What Variables Affect Out-of-Distribution Generalization in Pretrained Models?
Authors: Md Yousuf Harun
Kyungbok Lee
Jhair Gallardo
Giri Prashanth
Christopher Kanan
Venue: NeurIPS 2024 poster (2024)
Keywords: Image Embeddings
Out-of-Distribution Generalization
Tunnel Effect
Neural Collapse
Primary area: evaluation
TL;DR: We identify what variables matter most in out-of-distribution generalization of embeddings and we show that the tunnel effect hypothesis proposed in NeurIPS-2023 is not universal.

Abstract: Embeddings produced by pre-trained deep neural networks (DNNs) are widely used; however, their efficacy for downstream tasks can vary widely. We study the factors influencing transferability and out-of-distribution (OOD) generalization of pre-trained DNN embeddings through the lens of the tunnel effect hypothesis, which is closely related to intermediate neural collapse. This hypothesis suggests that deeper DNN layers compress representations and hinder OOD generalization. Contrary to earlier work, our experiments show this is not a universal phenomenon. We comprehensively investigate the impact of DNN architecture, training data, image resolution, and augmentations on transferability. We identify that training with high-resolution datasets containing many classes greatly reduces representation compression and improves transferability. Our results emphasize the danger of generalizing findings from toy datasets to broader contexts.

What Variables Affect Out-of-Distribution Generalization in Pretrained Models?
Md Yousuf Harun 1.*
Kyungbok Lee 2.*
Jhair Gallardo
Giri Krishnan Rochester Institute of Technology
Christopher Kanan 2 UUniversity of Rochester
Georgia Tech
Abstract
Embeddings produced by pre-trained deep neural networks (DNNs) are widely used; however, their efficacy for downstream tasks can vary widely. We study the factors influencing transferability and
(OOD) generalization pre-trained DNN embeddings through the lens of the tunnel effect hypothesis, which is closely related intermediate neural collapse. This hypothesis suggests that deeper DNN layers compress representations and hinder OOD generalization. Contrary earlier work, our experiments show this is not universal phenomenon. We comprehensively investigate the impact of DNN architecture, training data, im- age resolution, and augmentations transferability. We identify that training with high-resolution datasets containing many classes greatly reduces representation compression and improves transferability. Our results emphasize the danger of generalizing findings from toy datasets to broader contexts.
Introduction
Understanding deep neural network (DNN) representations has been a central focus of the deep learning community. It is generally accepted that a DNN's ' initial layers learn transferable universal features, with deeper layers being task-specific with evidence for the tunnel effect hypothesis:
[
At NeurIPS-2000 2023, 9 challenged this view
The Tunnel Effect Hypothesis: overparameterizee N-layer DNN forms two distinct groups:
1. The extractor consists of the first K layers, creating linearly separable representations. 2. The lunnel comprises the remaining N- K layers, compressing representations and hindering OOD generalization.
To test the tunnel effect hypothesis, they trained models on an in-distribution (ID) dataset and compared linear probes trained and evaluated on either ID or OOD datasets for embeddings produced by each DNN layer. They showed that accuracy increased monotonically, whereas OOD accuracy rapidly decreased after the extractor (Fig D. The likely cause of the tunnel effect is intermediate neural collapse [0]. Both [10] and g showed that collapsed/tunnel layers could be static without needing learning. If these results universal, they suggest universal visual features learned in early layers and using embeddings from the penultimate layers pre-trained DNNs, need to be rethought. However, both [9] and (10) limited their experiments to datasets with low-resolution images and relatively few categories (CIFAR-10, 10, MNIST), Given the widespread use of embeddings from pre-trained DNNs for downstream OOD tasks, we aim assess the universality of the tunnel effect and the variables that influence its strength
'Equal contribution. Corresponding author: Md Yousuf Harun (mh1023 @ rit.cdu) Project website and code: https:://oosuuf00 oood//
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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If the tunnel effect is stronger in models trained on toy datasets like CIFAR-10 but diminishes for large- scale datasets, this may explain why many algorithms evaluated only on toy datasets are ineffective on larger datasets such as ImageNet. This disparity has persisted across problem settings, including open set classification [1] active learning [2], OOD detection
13] uncertainty quantification [14]
dataset distillation [1]. and continual learning (16418].
Our paper makes the following contributions:
1. We define metrics to measure the strength of the tunnel effect and use a SHAP- -baeed analysis to assess each variable's 's impact, e.g., image resolution, number of semantic classes, and DNN architecture. Using 64 pre-trained ID backbones and 8,604 linear probes, we identify conditions that exacerbate, reduce, and eliminate the tunnel effect.
2. Using our metrics, we find that widely used ImageNet-1K IK pre-trained CNN and ViT backbones do not exhibit tunnels, except for ResNet-50.
3. In contrast to [9. we find that the tunnel strongly impacts forgetting in continual learning. This suggests the generality of many continual learning systems depends on tunnel strength, which is heavily influenced by architectural and training dataset choices.
4. We establish a link between impaired OOD generalization and the characteristics of widely used toy datasets, with both resolution and a small number of classes exacerbating the tunnel effect. We propose revised tunnel effect hypothesis, in which the tunnel's 's strength influenced by training data diversity.
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and CNNs, whereas ViT models are now widely used. Second, their experiments only use 32 32 images, and we hy- pothesize that higher resolution images could mitigate the tunnel effect by promot- ing learning hierarchical representations. Third, they do not control for the impact of data augmentation, where data augmen- tation is known to improve OOD general- ization 24 Lastly, they define tunnel as starting at the layer where a linear probe on the ID dataset achieves at least 95% of the final ID accuracy, ignoring OOD gen- eralization. This is problematic since OOD generalization is central to their tunnel ef- fect definition. Here, we measure tunnel effect strength using OOD performance.
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The tunnel effect. The tunnel impedes OOD generalization, which we study using linear probes trained on ID) and OOD datasets for each layer. In this example, identical VGGm-1 17 architectures are trained identical ID datasets, where only the resolution is changed. Probe accuracy on OOD datasets decreases once the tunnel is reached (denoted by )), where the model trained on low-resolution (32 x 32) images cre- ates longer tunnel (layers 9-16) than the one (layers 13-16) trained on higher-resolution (224 x 224) images. The Y-axis shows the normalized accuracy. The OOD curve is the average of OOD datasets (Sec. 3.3). with the standard deviation denoted with shading.
Figure 1:
2.2 Learning Embeddings that Generalize
Pretrained DNNs are widely used to produce embeddings for downstream tasks, c.g., DNNs trained on ImageNet generalize effectively many computer vision tasks 225 Several studies 28:31 observe that ImageNet ID accuracy is highly predictive of OOD accuracy, while others [22 32
find that observation does not always hold. Another example is CLIP [35,, which has better OOD
generalization due to larger and more diverse training data [36] We disentangle the role of data quantity versus the level of semantic variability.
Many works suggest that representations learned earlier layers are more universal across image
datasets whereas later layers are more task-specific 1 32 This observation has guided the development of many transfer and continual learning methods. We revisit this phenomenon by
studying the impact of DNN architecture OOD generalization.

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Previous studies have focused on independently analyzing variables that may impact OOD general- ization B 4
22 32 36/40] However, there still a significant gap in our current understanding regarding each variable's s relative importance. Our study bridges this gap.
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3 Methods
3.1 Measuring the Tunnel Effect
Following [2], we use linear probes for our tunnel effect analysis. Linear probes are widely used
to evaluate the transferability of learned embeddings to OOD datasets [2 41452. After supervised training DNN on an ID dataset, we train ID and OOD linear probes on embeddings produced by each layer. Embeddings for each layer are produced via global average pooling. Additional details are given in Appendix A.2 We use the linear probes to measure the strength of the tunnel effect.
In [ authors showed that OOD accuracy decreased in the tunnel, whereas ID accuracy showed a monotonically increasing trend. However, they did not evaluate the strength of the tunnel and defined the start of the tunnel as when the ID probe reached either 95% or 98% of the final ID accuracy. Instead, we propose three metrics that enable us to measure the tunnel's strength, which are tied to OOD accuracy rather than ID accuracy. These metrics are computed for each OOD dataset. Our findings suggest that defining the start of the tunnel based on ID accuracy is ineffective, In Fig. [ ID accuracy for 32 x 32 images reaches 95% of the final accuracy at layer 14, while OOD accuracy degrades starting at layer 9. We use normalized accuracy curves in the main text to compare models across OOD datasets and resolutions, where each linear probe curve is divided by the highest value.
Metric 1: % OOD Performance Retained. We measure the magnitude of the tunnel effect by evaluating the OOD performance through layer-wise linear probing. For given OOD dataset, and a network with N layers, we find the layer that achieves the highest OOD linear probe accuracy, denoted as Im- The linear probe accuracy of Lm is denoted as a. Then, we denote the OOD accuracy of the linear probe at the penultimate layer (N-1 as Op. We assume that 4m is the start of the tunnel Im < (N-1 and am dp. For an OOD dataset, the % OOD performance retained, w.r.t. the start of the tunnel defined as 100 X (tp/am) Higher r means better OOD generalization, hence a weaker tunnel and vire-versa. When d amm there is no tunnel.
Metric 2: Pearson Correlation. Linear probe accuracy of both ID and OOD datasets should display similar trends (higher correlation) in the extractor layers. However, they should have a low correlation for the tunnel. To quantify this, we use Pearson correlation (p) between ID and OOD accuracy curves. where a higher correlation indicates less tunnel effect. Additional details are given in Appendix A.8
Metric 3: ID/OOD Alignment. A strong model should have higher ID and OOD accuracy, whereas a weak model may show poor accuracy on ID or OOD or both. To capture the characteristic of a model in terms of how strongly it performs on both ID and OOD, we introduce metric, called ID/OOD Alignment, denoted by A. To formalize, we denote ID and OOD accuracy by Ond and aoodd respectively. Chance accuracy (random guess) for ID and OOD datasets are denoted by Cid and Good. respectively. Finally, we define the metric as A = (asd caa) X (Qoo Cood), where A. aidd Good Cia. Good E [0, 1]. Higher A means greater alignment between ID and OOD accuracy.
3.2 Variables Investigated for Their Role in OOD Generalization
We study the role of image augmentation. training classes, training samples, image resolution, and DNN architecture on the tunnel effect, with the details for each given in the next paragraphs.
studied the impact of augmentation independently on OOD generalization whereas its impact on the tunnel effect has not been studied. To address this, we conducted 5/2 experiments, where half of them were trained with augmentations and half without. These are done for every combination of the other variables we study. We used random resized crop and random horizontal flip augmentations.
Augmentation. Prior work 22 2
Number of Classes. In 2 the tunnel effect was shown to decrease as the number of classes and training samples increased. We aim to disentangle these two variables. We conducted 48 experiments with ImageNet-1000 where we kept the training set fixed at 10,000 samples but varied the class counts: 10 (1000 images per class), 50 (200 images per class), and 100 (100 images per class).
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Number of Samples. We conducted 64 experiments using ImageNet- 100 to assess the impact of the number of samples on the tunnel effect. We varied the number of training data per class from 100, 200, 500, and 700 while keeping the number of classes fixed at 100.
Resolution. Since [ only studied 32 x 32 image datasets, the impact of image resolution on the tunnel effect is unknown. We hypothesized that higher resolutions would result in more hierarchical features, resulting in reducing the tunnel effect. To test this, we trained models on ImageNet-Ile 100 with 32 x 32, 64 x 64, 128 x 128, and 224 x 224 images, while keeping the number of parameters for each architecture constant. We conduct 48 experiments per resolution (192 total).
DNN Architecture Variables. We study the tunnel effect in eight DNN architectures drawn from three families: VGG [53], ResNet [54], and ViT (55]. We study the role of the size of the & x l stem, which is the size of the first CNN filter or the ViT's patch size. Because over-parameteriizaton is central to the tunnel effect hypothesis, we measure the vver-perameterization level [56). 7 = P/N, where P is the number of DNN parameters and N is the number of ID training samples. We conducted 416 experiments to assess the impact of architecture type, depth, over-parameetrrizatoon level, stem style, and spatial reduction.
We ensure that each DNN architecture uses the same number of parameters across image resolutions. To do this for the VGG family, we created VGGm, which replaces the two fully connected layers before the output layer with a ResNet-style global average pooling layer. Since the original VGG is designed for high-resolution images (224 224), it includes the max-pool in all 5 stages to progressively reduce the spatial dimension, s of the features (s X s X c) across VGG layers. To capture this, we introduce a variable named spatial reduction by which a stem layer (first layer) reduces the spatial dimension of input images. Spatial reduction, & is defined as the ratio of the output spatial dimension Sout to the input spatial dimension 8in i.e., Φ Sout/ Sin- For instance, spatial reduction at layer that reduces the spatial dimension from 32 x 32 into 16 x 16 becomes 0.5, whereas a DNN that did no spatial reduction would have é We also created another variant, VGGm to study the impact of spatial reduction on the tunnel effect. The difference between VGGm (ø = 0.5) and is that VGGm includes max-pool in all stages whereas VGGm* omits max-pool in the first 2 stages for 32 x 32 input resolution. Compared to VGGm, VGGm* achieved higher ID accuracy on ImageNet- 100 (see Ta)le For ResNet, we use the original ResNet architecture [54] To keep model size constant across resolutions for ViT models, we use fixed patch size of 8 x 8 with the number of patches being larger for higher-resolution images. Following [57] sin-cos position embeddings to encode spatial information.
VGGmt (ó-
we used 2D
3.3 Datasets
ID Datasets. In our main experiments, we train DNNs on 3 ID datasets: 1) ImageNet- 100 [58] a
subset (100 classes) of ImageNet-1K, 2) CIFAR-IO [59], and 3) and COF [60]. For these experiments, 52 DNNs were trained on ImageNet- 100, 8 on CIFAR- and on CIFAR-10 10 (64 DNNs total), where resolution, augmentation, etc., were varied described earlier. ID and OOD linear probes are trained and evaluated for each DNN layer. For our experiments on downloaded ImageNet- IK pre-trained DNNs, ID linear probes were trained training subset consisting of 50 images per class (50,000 images). Standard test sets are used for all ID datasets.
OOD Datasets. To assess OOD generalization with linear probes, we use 9 OOD datasets: NINCO 61), ImageNer-R R 622. CIFAR- 100 (60) CIFAR-IO [59]. Oxford 102 Flowers (3), CUB- 200 [64], Aircrafts (65], Oxford-IlIT Pets (66. and STL-10 67 (see Appendix B). Eight OOD datasets are used with DNNs trained on each ID dataset, where CIFAR-10 is omitted for DNNs trained on ImageNet variants. When using CIFAR-10 or CIFAR- 100 as the ID dataset, the other CIFAR dataset used for OOD experiments since their classes do not overlap.
Resolution & ID Accuracy. All DNNs trained on CIFAR-10 or CIFAR- 100 are trained and evaluated with 32 x 32 images. For DNNs trained on ImageNet variants, all ID and OOD images were resized to the resolution with which the DNN was trained. See Table for the resolution used for each DNN and their ID accuracy with and without augmentations.

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ID Class Count
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SHAP Slope
(a) OOD performance retained as target
(b) ID/OOD aligument as target
Figure 2: SHAP Results. SHAP slope shows the individual contribution of variables to various targets. Positive values indicate enhanced OOD generalization, and vice-versa for negative values.
3.4 Statistical Analysis
For each of the 64 DNNs trained on an ID dataset in our main results, we compute our OOD generalization metries on each OOD dataset, resulting in 512 values per metric. These values derived from 8,604 linear probes (ID and OOD). We study the impact of each variable on OOD generalization in isolation using paired Wilcoxon signed-rank tests constructed to control for the impact of other variables, and we use Cliff's Delta to measure effect sizes (68), which is appropriate for ratio data. For Cliff's Delta (6), follow the standard practice of defining a negligible effect for |ō| < 0.147, small effect for 0. s |8| 0.33, medium effect for 0.33 |o| < 0.474, and large effect for |ô| 2 0.474.
0.05, where pairs are
To jointly analyze and rank the contribution of each variable, use SHAP which determines the contribution of each input variable to its output [69] [70.. Following [71. we train Gradient Boosting Regression models to predict three output targets: a) % OOD performance retained, b) Pearson correlation, and c) ID/OOD alignment, from 8 input variables: 1) resolution, 2) augmentation, 3) ID class count, 4) spatial reduction, 5) stem, 6) CNN ViT, 7) over-parametrizatton level, and 8) depth. We then obtain SHAP values for each variable, where using Gradient Boosting Regression facilitates controlling for variable interaction effects (71]. Because SHAP magnitude does not indicate the direction of a variable's impact, for each of the 3 models, we fit linear regression model between each variable and its corresponding SHAP values to obtain its slope. Positive slopes indicate the variable improves the metric. We call this SHAP Slope. Details are given in Appendix A.9
4 Experiments & Results
4.1 Main Experiments
In [9. all architectures were trained with CIFAR-10 or CIFAR-100, and all experiments were conducted with 32 x images. Instead, most of our experiments use ImageNet-100 the ID dataset, where image resolution is varied. We also include experiments on CIFAR datasets. In our main experiments, for each of our 64 DNNs, we produced 8 OOD linear probe curves and ID linear probe curve (576 total), which required computing 8604 linear probes. From this, obtain 512 values for each of our 3 metrics under various conditions.
4.1.1 Overall Findings & SHAP Analysis
Results for our SHAP Slope analysis computed across all 512 OOD experiments are summarized in Fig. 2 which shows the impact of each variable on the % OOD performance retained and ID/OOD alignment. The SHAP Slope figure for Pearson Correlation is given in Appendix C since it has nearly identical trends to % OOD performance retained. The R² for % OOD performance retained, ID/OOD alignment predictions, and Pearson Correlation are 0.62, 0.44, and 0.73, respectively. Each variable's
httpp:://github..co//aatte
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Figure 3: Augmentation greatly reduces the tunnel effeet. (a), augmentation shifts the tunnel from layer 14 to 22, and in (b) from block 11 to 15. The OOD curve is the average of 8 OOD datasets with shaded area indicating 95% confidence interval. denotes the start of the tunnel.
positive/negative impact is consistent across all 3 of our SHAP analyses. Our main findings are given below, with additional findings in Appendix C
Our metrics reveal that increasing the ID class count, higher resolutions, and using augmentations improve OOD generalization. For OOD performance retained and Pearson Correlation, increasing the number of ID classes had the greatest impact, whereas, for ID/OOD alignment, increasing resolution did. This is likely because ID/OOD alignment curves are not normalized using the best OOD accuracy, resulting in resolution's 's role being obscured for the other two metrics. Across metrics, using augmentations had the second greatest positive impact. These results indicate that increasing between-class diversity (more classes), greater within-class diversity (augmentations), and higher image resolutions improve OOD generalization.
While [9] argued that the primary source of the tunnel effect is aver-parameterization,, our results indicate plays minor role compared other factors. Our results indicate that using larger stem and excessive DNN depth somewhat impair generalization. For all metrics, the choice of ViT or CNN had the least impact on OOD generalization, consistent with the hypothesis that much of the reported benefits of ViTs for image classification are due to training with larger datasets, stronger augmentation policies, and other tricks [72].
Using the average % OOD performance retained across the 8 OOD datasets to analyze all 64 of our DNNs, 4 had negligible (non-existent) tunnels, 8 had weak tunnels, 13 had medium tunnels, and 39 had strong tunnels. We use intervals of [100%, 95%] for negligible, [90%. 95%) for weak, [80%, 90%) for medium, and [0%, 80%) for strong tunnel. This demonstrates that the tunnel effect is universal and depends on variables. Next, we dive into the factors that influence tunnel effect strength.
4.1.2 Augmentation Results
In Fig. example linear probe plots illustrate that augmentations play major role in reducing the tunnel effect. To further analyze the impact of augmentation on OOD generalization, we compared of our experiments in which augmentation was used omitted with all other variables controlled using paired Wilcoxon Signed-Rank tests (256 paired experiments, 512 total). For % OOD performance retained, augmentations significantly decreased the tunnel effect with 64.26% retained without augmentations and 78.41 %% with (p < 0.001), which had medium effect size (1o) = 0.370). For Pearson correlation, augmentations also had significant effect where p increased from 0.77 to 0.86 (p < 0.001), with a medium effect size (16) = 0.374). For ID/OOD alignment, augmentations increased alignment from 0.15 to 0.25 (p < 0.001), with a medium effect size (0o) 0.357).
4.1.3 Resolution Results
Illustrative examples showing how increasing resolution improves OOD generalization are given in Fig. study resolution further, we conducted paired tests between models trained with 32 32 images and those trained with 64 x 64, 128 x 128, or 224 X 224 images (48 paired experiments per resolution comparison, total). All models were trained on ImageNet- 100. Mean effect sizes (0) and valuue given in Table Average values for the metries computed for each resolution

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Table Higher resolution images reduce the tunnel effect. Pairwise statistical analysis between
DNNs trained on (32 x 32) images vs. higher resolution images.
Resolution
% OOD Perf. Retained
Pearson Correlation
ID/OOD Alignment
Eff. Size (16)
p-val
Eff. Size ([6)
p-val 1
Eff. Size (Jő)) 1
p-val
32" vs 61
negli. (0.002)
0.315
negli. (0.023)
0.572
small (0.326)
< <0.001
32"
vs 128
small (0.171)
0.001
small (0.240)
0.006
large (0.567)
< 0.001
32 vs 224
small (0.198)
0.005
small (0.280)
0.011
large (0.625)
< 0.001
Layer 7 (32x32)
Layer 8 (32x32)
Layer 9 (32x32)
Layer 10 (32x32)
Layer 7 (224x224)
Layer (224x224)
Layer 9 (224x224)
Layer 10 (224x224)
Figure 4: High-resolution model does not exhibit representation compression. The t-SNE comparison between VGGm-11 models trained on low- (Ist row) and high-resolution (2nd row) images of the same ID dataset (ImageNet-100) in an augmentation-free setting. Layer 8 marks the start of the tunnel VGGm-11 trained on 32 X 32 images whereas 224 x 224 resolution does not create any tunnel. Layer 10 is the penultimate layer. The tunnel layers (layers 8-10) progressively compress representations for 32 x 32 resolution whereas corresponding layers for 224x 224 resolution do not exhibit similar compression. For clarity, we show 5 classes from ImageNet- 100 and indicate each class by a distinct color. The formation of distinct clusters in the 32 x 32 model is indicative of representation compression and intermediate neural collapse [00] which impairs OOD generalization.
given in Table 12 The findings are consistent with our SHAP analysis: training on higher-resolution images improves OOD generalization, whereas low-resolution datasets increase tunnel effect strength. Additional results are given in the Appendix C.13
t-SNE analysis for various layers from VGGm-1 11 models trained on 32 x 32 and 224 x 224 images given in Fig. E The low-resolution model exhibits much greater intermediate neural collapse [10] and representation compression than the high-resolution model. This is likely why many OOD detection algorithms that work well for CIFAR fail for higher-resolution datasets [I]] These results highlight the dangers of extrapolating findings from low-resolution datasets to all of deep learning.
4.1.4 DNN Architecture Results
Spatial Reduction. Our SHAP analysis revealed that lower values for spatial reduction (d) hurt OOD generalization. To further study this, we conducted paired tests between VGGm-11 and VGGm-l 17, which both have 6 = 0.5, and VGGmf-11 and VGGm (ø = 1.0). All 4 DNNs are trained on ImageNet- 100 at 32 x 32 resolution, with and without augmentations, and each evaluated on the OOD sets (32 paired experiments, 64 total). In terms of % OOD performance retained, the VGGm models retained 84.40% whereas the VGGm models retained 64.85% (p 0.001), with a large effect size ()0) 0.531). Similarly, Pearson correlation significantly decreased from 0.92 to 0.72 (p < 0.001), with large effect size (16) 0.536), and ID/OOD alignment significantly decreased from 0.26 to 0.18 (p 0.001), with medium effect size (1o) 0.361). Fig. 5 provides example
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normalized accuracy curves. VGGm-11 exhibits a strong tunnel spanning from layer to 10 (Fig. 5a whereas no tunnel present in VGGm#-11 (Fig. (5).
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Figure 5: The tunnel effect is not universal. In (a), VGGm-11 consisting of max-pool in all stages (ő = 0.5), creates a tunnel (layers 7-10, gray-shaded area). In (b), the same VGGm-11 I without max-pool the first 2 stages (ø = 1, called VGGmf-11), eliminates the tunnel for all OOD datasets.
Stem. Our SHAP results indicate that increasing stem size hurts OOD generalization. To further study this, we conducted a paired test over 64 paired experiments between ResNet-18, which uses a 7 x stem, and VGGm-17, 17, which uses X 3 stem. Increasing the stem from 3 to 7 significantly decreased the % OOD performance retained from 76.74% to 66.66% (p < 0.001), with a small significant difference (p = 0.145). For ID/OOD alignment, increasing the stem significantly reduced the score from 0.27 to 0.21 (p 0.001), with a small effect size (15l = 0.226). Fig. 12 provides box plots of % OOD performance retained and ID/OOD alignment for the three stem values.
effect size (1ō] 0.306). However, for Pearson correlation, there
Depth. Our SHAP analysis revealed that increasing depth impairs OOD generalization. As shown in Fig. [0] increasing depth impairs OOD performance retention for each architecture family. To study this further, compared VGGm-11 11 and VGGm-17 using 48 paired experiments (96 total), Increasing depth significantly decreased % OOD performance retained from 89. 19% to 69.41 % (p- 0.001), with large effect size (oō = 0.539). Likewise, Pearson correlation significantly decreased from 0.94 to 0.80 (p < 0.001), with a large effect size (15) = 0.497). ID/OOD alignment also significantly decreased from 0.28 0.25 (p- 0.001) with a small effect size (10) 0.161).
wver-parameterization Level. Our SHAP analysis showed that over-parameterriztion level nega- tively impacts OOD generalization. Fig. 11 shows how increasing the over-parameterrizatin level de- creases % OOD performance retained. We conducted paired tests between VGGm-11 (7 = 74.7) and ResNet-34 (y 168.4) to study this further (32 paired experiments). Increasing recettrratttiinoiooonn significantly reduced % OOD performance retained from 87.22% to 62.78% (p < 0.001), with a large effect size (lol 0. 0.680). Likewise, the Pearson correlation
significantly reduced from 0.93 to 0.82 (p < 0.001), with a large effect size ()0) 0.370). Lastly, ID/OOD alignment significantly dropped from 0.29 0.20 < 0.001), with medium effect size (16) 0.340).
4.1.5 ID Dataset Size vs. Total Classes
Our SHAP analysis shows that ID class count positively impacts OOD generalization. To further analyze this, we trained VGGm-11 11 on different subsets of ImageNet- 100 with 32 x 32 images where we kept the training dataset fixed at 10,000 samples but varied the class counts: 10 (1000 samples per class), 50 (200 samples per class), and 100 (100 samples per class). Experiments were done with and without augmentations. As shown in Fig. G increasing the number of classes greatly reduces the tunnel effect (Figs. (6a and (6bb. To examine the role of the dataset size, vary the number of samples per class from T00, 200, 500, and 700 while keeping the class count constant at 100, which has relatively small impact on the tunnel effect (Figs. 6c and 6d).
4.2 Analysis of Widely Used Pre-trained Backbones
We also studied OOD generalization for eight widely used ImageNet- 1K pre-trained CNN and VIT backbones trained with either supervised learning (SL) or self-supervised learning (SSL). We studied
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0.6
100 samples per class
0.6
100 samples per class
200 samples per class
200 samples class
0.4
500 samples per class
500 samples per class
0.2
700 samples per class
0.2
700 samples per class
2
10
Layer
Layer
(c) # Samples without augmentations
(d) Samples with augmentations
Figure 6: Training on more classes greatly reduces the tunnel effect, whereas increasing dataset size has less impact. (a) and (b) Results with a fixed number of samples but a varied number of classes. (c) and (d) Results with a fixed number of classes but a varied number of samples per class.
ResNet-50 (1 SL and 1 SSL 773), 4 ViT-B (1 SL and 3 SSL (50 74 75 and ConvNeXI-B (1 SL and SSL (76)) models. We trained linear probes on ImageNet- (ID) and our OOD datasets (1980 linear probes total), resulting in 72 values per OOD metric. As shown in Fig. 17 and Table 9 the tunnel effect is absent in most models and is weakly present in both SL and SSL ResNet-50. Additional results are given in Appendix C.II Appendix Appendix/A.6finclue A.6lincludes implementation details.
4.3 Continual Learning Results
Catastrophic forgetting is a central focus in continual learning 17 77].
Many methods assume
forgetting occurs mostly in later layers with earlier layers serving universal features [16] 78 79 The original tunnel effect paper challenged this [9]. They trained VGG-19 on two tasks sequentially, where the first task included half of the CIFAR-10 10 classes and the second task included the other half. After training on each task, the tunnel and extractor were saved. They found no forgetting when tunnels were swapped, indicating no learning occurred in the tunnel for task 2, and they found reduced forgetting when fine-tuning the extractor alone. These findings are worth assessing beyond CIFAR-10. 10. We ask: What is the role of the tunnel in mitigating forgetting?
We replicated their general approach by training ResNet- 18 on ImageNet- 100, where the first task had the first 50 classes and the second had the rest. After learning each task L, we saved the extractor E, tunnel Te. and the classification head. We conducted this experiment with 32 x 32 and 224 x 224 images. Using the tunnel definition from [9), tunnels Ti and T2 correspond to layers 14-17 for 32 x 32 images and 15-17 for 224 224 images. See Appendix A.7 for additional details.
Results are given in Table 2 Unlike the findings in 19. when we swapped tunnels Ti and T2, accuracy was greatly reduced for both resolutions, indicating that essential learning happened within the tunnel. Next, we replicated their fine-tume fine-tuning experiments. If fine-tuning E₂ alone reduces forgetting more than fine-tuning Eg with T2. suggests the tunnel has a detrimental impact on mitigating forgetting. We found that fine-tuning Fg alone improved task accuracy less than fine-tuning Eg + Ti, indicating T3 helps reduce forgetting. Our findings, which contradict [9. suggest the "tunnel" plays an essential role in mitigating catastrophic forgetting, consistent with prior work (5).

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Table 2: Continual Learning Results. The tunnel is task- susk-specific and impacts forgetting. E, and T, denote the extractor and tunnel, respectively, for tasks t e 2). Orange indicates original task accuracy. Red and blue indicate degraded or maximally enhanced accuracy, respectively. Fine-tuning (FT) aims to recover 1st task performance (gray); therefore, the 2nd task columns are empty.
Combination
32 32 Resolution
224 x 224 Resolution
1st Task T
2nd Task 1
1t Task 1
2nd Task
E1 + 1 E + T2 Eg + T2 Eg + Ti
64.04
21.20
74.36
23.24
37.64 (1 26.40)
35.64
54.32 (J 20.04)
35.68
20.44
68.16
20.44
78.00
29.84
23.84 (1 44.32)
21.56
46.08 (1 31.92)
Eg + (FFT)
51.40 (1 30.96)
57.24 (1 36.80)
(F()
45.60 (1 25.16)
52.48 (1 32.04)
5 Discussion & Conclusions
We conducted extensive experiments to investigate the generality of the tunnel effect in a wide range of transfer settings. Our study indicates that the best way mitigate the tunnel effect, and thereby increase OOD generalization, is to increase diversity in the ID training dataset, especially by increasing the number of semantic classes, using augmentations, and higher-resolution images; hence, we revise the tunnel effect hypothesis as follows:
The Tunnel Effect Hypothesis: An overparameterized N-layer DNN forms two distinct groups:
1. The extractor consists of the first K layers, creating linearly separable representations.
2. The tunnel comprises the remaining N K layers, compressing representations and hindering OOD generalization.
K is proportional to the diversity of training inputs, where if diversity is sufficiently high, = K.
Earlier works on the tunnel effect ( and intermediate neural collapse 10 exclusively used 32 32 images for ID training. We found that while DNNs trained on CIFAR always exhibited the tunnel effect, the tunnel effect was greatly reduced for ImageNet- at higher resolutions. This discrepancy helps explain why methods validated on CIFAR and similar datasets may not generalize in many scenarios IHIS. We urge the community to use high-resolution datasets with 100 or more categories to improve the generality of findings, especially for studies related to representation learning, neural collapse, and OOD detection/generalization.
Limitations & Future Work. While our work validates the existence of tunnels, future research should focus on developing theoretical frameworks help explain the tunnel effect. We rigorously studied OOD generalization on vision datasets with supervised learning. Future work could study where the tunnel effect has not yet been studied. While we studied pre-trained SSL backbones. we could not do our SHAP analysis without having more SSL backbones. Valuable insights for SSL could be obtained by conducting carefully controlled paired experiments, done in our main experiments. This would require probing at least four different SSL algorithms for each variable analyzed, where training each SSL DNN would require over 10x more time than our supervised DNNs. Additionally, SSL methods employ more advanced augmentation policies than ours, where we used madoom-rsiieed crops and horizontal flips. Replicating our SHAP analysis with multiple augmentation policies could reveal whether the OOD generalization capabilities of SSL algorithms are due to their augmentation policies versus their objective functions. Lastly, identifying regularizers or other techniques that mitigate tunnel formation should be sought for continual learning methods that start from scratch using small initial sets. This could greatly improve forward transfer, leading more efficient continual learning methods [3] 86)
non-vision, multi-modal 80, and biased datasets 81 82
Acknowledgments and Disclosure of Funding
This work was partly supported by NSF awards #2326491, #21 #2125362, and #2317706. The views and conclusions contained herein are those of the authors and should not be interpreted as representing any sponsor's official policies or endorsements. We thank Junyu Chen for feedback on an early draft of this manuscript.
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Appendix
We organize additional implementation details and supporting results follows:
Appendix (eannddxx/]descrbbbsss the implementation details and hardware used for training. It describes the DNN architectures (VGG, ResNet, and ViT), feature extraction for linear probing, training, and evaluation details of both pre-training and linear probing in various experiments. The implementation details of continual learning experiments and analysis the widely used pre-tree tre-trained models are also described. The implementation details of the SHAP slope analysis are also provided.
Appendix B provides details the datasets used in this paper. We used total of 4 ID datasets and OOD datasets.
Appendix C presents additional supporting results for the Pearson correlation metric. It includes additional SHAP results. reports the performance of various models terms of OOD accuracy, % OOD performance retained, Pearson correlation, and ID/OOD alignment in various settings. It presents analyses of how variables impact the tunnel effect and OOD generalization.
Appendix repoorts the in-distribution performance of various models (VGGm, VGGmf, ResNet, ConvNeXt, and ViT) on various II) datasets (ImageNet-10M) ImageNet-IK, CIFAR- 10, 100)
Appendix reports additional statistical results for different variables and interventions.
Appendix includes the list of 100 classes in the imageNet-100 100 dataset and confirms there is no overlap between ID and OOD datasets.
A Implementation Details & Computational Resources
In this section, we use several acronyms such as WD : Weight Decay, LR Learning Rate, GAP : Global Average Pooling, SSL : Self-Supervised Learning, SL : Supervised Learning, ID : In- Distribution, and OOD: Oftttr-Diisributtion We implemented our code in Python using PyTorch.
A.1 DNN Architectures
To assess how the depth of DNN affects the tunnel effect, we create a deeper variant of each DNN architecture by increasing the number of layers (CNN) blocks (ViT) while keeping other configurations identical.
VGGm. We modify the VGG-13 (or VGG-19) architecture to create VGGm-11 (or VGGm-17). This is done by adding an adaptive average pooling layer (m..AdaptiveArgPool2d,, which allows the network to accept any input size while keeping the output dimensions the same. Additionally, we include single fully connected (FC) layer rather than three fully connected layers, resulting in the VGGm-11 11 (or VGGm-17) structure. In particular, VGGm has the final FC classifier layer without the additional two FC layers before the final layer. The number parameters of VGGm-11 (or VGGm- 17) is the same across all input resolutions.
ResNet. To maintain the same number of parameters across all input resolutions, we use the original and unmodified ResNet- 1 18/34 (54] Thus ResNer- 18/3 consists of 7 x 7 convolution with stride 2 in the stem layer (first layer) followed by maxpool layer.
VIT. We select ViT-Tiny (5.61M parameters) for our main experiments with varying resolutions. To maintain exact same number of parameters across all resolutions, we use fixed patch size of 8 x with varied number of patches due to spatial dimensions. The number of patches or image tokens for x 32 and 224 X 224 resolutions are 16 and 784 respectively. We use an embedding dimension of 192, a depth of 12 (i.e., 12 ViT blocks) and 3 heads. We also created another deeper variant with depth of (i.e., 18 ViT blocks), referred to as ViT-Tiny+ (8.39M parameters). To maintain the same number of parameters across all input resolutions, following [57] we omit the learnable position embeddings and instead use the fixed 2D sin-cos position embeddings. Other details adhere to the original ViT paper [55].
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A.2 Feature Extraction For Linear Probing
In experiments with CNNs, at each layer 1, for each sample, extract features of dimension H2 x W, x C₁, where Hi W,, and C₁ denote the height, width and channel dimensions respectively. Next, following [37], apply 2 x 2 adaptive average pooling each spatial tensor (H₁ x Wi). After average pooling, features of dimension 2 x 2 x Cj are flattened and converted into vector of dimension 4 Finally, linear probe trained on the flattened vectors. In experiments with ViTs, following [87], we apply global average-pooling (GAP) to aggregate image tokens excluding the class token and train linear probe on top GAP tokens.
A.3 VGGm Experiments
VGGm ID Training: For training VGGm- 11/17 on ImageNet-100, we employ the AdamW optimizer with an LR of x 10 and WD of 5 x 10 for batch size 512. The model is trained for 100 epochs using the Cosine Annealing LR scheduler with linear warmup of 5 epochs. We use label smoothing of with cross-entropy loss. For CIFAR-10 and CIFAR-100 datasets, we use an LR of 0.01 for batch size 512. We train VGGm-11 for 100 and 70 epochs in experiments without augmentations and with augmentations respectively. Whereas VGGm-17 17 is trained for 100 epochs in both settings without augmentations and with augmentations.
Varying Number of Classes and Sample Size: VGGm-11 uses LR of 8 10T3 and WD of 5 x 10" VGGm-17 17 uses WD of 1 10 instead of 5 10 For both with and without augmentation, We train VGGm-11 for 100 epochs and VGGm-17 for 200 epochs.
VGGm Linear Probing: We use the Adam optimizer with a flat LR of x 10 3 and a WD of 0 for batch size 128. The linear probes are trained for 30 epochs. We use label smoothing of 0.1 with the cross-entropy loss.
A.4 ResNet Experiments
ResNet ID Training: For training ResNet-11/34, we employ the AdamW optimizer with LR of 0.01 and a WD of 0.05 for batch size 512. The model is trained using the Cosine Annealing LR scheduler with linear warmup of 5 epochs. We use label smoothing of 0.1 with cross-entropy loss. We use 100 epochs to train ResNet- 18 in experiments without augmentation. In experiments with augmentations, train 18 for 80 epochs using random resized crop and random horizontal flip augmentations. The ResNett-3 models are trained for 100 epochs in experiments with and without augmentations.
ResNet Linear Probing: In the linear probing experiment, we use the AdamW optimizer with an LR of x 10 and a WD of for batch size 128. The linear probes are trained for 30 epochs. We use label smoothing of 0.1 with cross-entropy loss.
A.5
VIT Experiments
For VIT training, we follow the codebase of DeiT 88 and A-VIT 89 We also use timm library 90]
VIT ID Training: For training ViT-Tiny/ViT-Tiny++ we employ the AdamW optimizer with an LR of 8 x 10"4 and WD of 0.05 for batch size 96. We use the Cosine Annealing LR scheduler with linear warm-up (5 epochs). We also use label smoothing the ViT-Tiny for 100 and 40 epochs in experiments without augmentations and with augmentations respectively. Whereas the ViT-Tiny+ is trained for 100 and 60 epochs in experiments without augmentations and with augmentations respectively. In the experiments with augmentations, we use random resized crop and random horizontal flip. Following [57 87,. we omit class token and instead use GAP token by global average-pooling image tokens for classification head.
0. with cross-entropy loss. We train
VIT Linear Probing: We use the AdamW optimizer with LR of 0.01 and WD of 1 x 10 for batch size 512. The linear probes are trained for 30 epochs. We use label smoothing of 0.1 with cross-entropy loss.
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Table Augmentations used for training various large pre- pre-trained models.
Model
Augmentations
SWAV ResNet-50
Random crop, horizontal flip, color distortion. Gaussian blur
MAE VIT-B
Crop, horizontal flip, masking
MUGS ViT-B
Random crop, color jitter, Gaussian noise, horizontal flip, gray scaling, auto-aug
DINO VI VīT-B
Color jittering, Gaussian blur, solarization, multi-crop
FCMAE ConvNeXI-B
Random crop, RandAug, masking
SL ResNet-50
Random erase, mixup, cutmix, auto-aug Mixup, cutmix, RandAug, Random Erasing Mixup, cutmix, auto-aug
SL ConwNeXt-B
SL VIT-B
Note that, in all cases, we maintain the over-parameterizatton level where the DNN model size (number of parameters) exceeds the number training samples ( > 1). After ID training, we select
the model checkpoint that achieves the best top-1 accuracy (%) on the validation dataset.
A.6
Pre-trained Model Experiments
We describe the implementation details of large pre-trained model analyses that are presented in We list the augmentations used by various pre-trainen pee-tra models in Table
Sec. 4.2
Since it computationally expensive use the full ImageNet-1K 1K (ID) dataset for layer- wise linear probing experiments, we use a subset of ImageNet-16 K as the training dataset where we randomly sampled 50 images per class from the ImageNet- 1K dataset. During the evaluation, we used the original ImageNet- 1 validation dataset (50 images per class). For OOD linear probe experiments, we used the same OOD datasets e.g., CIFAR-100, Flower- 102, NINCO, Aircrafts- Oxford Pets-37, STL-10, CUB-200, and ImageNet-R.
Datasets.
VIT. For all ViT pre-traines pre-trained models, we use ViT-Base (85.8M parameters) with depth of 12 and 16x16 patch size.
Pre-trained Model Download Links. The links download pre-trained models given below: DINO V/ ViT-B
http:/facccccctttto tot//imm/vitt.../m/ base allase_pptcche 224
dino MAE VTT-B: htttps:/huugingg::ee
co timm/vit. serittbbbee_peeee paase_patchi._.. 2eeechhl___e____2eeee mae. MUGS
ViT-B:
co hotpo/ocecccccoooooaaa/a///g SwAV ResNet-50 (800 epochs): https
co co//iimm/convnexxt>___eee.. swav] FCMAE ConvNeXI-B: https://ugginnffan
ft it_inkk] ConvNeXi-B
facceboot/convneettbaa---- 224 ResNer-50 (IMAGENETIK V2): https://pyton: org/
vision/stablee/mddels. html
and ViT-B (IMAGENETIK VI); https: /ttps://pytorch. org/
7B500//aann/mmmoll//ggonrtttdd wtw.seedddttocviiiiiooo.o models. vit___16. 1it_b_16.html
Pre-trained Model Linear Probing. We attach linear probe layer to each block of ViT models and each Conv2d layer of CNN models. In the ConvNeXt block, which has three layers, only the 7x7 layer uses Conv2d. Therefore, using the Conv2d layer results in one layer per ConvNeXt block for linear probing. We use the AdamW optimizer with WD of 0 and batch size of 512. Linear probes are trained for 30 epochs using cross-entropy loss with label smoothing of 0.1. For all ViT models and ResNet-50 Supervised model, the LR is 5 x 10 And, for the ResNet-50 50 SwAV model and both ConvNeXt models, the LR is 10
A.7 Continual Learning Experiments
We describe the implementation details of continual learning experiments that are presented in Sec. 4.3
We adapt the experimental design from (9] for this study. We use the same linear probing approach and definition of the tunnel to identify tunnels in ResNet-18 18 models during continual learning experiments. We train the model two subsequent tasks and each task contains non-overlapping 50 ImageNet classes.
Continual Learning. We employ the Adam optimizer with LR of 0.01 and WD of 0.05 for batch size 512. The model trained for 50 epochs using the Cosine Annealing LR scheduler with linear warmup of 5 epochs (for the first task). We use label smoothing of 0. with cross-entropy loss.
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Tunnel Layers. For 32 x 32 resolution, tunnels Ti and T2 correspond to ResNet layer 14-17. For 224 x 224 resolution, tunnels Ti and T2 correspond to ResNet layer 15-17.
Finetune. In this experiment, we use the A optimizer with LR of 0.01 and WD of 5e-2 for batch size 512. The number of epochs is 50. We use label smoothing of 0.1 with cross-entropy loss. A Step LR scheduler is used. In particular, we reduce LR by a factor of 0,1 at predefined milestones, which are set occur the 20th and 40th epochs.
In all experiments, we use image augmentations namely random resized crop, random horizontal flip, mixup 191], and cutmix [92]. For mixup and cutmix augmentations, we participation probability of 0.6 and 0.4 respectively. We set coefficient 3 1.0 for cutmix and coefficient a 0.1 for mixup.
We adapt image pre-processing steps from 89 for various image resolutions. We use the same number of network parameters, hyperparameters, and identical settings for all image resolutions. For a fair comparison, we choose hyperparameters to maximize the performance of all compared methods or models.
A.8 Evaluation Metries
Accuracy, For accuracy in all experiments including ID training and ID or OOD linear probing, we the best top-1 accuracy (%)
Pearson Correlation. We compute the Pearson correlation p between accuracy and OOD accuracy using the following equation,
P Σ (z. () v)
(I)
(x; x)² (1= 7)²
In this formula, 2; represents the ID accuracy at the i-th layer, and y represents the OOD accuracy at the i-th layer. T and are the average of ID and OOD accuracy over layers, respectively. The index i spans from the first layer (1) to the penultimate layer (n) of models since ID and OOD accuracy are computed at each layer. P E [-1, 1]. where م 1 indicates perfect positive linear relationship, and = indicates a perfect negative linear relationship.
Wilcoxon Signed-Rank Test. To measure the significance of the difference between the two groups we performed Wilcoxon signed-rank test between the two groups. We compared % OOD performance retained, Pearson correlation, and ID/OOD alignment metrics between each pair. We used the wilcoxon function from the sticy.stats python library.
The effect size (Cliff's Delta) quantifies the statistical difference between the two sets. bigger effect size denotes a bigger difference and the order is negligible < small medium < large. We computed Cliff's Delta for % OOD performance retained, Pearson correlation, and ID/OOD alignment metrics to measure the effect size between the two groups We used the cliff's _dela function from the cliffs _eeta python library (https: //gi:::///iti htgggtttuuu.... com wweilernsttcliffsleee.
Cliff's Delta.
Reasons for Multiple Metrics. The Pearson correlation metric gauges the correlation between ID and OOD accuracy, indicating tunnel behavior (low correlation), but doesn't testt't quantify the tunnel effect's s magnitude. The % OOD performance retained metric assesses the tunnel effect's magnitude and identifies tunnel layers but solely compares OOD performance between the highest and penultimate layers, neglecting ID accuracy. The ID/OOD alignment metric addresses this by considering both ID and OOD accuracy. To ensure robustness, we employ all metrics to comprehensively capture ID and OOD performance and their relation the tunnel effect.
A.9 SHAP Slope Analysis Details
We describe the implementation details of SHAP slope analyses that are presented in Sec. 4.1.1 For SHAP analysis, categorical variables (e.g., CNN vs ViT) are treated as one-hot vectors, while non- categorical values are transformed into ordinal numbers. We calculate SHAP values on a Gradient Boosting Regression model, which is trained our set of 512 experiments to predict metric from the manipulated input variables already described in the main section of this work. We use the Huber loss train the Gradient Boosting Regression model.
While SHAP values themselves can give us insights into the impact each variable, their interpreta- tion from commonly used plots like SHAP mean absolute bar plot (Fig. 7a) SHAP Beeswarm plot
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1900 Nocordaa relaneet
0291
008
Sate faduction
Thee sbon
Ovatfrrm: unnil
ON xT
600
023
045 000 2:1 2.30
-D0 -it 01
Depth
(a) SHAP mean absolute bar plot
(b) SHAP Becswarm plot
(c) Linear for depth
Figure 7: Examples of SHAP analysis. SHAP analysis plots for the % OOD performance retained metric and an example of the slope calculation for the depth. (a) Mean absolute SHAP bar plot, (b) Beeswarm plot, and (c) SHAP values normalized ordinal values of depth.
(Fig. 7b) is limited. We want show both the impact and the relationship direction of each variable with the predicted metric. To do this, for each variable, we fit a linear model on the obtained SHAP values and the normalized ordinal values of the variable. An example can be seen in Fig. 7c In this way, the value of the slope tells us the impact of the variable on the predicted metric, while the sign of the slope tells the direction. For each metric, we L1 normalize the slope values. A positive slope means that increasing the variable's 's value increases the predicted metric, while a negative slope means that increasing the variable's ss value decreases the value of the predicted metric. A bigger value in any direction indicates that the predicted metric is more sensitive to the corresponding variable. We coined the plot containing the slopes for each variable as the "SHAP Slope" plot.
A.10 Compute Resources
We trained a total of 64 backbones and 10,652 linear probes to finalize manuscript. We ran all experiments using four NVIDIA A5000 GPUs, including training backbones and linear probes. The aggregated compute time is ~ ~1,161 (wall clock) hours (48 days).
B
Datasets
All datasets are widely used and publicly available. We provide a link to the license if it exists. unable to identify the license for CIFAR-10, CIFAR-100,
Despite their widespread use, ImageNet- KK CUB-200, Aircrafts- 100, Flowers- 102, and STL-10 datasets.
We used 11 datasets in total in our paper and they are ImageNet- 1,, ImageNet- ImageNet-R, CIFAR- 10, CIFAR-100, NINCO, CUB-200, Aircrafts, Oxford Pets, Flowers- 102, and STL-10. The dataset details are given below:
CIFAR-10. CIFAR-10 [59] dataset contains 32 x 32 color images with 10 classes. It comprises total of 60,000 images and each class has 6,000 images. The dataset is split into 50,000 training images and 10,000 test images. CIFAR- 10 is a public dataset but does not specify any particular license hattps://wxx toronto edueedduiiii cifar cimfr.
CIFAR-100. CIFAR-I00 [60] dataset is similar to CIFAR-IO but with 100 classes. And, each class has 600 images. It comprises total of 60,000 images. The training and sets contain 50,000 and 10,000 images respectively, Note that the classes in CIFAR-100 are mutually exclusive with those in CIFAR-IÓ. CIFAR-100 public dataset but does specify any particular license hnttps://wwer cs. toronto. edu cifar html).
ImageNet-1K. Imagenet-IK is widely-used large-scale dataset with 1000 object categories and over 1.2 million training images (224 x 224). The test set contains 50000 images. ImageNet- dataset available for free to researchers for non-commercial use. There no particular license specified by creators pattps://images /ttp://een...orgggg/aag////////a chaleeeleeee//LL//////
org
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ImageNet-100. ImageNet- 100 [58] is a subset of ImageNet- IK and contains 100 ImageNet classes. consists of 126689 training images (224 X 224) and 5000 test images. The dataset available to use for research purposes under a BSD 2-Clause License: https: //ggttttuubbu. com wwom/Hobbiiii Hobbitoobboo CHC//Blobbmmaster/LCCCSSSS The class names of ImageNet- 100 dataset are given Sec.
NINCO (No ImageNet Class Objects). NINCO [6]] is dataset with 64 classes. The dataset curated to use as an out-of aut-of-distribution dataset for ImageNet- IK in-distribution dataset. NINCO dataset has 5878 samples and the classes do not overlap with ImageNet classes. We split 5878 samples into 4702 samples for training and 1176 samples for evaluation. We do not have a fixed number of samples per class for training and evaluation datasets. The dataset is available to use for research purposes under an MIT license: btttps://github /githubtt....gg. coml
ImageNet- Setggeeet-nniiiion (ImageNet-R). ImageNet-R incorporates distribution shifts using different artistic renditions of object classes from the original ImageNet dataset [62]. We use a variant of ImageNet-R dataset from [94]. ImageNet-R is a challenging benchmark for continual learning, transfer learning, and OOD detection. It consists of classes with different styles and intra-class diversity and thereby poses significant distribution shifts for ImageNet- pre-tree rre-trained models [94). It contains 200 classes, 24000 training images, and 6000 test images. The dataset available to use for research purposes under an MIT license: https: /et::://ghtttttt com www/hendrycks/////ocoocoooccooae master/LICENSE
CUB-200. CUB-200 is composed of 200 different bird species [64]. The CUB-200 dataset comprises a total of 11,788 images, with 5,994 images allocated for training and 5,794 images for testing. CUB-200 is public dataset but does not specify any particular license (http) //www.vision vision. caltech. edu aalu/datasets/cull _ 2001/_
Aircrafts-100. The Aircrafts or FGVCAircrafts dataset 66 consists of 100 different aircraft categories and 10000 high-resolution images with 100 images per category. The training and test sets contain 6667 and 3333 images respectively. Aircrafts dataset is available for nomccommeraaal research purposes only and does not mention a particular license (http: btttp://wwy http:://ww.rroote robots. ox ac uk/ wwwtaaaaaaaaarrrrraaaeae
Oxford Pets-37. The Oxford Pets dataset includes a total of 37 various pet categories, with an approximately equal number of images for dogs and cats, totaling around 200 images for each category [66]. The dataset available to use for commerciaa/research purposes under a Creative Commons Aitribution-ShareAlin 4.0 International License: https: http::////wwww.....//// robots. ac. uk/ "vgg/data/pets/
Flowers1022 The Flowers- 102 dataset contains 102 flower categories that be easily found in the UK. Each category of the dataset contains 40 to 258 images (3) Flowers- 102 is public dataset but does not mention a particular license (https://wwzz www.:w.wwbbbo..oo ac. uk/ data. f flovers/102/).
ST0-10. STI.-10 has 10 classes with 500 training images and 800 test images per class 67 STL- 10 is public dataset but does not specify any particular license (https: :/cps:///s.. stanford. edu/ aacoates/st110//
C Results & Insights
C.1 Additional SHAP Results
We calculate the Pearson correlation metric over all 512 experiments, using the formula described in Sec. A.8 Fig. 8 shows the SHAP Slope plot for the Pearson correlation metric. The gradient-
regression model got a R² of 0.73 when predicting this metric. The variables follow similar trend as seen in Sec. [.1.] for OOD performance retained metric, where ID class count, augmentation, spatial reduction, and resolution have positive impact on Pearson correlation. Again, ID class count stands out as the most influential variable for Pearson correlation, suggesting that input diversity enhances OOD generalization. In contrast, depth, overtearratttriization level, stem, and CNN vs
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ID Class Count
0.55
Augmentations
0.10
Spatial Reduction
Resolution
0.04
CNN ViT
-0.01
Stem
-0.01
OverParam. Level
Depth
-0.17
-022
0.0
0.2
0.4
SHAP Slope
Figure 8: SHAP results for Pearson correlation. SHAP slope shows the individual impact of variables on the Pearson correlation target. A positive value indicates enhanced OOD transferability and reduced tunnel effect.
ViT variables negatively impact Pearson correlation. Depth shows the negative impact among others.
C.2 Assessing The Tunnel Effect
We conduct 224 experiments ImageNet-1000 exploring various model architectures, and resolutions (32 x 32 and 224 x 224), with and without augmentations, and evaluate them on different OOD datasets mentioned Sec. 3.3] Additionally, to examine resolution in more fine- ane-grained manner. we conduct 96 experiments with resolutions of 64 x 64 and 128 x 128 using VGGm- 17, ResNet-1e 18, and ViT-T+, also ImageNet-100 and the same OOD datasets. We conduct 96 more experiments on ImageNet- 100, varying class numbers while keeping image numbers constant, and vice versa. To compare the effect of the dataset, we perform 64 experiments on CIFAR- 10 and CIFAR-100 as ID datasets with their native resolution (32 X 32), exploring VGGm-11 and VGGm- 17 models, with and without augmentations, and evaluate them on all OOD datasets. do the same for VGGmt-11 I and VGGm+-17 on CIFAR-100, resulting in another 32 experiments. This totals 512 OOD experiments.
In this section, we summarize results in terms of OOD accuracy and three metrics e.g., % OOD performance retained, Pearson correlation, and ID/OOD alignment. This helps analyze the strength of the tunnel effect and OOD generalization various transfer settings. The following subsections present results in terms of different metrics and discuss the findings.
C.2.1 OOD Accuracy
In Table compare OOD accuracy among models trained the ImageNet-100 ID dataset with varied resolutions. The insights derived from three metrics regarding the influence of variables on the tunnel effect are consistent with observations of OOD accuracy. Models exhibiting weaker or negligible tunnel effects tend to attain higher OOD accuracy compared to those with stronger tunnel effects.
C.2.2 OOD Performance Retained
In Table we compare % OOD performance retained among models trained on the ImageNet-100 100 ID dataset with varied resolutions. Models exhibiting weaker or no tunnel effect tend to achieve higher % OOD performance retained compared to those displaying stronger tunnel effect.
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Table 4: OOD Accuracy. We report average results with 95% confidence intervals (CT). ImageNet-R is abbreviated as IN-R. denotes over-paramen parameterization level.
Image Size
OOD Accuracy (8)
NINCO
IN-R
CUB
Airerafts
Flowers
Pets
CIFAR
STL
Avg.
CT
Aug
VGGm7-11
74.67
32"
54.51
21.57
19.54
75.89
40.94
24.03
VGGm-11
74.67
32"
51.33
15.22
16.32
13.11
39.08
68.85 08.86
36.68
21.07
52
VGGm-11
74.67
221"
63.86
12.02
VGGmf-17
158.5
32
43.20
16.32
12.94
9.24
25.98
40.50
40.94
73.47
32.82
15.51 50.13
VGGm-I1 17
138.5
32
31.80
8.43
6.94
3.99
15.00
24.21
28.07
60.42
22.36
7.27 37.45
VGGm-17
158.5
221"
50.51
17.52
12:15
9.51
25 98
32.30
53.15
77. 9-1
34.88
15.41 51.32
VIT-T
44.28
32
47.62
11.22
21.45
11.46
39.41
30.67
27.12
60.62
32.32
17.98 46.66
VII-T
44.28
224"
54.42
11.25
16.15
9.15
26.47
33.11
39 998
65.31
31.98
15.35 48.61
T+
66.23
132"
46.68
10.68
19.00
10.98
355.59
37.68
24.83
59.78
30.65
16.42 44.89
VII-T+
66.23
221"
50.60
8.68
11.
7.05
21.76
30.19
33.
59.88 81
97.98
12.06 13.91
ResNet188
$8.56
32
24.06
5.68
4.47
4.86
9.71
20.05
16.87
48.69
16.87
4.71 20.04
ResNet-18
$8.36
224"
54.85
38.80
21.06
17:28
43.73
38.56
533.28
74.46
40:25
23.39
56.92
ResNet-34
168.37
24.40
4.15
4.73
4.92
18.50
13.63
45.61
15.08
4.19 27.17
ResNet-34
168.37
224
52.98
17.02
15.03
49.77
71.90
Aug
VGGm#-11
74.67
32
65.99
22. 22
32.24
21.81
66.47
56.1
56.50
80.89
50.15
32.
68.20
VGGm-11 11
74.67
332
62.59
18.62
26.27
14.49
56.47
47.67
49.88
76.86
44.11
25.98
62.23
VGGm-11
74.67
221"
70.49
21.17
33.09
28.62 62
70.59
50.92
08.03
85.43
53.92
33.11 72.69
VGGmf-17
158.5
32
63. 10
19.15
27 87.87
15.39
55.78
52.18
58.1
82.18
46.72
27.57 65.87
VGGm-17 17
158.5
322
53.06
12:13
16.34
7.98
40.58
37.01
46.55
74.39
36.04
17.45 54.64
VGGm-17
158.5
221"
71.68
22
22.59
61.12
50.15
69
85.39
51.91
31.81 71.98
VIT-T
44.28
322
49.40
22.11
10.89
41.47
24.94
60.17
32.59
17.92
VIT-T
44.28
224
06.75
17.45
35.31
17.04
51.55
74.29
45.80
66.23
322
54.08
13:25
24.15
30,09
64.50
35.55
VIF-T+
66.23
221"
72.02
18.80
37.78
17.75
79.04
19.99
R8sNet-18
68.56
32
51.19
13.17
19.61
11.49
39.22
41.75
36.47
65.91
34.85
19.29
50.41
ResNet-18
88.56
224"
70.32
27.68
34.47
21.33
62.55
57.27
68.63
81.68
53.337
34.77
71.97
ResNot-34
168.37
32
49.37
12.10
18. 28
10.44
37 37.84
39.30
36.05
66. 08
33.59
17.89
49.30
ResNot-34
168.37
221"
70.83
23.27
30.79
22.62
58.24
52.61
66.99
83.79
51.14
32
70.01
C.2.3 Pearson Correlation
In Table 6
we compare the Pearson correlation among models trained on the ImageNet- 100 ID) dataset with varied resolutions. We observe that the Pearson correlation adeptly captures the tunnel effect across different models and settings.
C.2.4 ID/OOD Alignment
In Table we compare ID/OOD Alignment among models trained on the ImageNet- 100 ID dataset with varied resolutions. More performant models obtain higher ID/OOD alignment scores across various experiments compared to less performant models. The impact of different variables and interventions on the ID/OOD alignment shown in Fig. and Fig. 20
C.3 DNN Architecture
In this section, we analyze how DNN architecture impacts % OOD performance retained across transfer settings. To investigate this, We create boxplot (Fig. 9 that shows % OOD performance retained of each model trained on ImageNet-100 100 ID dataset with resolutions 32 x 32 and 224 x 224. We find that DNN architecture greatly impacts the OOD generalization. Among CNNs. VGGm-Il shows superior performance. In terms of CNN vs. VIT, ViTs perform better than CNNs when augmentations are used. Augmentations benefit both CNNs and ViTs, but ViTs seem benefit more from augmentations.
C.4 DNN Depth
In this section, we analyze how DNN depth impacts the tunnel effect. Fig. 10 shows that smaller models have higher OOD performance retained than larger (deeper) models. Therefore, the depth of DNN has adverse impact OOD generalization and the tunnel effect.
24

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Table 5: % OOD Performance Retained. We report average results with 95% confidence inter- vals (CI). A higher % OOD performance retained indicates a lesser tunnel effect and better OOD generalization. ImageNet-R abbreviated as IN-R. 7 denotes over-parameterizatoon level.
Model
Image Size
% OOD Performance Retained
NINCO
IN-R
Airerafts
Flowers
CIFAR
Avg.
Ang
VGGml-1 11
74.87
32
88.68
94.05
74.23
$1.68
72.62
100.00
80.15
97.65
87.26
78.80 95.62
VGGm-11
14.87
32a
88.08
75.39
65.28
59.32
89.10
94.85
$4.06
92.95
78.63
87.78
89.48
VGGm-11
74.67
224
80.55
87.97
76:40
62.93
64.46
100.00
87.20
98.12
85.70
76.23
96.18
VGGm
158.5
32
70.36
75.05
45.90
34.57
41.67
$0.80
77.19
94.21
64.97
47.49
82.45
VGGm-17 17
158.5
32
57.45
44.58
25.94
15.15
27.67
67.06
47.60
83.65
46.15
27.44
64.96
VGGm-17
158.5
224
75. 19
72.78
44.22
32.02
36.20
84.27
70.23
93.73
63.83
44.72
82 94
VIT-T
44.28
96.05
89.02
92. 62
92.49
96.17
97.33
99.42
98
95.25
92.33
98.
VIT-T
44.28
224
60.76
43.17
42.42
40.91
74.85
76.20
96.91
63.56
47.83 79.28
VTT-++
66.23
322
95.15
87.93
$7-86
67.98
90.52
91.83
97.21
97.57
98.58 96.38
V/T-T+
66.23
22/1"
76.18
50.88
32.23
32.87
34.00
65.73
08.72
81.07
56.30
38.79 71.80
R8sNet-18
88.56
32
49.91
38.35
19.74
22.31
23.57
58.56
44.33
75.56
41.20
25.22 - 57.36
ResNet-18
88.56
224
86.35
72.49
74.98
66.06
17.97
92.33
80.69
95.46
80.79
72.60 88.90
ResNet-34
168.37
61.34
28 05.65
20.30
22.01
21.60
48.78
42.83
72.67
38.02
23.32 53.
ResNet-34
168.37
224
79.16
60.31
51.65
40.67
48.02
83.19
90.14
50.26 79.46
Aug
VGGmi-11
74.87
32"
100.00
100.00
99.52
96.42
96.86
100.00
99.08
100.00
98.98
97.77
100.20
VGGm.11
74.67
322
98.00
90.59
$1.52
56.16
$6.49
97.91
87.40
97.42
86.94
75.64 08
VGGm-11
221"
96.73
100.000
92.66
100.00
99.
VGGmi-17
158.5
'32"
92.98
84.24
83.98
56,81
$2.94
100.00
91.13
99.43
86.44
75.25 97. 77.65
VGGm-17 17
158.5
32
83.53
55.70
48.
31.80
61.96
87.63
65.06
93.28
66.00
48.84
83.15
VGGm-17
158.5
221
98.02
87.66
80.94
71.37
83.31
1001.00
91.74
99.12
89.06
50.74
97.
VIT-T
44.28
.32"
97.48
97.18
94.26
90.75
91.76
97.88
98.82
98.87
95.87
93.22
98. 48
VIT-
224
95.50
90.21
99.38
67.25
90.52
95.88
96.19
98.23
90.27
90.13 96.41
VIT-T+
'32
97.55
91.02
VIT-T+
66.23
224"
98.37
89.32
57.49
87.97
89.13
97.35
95.56
99.03
91..0
58,99 97.11
ResNet-18 18
$8.56
'32"
80.03
63.15
58.80
50,50
69.20
85.28
74.14
90.17
71.80
60.55 83.11
ResNet-18
88.56
224
90.03
85.84
$3.10
72.85
85.64
95.85
91.49
97.88
88.20
$1.00 94.80
ResNet-34
168.37
332"
80.97
57.26
56.63
43.02
68.08
80.93
71.63
89. 99.90
68.55
55.87 81.24
R4sNet.34
168.37
224"
91.24
71.19
68.60
55.16
74.16
91.98
96.40
79.21
67.62 90.80
C.5 Overparameteriration Level
In this section, we investigate the relationship between overparameterization level and % OOD performance retained. We use experimental results from models trained on ImageNet-100) ID dataset with resolutions 32 32 and 224 x 224 for this analysis. To do this, we compute average % OOD performance retained across overparameterization levels and create boxplot using this data. Fig. II shows that % OOD performance retained decreases as wver-parameterization level increases. Therefore, overparameterization level has an adverse impact on OOD generalization.
C.6
Stem
This section analyzes how the stem affects tunnel formation. We use experimental results of models trained on ImageNet-100 ID dataset with resolutions 32 x 32 and 224 x 224. For CNNs, the stem represents kernel size (3 x 3 and 7 7) at the stem layer whereas, for ViT's it is patch size (8 x 8). Fig. 12 reveals that increasing stem hurts % OOD performance retained. In particular, when comparing CNNs (VGGm's 's 3 x 3 and ResNet's 7 X 7). increasing stem from 3 7 decreases average % OOD performance retention. However, ViTs (8 x 8) perform better than CNNs. On the other hand, stem significantly impacts ID/OOD alignment. Across all compared models, increasing stem shows significant negative impact on ID/OOD alignment.
C.7 Augmentation
In this section, we study how augmentation affects the tunnel effect. We used all 512 experiments to assess the impact of augmentation. 256 experiments used augmentations and another 256 experiments did not use any augmentation. In experiments with augmentation, we used random resized crop and random horizontal flip. Fig. 13 exhibits that increasing augmentation greatly improves % OOD performance retained.
25

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Table 6: Pearson Correlation. We report average results with 95% confidence intervals (CT). A higher Pearson correlation indicates a lesser tumnel effect and better OOD generalization. ImageNet-R abbreviated as IN-R. y denotes over- warrperrameteiization level.
Model
Image Size
Pearson Correlation Aircrafts
NINCO
IN-R
CUB
Flowers
Pets
CIFAR
STL
Avg.
No Aug
VGGmf-11
74.67
32'
0.93
0.98
0.88
0.91
0.87
0.98
0.93
0.97
0.93
0.90
0.97
VGGm-11
74.67
322
0.96
0.93
0.85
0.85
0.87
0.98
0.92
0.95
0.91
0.87 0.98
VGGm-11
74.67
224
0.92
0.97
0.86
0.88
0.81
0.99
0.92
0.96
0.91
0.86 0.96
VGGmff
158.5
322
0.84
0.94
0.76
0.71
0.70
0.96
0.87
0.95
0.84
0.75 0.93
VGGm- 17
158.5
322
0.62
0.61
0.38
0.38
0.35
0.88
0.55
0.86
0.58
0.41 0.75
VGGm-17
158.5
221
0.81
0.92
0.69
0.96
0.62
0.97
0.81
0.95
0.81
0.70 0.92
VIT-T
41.28
322
0.91
0.97
0.97
0.96
0.91
0.99
0.97
0.96
0.96
0.95 0.98
VIT-T
44.28
224
0.75
0.70
0.53
0.55
0.40
0.90
0.61
0.83
0.66
0.52 0.79
V
66.23
32'
0.95
0.95
0.93
0.87
0.88
0.97
0.97
0.95
0.94
0.90 0.97
VIT-T+ 66.23
224
0.68
0.59
0.46
0.41
0.12
0.83
0.62
0.74
0.60
0.18 0.72
ResNet-18
88.56
32"
0.83
0.76
0.09
0.71
0.68
0.90
0.77
0.92
0.78
0.71 0.86
ResNet-18
88.56
224
0.97
0.97
0.96
0.93
0.97
0.98
0.96
0.99
0.96
0.95 0.98
ResNet-34
168.37
322
0.78
0.68
0.58
0.62
0.48
0.83
0.72
0.87
0.69
0.59 0.80
ResNet-34
168.37
224
0.87
0.90
0.84
0.81
0.74
0.98
0.79
0.91
0.86
0.79
0.92
Aug
VGGmf-11
71.67
32
0.95
0.99
0.98
0.95
0.91
0.99
0.95
0.95
0.96
0.95 0.98
VGGm-11
74.67
322
0.97
0.95
0.94
0.78
0.93
0.99
0.92
0.97
0.93
0.88 0.98
VGGm-11
74.67
224
0.96
0.99
0.98
0.95
0.95
0.99
0.97
0.97
0.97
0.96 0.98
VGGmf-17
158.5
32'
0.94
0.96
0.94
0.78
0.90
0.99
0.94
0.97
0.93
0.87 0.98
VGGm-17
158.5
32
0.85
0.62
0.60
0.30
0.61
0.97
0.62
0.93
0.69
0.51 0.87
VGGm
158.5
224
0.95
0.97
0.94
0.86
0.91
0.99
0.95
0.94
0.91 0.97
VTT-
44.28
y22
0.96
0.99
0.99
0.95
0.97
0.99
0.99
0.98
0.96 0.99
VIT-T
44.28
224
0.95
0.99
0.98
0.98
0.98
0.99
0.95
0.97
0.96 0.99
VIT-T+
06.23
322
0.96
0.99
0.98
0.96
0.97
1,00
0.99
0.99
0.98
0.97 0.99
VIT-T+
06.23
224
0.97
0.98
0.98
0.98
0.96
0.99
0.94
0.98
0.97
0.96
0.99
ResNet-18
88.56
32"
0.96
0.90
0.91
0.83
0.92
0.98
0.91
0.96
0.92
0.88
0.96
ResNet-18
88, 56
2
0.98
0.98
0.97
0.95
0.99
0.97
0.99
0.99
0.98
0.96 0.99
ResNet-34
168.37
322
0.90
0.81
0.79
0.11
0.77
0.98
0.82
0.92
0.80
0.66
0.91
R4
168.37
224
0.93
0.96
0.95
0.84
0.87
0.99
0.94
0.94
0.93
0.89
0.97
C.8 ID Class Count
This section explores the relationship between the ID class count and the tunnel effect. We use experimental results from the VGGm-11 models trained with ImageNet-100 CIFAR-IO, and CIFAR- 100 using 32 x 32 resolution and image augmentations. Fig. didpllay how the number of ID classes affects the tunnel effect and OOD performance. We see that more ID classes reduce the strength of the tunnel effect and enhance OOD generalization.
For the statistical analysis, we consider 16 paired experiments (32 total) comparing CIFAR-10 and CIFAR-100 datasets (ID). The compared models are VGGm-11, VGGm-17, VGGm+-1 and VGGm+-17. Increasing the number of CIFAR classes from 10 to 100 increased % OOD performance retained from 35.81% % to 73.42% (p < 0.001), with large effect size (10) 0.758). Similarly, the Pearson correlation was improved from 0.54 to 0.88 (p < 0.001), with a large effect size ()8) = 0.742). And, ID/OOD alignment reached 0.22 from 0.12 (p 0.013), with a large effect size (io) 0.531).
C.9 Number of ID Training Classes vs. ID Dataset Size
Fig. 15 shows OOD performance for various dataset configurations with varied classes and samples per class. Increasing class counts significantly impacts OOD performance, whereas, increasing the number of training samples has less impact.
C.10 The Tunnel Effect Is Not Specific To CIFAR-10
In Fig. 16 and Fig. 14 we observe that the tunnel effect is present in various ID datasets e.g.. ImageNet- 100, CIFAR-10, 10, and CIFAR-100. Therefore, the tunnel effect is not a characteristic of particular ID dataset such CIFAR-10.
26

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Table 7: ID/OOD Aligmment. We report average results with 95% confidence intervals (CI). higher ID/OOD alignment indicates a lesser tunnel effect and better OOD generalization. ImageNet- Ris abbreviated as IN-R. 7 denotes over-parametteriztion level.
Model
Image Size
DDOOD Alignment
NINCO
IN-R
CUB
Aircrafts
Flowers
Pets
CIFAR
STL
Avg.
No Aug
VGGmf-11
74.67
32'
0.32
0.09
0.26
0.28
0.23
0.14 0.33
VGGm-11
74.67
322
0.25
0.07
0.09
0.08
0.19
0.21
0.30
0.17
0.10 0.24
VGGm-11
74.67
224
0.45
0.14
0.13
0.13
0.31
0.47
0.29
0.52
0.30
0.17 0.44
VGGmff
158.5
322
0.27
0.10
0.08
0.05
0.16
0.24
0.25
0.40
0.19
0.10 - 0.29
VGGm 17
158.5
322
0.15
0.04
0.03
0.02
0.07
0.13
0.12
0.26
0.10
0.04 0.17
VGGm-17
158.5
2214
0.39
0.13
0.09
0.07
0.20
0.10
0.25
0.54
0.26
0.12 0.39
VIT-T
41.28
32"
0,16
0.04
0.07
0,04
0.14
0.09
0.14
0.18
0.11
0.06 0.15
VIT-T
44.28
224
0.33
0.07
0.10
0.95
0.16
0.23
0.20
0.34
0.18
0.09
0.27
V
66.23
32'
0.16
0.04
0.06
0.03
0.12
0.08
0.13
0.17
0.10
0.06 0.14
VIT-T+
66.23
224
0.29
0,05
0.07
0.04
0.12
0.18
0.17
0.29
0.15
0.07 0.23
ResNet-18
88.56
32"
0.08
0,02
0.01
0,01
0.03
0.05
0.06
0.13
0.05
0.02 0.08
ResNet-18
88.56
224
0.36
0.12
0.14
0.11
0.29
0.34
0.25
0.43
0.26
0.16 0.35
ResNet-34
168.37
322
0.07
0.01
0.01
0.01
0.03
0.03
0.05
0.10
0.04
0.01 0.07
ResNet-34
168.37
224
0.34
0.10
0.11
0.09
0.21
0.31
0.22
0.22
0.12 0.32
Aug
VGGmf-11
71.67
32
0.14
0.15
0.22
0.14
0.11
0.37
0.37
0.48
0.32
0.21 0.14
VGGm-11
74.67
32"
0.38
0.11
0.16
0.08
0.35
0.29
0.29
0.42
0.26
0.16 0.36
VGGm-11
74.67
224
0.55
0.19
0.26
0.22
0.55
0.52
0.40
0.60
0.41
0.27 0.55
VGGmf-17
158.5
32'
0.44
0.13
0.20
0.10
0.39
0.40
0.37
0.52
0.32
0.19 0.44
VGGm-17
158.5
32
0.33
0.08
0.10
0.05
0.26
0.28
0.23
0.42
0.22
0.11 0.33
VGGm
158.5
224
0.59
0.24
0.42
0.42
0.26 0.58
VIT-
y22
0.17
0.07
0.03
0.14
0.10
0.06 0.15
224
0.39
0.10
0.26
0.39
0.26
0.17 0.36
VIT-T+
06.23
322
0.21
0.05
0.09
0.04
0.17
0.11
0.17
0.22
0.13
0.08
0.19
VIT-T+
06.23
224
0.49
0.13
0.26
0.13
0.44
0.40
0.32
0.48
0.33
0.21 0.45
ResNet-18
88.56
32"
0.24
0.06
0.09
0.05
0.19
0.16
0.20
0.27
0.16
0.09
0.23
ResNet-18
88, 56
2212
0.55
0.22
0.27
0.16
0.50
0.53
0.15
0.60
0.11
0.27 0.55
ResNet-34
168.37
32
0.23
0.05
0.08
0.04
0.17
0.15
0.18
0.26
0.15
0.08
0.21
R4
168.37
224
0.56
0.18
0.25
0.18
0.46
0.52
0.42
0.60
0.40
0.26
0.54
Table 8: OOD Accuracy of Large Pre-trained Models.
We report average results with 95%
confidence intervals (CT). ImageNet-R is abbreviated IN-R. denotes over-parameteriizaion level.
Model
0OD Accuracy (%)T
NINCO
IN-R
CUB
Aircrafts
Flowers
Pets
CIFAR
STL
Avg.
SSL Models
SwAV ResNet-50
19.98
80.78
35.87
43.84
18.39
50.88
67.84
77.98
94.91
58.81
37.73
79.90
DINO VIT
66.97
88.78
50.00
55.02
37.95
87.06
80.29
66.75
96.61
72.81
55.04
90.58
MAE VIT-B
66.97
84.27
43.35
31.26
27.27
77.84
68.31
79.04
95.21
63.32
42.27
84.37
MUGS VIT-B
66.97
94.22
64.33
81.74
53.26
92.25
85.83
93.92 03.92
99.00
83.09
69
96.25
ConvNextV2
69.47
91.21
67.48
65.33
26.55
51.90
83.26
91.52
98.70
72.37
52.85
99.89
Models
ResNer-50
19.98
88.10
47.03
45.69
17.22
60.00
66.01
89.86
97. 28
63.90
41.70 - 86.09
VIT-B
66.97
88.52
52.48
48. 48.43
29.52
83.73
80.59
86.18
96.85
70.79
51.22 90.35
ConvNextV1
69.17
90.31
65.95
63.48
30.24
53.04
81.35
91.63
98.18
71.80
53.03
90.56
C.11 Large Pre-trained Models Do Not Exhibit The Tunnel Effect
With the prevalence of large pre-trained models, many research and applications are driven by these models. They show impressive transferability, especially those trained with SSL methods. Our goal is explain this phenomenon using the tunnel effect hypothesis. Although the tunnel effect is hypothesized to present in all over weer-araameterized DNNs, in [9), only supervised DNNs were studied. Using pre- pre-trained models, we study both SSL and SL models. For SSL pre- trained models, we study the following:
ResNet-50 pre-trained with SWAV 73
ViT-B pre-trained with DINO V1
75
ViT-B pre-trained with MAE 50
ViT-B pre-trained with MUGS
74 and
27

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Average OOD Performance Retained
Average % OOD Performance Retained
VGGm-11
VGGm-17
ResNet-10 18
ResNet-34
VIFT
VIT.T+
VGGm-11
VGGm-17
ResNet-18 18
ResNet:3
VITT
ViT-T
(a) No Augmentation (32 X 32)
(b) Augmentation (32 x 32)
Performance Retained
Performance Retained
Average OOD
Average % OOD
VGGm-11
VGGm-17 17
ResNet-18 18
ResNet-34 34
VITT
VITT+
VGGm-11
VGGm-17
ResWet-18
R4
VIT-T
VIT:T
(c) No Augmentation (221 x 224)
(d) Augmentation (221 x 22/)
Figure 9: Box-plots of OOD Performance Retained. The figure shows the OOD performance retained, computed across models trained on ImageNet- 100 at resolutions 32 x 32 and 224 x 224, both with and without augmentation.
Table 9: % OOD Performance Retained of Large Pre-trained Models. We report average results with 95% confidence intervals (CI). ImageNet-R abbreviated as IN-R. y denotes over- parameterization level.
Model
% OOD Performance Retained
NINCO
IN-R
CUB
Airerafts
Flowers
Pets
CIFAR
STL
Avg.
CT
SSL Models
SwAV ResNet-50
19.98
95.77
83.12
87.83
58.10
00.85
94.91
100.00
100.00
86.20
73.90
98.59
DINO
100.19
MAE WIT-B
66.97
98.99
98.52
91.28
100100
96.24
98.61
100.00
100.00
97.91
95.52
100.36
MUGS VIE-B
100.00
100.00
ConNNexTV2
69.47
97.90
99.39
92.66
84.61
99.31
90.49
99.70
99.96
96.38
90.61
100.14
Models
ResNet-50
19.96
96.73
92.01
73.98
37.30
65.67
91.12
99.49
99.82
62.00 02.00
64.15 - 99.85
VIT-B
66.97
89.43
95.60
94.90
87.31
93.74
98.96
100.00
99.60
98.
92.65
99.71
ConvNexiV1
69.47
98.52
08.19
92.71
90.00
89.27
98.87
99.36
99.67
95.85
92
99.46
ConvNeet-B V2 pre-trained with FCMAE 76
For SL pre-trained models, we study ResNet-50 [54], ConvNext-B VI [72. and VIT-B [55] which are pre-trained with SL loss and data labels. We carry out 72 experiments in total of which 27 for SL models and 45 are for 5 SSL models. All SL and SSL models are pre-trained and fine-tuned (SSL only) on ImageNet-INe IK dataset. In total, trained 1980 linear probes for ID and OOD datasets. Appendix A.6 gives additional details and model configurations.
Due to limited computational resources. we could not pre-train our own SSL models to do rigorous paired analysis. SSL training approximately 16x more expensive than SL. considering multiplica- tive factors, e.g., 8x more epochs and 2x more forward passes. Thus, we could only evaluate publicly available pre-trained models released by their creators. We find that SHAP analysis appears to be less informative due to the small sample size and because most of the pre- rre-trained models do
28

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95.0
80.0
Performance Retained
Average OOD Performance Retained
Average % OOD
05.0
75.0
80.0
70.0
65
65.0
80.0
60.0
55.0
VGGm-11
VGGm-17
ResNet-18
ResNet-34
VGGm
(b) ResNet
Performance Retained
Average % OOD
83.0
80.0
75.0
60.0
VIT-T
VIT-T+
(c) VIT
Figure 10: Impact of Depth. The figure shows how depth impacts the tunnel effect in terms of OOD performance retained. Increasing depth decreases the OOD performance retention and intensifies the tunnel effect. The Y-axis shows the average with 95% confidence interval.
100
Average % OOD Performance Retained
00
60
00
8
20
44.28
66.23
74.67
88.56 158.5 168.37
Overparameterization Level
Figure 11: Over-parameteriizaion level. This figure exhibits OOD performance retained com- puted across over-paramettrrizaton levels. This based models trained ImagerNet- 100 resolutions 32 x 32 and 224 x 224. Increasing the over-parameterizztion level reduces the % OOD performance retained and intensifies the tunnel effect.
not exhibit the tunnel effect, resulting in less variability. Therefore, we focus on OOD linear probe analysis.
Fig. and Table we observe that tunnel not present in most cases except for the ResNet-50 models. As shown in Table & the SSL method, MUGS achieves the highest average OOD accuracy among all methods. In terms of DNN architecture, ViT-B exhibits better OOD performance than ResNet-50. Interestingly, among CNNs, ConvNeXt-B, which adapts design choices from Swin-
29

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Performance Retained
100
Average ID O0D Alignment
0.6
Average % OOD
80
0.2
0.1
0.0
Stem
Stem
(a) % OOD Performance Retained
(b) IDIOOD Alignment
Figure 12: Stem. This figure exhibits % OOD performance retained and ID/OOD alignment computed stems and averaged across OOD datasets. This is based models trained ImagerNet-100 (ID) with 32 x 32 and 224 x 224 resolutions. When comparing CNNs (VGGm's x 3 and ResNet's x 7), increasing stem exhibits negative impact on % OOD performance retained. Across all models, increasing stem negatively impacts ID/OOD alignment.
100
Performance Retained
Average % OOD
80
60
40
20
Augmentation
Figure 13; Augmentation. This figure exhibits % OOD performance retained to assess the impact of augmentation. The comparison made between 256 experiments without augmentation and 256 experiments with augmentations. Augmentation greatly enhances the % OOD performance retained and reduces the tunnel effect.
transformer 995 shows better OOD performance than ResNet-50. They also rival ViTs. This corroborates our argument that DNN architecture matters for OOD performance.
The comparison between SSL and SL. models is not straightforward as there are multiple factors involved, c.g., pretext tasks, training epochs, augmentations, and so on. Except for MAE, other SSL methods exhibit strong OOD performance compared to SL counterparts (Table Sb. Previous works [52 [6] also found that MAE performs poorly in linear evaluation. When we compared SL vs. SSL models in the same family, in terms of average OOD accuracy, SSL (71.42%) outperforms SL (68 83%). As illustrated in Fig. I8 SSL models perform better than SL models in terms of % OOD performance retained. We report the ID accuracy of these models in Table TO Given that SSL methods employ more augmentations than their SL counterparts (see Table 3 the performance improvements of SSL methods over SL. ones are likely, in part, due to stronger augmentations, which also argued in prior studies (97 198.. While complimenting earlier works, our work confirms that large pre-trained models do not form tunnels, adding valuable perspectives to current knowledge.
30

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1.0
Normalized Accuracy
0.8
0.6
0.4
0.2
CIFAR-101OOD)
CIFAR-10OII))
CIFAR-100:00D)
imageNet-100/I))
ImageNet-100(000)
0.0
4
Figure 14: ID class count. This figure compares the OOD and ID linear probe accuracy for VGGm- 11 models across three ID datasets (32 x 32 resolution): CIFAR-10, CIFAR-100, and ImageNet- 100. The OOD curve is the average of OOD datasets and the shaded The strength of the tunnel weaker for ImageNet- 100 and CIFAR-10 100 compared to CIFAR-10.
denotes standard deviation.
Average OOD Accuracy
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
5:1000
C:50 C:100
C:100
Dataset Confiquation
Figure 15: Class Count Data Quantity. The figure shows the trend that models trained with more classes and more samples have better OOD accuracy (%). We use C and S to denote the number of classes and number of samples per class respectively, the X-axis of the figure.
C.12 Examining Actual Accuracy
We also examine the impact different variables and interventions the performance, OOD performance, and ID/OOD alignment by analyzing the actual accuracy (no normalization). We show these results in Fig. 19 and Fig. 20 We observe that the actual accuracy trends are consistent with our previous findings where variables that improve (degrade) OOD generalization also show higher (lower) ID/OOD alignment.
C.13 Additional Resolution Results
Here we present additional resolution results. The image resolution shows a significant impact on the tunnel effect and OOD transferability. As shown in Fig. 19a higher resolution images achieve higher performance in terms of ID accuracy, OOD accuracy, and ID/OOD alignment.
CNN. Fig. 21 and Fig. 22 show the results for VGGm-17 models trained on ImageNet- 100 with varied image resolutions experiments with and without augmentations. The tunnel effect decreases with the increase in image resolution in all experiments.
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CRIPL
33
(a) VGGm-11, CIFAR-10
(b) VGGm-111 CIFAR-100
(c) VGGm-11, ImageNet-110
Colect
Colen
(d) 17, CIFAR-10
(c) VGGm-17, CIFAR-100
(f) VGGGm117 17, ImageNet- 100
Figure 16: The tunnel effeet not specific particular ID dataset. The OOD linear probe accuracy for VGGm models trained on various ID datasets: CIFAR-10 10, CIFAR-100, and ImageNet- 100 with low resolution (32 32) images in augmentation free settings. The gray shaded area denotes the tunnel. The tunnel effect is prominent in all low-resolution settings.
VIT Blak
VST BEak
122 26:4
(a) SwAV Re
(b) MAE VIT-B
(c) MUGS VIT-B
(d) DINO VI VIT-B
(e) FCMAE ConvNeXi-B SL ResNet-50
SL ConvNeXt-B
(h) SL VIT-B
Figure 17: OOD performance of large pre-trained models. We show normalized linear probe accuracy the ID (ImageNet-IK)) and OOD datasets. The OOD curve is the average OOD datasets. Shaded area denotes the standard deviation. Most models do not show any tunnel effect.
VIT. Fig. 23 and Fig. 24 show the results for ViT-T+ models trained on ImageNet- 100 with varied image resolutions in experiments with and without augmentations. When augmentation is omitted, low-resolution inputs show a weaker tunnel effect than high-resolution inputs. However, both low- and high-resolution inputs significantly mitigate the tunnel effect when augmentations are used.
Rank Analysis. We examine the numerical rank of the representations evaluated on the dataset, following prior work [9]. In Fig. 25 we observe that a model trained on high-resolution images maintains higher rank than a model trained on low-resolution images, corroborating our previous findings (Sec. 4.13). The representations rank for resolution 32 x 32 plummets after the extractor, exhibiting the neural collapse phenomenon [00] whereas resolution 224 224 retains a much higher rank in the corresponding layers. The degradation in OOD accuracy and ID representation rank is more pronounced for oowrresolution images than for high-resolution images. As a result, model trained on low wow-resouution images exhibits stronger tunnel effect than trained on high-resolution images.
32

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% 00D Performance Retained
% 0OD Performance Retained
120
30
30
Dio Vi wiaa
SOMAE convirts frea
HuGs wisa
Con sette
Ruseet 30
vit
Suiu Rectier-30
Self-Supervised
Supervised
(a) SSL vs SL.
(b) Comparison among pre-trained models
Figure 18: Summary plots for large pre-trained models. The left figure exhibits % OOD per- formance retained computed across training methods (SL and SSL). The right figure displays % OOD performance retained computed across distinct architectures. SSL models show higher OOD performance retained than SL models.
Avg. ID Acc. Avg. OOD Acc. 10/000 Align.
Avg. ID Acc.
Avg. ID Acc.
Avg. OCO Acc
Arg. 0C0 Acc.
IDA0OD
IDV00D
0.74
Accurag
00.6
2.0
0.0
0:51
0.29
0:17
2.18
0.12
0.09
0.12
0.0
32x32
Res. 224x224
0.0
0.0
Classes
classes
(a) Resolution
(b) Augmentation
(c) ID Class Count
Figure 19: Dataset variables. Impact of resolution, augmentation, and ID class count on ID accuracy, OOD accuracy, and ID/OOD aligmment. This analysis based on actual accuracy (no normalization) averaged over models and datasets. The accuracy and alignment score range from 0 to 1.
Avg. Avg. Acc. ID/000 Align.
Avg.
Aug.
Avg:
ID/OOD Allgn.
IDVOOD Alian.
0.8
0.8
0.8
0.73
0.M
0.7
Accuracy
Accuracy
0.59
0.41
0:35
0.35
0.31
025
0.29
3.29
0.2
0.2
0.2
0.2
D-11 (v- 74.1
D-17 (y- 158.51
6 0.5
3.0
Kernel 3x3
Karnal 7x7
(a) Depth & Overparam. Level
(b) Spatial Reduction
(c) Stem
Figure 20: DNN architecture variables. Impact depth (D), overparameterization level (7), spatial reduction (o), and stem on ID accuracy, OOD accuracy, and ID/OOD alignment. This analysis is based on actual accuracy (no normalization) averaged over models and datasets. The accuracy and alignment score range from to 1.
33

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0.9
0.
0.0
0.5
Imageten:
CIARR
Outord
Ostrrs
Rower
STL
Fowcr
STL
KINCO
Imagehee (0)
04
CUS
NMOO
IrageNet00)
0.3
Layar
(a) Resolution 32 x 32
(b) Resolution 64 x 64
0.8
0.5
ImageNet-R
CIRAR
OPAR
Oxtordl
FloeY
STL
Plavor
STL
NINCO
(n2perle110)
NENDO
Inagchor)0)
04
(c) Resolution 128 x 128
(d) Resolution 224 X 224
Figure 21: The OOD linear probe accuracy for similar sized VGGm-17 models trained on ImageNet- 100 dataset with varied image resolutions in augmentation-free settings. The OOD degradation reduces with the increase in image resolution.
0.5
0.5
CIAAR
Octerd
CIAR
Outordl
Rover
STL
Flower
STL
NINCO
Imageker (E)
NINDO
Imageher
0.1
Loyer
(a) Resolution 32 x 32
(b) Resolution 64 x 64
1.0
0.5
0.5
0.7
0.7
0.0
05
CIFAR
Outord
CIRAR
Outordl
0.2
Rower
STL
Flower
STL
0.1
NINCO
imsgeteer (0)
NINDO
Imageher (6)
00
Loyer
(c) Resolution 128 x 128
(d) Resolution 224 x 224
Figure The OOD linear probe accuracy for similar sized VGGm-17 models trained on ImageNet- 100 dataset with varied image resolutions while using image augmentations. The OOD degradation reduces with the increase in image resolution.
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008
ImageNen-R
CIFAR
Aevihs
Arcoots
Floer NINCO
Oxtard Pet
64
Flwcr
Osbod Pot
STL
NMOO
imapetee
IrageNer 0D)
VIT Black
Book
(a) Resolution 32 x 32
(b) Resolution 64 x 64
0.8
0.7
Nomabest
bool
R
ImageNer-
CIAAR
Arcooss
Rover
Oxtond Pct
Flwer
Osbod Pet
NINCO
STL
NNOO
Imagetee
CUS
PrageNer 0D)
03
VIT Black
Bock
(c) Resolution 128 x 128
(d) Resolution 224 x 224
Figure 23: The OOD linear probe accuracy for similar sized VIT-T+ models trained on ImageNet- 100 dataset with varied image resolutions in augmentation-free settings. The OOD degradation reduces with the increase in image resolution.
0.5
0.9
0.6
20.
0.0
00
CIFAR
Alrrnts
CRAA
Rower
Outord Per
04
Flwwer
Ootordl Pet
NINCO
NINDO
Imageteer
VTT Block
Blook
(a) Resolution 32 x 32
(b) Resolution 64 x 64
0.5
0.9
0.6
0.0
0.7
0.0
0.5
0.5
CIFAR
Alrrms
CIRAR
Arrats
Rower
Ovtord Per
Ootordl Pet
NINCO
NINDO
Imageher
VT
Block
Book
(c) Resolution 128 x 128
(d) Resolution 224 x 224
Figure The OOD linear probe accuracy for similar sized VTT-T+ models trained on ImageNet- 100 dataset with varied image resolutions while using image augmentations. The OOD degradation reduces with the increase in image resolution.
35

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5000
Tunnel Layers
Tunnel Layers
0.0
7000
5000
0.7
0000
Nomerion Rank
Accurary
5000
0.5
3000
0.2
0.3
Acpurasy racy
2000
Acpuracy
03
Aug. OOD Accuracy
Avg. OGD Accuracy
1000
Numerical
B 3
10
0.0
10
VGGm Layer
VGGm Layer
(a) Resolution 32 x 32 (strong tunnel effect)
(b) Resolution 224 x 224 (weak tunnel effect)
Figure 25: High-resolution model maintains a high representation rank. This figure corresponds to Fig. in the main text. In this setting, identical VGGm- architectures are trained on identical ID datasets (100 ImageNet classes), where only the resolution is changed. The Y-axis shows the actual accuracy (no normalization) of linear probes trained on ID) and OOD datasets. The OOD curve is the average of OOD datasets (Sec. (.3). with the standard deviation denoted with shading. The Y-axis also shows the numerical rank evaluated on the ID dataset. Here the OOD accuracy and ID representation rank align with the dynamics of the tunnel effect: the stronger the tunnel effect, the lower the OOD accuracy and ID representation rank.
D In-Distribution Performance
In this section, we present the ID performance of all pre-trained DNNs. Table I0 shows the ID performance of 8 large-scale offtthe-shelf models pre-tained on ImageNet- IK dataset.
Table 10: ID performance of large pre-trained models. Reported is the best top-1 accuracy (%) on ImageNet- IK dataset (224 x 224).
Model
Accuracy
SSL
SWAV ResNet-50
75.3
DINO VI ViT-B
78.2
MAE VIT-B
83.6
MUGS VIT-B
80.6
FCMAE ConvNeXtV2
84.9
SL
ResNet-50
80.9
ViT-B
81.1
ConvNettV1
83.8
Table 11 presents the results for each the 64 DNN models studied in our main results. For each model and ID dataset combination, it gives the ID accuracy for the resolution/angmentatiion combination.
On ImageNet-100, for ViT-T+, ResNet- 18, and VGGm-17 17, 8 models were trained per DNN archi- tecture resolution 2 augmentation policies). The total is DNNs. For same dataset, models were trained per DNN architecture, namely, ViT-T, ResNet-34, and VGGm-11 (2 resolution x augmentation policies). The total 12 DNNs. An additional models were trained per architecture for VGGmf-11 and VGGm/-17 (I resolution 2 augmentation policies). The total is 4 DNNs. Overall, 40 DNNs were trained for ImageNet-100.
On CIFAR-100, for VGGm-11 -16 VGGm VGGm17, and VGGm 17, 2 models were trained per architecture resolution augmentation policies). The total is DNNs.
On CIFAR-10, for VGGm-11, 1, VGGm- 17, 2 models were trained per architecture (1 resolution x augmentation polices). The total is 4 DNNs.
On ImageNet Subsets, for VGGm-11, 12 models were trained (1 resolution times dataset configu- rations x 2 augmentation policies). The total is 12 DNNs.
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Table 11: ID performance DNNS trained on CIEAR-10, CIFAR-100, ImageNet-100 and ImageNet Subsets. Reported is the best top-1 accuracy (%) for experiments with varied resolution and augmentation policies. The total number of DNN parameters in Million and denoted by # P. For each ID dataset, we group results based on DNN architecture. The sum of rows indicates the total number of DNNs i.e., 64.
ID Dataset
Model
#P
Resolution
No Aug
Aug 1
32
36.48
35,28
ViT-T
5.61
224
62.50
60.72
32
35.64
41.14
VIT-T+
8.39
64
47.18
56.64
128²
56.84
66.60
224
59.38
70.24
32
34.38
49.70
ResNet-18
11.22
64
45.56
66.08
ImageNet-100
128²
59.90
76.94
224
68.80
81.74
32
32.10
50.80
ResNet-34
21.33
224
68.86
83.12
32
52.22
63.74
VGGm-11
9.46
224
78.74
83.02
32"
52.02
65.78
VGGm-17
20.08
64
66.10
77.88
128
75.62
84.76
224
80.28
86.28
VGGm+-11
9.46
32"
63.12
70.28
VGGm*-17
20.08
32
65.76
74.40
VGGm-11
9.46
32"
63.78
72.36
CIFAR-100
VGGm-11 17
20.08
32
60.91
70.92
VGGm+-11
9.46
32
71.18
76.00
VGGm+-17
20.08
32²
70.23
76.19
VGGm-11
9.46
32
88.05
93.04
CIFAR-10
VGGm-17
20.08
32"
88.20
92.69
ImageNet Subsets
10 classes & 1K samples
70.2
77.0
50 classes & 200 samples
37.2
50.7
100 classes & 100 samples
VGGm-11
9.46
32
26.1
33.2
100 classes 200 samples
32.8
45.0
100 classes & 500 samples
44.7
57.1
100 classes 700 samples
47.5
61.6
E
Additional Statistical Results
In this section, we report additional statistical results for different variables and interventions. Table includes average results with confidence interval. Table [3 reports effect size (Cliff's s Delta) and p-value (Wilcoxon signed-rank test) for various pair comparisons where #E denotes the number of paired experiments (total number of experiments is 2 x E).
37

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Table Average Results, We report average results in metries with a 95% confidence interval (CI) for different variables and interventions.
Variable % OOD Performance Retained 7
Pearson Correlation 1 CI
ID/OOD Alignment f
Avg.
CI
Avg.
Avg.
CI
Resolution 32
68.63
61.18 76.09
0.81
0.76 0.87
0.13
0.10 0.15
64
69.78
63.48
76.08
0.83
0.78 0.88
0.20
0.16 - 0.24
128
77.25
82.68
0.88
0.83 0.92
0.28
0.23 0.32
224
78.37
72.66 84.08
0.88
0.83 0.92
0.30
0.25 0.35
Augmentation
No Aug.
64.26
61.20
67.31
0.77
0.74 0.80
0.15
0.14 0.17
Aug.
78.41
75.65 81. 16.6
0.86
0.84 0.89
0.25
0.23 0.27
Stem
3
76.74
71.21 82.27
0.84
0.80 0.89
0.27
0.23 0.31
66.66
61.09
72.23
0.87
0.83 0.90
0.21
0.17 0.25
85.35
80.81 89.90
0.88
0.84 0.92
0.17
0.14 0.20
DNN Arch.
VGGm
75.38
71.10 79.66
0.85
0.82 0.88
0.27
0.21 0.31
ResNet
68.97
64.64
73.30
0.89
0.87 0.91
0.22
0.19 0.25
ViT
81.66
77.45 85.88
0.85
0.80 0.89
0.18
0.15 - 0.20
Spatial Reduction
84.40
80.25 88.54
0.92
0.90 0.94
0.26
0.23 0.30
0.5
64.85
59.06 70.63
0.72
0.66 0.78
0.18
0.15 0.21
Depth
89.19
85.71 92.66
0.94
0.92 0.95
0.28
0.24 0.33
12
86.99
80.94 93.04
0.89
0.84 0.95
0.16
0.13 0.20
17
69.41
62.56 76.25
0.80
0.74 - 0.85
0.25
0.20 - 0.30
18( ResNet) 18(VIT)
70.53
62.50 78.56
0.91
0.88 0.94
0.22
0.16 - 0.28
83.72
76.65 90.79
0.87
0.81 0.94
0.18
0.13 0.22
34
62.78
54.88 70.69
0.82
0.77 0.87
0.20
0.14 0.26
Overparam Level
44.28
86.99
80.94 93.04
0.89
0.84 0.95
0.16
0.13 0.20
66.23
83.72
76.65 90.79
0.87
0.81 0.94
0.18
0.13 0.22
74.67
87.22
82.62 91.82
0.93
0.91 0.95
0.29
0.23 - 0.34
88
70.53
62.50 78.56
0.91
0.88 0.94
0.22
0.16 - 0.28
158.5
66.26
57.39 75.13
0.76
0.68 0.83
0.25
0.18 - 0.32
168.37
62.78
54.88 70.69
0.82
0.77 0.87
0.20
0.14 0.26
ID Datasel
ImageNet-100
82.78
75.47 90.10
0.92
0.89 0.95
0.22
0.16 0.28
CIFAR-10
35.81
22.60
0.54
0.42 0.65
0.12
0.04 0.20
CIFAR-100
73.42
64.62 82.22
0.88
0.84 0.93
0.22
0.15 0.29
Classes Samples
C10 $1000
29.61
24.01 35.21
0.42
0.37 - 0.47
0.06
0.03 - 0.08
C200
$200
68.72
61.34 76.
0.84
0.79 0.88
0.11
0.07 0.15
C100_S10
79.57
72.81 86.33
0.91
0.87 0.94
0.08
0.05 0.11
C100 $200
74.28
66.78 81.78
0.89
0.85 0.93
0.11
0.07 0.15
C100_$500
78.04
69.83 86.24
0.90
0.86 0.94
0.17
0.12 0.23
C100_S700
77.19
68.20 86.18
0.87 0.95
0.19
0.13-
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Table 13: Effect Size & p-value. bigger effect size, |8| indicates a bigger statistical difference between each pair and the order is negligible (N) < small (S) < medium (M) < large (L).
Pair
% OOD Perf. Retained
Pearson Corr.
IDIOOD Alignment
|8|
p p-value
18
p- value
[6] 1
p-value
#
Aug. Aug. vs No Aug.
MM
0.001
0.374((
< 0.001
0.357(
< 0.001
256
Spatial Red. I vs 0.5
O.53I(L)
0.001
(.536(
< 0.001
0.36I(M))
< 0,001
64
Resolution
32" vs 61
0.002(N)
0.315
0.023(IN)
0.572
0.326((S)
< 0.001
32 128
0.171(5)
0.001
0.240(5)
0.006
0.567(L)
0.001
48
32 vs 221
0.198(S)
0.005
0.280(5)
0.011
0.625(L)
0.001
64" vs 1282
0,208(S)
0.001
0.222(55)
0.001
0.283((S)
< 0.001
48
64" vs 224"
0.250(S)
0.001
0.251(S)
0.077
0.351(AM)
0.000
128 vs 224 Stem
0.059(NN
0.741
0.042(NV)
0.947
0.102(N)
0.035
48
3 vs
0.306(S)
0.001
(.004(N0
0.145
0.226(
0.001
64
3 8
(.249(5)
0.014
0.293(S)
0.092 1
(.346(M)
0.001
64
7 8
0,580(2 L)
0.001
(.250((S)
0.133
0.083(N)
0.001
64
Depth
11 vs 12
0.041(N)
0,978
0,150(5)
0.963
0.475 L)
0.001
32
11 vs 17
0.539(L) (L)
10000
0.497(L)
0.001
0.161(9)
0.001
48
11 vs 18( ResNett
0.520(L) L)
10000
0.025(N)
0.322
0.285(
0.001
32
11 vs 18(VI7) 11 vs 31
(N)
0,312
0.031(N)
0.846
0.443( M)
<
0.001
32
0.680(L)
10000
0.570(L)
< 0.001
0.340(
0.001
32
12 vs 17
0.534(L)
1,000
0.533(L)
0.013
0.250
0.001
32
12 vs 18( (eRcsNet)
0.574(L)
0.003
0.123(N)
0.625
0.125(N)
0.002
32
12 vs I8(VIT)
0.128(N)
1,000
0.088(N)
0.010
0.020(N)
0.190
32
12 vs
0.689( L)
1.000
0.471(M)
0.052
0.070(
0.024
32
17 vs 18( ((ReNN)) vs 18(VIT)
(.090(N)
0,262
0.516(L)
0.001
0.100(N)
0.003
32
0.472(M)
0.000
0.457(M)
0.025
0.217(8)
0.001
17 v4 34 18(Res.) 18(VIT)
0.113(N)
0.062
0.096(NV)
0.005
0.178((8)
0.001
0.465(M)
0,017
0,000
0.021((V)
0.818
0.102(N)
0.004
18(ResNel) 34
0.242(S)
0.443(M)
0.001
0.072(N)
0.001
18(V:T) vs
O.590(L)
0.001
0.387(
0.106
0.037(N)
0.045
Overparam Level
44.28 66.26..
0.128(N)
0.001
0.088(N)
0.010
0.020(NN
0.190
44.28 74.67
0.041(N)
0.978
0.150(5)
0.963
0.475
0.001
44.28 88.56
0.574(L)
0.003
0.123( NN)
0.625
0.125(N)
0.002
44.28 158.5
0.534(L) L)
10000
(.533(L)
0.013
0,250(
0.001
10,00
44.28 168.6666 37
0.689 L)
0.471(M)
0,052
0.070(N)
0.024
32
66.23 74.67
0.051(N)
0.512
0.031((N)
0.846
0.443(M
0.001
66.23 56
0.465 (M)
0.017
(.021(N)
0.818
0.102(N)
0.004
32
66.23 158.5
0.472(M)
10000
0.457(
0.025
0.217(8)
0.001
32
66.23 168.37
0.590(L) L)
2 10000
0.387 M)
0.106
0.037(N)
0.045
32
10000
74.67 vs 88.56
74.67 158.5
O.520(L)
0.531(L)
2
10000
0.025(N)
0.553(L)
< 0.001
0.322
0.174(8)
0.285(S)
0.001
0.001
32
32
74.67 vs 168.37
0.680(L)
10010
0.570(L)
0.001
(.340(M)
0.001
32
88,56 158.5
0.090(N)
0.262
0.516(L)
< 0.001 1001
0.100(N)
0.003
32
88.56 vs 168.37
0.242(S)
0.001
0.443(
< 0.001
0.072(N)
0.001
32
158.5 vs 168.37
0.113(N)
0.062
0.096(N)
0.005
(S)78(S)
< 0.001
32
ID Dataset
Imagenet-100 vs cifar-10
0.805(L)
0.001
0.766(L)
< 0.001
0.547(L)
0.011
16
Imagenet-100 100 vs cif
0.352(M)
0.001
0.320(S)
0.005
0.023(N)
0.211
16
ci vs cifar-100
0.758(L)
0.001
0.742(L)
< 0.001
0.531(L)
0.013
16
Classes Samples
e10 s10_s1000 vs cs000
c10_s1000 vs c100_s100
c10 s1000 vs c50 c20_ $200
1.000
0.969(L) L)
1.000(L)
000
0.001
10000
10000
1.000(L)
1.000L)
1.00 L)
< 0.000
< 0,001
< 0.001
L000
0.453(M)
0.477 L))
0.309
10000 >
<
0.001
0,000
1000
16
16
16
10000
L0000
1 1000 0000 >
c10_s1000 vs c100_s500
c10_s1000 vs c100_s700
c50_s200 vs c100_s100
0.422(M)
0.984(L)
0.992(1)
10000
10000
1
O. 0.469
1.00 L.
1.00(L)
4
4 0,000
2 L,000
L000
0.223(S)
0.707
0.754(L)
1000 000 >
0000
1000 10000
16
16
c50_s200 vs c100_s200
0.242(S)
1000 >
T000
0.352(M))
< 0.000
0.023(N)
0.324
T000 10000
c20_s200 vs c100 s500
(M391(M)
10000 >
(.492(L)
< 0.001
0.402(M)
0.001
c50_s200 vs c100_s700
(.367(M)
1
0.500(L) L)
0.001
0.453(M)
0.001
c100_s100 c100_s200
0.219(S)
0.001
0.180(5)
0.40 0.495 9
0.00 0.065
0.250(8)
0.001
c100_s100 c100_s500 $500
0.047(NN)
0.375
0.016(N)
0.562(L)
0.001
c100_s100 cs000__7000
0.062 N)
0.323
0.055
0.617(
0.001
c100 s200 s500
0.203(S)
0.004
0.211(S)
0.004
0.383(M)
0.001
16
c100_s200 c100_s700
(8
0.039
0.250(5)
0.013
0.434(M)
< 0.001
16
c100_s500 c c100_s700
0.008(N)
0.404
0.141((N)
0.065
0.113(N)
0.001
16
39

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F
Classes of ImageNet-100 ID Dataset
We list the 100 classes present in the ID dataset, ImageNect1000 [58]. This list can also be found at: txt
https://githen cww/Hobbiit hwwp:/obbiooooog///o/ooooooooo/e http:////....oooo/o/t/////aaaaaa
Rocking chair, pirate, computer keyboard, Rotweeilrr Great Dane, tile roof. harmonica, langur, Gila monster, hognose smake, vacuum, Doberman, laptop, gasmask, mixing bowl, robin, throne, chime, bonnet, komondor, jean, moped, lub, rotisserie, African hunting dog, kuvasz, stretcher, garden spider, theater curtain, honeycomb, garter snake, wild boar, pedestal, bassinet, pickup, American lobster, sarong, mousetrap, coyole, hard disc, chocolate sauce, slide rule, wing, caudiflower, American Staffordshire terrier, meerkat, Chihuahua, lorikeet, bannister, tripod, head cabbage. stinkhorn, rock crab, papillon, park bench, reel, toy terrier, obelisk, walking stick, cocktail shaker, standard poodle, cinema, carbonara, red fox, little blue heron, gyromitra, Dutch oven, hare, dung beetle, iron, bottlecap. lampshade, mortarboard, purse, boathouse, ambulance, milk can, Mexican hairless, goose, boxer, gibbon, football helmet, car wheel, Shih-Tzu, Saluki, window screen, English foxhound, American coot, Walker hound, modem, vizsla, green mamba, pineapple, safety pin, borzoi, fibby.iidler crab, leashopper, Chesapeake Bay relriever, and ski mask.
Is there any semantic class overlap between ID and OOD datasets? There is no semantic class overlap between ImageNet- 100 (ID dataset) and 8 other OOD datasets e.g.. CIFAR-10, CIFAR-100, NINCO-64, CUB-200, Aircrafts- 100, Oxford Pets-37, Flowers- and STL-10.
Only ImageNet-R (consisting of 200 classes) has 19 classes that overlap with ImageNet-100. This is expected and we know that ImageNet-R includes classes from ImageNet-IK IK dataset but incorporates significant distribution shifts using artistic renditions. The overlapping classes are: Gasmask, Ameri- can lobster, Standard poodle, Red fox, Head cabbage, Harmonica, Ambulance, Gibbon, Pineapple, Chihuahua, Tabby, Pirate, Rotweeiler, Lorikeet, Boxer, Pickup, Goose, Shih-Tzu, and Meerkat.
Also, there is no overlap between CIFAR-10 and CIFAR- 100 so using one as ID and the other OOD retains OOD challenges. is evident that OOD evaluations all our experiments are substantially robust due to dissimilar classes and significant distribution shifts between ID and OOD datasets.
40

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47


Reviews:
[{"review_id": "Dv5FsJGJAF", "reviewer": "Reviewer_tyj4", "summary": "This paper studies the factors influencing out-of-distribution (OOD) generalization of pre-trained DNN embeddings through the lens of the tunnel effect hypothesis, which suggests deeper DNN layers compress representations and hinder OOD performance.", "questions": "please refer to the weakness.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The paper includes a sufficient amount of experiments, offering detailed and substantial content.\n\n- The main purpose of the paper is clear and easy to understand.", "weaknesses": "- The technical contribution is limited. The experiments on OOD generalization discussed in the paper are rather trivial and do not yield sufficiently insightful conclusions.\n\n- The paper is poorly written. As an evaluation-focused study, it fails to effectively organize the relationship between the arguments and experiments, making it rather disorganized.\n\n- The paper does not provide significant theoretical contributions, focusing primarily on empirical results without delving into the underlying theoretical frameworks or offering new theoretical insights.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thorough reviews and insightful feedback. We have carefully considered your concerns and tried to address them. Below, we have provided detailed responses to each review separately.\n\n# Weaknesses\n\n**W1. Limited Technical Contributions**\n\n- We believe our work presents substantial scientific contributions with valuable insights. The main contribution of our work lies in conceptualizing and offering a cohesive perspective on how representations form within deep neural networks (DNNs).\n- The tunnel effect, a recently discovered phenomenon in DNNs, enhances our understanding of out-of-distribution (OOD) generalization. Although initially identified in prior work [1], our research revises and strengthens the hypothesis through in-depth analysis, placing it within a broader context.  Our work replicates their findings for small datasets but finds that the strength of the tunnel effect greatly diminishes due to augmentations, resolution, and number of classes.\n- To the best of our knowledge, we are the first to conduct a comprehensive study to disentangle and precisely measure the impact of different variables on OOD generalization through the lens of the tunnel effect hypothesis.\n## Our key scientific contributions include:\n1. **Novel Evaluation Framework.** We introduced a novel SHAP-based evaluation framework that uses multiple metrics to reveal the intricate interactions among variables and their influence on OOD generalization. Our framework enables a more nuanced assessment and comparison of various models' OOD capabilities.\n2. **Broader Exploration of the Tunnel Effect Hypothesis.** We examined the tunnel effect across different settings, including supervised and self-supervised learning, various architectures, and datasets, and revised the tunnel effect hypothesis to align it with broader contexts.\n3. **Insightful Findings.** We revealed how different variables impact the tunnel effect individually and collectively, offering essential insights for designing architectures and training pipelines to enhance OOD generalization. Our experiments yielded significant insights, such as how the tunnel effect varies across the same architecture and dataset (Figs. 1-4).\n4. **Continual Learning Perspectives.** Our findings demonstrated the tunnel effect's role in mitigating catastrophic forgetting in continual learning (CL) scenarios. In contrast to previous work [1], we find that the tunnel plays a task-specific role and significantly impacts forgetting in CL. Our findings provide invaluable perspectives on mitigating catastrophic forgetting for the CL research community.\n5. **Explanation for Scaling Issues.** We provided the first evidence that the inherent characteristics of toy datasets exacerbate the tunnel effect, hindering the learning of reusable features and limiting generalization to larger, real-world datasets. Our work questions the generalizability of results obtained from toy datasets and underscores the importance of conducting diverse tests in deep learning research to ensure algorithm scalability.\n\n**W2. Poor Writing and Organization**\n- We carefully crafted our paper to clearly communicate our research outcomes. After numerous revisions and months of refinement, we believe the paper is well-organized, making it easier to understand the motivation, methodology, and conclusions of each experiment and analysis. However, we will address the reviewers' concerns and further revise the paper to enhance the clarity and quality of our presentation.\n\n**W3. Lack of Theoretical Contributions**\n\n- Our work builds on a prior NeurIPS paper [1] that empirically examined the tunnel effect phenomenon. To align the tunnel effect with broader contexts, we conducted a much more comprehensive study than [1]. We carefully measured tunnel effect strength and controlled for all relevant variables. \n- While theoretical contributions are undoubtedly important, we believe theory requires empirical science to come first. Our empirical findings significantly contribute to the field and will inspire future theoretical research. We will mention the limitations regarding theoretical contributions in our paper as follows:\n\n> Our work empirically examines the tunnel effect and OOD generalization without presenting theoretical insights. Future research may develop theoretical frameworks to explain the revised tunnel effect in the context of OOD generalization.\n\nThank you again for your valuable comments and suggestions. We hope our responses have addressed your concerns. Please let us know if you have further questions.\n\n**Reference**\n- [1] Masarczyk et al., The Tunnel Effect: Building Data Representations in Deep Neural Networks, NeurIPS 2023.", "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": "", "extra_scores": {}}, {"review_id": "2Dg1fxzyma", "reviewer": "Reviewer_gM3N", "summary": "This paper studies how well self-supervised models transfer after self-supervised pretraining.  Using linear probe experiments on top of frozen encoders, and by varying the depth in the model being fed to the linear probe, they study the effect of network depth on ID performance and OOD (transfer learning) performance.  They find that the previously studied \"tunnel effect hypothesis\" can be diminished by increasing the diversity of pretraining data (which they demonstrate using data augmentation).", "questions": "How can we interpret these results in the context of other methods like SSL, where the learning goals seem to be more directly targeting removal of any tunnel effects?", "limitations": "Yes.", "rating": 5, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The paper builds on previous works to clarify their results and provide important additional context.", "weaknesses": "Scope:  The results of the paper seem fairly narrowly scoped.  I am not sure how these findings can really inform pretraining in ways that aren't already well understood (e.g. \"use more diverse data\" is already a fairly well established paradigm).  Thus it seems like the impact of this paper is fairly limited.\n\nExperimental evaluation seems somewhat limited:  While the authors do run a large number of individual training runs, it is not clear to me that they performed a particularly wide experimental study.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful review, comments, and feedback. We have carefully considered your concerns. Below, we have responded to your comments, and we hope these will address your concerns.\n\n# Weaknesses\n\n**W1. The scope of results seems narrow, reflecting known findings**\n- Our work is much more comprehensive and rigorous than the NeurIPS'23 paper [1] that identified the tunnel effect. In contrast to [1], we examined the tunnel effect in much wider settings incorporating 11 datasets, 3 metrics, 8 variables, several DNN architectures (VGG, ResNet, ViT), model scales (shallow, deeper), and various testing conditions. We are the first to quantify each variable's impact on the tunnel effect. Our findings both support the original tunnel effect while finding that it does not always hold and that its strength varies considerably depending on these variables that were ignored in prior work [1].\n- Our results and findings have a significant impact on the out-of-distribution (OOD) generalization and relevant areas of deep learning. While previous works on OOD find that larger and more diverse datasets help learn more invariant features and improve OOD performance (as discussed in Sec. 2.2), our work is _uniquely_ positioned to reveal the _relative_ contribution of each variable e.g., resolution, class, dataset size, and augmentations toward OOD generalization. So while some of the variables we study are known to impact OOD generalization, the relative contribution of each variable had not been quantified before our study.\n\n**W2. Experimental evaluation seems somewhat limited**\n- We conducted the most comprehensive study to date to unravel the intricate relationships between different variables and OOD generalization, _significantly_ expanding upon prior work [1]. For each OOD experiment and analysis, we utilized eight different OOD datasets and assessed various deep neural network architectures, including CNNs and ViTs, across different scales. We are the first to study the tunnel effect in ViTs and widely used self-supervised learning (SSL) models.\n- While additional experiments could provide further insights, we believe the breadth and depth of our experiments do not compromise the quality of our findings. We think our experimental results and statistical analyses robustly support our primary findings and hypothesis, with implications that extend beyond the scope of our specific study.\n- As discussed in Appendix A.10, our work involved training 64 different backbones and training/analyzing 10,652 linear probes, resulting in an aggregate compute time of $\\sim$ 1,161 hours (48 days). This demonstrates the substantial effort invested in our experimental evaluation.\n\n**Reference**\n- [1] Masarczyk et al., The Tunnel Effect: Building Data Representations in Deep Neural Networks, NeurIPS 2023\n\n# Questions\n\n**How can these results be interpreted in the context of SSL, where the learning goals target the removal of the tunnel effect?**\n\n- Thank you for your thoughtful question. Earlier work [1] introducing the tunnel effect solely focused on supervised learning (SL) setting. We also mainly focused on the SL setting and briefly studied self-supervised learning (SSL) models since SSL requires significantly more compute than SL. We spent 48 days of compute time on our comprehensive SL study. Conducting a similar study for SSL would require nearly 480 days of compute time ($\\sim10\\times$ more). As an academic lab, this extensive computation is beyond our current scope.\n- As discussed in Sec. 4.2 and Appendix C.11, our findings indicate that large-scale SSL models do not exhibit the tunnel effect. However, as mentioned in Sec. 5, due to limited compute resources, we were unable to control variables and perform a similar SHAP analysis on a variety of SSL models (at least 4). While our study focused on SL, the methods and evaluation framework we developed could be extended to SSL. In particular, analyzing the impact of different variables—especially augmentations—on the tunnel effect in SSL models could yield valuable insights.\n- Our results suggest that dataset diversity, particularly through augmentation, plays a critical role in mitigating the tunnel effect and enhancing OOD generalization (Fig. 3). This insight hints at the superior OOD generalization abilities of SSL models. Given that SSL methods typically employ more advanced augmentation techniques, expanding our SHAP analysis to disentangle these augmentation policies could help determine whether the OOD generalization capabilities of SSL models are primarily due to their augmentation strategies or their underlying objective functions.\n\nThank you again for your valuable comments, questions, and suggestions. We hope our responses have addressed your concerns. Please let us know if you have further questions.", "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": "", "extra_scores": {}}, {"review_id": "utrYx3fP6d", "reviewer": "Reviewer_WrHJ", "summary": "This paper investigates the \"tunnel effect\" in NNs introduced in a NeurIPS 2023 paper. According to the “tunnel effect” the deeper layers compress representations, limiting OOD generalization. The authors challenge the prior assumption that the tunnel effect is universal. They imply that it's heavily influenced by training data diversity.\nThey analyze a large number of NNs on various datasets with varying resolutions and introduce three metrics to quantify the tunnel effect's strength. Using a SHAP-based approach, they disentangle the impact of augmentation, number of classes, sample size, resolution, and the architecture.\nTheir experiments suggest that increasing the diversity of the training data (more classes, augmentations, and higher image resolutions) mitigates the tunnel effect and improves OOD generalization. Depth and overparameterization have the opposite effect. \nBased on these findings, they propose a revised tunnel effect hypothesis where its strength is inversely proportional to training data diversity.", "questions": "1. This citation has the wrong year and NeurIPS number: “Wojciech Masarczyk, Mateusz Ostaszewski, Ehsan Imani, Razvan Pascanu, Piotr Miło ́s, and Tomasz Trzcinski. The tunnel effect: Building data representations in deep neural networks. Advances in Neural Information Processing Systems, 36, 2024.”.\nPlease cross-check other references too.\n2. SHAP papers should be cited the first time it is mentioned in the text.\n3. Could you clarify a bit further the reasoning / logic behind the “Metric 3: ID/OOD Alignment”? I find it a bit hard to wrap my head around it in its current form. Specifically why you choose to have a product of the two values and the respective “baseline” values that are subtracted.\n4. What do you mean by “more hierarchical features” in L136? Isn’t the tunnel effect reduced because the size of the activation maps is increased, so the bottleneck is decreased?\n5. L275: Perhaps a more appropriate wording here would be \"7x7 kernel size\" instead of \"7x7 stem\"?", "limitations": "The limitations and societal impacts have been addressed.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Originality: This paper is original, in the sense that it challenges existing assumptions on  the universality of the tunnel effect hypothesis, which might have implications on understanding and improving NN’s OOD generalization ability. The authors propose a revised tunnel effect hypothesis which is a novel contribution.\n\nQuality: This paper is scientifically well-executed. The hypothesis is clear and the experiments are extensive (several NN architectures and dataset (configurations), which greatly helps to support their hypothesis. The SHAP-based analysis they performed to disentangle the relative importance of different variables is solid (through rigorous statistical analysis with Wilcoxon signed-rank tests and Cliff's Delta to measure effect sizes) and provides a quantitative measure of the effects.\n\nClarity: The paper is very well written and easy to follow. Figures and tables are very helpful to understand the key findings.\n\nSignificance: The paper’s findings may have significant implications for the “tunnel effect” hypothesis, though I am a bit skeptical of the new insights this brings us in terms of designing algorithms that have better OOD generalization properties.", "weaknesses": "Although the paper is a very solid work, the main worry that I have is about the confounding variables in the experiments and the revised hypothesis, which might limit the significance of the contribution:\n* For example, Figure 1 claims that the increased resolution mitigates the tunnel effect. But intuitively, if you increase the resolution of the image, you also increase the resolution of the activation maps in the bottleneck layers. Still this doesn’t tell us anything about the architectures per se. Yes, the tunnel effect can be “sidestepped” if you increase the resolution, but then you run into the same issues if you increase the depth.\n* OOD accuracy is measured on a number of datasets (NINCO [61], ImageNet-R [62], CIFAR-100 [60], CIFAR-10 [59], Oxford 102 Flowers [63], CUB- 173 200 [64], Aircrafts [65], Oxford-IIIT Pets [66], and STL-10 [67]). However, I wonder what such experiments tell us about the “kind” of OOD that we are testing for. For example, if one tests for compositional or systematic OOD generalization, it becomes very clear what the learnings are, and which particular flaws the models have. I feel that on these benchmarks it is hard to make the similar conclusions.\n* Certain findings I find limited in the sense that they are already known, e.g. “Our metrics reveal that increasing the ID class count, higher resolutions, and using augmentations improve OOD generalization”.\n* In these figures/results, typically normalized accuracy or performance retained are discussed. However, in ML it is also important to understand the actual accuracy, and these are not easy to find in the paper. Ideally for each figure/results discussion, the reader would be pointed to a table (in the appendix) that contains absolute numbers on the datasets. For example, it is claimed that \"overparametrization negatively impacts OOD generalization .. since increasing overparametrization decreases OOD performance **retained**\".\nHowever I feel that without the absolute numbers this claim cannot be made. E.g. if both the IID and OOD performance improved by increasing overparametrization, but the IID performance improved more than OOD performance, one cannot claim that OOD performance decreased, quite contrary.\n* L281: “Depth. Our SHAP analysis revealed that increasing depth impairs OOD generalization.” - Depending on how you increase depth (e.g. if you have pooling layers), to me this is an obvious consequence of additional compression that you may have in that case.\n* The paper claims that their continual learning results contradict [9] and suggest the “tunnel” plays an essential role in mitigating catastrophic forgetting. However, they only replicate the experiment with ResNet-18 on ImageNet-100. To strengthen this claim, the authors could expand the continual learning analysis to include different architectures and datasets.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful review, comments, and feedback. We have carefully considered your concerns and tried to address your concerns below.\n# Weaknesses\n**W1. Increased resolution mitigates the tunnel effect, but doesn’t increasing DNN depth in that setting bring the tunnel effect back?**\n- We find that resolution has a larger impact on the tunnel effect than depth, but based on our analysis and intuition, a very deep model could still exhibit the tunnel effect. Our work does suggest that for OOD generalization, shallower models may be preferable over deeper ones.\n- In our global rebuttal (Fig. 3), we show that higher resolution maintains a higher rank (evaluated on the ID dataset, following [1]) than low resolution, which corroborates our findings.\n\n**W2. Benchmarks might not reveal compositional or systematic OOD generalization**\n- We conducted a much more comprehensive study than prior work [1] that introduced the tunnel effect. We used a variety of 8 OOD benchmark datasets in each OOD experiment. We focused on evaluating the strength of the tunnel effect and quantifying the relative impact of variables on it. For more fine-grained analysis of compositional or systematic OOD generalization, more crafted datasets might be necessary, but designing such datasets remains outside the scope of our work. Thank you for your insightful comments.\n\n**W3. Some findings reflect things that are already known**\n- While previous research has shown that larger and more diverse datasets help learn invariant features and improve OOD performance, our study uniquely dissects the relative contributions of factors such as resolution, class counts, dataset size, and augmentations toward OOD generalization. So while some of the variables we study are known to impact OOD generalization, the relative contribution of each variable had not been quantified before our study.\n\n**W4. Actual accuracy is necessary besides normalized accuracy**\n- Following previous work [1], we used normalized accuracy to illustrate the tunnel effect. Otherwise, it is very challenging to interpret figures because some datasets are easier or harder, e.g., because they contain more or fewer classes. We reported the actual accuracy in the appendix (Tables 4 and 11) and verified that they are consistent with our findings (see global rebuttal).\n- We understand your concern regarding the ID and OOD accuracy. To address this issue, we introduced another metric ID/OOD alignment which combines ID and OOD accuracy (calculated as the product of ID and OOD accuracy). As shown in Fig. 2(b), our SHAP results with the ID/OOD alignment demonstrate that overparameterization negatively impacts OOD generalization.\n- We have included results based on actual accuracy in the global rebuttal. We see that the actual accuracy trends are consistent with our findings where variables that improve (degrade) OOD generalization also show higher (lower) ID/OOD alignment.\n\n**W5. Increasing depth impairs OOD generalization seems obvious**\n- Previous work [1] has reached a similar conclusion, but they did not quantify the impact. We agree that this conclusion might seem intuitive, but our goal was to quantitatively measure this phenomenon in a broader context. Also, previous studies independently analyzed depth without taking other variables into account that can impact OOD generalization. In contrast, we presented a more comprehensive study, assessing each variable’s relative importance.\n- While increasing depth impairs OOD generalization, we found that this variable's impact on OOD generalization is much smaller than other variables.\n\n**W6. Continual learning experiments could explore more architectures and datasets**\n- Prior work [1] suggested that the tunnel plays a task-agnostic role, but their observations were made in a toy setting with a small dataset. We revisited this to assess the generality of their finding in a more challenging setting with a larger dataset. This exploration was conducted as an auxiliary experiment and is not part of our main results.\n\n# Questions\n1. **Citation.** We will verify and correct the citations.\n2. **Citation for SHAP.** We will ensure that SHAP is cited the first time it is mentioned.\n3. **Reasons behind ID/OOD alignment metric.** The ID/OOD alignment metric combines ID and OOD accuracy to facilitate comparison. Ideally, a model should achieve high ID and OOD accuracy simultaneously (high ID/OOD alignment). This metric potentially alleviates the concern you raised in Weakness #4. We discussed the reasons for our metrics in Appendix A.8.\n4. **What did the authors mean by more hierarchical features?** \nWe hypothesize that higher resolution results in learning more hierarchical features, which reduces the tunnel effect. By \"more hierarchical features,\" we mean that higher resolution enables the network to learn a progression of information—from simple elements like edges and corners to more complex structures and object parts—across multiple stages of the network [2]. Your interpretation is also valid.\n5. **Stem or kernel.** In Sec 3.2, we referred to the $k\\times k$ kernel of the first layer as the $k\\times k$ stem. We will make the suggested revisions.\n\n**Reference**\n- [1] Masarczyk et al., The Tunnel Effect: Building Data Representations in Deep Neural Networks, NeurIPS 2023\n- [2] Yann LeCun et al., “Convolutional Networks and Applications in Vision,” ISCAS, IEEE, 2010\n\nThank you again for your valuable comments, questions, and suggestions. Please let us know if you have further questions.", "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": "", "extra_scores": {}}, {"review_id": "eLzYFoZ0vf", "reviewer": "Reviewer_gXLk", "summary": "The paper sets out to evaluate empirically the generality (referred to as \"universality\") of the \"tunnel hypothesis\", the idea that compression at later layers may hinder OOD performance.", "questions": "What does it mean to \"disentangle samples and classes\"?\n\nWhat is \"diversity of inputs\"?", "limitations": "Please define linear probe and probe accuracy and how it is used in the paper.  \n\nIt is very unclear how swapping tunnels might help you answer the question of mitigating forgetting.", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "Work on OOD learning, network probing and explainability is very relevant to the conference.", "weaknesses": "How empirical evaluations may provide any conclusive answer to the question of generality of a hypothesis is unclear to me. \n\nThe use of linear probing cannot be taken as the yardstick for this study. The validity of any result is further compromised by the choice of SHAP in the place of a sound knowledge extraction method for the evaluation of the results. SHAP is known to produce unreliable results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful reviews and feedback. We have carefully considered your concerns. Below, we have responded to your comments.\n# Weaknesses\n**W1. How do empirical evaluations support the generality of a hypothesis?**\n- We addressed this by considering a diverse range of experimental settings, including various deep neural network (DNN) architectures, datasets, and testing conditions. As noted in Appendix A.10, our work involved training 64 different backbones and training/analyzing 10,652 linear probes, resulting in an aggregate compute time of approximately 1,161 hours (48 days). This demonstrates the substantial effort invested in our experimental evaluation. Our experimental results and statistical analyses robustly support our primary findings and hypothesis.\n- Although we did not present theoretical perspectives, we believe our extensive evaluations demonstrated that our revised hypothesis is not just a product of specific conditions but is broadly applicable across various scenarios. While theoretical contributions are undoubtedly important, our work has a profound impact on the field and will inspire future theoretical research. We will mention the limitations regarding theoretical contributions in our paper as follows:\n> Our work empirically examines the tunnel effect and OOD generalization without presenting theoretical insights. Future research may develop theoretical frameworks to explain the revised tunnel effect hypothesis in the context of OOD generalization.\n\n**W2. How effective is linear probing for the OOD study?**\n- The previous work [1] introducing the tunnel effect hypothesis also relied heavily on linear probing for their analyses, further validating its effectiveness in this context.\n- As discussed in Sec. 3.1, linear probing is a widely recognized and standard evaluation technique across various domains, including transfer learning, OOD generalization, and self-supervised learning. We cited 13 papers that extensively use linear probing, although many more could be referenced.\n\n**W3. How reliable is SHAP analysis?**\n- According to NeurIPS'17 paper [2] that introduced SHAP and has been cited $\\sim$ 25K times, SHAP is a unified measure of feature importance, with theoretical guarantees that it achieves a unique solution with desired properties.\n- SHAP is widely used in machine learning [2-8] to explain DNNs, providing consistent and reliable interpretations compared to other methods such as SP-LIME, SpRay, GAA, and ACE [7]. Due to SHAP's consistent and superior performance compared to other methods, it is extensively used in the medical field [8].\n- SHAP allows us to control for variables where this careful pairing could not be done. Our SHAP analysis is consistent with our statistical findings using carefully controlled experiments.\n\n**References**\n- [1] Masarczyk et al., The Tunnel Effect: Building Data Representations in Deep Neural Networks, NeurIPS 2023.\n- [2] Scott M. Lundberg et al., A Unified Approach to Interpreting Model Predictions, NeurIPS, 2017\n- [3] Scott M. Lundberg et al., Explainable AI for Trees: From Local Explanations to Global Understanding, https://arxiv.org/abs/1905.04610 (2019)\n- [4] Lundberg, S. et al., An unexpected unity among methods for interpreting model predictions, https://arxiv.org/abs/1611.07478 (2016).\n- [5] Dubois, Yann, et al., \"Evaluating self-supervised learning via risk decomposition.\" In ICML, 2023.\n- [6] S. Mishra et al., Local interpretable model-agnostic explanations for music content analysis., ISMIR, Vol. 53, 2017, pp. 537–543.\n- [7] S., Rabia, et al., \"Explaining deep neural networks: A survey on the global interpretation methods.\" Neurocomputing 513 (2022): 165-180.\n- [8] Lapuschkin S, et al., Unmasking Clever Hans predictors and assessing what machines really learn. Nature communications 10, no. 1 (2019): 1096.\n\n# Questions\n**Q1. What does it mean to \"disentangle samples and classes\"?**\nIf we increase the number of classes, we could also increase the number of samples by just adding in more classes. So, when we increased the classes we kept the total size of the dataset constant. In contrast, [1] increased the classes and samples, so we wanted to disentangle these variables to know whether more classes or more samples mattered more for reducing tunnel effect strength.\n\n**Q2. What is \"diversity of inputs\"?**\nThe diversity of inputs/ dataset refers to factors such as augmentations (within-class diversity), semantic categories (between-class diversity), and resolution, which increase the variability of the training dataset.\n\n# Limitations\n**Please define linear probe and probe accuracy and how it is used in the paper.**\nWe discussed the motivation, significance, and process of linear probing in Section 3.1 (motivation and usage), Appendix A.2 (details of linear probing), and A.8 (accuracy). The linear probe training details are discussed in Appendices A.3, A.4, and A.5.\n\n**It is unclear how swapping tunnels might help answer the question of mitigating forgetting.**\nWe adopted this experimental design from [1]. Swapping tunnels allows us to isolate the impact of the tunnel itself on mitigating forgetting. For example, let a model be trained on task 1 (extractor $E_1$ and tunnel $T_1$) and then sequentially trained on task 2 (extractor $E_2$ and tunnel $T_2$). When evaluated on task 1, the model's accuracy degrades (forgetting) due to task 2. Here we ask: Does the tunnel $T_1$ contribute to this forgetting? If $T_1$ had no impact, the swapping wouldn’t impact forgetting, meaning $E_1$ with $T_2$ ($E_1+T_2$ without task-specific $T_1$) would achieve similar performance as $E_1+T_1$ and $E_1$ alone would impact forgetting. It turns out $T_1$ significantly impacts forgetting. Likewise, when evaluated on task 2, $E_2+T_1$ achieves lower accuracy than $E_2+T_2$, indicating $T_2$ impacts task 2 performance.\n\nThank you for your valuable comments & questions. Please let us know if you have further questions.", "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": "", "extra_scores": {}}]

Author rebuttal:
We thank the reviewers for their constructive feedback, valuable insights, and thoughtful questions. We have carefully
considered all comments and provided detailed responses to each review separately. We have revised our paper as we should. 
We hope our responses have addressed the reviewers' concerns. Please take a look at the attached PDF for additional analyses.

## Contribution and Impact
Below we have mentioned some points to highlight our work's key scientific contribution and impact.
- Our main contribution is a _significant_ expansion of the findings from the original tunnel effect paper [1], which did not measure many of the variables we investigated. We found that the formation of tunnels greatly influences out-of-distribution (OOD) generalization, and by quantifying the impact of each variable through our SHAP analysis—a method widely used in other areas of deep learning but largely overlooked in vision—we provide valuable insights into how OOD generalization can be further improved.

- In addition to OOD generalization, many algorithms, such as OOD detection methods, may benefit from understanding the tunnel effect. While our primary focus is on measuring the impact of each variable, we also highlight an important issue: the representations learned by deep neural networks for vision tasks can have very different properties by using augmentations, higher resolution, or more classes. By showcasing this impact, our paper contributes to addressing machine learning's replicability crisis, where an algorithm may fail to perform consistently across different datasets. Our work helps explain why such discrepancies occur in vision tasks.

**Reference.**
[1] Masarczyk et al., "The Tunnel Effect: Building Data Representations in Deep Neural Networks", NeurIPS 2023

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Meta-review: This paper provides a thorough investigation of a recently observed phenomenon in deep learning called the "tunnel effect." The hypothesis states that initial layers create linearly-separable representations, while subsequent layers (referred to as the "tunnel") compress these representations with minimal impact on overall performance. This paper verifies the existence of the tunnel effect and demonstrates that it can be mitigated with richer data. Additionally, the authors verify that representations created by compression layers can negatively impact out-of-distribution (OOD) generalization performance. These claims are supported across multiple architectures, datasets, and other learning settings (including self-supervised learning). Compared to the original paper that discovered this phenomenon, this submission offers a much broader empirical analysis.

The majority of reviewers find the paper borderline, with the exception of reviewer gM3N, who rates the paper as "accept." Concerns raised by reviewers with borderline ratings include a lack of theoretical support and unsurprising conclusions. In contrast, reviewer gM3N, who provided the most thorough review of this submission, believes the paper makes an important contribution with potential implications for understanding and improving OOD generalization ability, as it challenges existing assumptions about the universality of the tunnel effect hypothesis.

The overall rating for the paper is borderline accept. After reading all the reviews and responses, I tend to agree with reviewer gM3N. Not every paper needs a theoretical contribution, especially when it is thorough from an empirical standpoint, and I think the authors have done a reasonable job in their empirical investigation. I also believe that verifying the existence of the tunnel effect while also showing that it is not a universal effect, and doing so across different learning settings (as done in the paper), is a non-trivial contribution. I therefore recommend acceptance.
Decision: Accept (poster)