| best | last | best | last | best | last | best | last | best | last
Standard | 73.86 | 64.97 | 67.58 | 45.09 | 35.48 | 15.36 | 72.84 | 70.68 | 50.8 | 44.09
Coteaching | 76.11 | 74.08 | 72.06 | 69.37 | 30.97 | 16.92 | 74.78 | 73.61 | 56.06 | 52.78
Co-teaching+ | 75.66 | 69.84 | 72.03 | 51.07 | 31.01 | 13.65 | 74.66 | 67.61 | 56.4 | 41.32
PENCIL | 75.95 | 67.72 | 71.14 | 50.73 | 35.72 | 14.69 | 75.34 | 70.69 | 51.77 | 46.8
JoCoR | 82.51 | 82.22 | 77.19 | 76.94 | 23.19 | 22.19 | 81.17 | 80.68 | 48.59 | 45.08
MoPro | 77.7 | 76.07 | 70.04 | 59.68 | 50.84 | 44.23 | 81.55 | 80.67 | 57.75 | 50.63
MLC | 84.59 | 84.46 | 80.66 | 80.45 | 41.88 | 41.48 | 84.71 | 84.56 | 65.23 | 64.16
TABLE IV: Result on Clothing1M Methods |  Standard |  Co-teaching |  Co-teaching+ |  PENCIL |  JoCoR |  MLC
---|---|---|---|---|---|---
Accuracy |  64.68 |  68.51 |  58.79 |  66.53 |  69.79 |  69.8

####  V-A2 Baselines

We compare MLC with the following state-of-the-art algorithms. All the codes
for comparison were applied from the official implementation.

Standard This is the most basic training algorithm without any modification or
tricks to combating noisy labels.

Co-teaching This is the first algorithm in combating noisy labels with dual-
network. It combating noisy labels by mutual information exchange and small-
loss sample selection.

Co-teaching+ This is the algorithm based on the Co-teaching. It claims the
"Update by disagreement" strategy by disagreement sample selection.

PENCIL This is the most representative algorithm of learning and correcting
the label distribution simultaneously.

JoCoR This is the algorithm that claims the agreement updating by a joint
regular term, which can reduce the distance between networks.

MoPro This is the latest robust method that combine self-supervised learning
and supervised learning together.

####  V-A3 Network and Optimizer

For the experiments on MNIST, we use a two-layer MLP as the backbone[7]. The
batch size is set to 128 and uses Adam optimizer. For the 3-stage training, we
train MLC in a total of 320 epochs, including 30 warmup epochs and 180
finetune epochs. The learning rate is 0.001 at the beginning 140 epochs and
then decrease to 0.0001. The choice of label update parameter $\lambda$ is
listed in Table I.

On CIFAR-10, we use a six-layer CNN backbone. We train MLC 320 epochs in
total. The learning rate is 0.005 in 200 epochs and then decrease to 0.0001.

For the experiment on Clothing1M, we follow the setting of JoCoR, which has a
64 batch size of ResNet-18 backbone, optimized by Adam. The learning rate is
0.0001 and $\lambda$ is 4000.

####  V-A4 Measurement

We use the classification accuracy to measure network performance:

$Accuracy=\frac{number\ of\ correct\ prediction}{number\ of\ samples}$ (9)

Notably, we record the best test accuracy during training named as best and
the average test accuracy of the last ten epochs named as last. In our
experiments, it is not always that higher best accuracy is associated with
high last accuracy. We perform five trials training on MNIST and CIFAR-10 to
report their average results. Specifically, the comparison results of
Clothing1M are referenced from [11].

###  V-B Results

Table II and Table III show the classification accuracy of all comparison
methods on MNIST and CIFAR-10. MLC won first place under various noise
ratios/types in most cases. We found that noisy labels do degenerate the
accuracy of DNN classifiers from experimental results. As the noise ratio
increases, the accuracy of almost all the comparison methods decreases with
varying degrees. For instance, the accuracy (last) of the standard method are
reduced by more than 50% when the noise ratio equals 0.8 on MNIST and
CIFAR-10.

Fig. LABEL:fig:mnist_box and Fig. LABEL:fig:cifar10_box show the accuracy
(last) among five trials training results with various noise ratios and noise
types of MNIST and CIFAR-10. MLC outperforms comparison methods by higher
accuracy and more stable result. Surprisingly, the accuracy of Co-teaching is
usually higher than Co-teaching+. In Fig. LABEL:fig:mnist_box_a,
LABEL:fig:mnist_box_c, LABEL:fig:mnist_box_d and Fig. LABEL:fig:cifar10_box_a,
LABEL:fig:cifar10_box_c, LABEL:fig:cifar10_box_d, the Bright yellow box (Co-
teaching+) is lower and larger than the orange box (Co-teaching) and blue box
(JoCoR), which means that Co-teaching and JoCoR are more accurate and stable
than Co-teaching+ in most cases. Specifically, MoPro has the higher accuracy
in sn-0.8 of CIFAR-10 due to unsupervised feature learning but still suffers
from instability. In Fig. LABEL:fig:cifar10_box_d, LABEL:fig:cifar10_box_e,
the deep pink box (MoPro) is larger than the others. On the contrary, MLC has
lower accuracy variance under a large noise ratio since a certain disagreement
is required for mutually training two networks. For instance, in Fig.
LABEL:fig:mnist_box_b, LABEL:fig:mnist_box_e and Fig. LABEL:fig:cifar10_box_b,
LABEL:fig:cifar10_box_e, the sienna box (MLC) is smaller than the others.

Interestingly, co-training-based methods are usually higher than others in the
last accuracy, even if they are not guaranteed to obtain the best accuracy.
For example, in sn-0.8 of MNIST, PENCIL and Standard won the second and third
place of best accuracy. However, they were overtaken by the co-training-based
methods over 40% of the accuracy (last), which means they have fitted noisy
labels. In fact, single network methods are capable of higher accuracy but
easily memorize errors. In contrast, co-training-based methods are more
robust. The gap between best and last accuracy is much lower than others, but
there is still room to improve the best accuracy. By contrast. MLC obtain both
best and last accuracy owing to better mutually training.

Another observation is that the label correction method PENCIL can be worse
than Standard under pairflip noise. For instance, 0.45 pairflip noise in
MNIST. That might is caused by inaccurate label correction, which is related
to accurate class probability prediction. On the contrary, MLC performs better
than others under pairflip noise with the help of mutual learning.

The result of Clothing1M (Table IV) is similar to MNIST and CIFAR-10. MLC gets
the highest accuracy under real-world noise. Surprisedly, Co-teaching+ is
worse than Standard in a large gap. The classification accuracy of MLC is
slightly better than the two co-training methods and much higher than Co-
teaching+.

##  VI Conclusion

This study set out to determine the necessity of “Disagreement” for training
two networks to deal with noisy labels. The result shows that a certain degree
of variance helps to judge label accuracy on noisy datasets better. Based on
the observations, we designed a novel regularization term to ensure mutual
collaboration between networks. Moreover, we establish a noise-tolerant
framework named MLC with a mutual label correction mechanism and mutually
regularization. MLC achieves the state-of-the-art result under different noise
ratios/types of all datasets. In the future, it is expected that the proposed
method can be adjusted to adapt to the needs of imbalanced data.

## Acknowledgment

This work was supported by the joint project of BRC-BC (Biomedical
Translational) Engineering research center of BUCT-CJFH XK2020-07 and was
supported in part by the National Natural Science Foundation of China under
Grant No. 62101021.

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