How does a Neural Network's Architecture Impact its Robustness to Noisy Labels?
Authors: Jingling Li
Mozhi Zhang
Keyulu Xu
John P Dickerson
Jimmy Ba
Venue: NeurIPS 2021 Poster (2021)
Keywords: noisy labels
architectural inductive bias
algorithmic alignment
graph neural networks

Abstract: Noisy labels are inevitable in large real-world datasets. In this work, we explore an area understudied by previous works --- how the network's architecture impacts its robustness to noisy labels. We provide a formal framework connecting the robustness of a network to the alignments between its architecture and target/noise functions. Our framework measures a network's robustness via the predictive power in its representations --- the test performance of a linear model trained on the learned representations using a small set of clean labels. We hypothesize that a network is more robust to noisy labels if its architecture is more aligned with the target function than the noise. To support our hypothesis, we provide both theoretical and empirical evidence across various neural network architectures and different domains. We also find that when the network is well-aligned with the target function, its predictive power in representations could improve upon state-of-the-art (SOTA) noisy-label-training methods in terms of test accuracy and even outperform sophisticated methods that use clean labels.

How Does a Neural Network's Architecture Impact Its Robustness to Noisy Labels?
Jingling Li
Mozhi Zhang
Department of Computer Science University of Maryland College Park, MD 20740 j jinglinggee ingêcs umd edu
Department of Computer Science
University of Maryland College Park, MD 20740
mozhi @cs umd. edu
Keyulu Xu
Computer Science and Artificial Intelligence Laboratory (CSAIL) Massachusetts Institute of Technology (MIT)
Cambridge, MA 02139 keyulu@mit. .ddu
John Dickerson
Jimmy Ba
Department of Computer Science University of Maryland College Park, MD 20740 johnêcs. umd. edu
Department of Computer Science University of Toronto, Canada jbaêes. toronto.
Abstract
Noisy labels inevitable in large real-world datasets. In this work, we explore area understudied by previous works - how the network's architecture impacts its robustness noisy labels. We provide formal framework connecting the robustness of network to the alignments between its architecture and target/noise functions. Our framework measures a network's robustness via the predictive power in its representations the test performance of a linear model trained on the learned representations using small a network is more robust to noisy labels if its architecture is more aligned with the target function than the noise. To support our hypothesis, we provide both theoretical and empirical evidence across various neural network architectures and different domains. We also find that when the network well-aligned with the target function, its predictive power in representations could improve upon state-of-the-art (SOTA) boisy-label-training methods terms of test accuracy and even outperform sophisticated methods that use clean labels.
clean labels. We hypothesize that
Introduction
Supervised learning starts with collecting labeled data. Yet, high-quality labels are often expensive.
To reduce annotation cost, collect labels from non-experts [1] online queries [577], which are
inevitably noisy. To learn from these noisy labels, previous works propose many techniques, including
modeling the label noise 1-10), designing robust losses [1H144, adjusting loss before gradient
updates [3), selecting trust-worthy samples [12
22
24
31
designing robust architectures [32
39 applying robust regularization in training 40 using meta-learning to avoid over-fitting [46]
and applying semi-supervised learning 28 48
to learn better representations.
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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While these methods improve some networks' robustness to noisy labels, we observe that their effectiveness depends on how well the network's architecture aligns with the target/noise functions, and they are less effective when encountering more realistic label noise that is dlasedeepn or instance-dependent. This motivates us to investigate an understudied topic: how the network's architecture impacts its robustness to noisy labels.
We formally answer this question by analyzing how network's architecture aligns with the target function and the noise. To start, we measure the robustness of network via the predictive power in its learned representations (Definition I. as models with large test errors may still learn useful predictive hidden representations [52 [3 Intuitively, the predictive power measures how well the representations can predict the target function. practice, we measure by training a linear model on top of the learned representations using a small set of clean labels and evaluate the linear model's test performance
We find that a network having a more aligned architecture with the target function is more robust noisy labels due its more predictive representations, whereas a network having an architecture more aligned with the noise function is less robust. Intuitively, a good alignment between network's s architecture and a function exists the architecture can be decomposed into several modules such that each module can simulate one part of the function with a small sample complexity. The formal definition of alignment is in Section 2.3 adapted from 55
Our proposed framework provides initial theoretical support for our findings on a simplified noisy setting (Theorem 2 Empirically, we validate our findings synthetic graph algorithmic tasks by designing several variants of Graph Neural Networks (GNNs), whose theoretical properties and alignment with algorithmic functions have been well-studied (55 Many noisy label training methods are applied to image classification datasets, so we also validate our findings on image domains using different architectures.
Most of our analysis and experiments use standard neural network training. Interestingly, we find similar results when using DivideMix [49]. SOTA method for learning with noisy labels: for networks less aligned with the target function, the SOTA method barely helps and sometimes even hurts test accuracy; whereas for more aligned networks, it helps greatly.
For well-aligned networks, the predictive power of their learned representation could further improve the test performance of SOTA methods, especially on class-dependen or instance-depende label noise where current methods on noisy label training are less effective. Moreover, on Clothing M (58), a large-scale dataset with real-world label noise, the predictive power of well-aligned network's learned representations could even outperform some sophisticated methods that use clean labels.
In summary, we investigate how an architecture's alignments with different (target and noise) functions affect the network's 'ss robustness to noisy labels, which we discover that despite having large test errors, networks well-aligned with the target function can still be robust to noisy labels when evaluating their predictive power in learned representations. To formalize our finding, we provide a theoretical framework to illustrate the above connections. At the same time, we conduct empirical experiments on various datasets with various network architectures to validate this finding. Besides, this finding further leads to improvements over SOTA loisy-label-traiing methods on various datasets and under various kinds of noisy labels (Tables 10 in Appendix A).
1.1 Related Work
commonly studied type of noisy label is the random label noise, where the noisy labels are drawn i. from a uniform distribution. While neural networks trained with random labels easily overfit (59). has been observed that networks learn simple patterns first (52). converge faster on downstream tasks (53), and benefit from memorizing atypical training samples [60].
Accordingly, many recent works noisy label training are based on the assumption that when trained
with noisy labels, neural networks would first fit to clean labels 12 25 26 50 and learn useful
feature patterns [18 61 63). Yet, these methods are often more effective random label noise than
on more realistic label noise (i.e., class-dependent and instance-dependent label noise).
Many works on representation learning have investigated the features preferred by network during training [2 64 66), and how to interpret or control the learned representations on clean data [54] 64 67
69
Our paper focuses more on the predictive power rather than the explanatory power

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in the learned representations. We adapt the method in [54] to measure the predictive power in representations, and we study learning from noisy labels rather than from clean distribution.
On noiseless settings, prior works show that neural networks have the inductive bias to learn simple patterns [52] 66]. Our work formalizes what is considered simple pattern for a given network via architectural alignments, and we extend the definition of alignment in [5 to noisy settings.
2
Theoretical Framework
In this section, we introduce our problem settings, give formal definitions for "predictive power" and "alignment," and present our main hypothesis as well our main theorem.
2.1 Problem Settings
Let X' denote the input domain, which can be vectors, images, or graphs. The task is to learn an un- derlying target function f: X + y noisy training dataset S = {( y:)] U { út) Her, where == (xx denotes the true label for an input æ, and I denotes the noisy label. Here, the set I
contains indices with clean labels, and I' contains indices with noisy labels. We denote noise ratio in the dataset S. We consider both regression and classification problems.
[T') [S]
as the
Regression settings. We consider a label space y C IR and two types of label noise: a) additive label noise [70] : y + e, where e random variable independent from æ; dependet label noise: == g(x)) where g X'' - ) is noise function dependent on the input.
Classification settings. We consider discrete label space with C' classes: Y (1,2..... .C, and three types of label noise: a) uniform label noise: ÿ ~ Unif(1, C),, where the noisy label is drawn from discrete uniform distribution with values between 1 and C, and thus is independent of the true label; b) flipped label noise: ý is generated based on the value of the true label and does not consider other input structures; c) instance-dependent label noise: ý g(x) where g X' + y is function dependent on the input æ's internal structures. Previous works on noisy label learning commonly study uniform and flipped label noise. few recent works [7] 72) explore the instance-dependent label noise as it is more realistic.
2.2 Predictive Power in Representations
network's robustness is often measured by its test performance after trained with noisy labels. Yet, since models with large test errors may still learn useful representations, we measure the robustness of a network by how good the learned representations are at predicting the target function the predictive power in representations. To formalize this definition, we decompose a neural network ' into different modules N1, N2, ... where each module can be single layer (e.g., a convolutional layer) or a block of layers (e.g., residual block).
Definition 1. (Predictive power). Let : X y denote the underlying target function where the input æ E X' is drawn from distribution 'D. Let C = {(x,;, ys ys)) | denote small set of clean data (i.e., f(x:)). Given a network N with modules NG. let (xx) denote the representation from module N2 on the input (i.e., the output of Nf). Let denote the linear model trained with the clean set C where we use (x) as the input, and y/4 as the target value during training. Then the predictive power of representations from the module N, is defined as
Pf(f,N.C)=
E [((6)),
ænD
where is loss function used evaluate the test performance the learning task.
Remark. Notice that smaller PJ C) indicates better predictive power; i.e., the representations are better at predicting the target function. We empirically evaluate the predictive power using linear regression to obtain trained linear model I., which avoids the issue of local minima as we are solving convex problem; then evaluate L on the test set.

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2.3 Formalization of Alignment
Our analysis stems from the intuition that a network would be more robust to noisy labels if could learn the target function more easily than the noise function. Thus, we use architectural alignment to formalize what is easy to learn by given network. Xu et al. [55] define the alignment between network and a deterministic function via a sample complexity measure (i.e., the number of samples needed to ensure low test error with high probability) in PAC learning framework (Definition 3.3 (55) Intuitively, network aligns well with function if each network module can easily learn one part of the function with a small sample complexity.
in Xu et al.
Definition 2. (Alignment, simplified based on Xu et al. (55)). Net denote neural network with n modules Ny. Given a function f : X' + y which can be decomposed into n functions fy (e.g., f(x) (f. (x)) ))), the alignment between the network N and f is defined via
Alignment(N, f, y MA, Nf,
where MA, (f,, 6,0) d) denotes the sample complexity measure for Nj to learn fy with precision failure probability 8 under a learning algorithm Aj.
Remark. Notice that smaller Alignmenr(N (N f: c, 6) indicates better alignment between network N and function f. If ff is obtuse does not have structural decomposition, can choose 1, and the definition of alignment degenerates into the sample complexity measure for N to learn f. Although it is sometimes non-trivial compute the exact alignment for task without clear algorithmic structures, we could break this complicated task into sub-tasks, and would be easier to measure the sample complexity of learning each sub-task.
Xu et al. (55) further prove that better alignment implies better sample complexity and vice versa. Theorem 1. (Informal: (55)) Fix e and 8. Given a target function f : X - y and a network N. suppose { are Li.d. samples drawn from distribution D, and let :- f(x)). Then Alignment( (,,,,, M if and only if there exists a learning algorithm A such that
PAND [IINN,(()) f(x))I S 1121-
where IN,A is the function generated by A on the training data {x.4- V1 )
Remark. Intuitively, a function f (with a decomposition {fg}s) can be efficiently learned by network N (with modules {NgHy) iff each fy can be efficiently learned by Ng..
We further extend Definition 2 to work with random process F (i.e., set of all possible sample functions that describes the noisy label distribution).
Definition 3. (Alignment, extension to various noise functions). Given a neural network W and random process F, for each f E F. the alignment between A and f is measured via max, MA, (,,, 5) based on Definition Then the alignment between A and defined as
Alignment" (N,F,e, := sup max (f,,Ny,,e,), feF
where N can be decomposed differently for various f.
2.4 Better Alignment Implies Better Robustness (Better Predictive Power)
Building on the definitions of predictive power and alignment, we hypothesize that a network better-aligned with the target function (smaller Aligument(NN, f, 6)) would learn more predictive representations (smaller (f,,NCCC) when trained on a given noisy dataset.
Hypothesis 1. (Main Hypothesis). Let f > y denote the target function. Fix e, 6, a learning algorithm A, noise ratio, and noise function X' + y (which may be drawn from a random process). Let denote a noisy training dataset and C denote small set of clean data. Then for network N trained on S with the learning algorithm A.
Aligmmen(NN, f,,, - P,0,,N,C) 4,
(4)
where j is selected based on the network's architectural alignment with the target function (for simplicity, consider j in this work).

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We prove this hypothesis for simplified case where the target function shares some common struc- tures with the noise function (e.g., class-dependent label noise). We refer the readers to Appendix C for full statement of our main theorem with detailed assumptions.
Theorem 2. (Main Theorem; informal) For a target function f - y and a noise function
g X - Y. consider neural network N well-aligned with I such that P, C) is small when training N on clean data (i.e., PJ
NNN.C C) < e efor some small constant c). If there exists a function
on the input domain X such that I and g can be decomposed as follows: Vx E X, f(x) Jr (h(r))
with fr being a linear function, and g(z) = gr (h(x))) ) for some function gr. then the representations learned by N the noisy dataset still have good predictive power with P,f,,NCC <
We further provide empirical support for our hypothesis via systematic experiments on various architectures, target and noise functions across both regression and classification settings.
3 Experiments on Graph Neural Networks
We first validate our hypothesis on synthetic graph algorithmic tasks by designing GNNs with different levels of alignments to the underlying target/noise functions. We consider regression tasks. The theoretical properties of GNNs and their alignment with algorithmic regression tasks well- studied 57 73). To start, we conduct experiments on different types of additive label noise and extend our experiments instance-dependent label noise, which closer to real-life noisy labels.
Common Experimental Settings. The training and validation sets always have the same noise ratio, the percentage of data with noisy labels. We choose Error (MAE) as our loss functions. Due to space limit, the results using MAE are in Appendix [A.3] All training details are in Appendix [B.3] The test error is measured by mean absolute percentage error (MAPE), a relative error metric.
squared error (MSE) and Mean Absolute
3.1 Background: Graph Neural Networks
GNNs are structured networks operating on graphs with MLP modules [7 The input is graph g = (V. E) where each node u E V has a feature vector 2u, and we use (N) to denote the set of neighbors of GNNs iteratively compute the node representations via message passing: (1) the node representation h. is initialized as the node feature: h: æ.i (2) iteration k L..K, the node representations (k) are updated by aggregating the neighboring nodes' representations with MIP modules [8T). We can optionally compute a graph representation hg by aggregating the final node representations with another MLP module. Formally,
h (k)
Σ MEN(M)
MLP(() (n (k-1) (11-1),1!--111 11/
(5)
hg = MLP(K+1)
(K)
(6)
WEGT
Depending on the task, the output is either the graph representation hG or the final node representa- tions (K), We refer to the neighbor aggregation step for (kk as aggregation and the pooling step for hg as readout. Different tasks require different aggregation and readout functions.
3.2 Additive Label Noise
Hu al. [70] prove that MLPs are robust additive label noises with zero mean, if the labels are drawn i.i.d. from Sub-Gaussian distribution. Wu and Xu [82] also show that linear models are robust to zero-mean additive label noise even in the absence of explicit regularization.
this section, we show that GNN well-aligned to the target function not only achieves low test errors on additive label noise with zero-mean, but also learns predictive representations on noisy labels that are drawn from non-zero-mean distributions despite having large test error.
Task and A Architecture. The task is to compute the maximum node degree:
f(g) max vEN(u)
Σ
1.
5

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Module
Module(!)
30
hig MLP (2) (max
MLP (hw Hy))
25
KES
DEN
(()) i mmax
-15
WCS
PCN
10
22
f1()
Figure 1: Max-sum GNN aligns well with the task maximum degree. Max-sum GNN hg be decomposed into two modules: Module and Module and the target function f(g) be similarly divided as f()) = fa(fi( As the nonlinearities of the target function have been en- coded in the GNN's architecture, (C) can be eas- ily learned hg: f+) can be easily learned by (* and fa(-) is the same as !odule!
PCA visualization of hidden represen- tations from a max sum GNN trained with addi- tive label noise drawn from ((00 15) at 100% noise ratio. Each dot denotes single training ex- ample and is colored with its true label. The x-axis and y-axis denote the projected values the first and second principal components. As the colors change gradually from left to right, the largest prin- cipal component of the representations have clear linear relationship with the true labels.
Figure 2:
We choose this task as we know which GNN architecture aligns well with this target function 2 2-layer GNN with aggeegggen and sum-readout (max-sum GNN):
hg 2LP
max.eg
Σ
MLP(1) (bus (hr))
(8)
vEN(u)
h2 =
Σ vEV(u)
MLP
(9)
Figure demonstrates how exactly the max-sum GNN aligns with fG).. Intuitively, they are well- aligned the MLP modules of max-sum GNN only need to learn simple constant functions to simulate f(g). Based Figure 1 take the output of Module as the learned representations for max-sum GNNs when evaluating the predictive power.
Label Noise. We corrupt labels by adding independent noise drawn from three distributions: Gaussian distributions with zero mean (O, 40) and non-zero mean ((10, 15), and long-tailed Gamma distribution with zero-mean I(2, 1/15) 30. We also consider more distributions with non-zero mean in Appendix A.2
Findings. In Figure 3 while the max-sum GNN is robust to zero-mean additive label noise (dotted yellow and purple lines), its test error is much higher under non-zero-mean noise N(00, 15) (dotted red line) as the learned signal may be "shifted" by the non-centered label noise. Yet, max-sum GNNs learned representations under these three types label noise predict the target function well when evaluating their predictive powers with 10% clean labels (solid lines in Figure 3).
Moreover, when we plot the representations (using PCA) from max-sum GNN trained under 100%
noise ratio with e ~ (10,, 15), the representations indeed correlate well with true labels (Figure 2 This explains why the representation learned under noisy labels can recover surprisingly good test performance despite that the original model has large test errors.
The predictive power of -inttali-i max-sum GNNs is in Table (Appendix A.I
3.3 Instance-Dependen Label Noise
Realistic label noise is often instance-dependent For example, an option is often incorrectly priced in the market, its incorrect price (i.e., the noisy label) should depend on properties of the underlying stock. Such instance-dependen label noise is more challenging, as it may contain spurious signals that are easy to learn by certain architectures. In this section, we evaluate the representation' predictive power for three different GNNs trained with instance-dependent label noise.

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40
<- --N 40)
3
DeepSit
max max CNN
mi sum GNN
E- -(100 15)
12
Test Test MAPE (%)
30
T(2, 1/15) 30
Test MAPE (log
25
15-
3
10
1.
15
20
40 60 50 [00
Noise ratio (%)
0
20
40
60
80
100
Noise ratio (%)
Figure 4: Representations are more predictive for GNNs more aligned with the target func- tion, and less predictive for GNNs more aligned with the noise function. On the maximum node feature task, while all three GNNs have large test errors under high noise ratios (dotted lines), the predictive power (solid lines) in representations from Deepset (yellow) and max-max GNN (red) greatly reduces the test MAPE. In contrast, the rep- resentation's 's predictive power for max-sum GNN barely reduces the model's test MAPE (tiny gap between dotted and solid purple lines).
Figure Representations are very predictive for a GNN well-aligned with the target function under additive label noise. On the maximum de- gree task, the representations' predictive power (solid lines) achieves low test MAPE (< 5%) across all three types noise the max-sum GNN, despite that the model's test MAPE (dot- ted lines) may be quite large (for noise). We average the statisties over runs using different random seeds.
Task and Label Noise. We experiment with a new task compuunng the maximum node feature:
(()) == max g puullss
(10)
To create a instance-dependent noise, we randomly replace the label with the maximum degree:
(
max
Σ
(11)
vEN(w)
Architecture. We consider three GNNs: DeepSet 83 max-max GNN, and max-sum GNN. DeepSet can be interpreted special GNN that does not use neighborhood information:
hg = MLP(1)
mmxx,ecMLP(O)
(12)
Max-max GNN is a 2-layer GNN with max-aggregation and max-readout. Max-sum GNN the same as the one in the previous section.
DeepSet and max-max GNN are well-aligned with the target function f()), as their MLP modules only need to learn simple linear functions. In contrast, max-sum GNN is more aligned with g(G) than fG) since neither its MLP modules sum-aggregation module can efficiently learn the max-operation in f() 57)
Moreover, DeepSet cannot learn (()) the model ignores edge information. We take the hidden representations before the last MLP modules in all three GNNs and compare their predictive power.
Findings. While all three GNNs have large test errors under high noise ratios (dotted lines in Figure the predictive power in representations from GNNs more aligned with the target function DeepSet (solid yellow line) and max-max GNN (solid red line) significantly reduces the original models' test errors by 10 and 1000 times respectively. Yet, for the max-sum GNN, which is more aligned with the noise function, training with noisy labels indeed destroy the internal representations such that they are no longer to predict the target function - its representations' predictive power (solid purple line) barely decreases test error. We also evaluate the predictive power of these three types of randomly-initialized initialized GNNs, and the results are in Table (Appendix A.. A.I.
4 Experiments on Vision Datasets
Many noisy label training methods are benchmarked on image classification; thus, we also validate our hypothesis on image domains. We compare the representations' predictive power between MLPs and CNN-based networks using 10% clean labels (all models are trained until they could perfectly fit the noisy labels, a.k.a., achieving close to 100% training accuracy). We further evaluate the predictive
7

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CIFAR-Easy
0
2
100
Test. Accuracy (%)
5
80
8 (4) Class locations
40
MLP
CNN
Oh) The masked
2000
5000
7500
15 30
25
# of training samples
image
( "cal" image from CIFARIO
Figure 6: Sample complexity of MLPs and CNNs on CIFAR-Easy. Both MLPs and CNNs can achieve 100% test. accuracy given sufficient training examples, but MLPs need far fewer exam- ples than CNNs and thus are more sample-efficient CIFAR-Easy.
Figure 5: Synthetic Labels on CIFAR-Easy. For each image, we mask pixel the top left corner with pink color. Then the synthetic label for this image the location of the pink pixel/mask (i.c., the cat image in the above example has label 4),
power in representations learned with SOTA methods. Predictive power on networks that aligned well with the target function could further improve SOTA method's test performance (Section 4.2). The final model also outperforms some sophisticated methods on noisy label training which also use clean labels (Appendix A.4). All our experiment details are in Appendix B.4
4.1 MLPs vs. CNN-based networks
To validate our hypothesis, we consider several target functions with different levels of alignments to MLPs and CNN-based networks. All models in this section are trained with standard procedures without any robust training methods or robust losses.
Datasets and Label Noise. We consider two types of target functions: one aligns better with CNN-based models than MLPs, and the other aligns better with MLPs than CNN-based networks.
1). CIFAR-10 and CIFAR-100 [4] come with clean labels. Therefore, we generate two types of noisy labels following existing works: (1) uniform label noise randomly replaces the true labels with all possible labels, and (2) flipped label noise swaps the labels between similar classes (e.g.. deert dog+>cat) on CIFAR-10 10 [4). or flips the labels to the next class CIFAR- -10AR-100-R [
2). CIFyR-Easy a dataset modified on CIFAR-10 10 with labels generated by procedures in Figure
the class/label of each image depends on the location of a special pixel. We consider three types
of noisy labels on CIFAR-Easy: (1) uniform label noise and (2) flipped label noise (described as
above); and (3) instance-d label noise which takes the original image classification label as the noisy label.
Uniform Noise (CIFAR-10)
F Flipped Noise (CIFAR-10)
Uniffomm Noise (CIFAR-160)
Flipped Naise (CIFAR (CFFAR-100)
70
nocumcy
52
90
MLP
20
42
10
Noise ratio (%)
ratio (%)
Noise ratio (%)
Figure 7: CIFAR-10/100 with uniform and flipped label noise. Fach line indicates the raw test accuracy (dotted) and the predictive power in representations (solid) learned by a model trained across various noise ratios.
As CNN-based networks align better with image classification tasks than MLPs. their representations' predictive power (solid yellow and red lines) higher than that of MLPs (solid purple lines) on most noise ratios.
Architectures. On CIFAR-10/100, we evaluate the predictive power in representations for three architectures: 4-yer MLPs, 9-layer CNNs, and 18-layer PreAct ResNets [85]. On CIFAR-Easy compare between MLPs and CNNs. We take the representations before the penultimate layer when evaluating the predictive power for these networks.
As the designs of CNN-based networks (e.g., CNNs and ResNets) are similar to human perception system because of the receptive fields in convolutional layers and a hierarchical extraction of more
8

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Uniform Noise
Flipped Noise
Instance- Dennndent Noise
Test accuracy (%)
50-
60
40-
MLP
40
20-
CNN
50-
20-
50%
305
75%
90%
Noise ratio (%)
Noise ratio (%)
Noise ratio (%)
Figure 8: CIFAR-Easy with uniform, flipped, and instance-dependent label noise. Each line indicates the raw test accuracy (dotted) and the predictive power in representations (solid) learned by a model trained across various noise ratios. As MIPs align better with the target function than CNN-based networks on CIFAR-Ease their representations' predictive power MLPs (solid purple lines) consistently better than that of CNNs (solid yellow lines) across various noise ratios and noise types.
Table I: Comparison of different networks' test accuracies ( (%) CIFAR-10/11 We color test accuracy red if it lower than the test accuracy from vanilla training, and we color in green if it higher.
CIFARIO
CIFARIOO
Midal
Setting
Unifor
I|
Utifeem
Flpped
||
PC (MI Pt)
DivalaNi (X)
62.2
55.3
34,4
18.1
M4.2
56.8
44.0
32.8
25.0
13.9
7.2
31.5
22.3
1.3
Distridicks Preehiiine Power
10.6
39.0
14.8
18.7
18.5
11.1
11.6
11.1
13.0
Profet
Vovilla rointee
[2)
86-4
58.5
21.3
12.3
96.1
26-8
16.7
613
40.3
11.5
1.9
67A
45.3
24
DisideMic's & Predkctri Power
06.0
94.3
93.5
83.6
94.9
94.0
936
76.6
60.9
30.3
76.8
74.3
76.1
9-Kmeer CNN
Divdd-Mix
8U.5
91.4
55.7
91.3
25.5
78.3
90.9
88.8
544
15.3
71.4
69.0
51.8
72.9
71.
59.0
$3.0
0.3
Deridshii''s Prodecine Power
93.6
91.4
$1.8
93.1
26.3
702
690
and more abstracted features 86 87), CNN-based networks are expected to align better with the target functions than MLPs on image classification datasets (e.g., CIFAR-10/100),
On the other hand, on CIFAR-Easy, while both CNNs and MLPs can generalize perfectly given sufficient training examples, MLPs have a much smaller sample complexity than CNNs (Figure 6 Thus, both MLP and CNN well-alignes with the target function CIFAR-Easy, but MLP is better-aligned than CNN according to Theorem 2 Moreover, since the instance-dependen label on CIFAR-Fas -asy is the original image classificatinn label, CNN is also aligned with this instance- dependent noise function on CIFAR-Easy.
Experimental Results. First, we empirically verify our hypothesis that networks better-aligned with the target function have more predictive representations. As expected, across most noise ratios on CIFAR- 10/100, the representations in CNN-based networks (i.e., CNN and ResNet) are more predictive than those in MIPs (Figure under both types of label noise. Moreover, the predictive power in representations learned by less aligned networks (i.e., MLPs) sometimes are even worse than the vanilla-trained models' test performance, suggesting that the noisy representations on less aligned networks may be more corrupted and less linearly separable. On the other hand, across all three types of label noise CIFAR-Easy, MLPs, which align better with the target function, have more predictive representations than CNNs (Figure S).
Table 2: Comparison of different networks' test accuracies (%) on CIFAR-Easy We color a test accuracy in red if it is lower than the test accuracy from vanilla training, and we color it in green if it is higher.
Model
II
Flipped
Spurtoos meise
80%
90%6
48h5
50%
25%
5075
100%
4dayer (MLP)
Visiila trizzing
100,00
99.88
97.37
96.20
87.52
75.01
51.94
95.55
90:45
60.18
31.05
10:25
DivideMiis (3)
35.35
10. 00000*
59:50
16:33
100.00
$5.36
50.04
10010
100100
45.59
14.16
10.10
CNN
BivieMic'ss Preductio Power
Divadibii (1)
30000
200000
10000
10000
10300
100.00
10.00
10.05
92:25
95.33
98.43
50.00
96.76
96.55
10000
9652
99.59
14.59
10.09
16.70
10.14
10115
The phenomenon that DivideMix fails under 50% uniform noise but succeeds under 80% uniform noise is due to the unstable behaviors of DivideMix's 's division process, indicating that the predictive power in representations could be more stable measure of a model's robustness, the model can fail miscrably (a.k.a., performance close to random guessing), but its learned representation can still predict the target function well.

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We also observe that models with similar test performance could have various levels of predictive powers in their learned representations. For example, in Figure 8 while the test accuracies of MLPs and CNNs are very similar on CIFAR-Fasy under flipped label noise (i.e., dotted purple and yellow lines overlap), the predictive power representations from MIPs is much stronger than the one from CNNs (i.e., solid purple lines are much higher than yellow lines). This also suggests that when trained with noisy labels, if we do not know which architecture more aligned with the underlying target function, we can evaluate the predictive power in their representations to test alignment.
We further discover for networks well- well-aligned with the target function, its learned representations are more predictive when the noise function shares more mutual information with the target function. We compute the empirical mutual information between the noisy training labels and the original clean labels across different noise ratios on various types of label noise. The predictive power in representations improves as the mutual information increases (Figure T1 in Appendix (A) This explains why the predictive power for a network is often higher under flipped noise than uniform noise: at the same noise ratio, flipped noise has higher mutual information than uniform noise. Moreover, comparing across the three datasets in Figure [I] we observe the growth rate of network's s predictive power w.r.t the mutual information depends on both the intrinsic difficulties of the learning task and the alignment between the network and the target function.
4.2 Predictive Power in Representations for Models Trained with SOTA Methods
As previous experiments are standard training procedures, we also validate our hypothesis on models learned with SOTA methods on noisy label training. We evaluate the representations' predictive power for models trained with the SOTA method, DivideMix [49]. which leverages techniques from semi-supervised learning to treat examples with unreliable labels as unlabeled data.
We compare (1) the test performance for models trained with standard procedures on noisy labels (denoted as Vanilla training), (2) the SOTA method's test performance (denoted as DivideMix), and (3) the predictive power in representations from models trained with DivideMix in (2) (denoted as Mix's Predictive Power).
We discover that the effectiveness of DivideMix also depends on the alignment between the network and the target/noise functions. DivideMix only slightly improves the test accuracy of MLPs on CIFAR- 10/100 (Table I]. and DivideMix's s predictive power does not improve the test performance of MLPs, either. In Table 2 DivideMix also barely helps CNNs as they are well-aligned with the instance-dependent noise, where the noisy label is the original image classification label.
Moreover, we observe that even for nelworks well-aligned with the target function, DivideMix may only slightly improve or do not improve its test performance at all (c.g., red entries of DivideMix on MLPs in Table 2). Yet, the representations learned with DivideMix can still be very predictive: the predictive power can achieve over 50% improvements over DivideMix for CNN- models on CIFAR-10/100 (e.g., 80% flipped noise), and the improvements can be over 80% for MLPs on Casy (e.g., 90% uniform noise).
Tables I and 2 shows that the representations' predictive power on networks well aligned with the target function could further improve SOTA test performance. Appendix [A.4 further demonstrates that on large-scale datasets with real-world noisy labels, the predictive power in well-aligned networks could outperform sophisticated methods that also use clean labels (Table 9 and Table T0p.
5 Concluding Remarks
This paper is an initial step towards formally understanding how a network's 's architectures impacts its robustness to noisy labels. We formalize our intuitions and hypothesize that network aligee with the target function would learn more predictive representations under noisy label training. We prove our hypothesis on simplified noisy setting and conduct systematic experiments across various noisy settings to further validate our hypothesis.
Our empirical results along with Theorem Theorem[jsugges that knowing more structures of the target function can help design more robust architectures. practice, although an exact mathematical formula for a decomposition of a given target function is often hard to obtain, high-level decomposition of the target function often exists for real-world tasks and will be helpful in designing robust architectures direction undervalued by existing works on learning with noisy labels.
10

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Acknowledgments
We thank Denny Wu, Xiaoyu Liu, Dongruo Zhou, Vedant Nanda, Ziyan Yang, Xiaoxiao Li, Jiahao Su, Wei Hu, Bo Han, Simon S. Du, Justin Brody, and Don Perlis for helpful feedback and insightful discussions. Additionally, we thank Houze Wang, Qin Yang, Xin Li, Guodong Zhang, Yixuan Ren, and Kai Wang for help with computing resources. This research is partially performed while Jingling Li a remote research intern at the Vector Institute and the University of Toronto. Li and Dickerson were supported by an ARPA-E DIFFERENTIATE Award, NSF CAREER IIS- (IS-184627,, NSF CCF-1 1852352. NSF D-ISN #2039862. NIST MSE #20126334, NIH ROI NLM-01 3039--00, DARPA GARD #HR001 12020007, DoD WHS #HQ003420F0035,, and Google Faculty Research Award. Ba is supported in part by the CIFAR AI Chairs program, LG Electronics, and NSERC. Xu is supported by NSF CAREER award 1553284 and NSF III 1900933. Xu is also partially supported by IST ERATO JPMJERI20 and JSPS Kakenhi JP18H05291. Zhang is supported by ODNI, IARPA, via the BETTER Program contract #2019- 1905 1600005. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed implied, of ODNI, IARPA, the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.
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16


Reviews:
[{"review_id": "yEh-H-qe92x", "reviewer": "Reviewer_RRS5", "summary": "The key contribution of the paper is a notation of alignment between the architecture of the network and the target function. The paper develops theoretical analysis and a set of empirical experiments to demonstrate that networks with better alignment can learn better representations even with noisy labels.", "questions": "", "limitations": "", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "I find the paper’s idea very interesting and can be potentially very useful in more than one areas, i.e. network architecture search, training with noisy data, learning better representations. However, I am having more and more questions as I read through the paper (details to follow) and I am happy to increase my score if the authors can provide more explanations to resolve my concerns.\n\n### Originality\nThis work provides a bridge between an existing measurement, alignment [1], and Predictive Power [2]. The related work is well-cited.\n\n\n### Quality\nThe motivation of this work is intuitive and easy to understand but the analysis and the result in the current submission does not clearly explain (this could also be a problem in writing and I will clarify in the next paragraph) to me why these analytical and empirical results support the claim: *networks with better alignment have more predictive power*. I have following questions regarding both theorems  and the findings from the experiments:\n- About Theorem 1. A clear proof of Theorem 1 (or  Theorem 3 in the appendix) and its connection with [1] is missing. The author claims that Theorem 3 (from appendix) is a formal version of Theorem 3 and cites [1] as their proofs. However, it lacks a formal proof to elaborate more in formal math expressions in order to clarify which and how definitions and theorems in [1] are used to derive Theorem 3.\n\n- About Theorem 2. Is there a typo in the line 155 -156? Why “a network  N well-aligned with f” is equivalent to $P_j(f, N, C)$ is small as $P_j(f, N, C) < c$ is previously defined as predictive power instead of the alignment. Are there missing assumptions about C in Theorem 2? For example, there is no assumption stated in Theorem 2 about C but in the proof of Theorem 4, the formal version of Theorem 2, the authors further assume $|C|$ is larger than the input dimensions of $f_r$ (line 773). If  $|C|$ is necessary to prove the theorem then it would be necessary to provide the corresponding condition when the theorem will hold. \n\n- Is there a way tp empirically calculate the alignment score instead of a qualitative measurement based on assumptions? Statistical tests and even some graphs are convincing when validating a quantity A (alignment) is positively correlated with another quantity B (predictive power). However, it seems that alignment is not able to be empirically computed even for the simplest GNN case. The author instead provides qualitative descriptions of the alignment scores for all target networks evaluated in this paper, e.g. “max-sum GNN is more aligned”, “CNN-based models are expected to align better than MLPs”. These descriptions are not rigorously justified either by theorems or empirically justified by calculating the alignment score with its definition given in this paper. It would help to convince that there is indeed a positive correlation between the alignment and predictive power if the alignment can be quantitatively measured and evaluated. \n\n### Clarity\nThere are a few suggestions for improving the writing of this paper.\n- I am having a hard time separating which part of the analysis in section 2 is from a prior work (mostly from [1] and [2]) and which part is novel and should be considered as the main contributions of this paper. I would suggest separating the prior work and the paper’s work in a more obvious way. \n\n- I am not sure I understand the PCA experiment and its analysis. Can the authors explain more about the expected outcome of PCA and why it supports the claim made at line 210.\n\n### Significance\nThe result of this paper can be very useful and potentially significant for people to search network architecture in training noisy dataset if the paper can provide more clear theoretical and empirical justifications.\n\n\n[1] Xu, K., Li, J., Zhang, M., Du, S., Kawarabayashi, K., & Jegelka, S. (2020). What Can Neural Networks Reason About? ICLR 2020.\n\n[2] Alain, G., & Bengio, Y. (2017). Understanding intermediate layers using linear classifier probes. ArXiv, abs/1610.01644. ICLR 2017.\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors have limited descriptions about the limitation of the paper. By moving some graphs into the appendix the author may be able to add a separated paragraph in the main paper to discuss the limitation of their work.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "12"}, "extra_text": {}}, {"review_id": "srvzkKuiMHH", "reviewer": "Reviewer_AauR", "summary": "The paper studies robustness to noisy labels in the context of network architectures. It provides theoretical framework to study predictive powers of the representations trained with noisy labels, and defines alignment between network and target function using sample complexity to learn the task. The authors hypothesize that the representations learned by networks that are better aligned to for the target function, have higher predictive powers. They demonstrate this both theoretically and empirically.\n", "questions": "", "limitations": "", "rating": 8, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "This is a very well-written paper with valuable theoretical and empirical contributions. \n\nThe paper formalizes the concepts of predictive power and alignment of the network for a target task. Both of these are modular i.e., enables studying the network at intermediate levels/modules too. This setup helped showcase that the learned representations can be predictive despite being trained on noisy labels.\n\nThe authors hypothesize that the networks with lower sample complexity/better alignment to model the target function, learn representations with higher predictive power. This is a very intuitive statement: if the design/mechanisms used within the architecture are better aligned with the task, then it already has an inductive bias to model the task well. Of course, the interesting part here is that this is true even when the training samples are noisy. Theorem 2 formalizes this and the empirical results on graph networks and vision tasks provide empirical support to this claim.  \n\nOverall, this is a clearly written paper and the setup used here will be useful for future studies on network robustness.\n\nI have some comments/suggestions:\n\n[C1] Sec 3.2: High predictive power at 100% noise level is especially surprising. Untrained/Randomly initialized model would have been a good sanity check i.e., how much predictive power can be attributed to the architecture alone?  This would have been interesting for sec 3.3 too, to check if the architecture-alignment can be solely attributed to the architecture itself.\n\n[C2] It would have been very interesting to compare vision transformers against CNNs. A recent paper [1] shows that vision transformers are more akin to human vision in terms of the errors they make. So, this would be a relevant study here.\n\n[C3] Based on the formulations provided in the paper, lower values of predictive power (P) and Alignment(.) are better, but since they have positive connotations in “real life” one would expect higher values to be better. It makes things a bit confusing while reading. \n\n\n[1] Tuli, Shikhar, et al. \"Are Convolutional Neural Networks or Transformers more like human vision?.\" arXiv preprint arXiv:2105.07197 (2021).\n\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "While the checklist mentions that these are discussed in the supplementary materials, I could not find a section/untitled paragraphs dedicated to this.", "review_text": "", "extra_scores": {"ethical_concerns": "None", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}, {"review_id": "iPDlx9yTNbo", "reviewer": "Reviewer_8N9C", "summary": "This paper focuses on the connection between the neural network’s architecture and its robustness when learning with noisy labels. The authors provide both theoretical and experimental results to justify their claims. ", "questions": "", "limitations": "", "rating": 6, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Learning with noisy labels is one of the hottest topics in weakly supervised learning. This paper gives new insights into this topic. More specifically, the authors first borrow the tool named the predictive power which shows that how good the learned representations are at predicting the target function. Then the definition of alignment is introduced, and the connection between predictive power and alignment is built to describe the model robustness. The authors provide some theoretical analyses and extensive experimental results to support their claims. \n\n**Strength**\n- The motivation of this paper is clear. Prior works mainly focus on designing robust algorithms from the perspectives of loss/label correction and sample selection, etc. This paper aims to investigate the influence of the network’s architecture on model robustness. Such a perspective is novel, and the core idea is well motivated. \n- The experimental results are appreciated. To support their statements, the authors give detailed experimental results to show that better alignment could imply better robustness, and good representations could be learned even though there are noisy labels. The experiments are comprehensive, which include the MLP, GNN, and CNN architecture. Various types of label noise, e.g., additive, class-dependent, and instance-dependent label noise are also considered. \n\n**Weakness \\& Question**\n- The writing of this paper is not clear. Also, it is not very logical. It is a bit hard to understand this paper. The authors give too many notations and definitions in this paper. However, the core idea lacks enough descriptions at a high level. Also, the results are extensive. But the following analyses and discussions are not enough. \n- The definition of the alignment relies on the measurement of sample complexity. In this paper, how to measure it under deep networks? I notice Hypothesis 1 in Section 2.4. However, in Appendix, I found the formal version of Theorem 1 and the following analyses. Where are the details for justifying Hypothesis 1? Besides, more explanations for rationality are needed to be added. At the present stage, it seems that the authors only directly transfer the statements on clean data to the statements on noisy data. \n- Figure 2 is not very intuitive. The authors state that the representations have a clear linear relationship with true labels. More explanations are expected to be provided. In addition, the irrelevance between the raw test accuracy and the predictive power when using MLP is needed to be further justified. \n- The results on the 4-layer MLP in Table 2 are confusing. Why DevideMix can work well in the case of 80\\% uniform noise, but fail in the less challenging case, i.e.,  50\\% uniform noise? \n- The issues/concerns of proofs in Appendix C. \\\n(1) Although Theorem 3 is borrowed from [1], it would be better if three assumptions can be further explained. [1] Keyulu Xu et al. What can neural networks reason about? In ICLR, 2020. \\\n(2) The main theorem of this paper, i.e., Theorem 4 in Appendix C, is a bit weak. Expect three assumptions in Theorem 3, additional three assumptions are added. However, the rationality of these assumptions is not provided. The assumptions (b) and (c) are relatively intuitive. The assumption (a) is hard to understand. Why the models trained on clean data and noisy data would have the same $h(x)$. If the $f_r$ is regarded as an FC layer, $h(x)$ means the representations? And why they will be the same for the target function and noise function? It is somewhat confusing for me about this assumption. \\\n(3) As clean labels still are diagonally dominant in noisy labels, it is reasonable that deep networks trained noisy data still be very predictive. In the proof of Theorem 4, the authors state that ''we can ﬁnd a sub-structure (denoted as $\\mathcal{N}_{sub}$ in the network $\\mathcal{N}$ with sequential modules'' to learn the function $h$. However, definition 2 is used on clean data before. Is it an assumption on noisy data? If not, please justify it and add more discussions. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The core idea and theorem rely on strong assumptions, but the explanations are not enough. ", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "10"}, "extra_text": {}}, {"review_id": "Qy0JmTOQA5l", "reviewer": "Reviewer_NWJ7", "summary": "This paper investigates an interesting problem on how the network architecture is related to its performance under noisy labels. The paper offers a thorough foundation on the related topics and offers a good empirical discussion to support its main findings. Overall, it could be an interesting contribution to the community. ", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The paper offers a line of formal discussion and empirical investigation on the relationship between the alignment of the model architecture to the target functions and the robustness to the noisy labels. The overall methodology is interesting and the contributions seem solid, my major concern is that the main conclusion of the paper on \"a network is more robust to noisy labels if its architecture is more aligned with the target function than the noise\" seems quite intuitive; and the result on vision discusses CNN vs MLP seems a low-hanging fruit. Other than this major concern, I have several technical concerns. \n\n1. The results do not seem to necessarily indicate the relationship between \"the alignment of the model architecture to the target functions and the robustness to the noisy labels\", in contrast, in many places, it seems only about \"the alignment of the model architecture to the target functions and *test accuracy*\". For example, in Figure 7, I don't see additional information if we accept the fact that CNN and ResNet simply learn the target function better (independent of noise level). \n\n2. In Figure 8, I'm surprised to see that CNN suffers this much from the easy construction of the label, maybe some details of the model configurations and training procedures will be helpful to further review the results. \n     * My conjecture is that while we can see CNN as a over-complicated model for this scenario, the overcomplicateness does not seem matter that much statistically speaking. However, whether CNN will align with the noise label better might matter much and offer an explanation to the performance gap between CNN and MLP. However, even in this argument, the way the authors construct the noisy labels do not seem to suggest any intentionally alignment between the noises and the labels. \n\n3. Results in Table 3 does not seem a fair comparison because the vanilla performances of CNNs are much higher than the ones from MLP. Maybe reporting the increment will be better to present the main point. \n\n4. Some writings of the paper seem overconfident. \n     * One issue is is that while the authors indicate that their finding is that the alignment between architecture and target function is more important than the alignment between architecture and the noise function. It seems that there are no explicit discussions/experiments between the alignment and the noise functions, at least at the vision section. \n     * I was very excited when I read the first half of the paper because the alignment towards a target function is an open-research question nowadays, and a hard one. But later, the authors only use MLP vs CNN to simulate whether the alignment is done well or not seems an under-delivery of what's promised in the first half of the paper. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "yes. ", "review_text": "", "extra_scores": {"ethical_concerns": "none noted. ", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3.5"}, "extra_text": {}}, {"review_id": "M5-zT1ViBBb", "reviewer": "Reviewer_mMWd", "summary": "This work studied the connection between the neural network's architecture and its robustness to noisy labels. The architecture is quantified by its alignment with the target function, and the robustness is quantified by the predictive power of the learned representations. The authors propose a practical framework to compute the alignment and predictive power and hypothesize that the better alignment with the clean target function implies better predictive power and hence better robustness to noisy labels. They further conducted carefully designed experiments whose results support their hypothesis.", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "This paper is overall clear and well-written.\n\npros :\n1. in the study of learning with noisy labels, people often assume the expressiveness of the underlying neural network model and focus on the robust loss function designation or transition matrix estimation. This work addresses the effect of the neural network architecture concerning its comparability with the training data. It demonstrates that the predictive power of the learned representations relates to the network architecture in a non-trivial way.\n2. the authors proposed a practical framework to quantitatively measure the representation's predictive power and the alignment of the network with the training data. \n3. the authors conducted carefully designed experiments on synthetic tasks as well as real-world image classification tasks. The results support their hypothesis: better alignment implies better predictive power. They also provided proof of the hypothesis under a simplified scenario.\n\ncons:\n1. one important aspect of the alignment concept in this paper is that it not only measures the capacity of learning but also measures the easiness of learning. This should have some relation to the spectral bias of neural network models. Such spectral bias refers to a common belief that the neural network models tend to learn \"simple\" patterns first before overfitting to the noise during training. It would be better if the authors could discuss the connection between these two concepts.\n2. it is well-known that normally neural network is over-parameterized and can perfectly fit the noisy data during training. I wonder if the learned representations still possess good predictive power after the model is trained to perfectly overfit the noisy training dataset. I haven't found a description of whether the models achieve 100% training accuracy in the experiments. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Limitations and societal impact are addressed.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "5"}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper studies the connection between the architecture of deep neural networks and their robustness to noisy labels, which hasn’t been studied yet. A take-away message is that a well-designed architecture can help learn good representations even the training sample have label noise. Theoretical and empirical analyses are provided. Although Reviewers RRS5 and NWJ7 concern that the theoretical analysis is limited, the paper has certain merits in empirical contributions. All the reviewers agree that the paper is interesting. One reviewer commented that the work can be potentially very useful in several areas, such as network architecture search, training with noisy data, and representation learning, to which the meta-reviewer also agrees. Since the paper brings a unique spark that may potentially enlighten other researchers and benefit the machine learning society, the meta-reviewer is happy to recommend an accept. 

We ask the authors to carefully take the useful comments from reviewers in the final version, e.g., some writings that look overconfident should be revised. We also suggest the authors review an important topic in learning with noisy labels, i.e., modelling the label noise [r1], which has been exploited to correct loss [r2, r3] and should be useful in designing and validating the architecture of deep models by only exploiting the noisy data.

[r1] Yao et al. "Dual T: Reducing estimation error for transition matrix in label-noise learning."
In NeurIPS 2020.
[r2] Natarajan et al. "Learning with noisy labels." In NeurIPS 2013.
[r3] Liu et al. "Classification with noisy labels by importance reweighting." IEEE Transactions on pattern analysis and machine intelligence 38.3: 447-461, 2015.

Decision: Accept (Poster)