Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

* **Reducing image size sensitivity**.

The evidence to be evaluated is:Modifying the spatial size of an input to a convolutional layer by a factor \(\gamma\), will yield an output with size scaled by the same factor \(\gamma\). This modification does not require any change to the number of parameters of the given convolutional layer, nor its underlying operation. It was observed by practitioners and previous works that a network trained on a specific input dimension can still be used at inference using a modified image size to some extent (Simonyan and Zisserman, 2014). Moreover, evaluating with an image size that is larger than used for training can improve accuracy up to a threshold, after which it quickly deteriorates (Touvron et al., 2019). Although not explicitly trained to handle varying image sizes, CNNs are commonly evaluated on multiple scales post-training, such as in the case of detection (Lin et al., 2017; Redmon and Farhadi, 2018; Liu et al., 2020) and segmentation (He et al., 2017) tasks. In these tasks, a network that was pretrained with fixed image size for classification is used as the backbone of a larger model that is expected to adapt to a wide variety of image sizes. Recently, Tan and Le (2019) showed a computation-vs-accuracy trade-off in applying scaling to the image size used for convolutional networks training and evaluation.

In addition, previous works explored the notion of "progressive resizing" (Howard, 2018; Karras et al., 2017) -- increasing image size as training progresses to improve model performance and time to convergence.

Another related work by Touvron et al. (2019) demonstrated that CNNs can be trained using a fixed small image size and fine-tuned post-training to a larger size, with which evaluation will be performed. This procedure reduced the train-test discrepancy caused by the change in image size and allowed faster training time and improved accuracy -- at the cost of additional fine-tuning procedure and additional computations at inference time. In this work we will further explore the notion of using multiple image sizes at training, so the CNN performance will be resilient to test time changes of the image size.

For instance, a linear (Goyal et al., 2017) or square-root (Hoffer et al., 2017) scaling of the learning rate with respect to the batch size growth. Other modifications include per-layer gradient scaling schemes (You et al., 2017) and optimizer modifications (Ginsburg et al., 2019). Several works also explored using incremented batch-sizes (Smith et al., 2018) in order to decrease the number of training iterations required to reach the desired accuracy. Recent work (Hoffer et al., 2020) introduced the notion of "Batch Augmentation" (BA) -- increasing the batch size by augmenting several instances of each sample within the same batch. BA aids generalization across a wide variety of models and tasks, with the expense of an increased computational effort per step.

It was also demonstrated that BA may allow to decrease the number of training steps needed to achieve a similar accuracy and also mitigate I/O throughput bottlenecks (Choi et al., 2019).

The traditional practice of training convolutional networks using fixed-size images holds several shortcomings. As it is a common practice to use different image size for evaluation than that used for training (He et al., 2017; Lin et al., 2017; Redmon and Farhadi, 2018), it was observed by Touvron et al. (2019) and empirically verified (Figure 1) that classification accuracy may degrade above or below a certain size threshold. Similarly, we observed this phenomenon in a wide variety of common networks (Appendix Figure 4).

To remedy these issues, we suggest a stochastic training regime, where image sizes may vary in each optimization step.

We hypothesize that a considerable part of the training of convolutional networks can be performed at a lower image size than the target size used at test time.

We see that gradients computed across different sizes of the same images have a stronger correlation than those obtained across different images.

This observation suggests that smaller image gradients can be used as an estimate to the full image gradients, with a smaller computational footprint. Therefore, using large images along the entire training process may be sub-optimal in terms of computational resource utilization.

We propose "MixSize", a stochastic training regime where input sizes can vary. In this regime, we modified the spatial dimensions \(H,W\) (height and width) of the input image size2, as well as the batch size.

We will show that using our MixSize regime can have a positive impact on the resiliency of trained networks to various images sizes at evaluation time by demonstrating better accuracy across a wide range of sizes. This entails a considerable saving in computational burden required for inference, especially when using smaller models. Furthermore, given a fixed budget of computational and time resources (per step), we can now modify our regime along spatial and batch axes.

MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

To easily adapt training regimes to the use of MixSize as well as improve their final performance, we continue to describe three methods we found useful: **step-wise size sampling, gradient smoothing** and **batch-norm calibration**. Considering our findings on correlation of gradients across different image size in early training, we were initially motivated to consider a training variation where size is progressively enlarged (Howard, 2018; Karras et al., 2017). In this method we consider increasing image size from small to large, where each image size is used for a predefined number of epochs out of total number of training epochs required.

We therefore considered two alternatives for image size variations, where size is randomly sampled and changed throughout training: * Sampling image size per epoch

* Sampling image size per training step These sampling methods can be seen as a stochastic alternative to long and short cycle multigrid approach suggested by Wu et al. (2020). We found that random sampling regimes perform better than scaling image size from small to large, keeping accuracy high across all used sizes at evaluation (Appendix E). While sampling both at epoch and step time frames performed similarly, replacing sizes on each step converged faster and exhibited less noise in measured test accuracy. Considering these findings, we continue to perform our experiments using the third regime - sampling image size per training step.

This further suggests that the optimization regime should be adapted to smaller spatial sizes, in a manner similar to learning-rate adaptations that are used for large-batch training.

Here we suggest changing both the spatial size as well as the batch size, which is also expected to modify the variance of gradients within each step and further complicates the choice of optimal scaling.

We suggest an alternative solution to previous approaches, which we refer to as "Gradient smoothing". Gradient smoothing mitigates the variability of gradient statistics when image sizes are constantly changing across training.

Gradient smoothing, however, is designed to adapt globally (across all layers) to the batch and spatial size modification and can be used regardless of the optimization method used. We found gradient smoothing to be beneficial in \(B^{+}\) regimes, where multiple varying batch sizes are used, as the effective learning rate is also modified according to common practices. We observed that gradient smoothing reduces the gap between gradient norms of different sizes (see Appendix Figure 6) and allow the use of an average learning rate scaling (weighted across batch sizes).

As demonstrated by Touvron et al. (2019), using a different image size at evaluation may incur a discrepancy between training and evaluation protocols, caused by using different data pre-processing.

In contrast, we surmise that for networks trained with mixed-regimes, discrepancy issues mainly arise from the use of the batch-norm layers (Ioffe and Szegedy, 2015) and can be solved by targeting them specifically. Batch-norm layers introduce a discrepancy between training and test evaluations (Ioffe, 2017), as at inference a running estimate of the mean and variance (of training data) are used instead of the actual mean and variance values. This difference is emphasized further in the use of varying imagesize, as changing the spatial size of an input map can significantly modify the measured variance of that map. While a fine-tuning process per image size can eliminate this discrepancy (Touvron et al., 2019), it required significant amount of computation and labeled data. We offer a simpler alternative. For each evaluated size, we calibrate the mean and variance estimates used for that size by computing an average value over a small number of training examples.

Interestingly, we highlight the fact that although this process has little to no effect on models trained using a fixed-size input, it does improve our mixed-size models considerably on a wide range of image sizes.

\[S^{(28)}:\ S=\begin{cases}40,&\text{w.p.}\quad p=0.2\\ 32,&\text{w.p.}\quad p=0.3\\ 24,&\text{w.p.}\quad p=0.3\\ 16,&\text{w.p.}\quad p=0.2\end{cases}\] The regime was designed to be centered around the mean value of \(28\).

While the original training regime consisted of images of size \(224\times 224\), our proposed regime makes for an average image size of \(\hat{S}\times\hat{S}=144\times 144\). This regime was again designed so that the reduced spatial size can be used to increase the corresponding batch size or the number of BA duplicates, as described in Section 3.

We see that our MixSize regimes yield two possible improvements:* Reduced number of training steps to achieve a similar test accuracy using \(B^{+}\) regime.

\(B+\) enables larger batches on average, hence the reduction in training steps, while \(D+\) leverages benefits of batch-augmentation to achieve better accuracy within the same compute. The ResNet-50 model benefits the most from our MixSize regime on the ImageNet model and so we chose it for further exploration.

We enlarge the batch size used for each spatial size by a factor of \(\frac{224^{2}}{S^{2}}\) such that \(S^{2}\cdot B\) is kept approximately fixed.

As can be seen in Figure 2, regime \(B^{+}\) enables training with approximately \(2.7\times\) fewer training steps, while reaching an improved accuracy of \(76.61\%\). As sizes were chosen to reflect in approximately equal computational cost per iteration, \(B^{+}\) regime offers a similar improvement in total wall-clock time.

Next, we examine how MixSize affects the resulting model resiliency to changes in the image size during test-time. We evaluated the models by varying the test-time image sizes around the original \(224\) spatial size: \(S=224+32\cdot m\), for \(m\in\{-6,...,6\}\). The common evaluation procedure for ImageNet models first scales the image to a \(256\) smallest dimension and crops a center \(224\times 224\) image. We adapt this regime for other image sizes by scaling the smallest dimension to \(\lfloor\frac{8}{7}S\rfloor\) (since \(\frac{8}{7}\cdot 224=256\)) and then cropping the center \(S\times S\) patch. Models trained with a mixed regime were calibrated to a specific evaluation size by measuring batch-norm statistics for \(200\) batches of training samples.

However, due to the decreased average size, we were able to leverage more than \(1\) duplicates per patch on average, which improved the model's top-1 accuracy to \(77.14\%\) at size \(224\). Furthermore, we find that the model performs much more favorably at sizes smaller than \(224\), scoring an improved (over baseline) accuracy of \(76.43\%\) at only \(160\) spatial size.

Figure 2(a) demonstrates that while all three models (Fixed with \(S=224\), \(S^{(144)}\) and \(S^{(208)}\)) were trained with the same compute and memory budget, mixed-size regimes offer superior accuracy over a wide range of evaluation sizes.

As can be seen in Figure 2(b), mixed-regime trained models offer a wider range of resolutions with close-to-baseline accuracy (within a \(2\%\) change) and perform better than their fixed-size counterparts at all sizes.

Stochastic regime benefits are threefold: (1) reduced number of training iterations; or (2) improved model accuracy (generalization) and (3) improved model robustness to changing the image size.

Given a computational and time budget, stochastic size regimes may enable to train networks faster, with better results, as well as to target specific image sizes that will be used at test time. As the average size chosen to train is reflected in the optimal operating point for evaluation resolution, mixed regimes can be used to create networks with better performance across multiple designated use cases. We used 6 common networks (Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016; Huang et al., 2017; Mahajan et al., 2018; Sandler et al., 2018) pretrained on the ImageNet dataset at a resolution of \(224\times 224\) and measured their accuracy on varying sizes. As can be seen, these networks show similar patters of sensitivity to the evaluation size, suggesting this is caused by the training protocol (which is similar for all), rather than the used model.

In order to adapt to varying input scales, we add an additional augmentation step, that resizes the images using bilinear interpolation to \(S\times S\), depending on a sampled size for each step.

This improvement can be attributed to a regularization effect induced by changing image sizes during training, also manifested by an increase in training error throughout its progress.

We can see that gradient smoothing helps to reduce gap between gradient norms at difference batch sizes and improves training and validation accuracy. We consider training regimes with varying image sizes, such that the average image size is smaller than the desired evaluation size. For example, for the height dimension \(H\), we wish to obtain an average size of \(\bar{H}=\sum_{i}p_{i}H_{i}\) such that \(\bar{H}<H_{o}\).

* Increase image size from small to large (progressive resizing), where each image size is used for number of epochs \(E_{i}=p_{i}E_{\mathrm{total}}\), where \(E_{\mathrm{total}}\) is the total number training epochs required.

* Using a random image size for each epoch, keeping the epoch number for each size at \(E_{i}\)

* Sampling image size per training step at probability \(p_{i}\)

In both CIFAR10 (Figure 8) and ImageNet (Figure 9) sampling methods exhibit better accuracy than a progressive resizing regime. This is most apparent when the final size used at training is larger than target size for inference (on which test accuracy is measured).

Input: Figure 1: Top-1 test accuracy per image size, models trained on specific sizes (ResNet50, ImageNet).

Input: Figure 9: Test accuracy vs epoch (ResNet50 on ImageNet, B+ with s(144)) for progressive resizing (small to large) compared to per-step sampling.

Input: Figure 2: Training (dotted) and test accuracy on ImageNet using suggested regimes (224 evaluation size). All regimes required similar resources per step. B+ regime required ≈ 2.7× less steps per epoch.

Input: Figure 8: Test accuracy vs step (ResNet44 on CIFAR10,B+ with s(28)) for 3 size sampling regimes: (1) From small to large (2) Sample each Epoch (3) Sample each step. All methods reached a similar accuracy, but sampling each epoch was less noisy and did not require hyper-parameter tuning.

Input: Figure 6: Impact of gradient smoothing on CIFAR10, ResNet-44. The training regime includes two image sizes: 32 × 32 and 16 × 16 (average size is S = 24). Using a B+ regime creates two batch sizes: 256 and 2, 048 respectively. Gradient norm values are shown with and without Grad-smoothing. Solid lines are gradients for S = 32 while dotted lines are for S = 16. Gradient smoothing helps to reduce gap between gradient norms at difference batch sizes.

Input: Figure 4: Top-1 accuracy over ImageNet validation set per evaluation image size.

Input: Figure 3: (a): Test accuracy on validation set per image size, all models trained using the same computational and memory resources (regime D+). (b): Test accuracy per Gflop (at evaluation).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, the claim "Reducing image size sensitivity" appears well-stated and supported by comprehensive empirical evidence. The research demonstrates:

1. Clear documentation of how CNNs trained on fixed image sizes show sensitivity to evaluation at different sizes (Fig 1, 4)
2. Thorough experimental validation of their MixSize approach improving robustness across different image sizes (Fig 2, 3)
3. Multiple supporting experiments showing the benefits of gradient smoothing, batch-norm calibration, and different sampling strategies
4. Quantitative results demonstrating improved accuracy and computational efficiency
5. Careful acknowledgment of limitations and clear explanation of methodology

The claim is neither exaggerated nor overstated, with results thoroughly backed by data.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

* **Reducing image size sensitivity**.

The review comment to be evaluated is:

The paper proposes the use of mixed image sizes during training. They argue empirically that such an approach improves generalization for both fixed image size (e.g. 224 in ImageNet) as well as for variable image size. The proposed training algorithm maintains the same computational budget at each step by either changing the batch size or by using more/less augmentation. They show that adjusting the batch size leads to a faster training but using augmentation leads to a better test accuracy (hence a tradeoff).

However, in order for their proposed method to work, the authors also propose modifications to standard training procedures (i.e. smoothing the gradient, adjusting the batchnorm layers) but without carrying out an ablation study that shows the impact with/without each of these steps. My particular concern is in the use of "gradient smoothing". If I understand it correctly, this is not very different from using momentum, which is known to reduce the variance and improve generalization. However, the authors use gradient smoothing only in their proposed method and do not use it in the baseline method (why not?). It is possible that the reported improvements (e.g. for fixed image size) come solely from this step.

The other concern is when sampling the image size per step. The authors  propose distributions that seem odd in their experiments (e.g. why is p=0.6 for size 128 in ImageNet which is much larger than others, and why not uniform in CIFAR10). It is important to know if the results are sensitive to the choice of the distribution, to make sure that the benefit is not due to random chance. Also, if this distribution needs to be fine-tuned, then the discussion about improving the training time would be meaningless.

The last issue is the robustness to different image sizes. Figure 3(a) shows  that if the average image size during training is small, the network will perform better for small images but not for large images. Conversely, if the average image size during training is large, it will perform better for large images, but not for small images. If the concern here is around using mixed-image sizes at inference time, then the red curve in Figure 3(a) shows that a fixed image size is reasonably robust. If one knows in advance that the average image size would be smaller than 224, one can train with a fixed image size that is smaller.

One minor last remark (feel free to ignore) regarding the motivation: the authors study the correlation between the full gradients for the same image with different sizes, on the one hand, and for different images with the same size, on the other hand. They conclude that the first case (different sizes) shows a stronger correlation, which is true according to Table 2, but this statement omits the fact that most correlations were low anyway. For example, for partially trained network, it is 0.08 vs. 0.02. I do not think that one can use such figures to conclude that "smaller image gradients can be used as an estimate to the full image gradients".

The improvement in test accuracy is very promising but I believe, some ablation is needed to identify exactly where this improvement comes from and whether it can be obtained using simpler approach (e.g. smoothing the gradient alone or using augmentation alone, etc).

The evidence to be evaluated is:Modifying the spatial size of an input to a convolutional layer by a factor \(\gamma\), will yield an output with size scaled by the same factor \(\gamma\). This modification does not require any change to the number of parameters of the given convolutional layer, nor its underlying operation. It was observed by practitioners and previous works that a network trained on a specific input dimension can still be used at inference using a modified image size to some extent (Simonyan and Zisserman, 2014). Moreover, evaluating with an image size that is larger than used for training can improve accuracy up to a threshold, after which it quickly deteriorates (Touvron et al., 2019). Although not explicitly trained to handle varying image sizes, CNNs are commonly evaluated on multiple scales post-training, such as in the case of detection (Lin et al., 2017; Redmon and Farhadi, 2018; Liu et al., 2020) and segmentation (He et al., 2017) tasks. In these tasks, a network that was pretrained with fixed image size for classification is used as the backbone of a larger model that is expected to adapt to a wide variety of image sizes. Recently, Tan and Le (2019) showed a computation-vs-accuracy trade-off in applying scaling to the image size used for convolutional networks training and evaluation.

In addition, previous works explored the notion of "progressive resizing" (Howard, 2018; Karras et al., 2017) -- increasing image size as training progresses to improve model performance and time to convergence.

Another related work by Touvron et al. (2019) demonstrated that CNNs can be trained using a fixed small image size and fine-tuned post-training to a larger size, with which evaluation will be performed. This procedure reduced the train-test discrepancy caused by the change in image size and allowed faster training time and improved accuracy -- at the cost of additional fine-tuning procedure and additional computations at inference time. In this work we will further explore the notion of using multiple image sizes at training, so the CNN performance will be resilient to test time changes of the image size.

For instance, a linear (Goyal et al., 2017) or square-root (Hoffer et al., 2017) scaling of the learning rate with respect to the batch size growth. Other modifications include per-layer gradient scaling schemes (You et al., 2017) and optimizer modifications (Ginsburg et al., 2019). Several works also explored using incremented batch-sizes (Smith et al., 2018) in order to decrease the number of training iterations required to reach the desired accuracy. Recent work (Hoffer et al., 2020) introduced the notion of "Batch Augmentation" (BA) -- increasing the batch size by augmenting several instances of each sample within the same batch. BA aids generalization across a wide variety of models and tasks, with the expense of an increased computational effort per step.

It was also demonstrated that BA may allow to decrease the number of training steps needed to achieve a similar accuracy and also mitigate I/O throughput bottlenecks (Choi et al., 2019).

The traditional practice of training convolutional networks using fixed-size images holds several shortcomings. As it is a common practice to use different image size for evaluation than that used for training (He et al., 2017; Lin et al., 2017; Redmon and Farhadi, 2018), it was observed by Touvron et al. (2019) and empirically verified (Figure 1) that classification accuracy may degrade above or below a certain size threshold. Similarly, we observed this phenomenon in a wide variety of common networks (Appendix Figure 4).

To remedy these issues, we suggest a stochastic training regime, where image sizes may vary in each optimization step.

We hypothesize that a considerable part of the training of convolutional networks can be performed at a lower image size than the target size used at test time.

We see that gradients computed across different sizes of the same images have a stronger correlation than those obtained across different images.

This observation suggests that smaller image gradients can be used as an estimate to the full image gradients, with a smaller computational footprint. Therefore, using large images along the entire training process may be sub-optimal in terms of computational resource utilization.

We propose "MixSize", a stochastic training regime where input sizes can vary. In this regime, we modified the spatial dimensions \(H,W\) (height and width) of the input image size2, as well as the batch size.

We will show that using our MixSize regime can have a positive impact on the resiliency of trained networks to various images sizes at evaluation time by demonstrating better accuracy across a wide range of sizes. This entails a considerable saving in computational burden required for inference, especially when using smaller models. Furthermore, given a fixed budget of computational and time resources (per step), we can now modify our regime along spatial and batch axes.

MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

To easily adapt training regimes to the use of MixSize as well as improve their final performance, we continue to describe three methods we found useful: **step-wise size sampling, gradient smoothing** and **batch-norm calibration**. Considering our findings on correlation of gradients across different image size in early training, we were initially motivated to consider a training variation where size is progressively enlarged (Howard, 2018; Karras et al., 2017). In this method we consider increasing image size from small to large, where each image size is used for a predefined number of epochs out of total number of training epochs required.

We therefore considered two alternatives for image size variations, where size is randomly sampled and changed throughout training: * Sampling image size per epoch

* Sampling image size per training step These sampling methods can be seen as a stochastic alternative to long and short cycle multigrid approach suggested by Wu et al. (2020). We found that random sampling regimes perform better than scaling image size from small to large, keeping accuracy high across all used sizes at evaluation (Appendix E). While sampling both at epoch and step time frames performed similarly, replacing sizes on each step converged faster and exhibited less noise in measured test accuracy. Considering these findings, we continue to perform our experiments using the third regime - sampling image size per training step.

This further suggests that the optimization regime should be adapted to smaller spatial sizes, in a manner similar to learning-rate adaptations that are used for large-batch training.

Here we suggest changing both the spatial size as well as the batch size, which is also expected to modify the variance of gradients within each step and further complicates the choice of optimal scaling.

We suggest an alternative solution to previous approaches, which we refer to as "Gradient smoothing". Gradient smoothing mitigates the variability of gradient statistics when image sizes are constantly changing across training.

Gradient smoothing, however, is designed to adapt globally (across all layers) to the batch and spatial size modification and can be used regardless of the optimization method used. We found gradient smoothing to be beneficial in \(B^{+}\) regimes, where multiple varying batch sizes are used, as the effective learning rate is also modified according to common practices. We observed that gradient smoothing reduces the gap between gradient norms of different sizes (see Appendix Figure 6) and allow the use of an average learning rate scaling (weighted across batch sizes).

As demonstrated by Touvron et al. (2019), using a different image size at evaluation may incur a discrepancy between training and evaluation protocols, caused by using different data pre-processing.

In contrast, we surmise that for networks trained with mixed-regimes, discrepancy issues mainly arise from the use of the batch-norm layers (Ioffe and Szegedy, 2015) and can be solved by targeting them specifically. Batch-norm layers introduce a discrepancy between training and test evaluations (Ioffe, 2017), as at inference a running estimate of the mean and variance (of training data) are used instead of the actual mean and variance values. This difference is emphasized further in the use of varying imagesize, as changing the spatial size of an input map can significantly modify the measured variance of that map. While a fine-tuning process per image size can eliminate this discrepancy (Touvron et al., 2019), it required significant amount of computation and labeled data. We offer a simpler alternative. For each evaluated size, we calibrate the mean and variance estimates used for that size by computing an average value over a small number of training examples.

Interestingly, we highlight the fact that although this process has little to no effect on models trained using a fixed-size input, it does improve our mixed-size models considerably on a wide range of image sizes.

\[S^{(28)}:\ S=\begin{cases}40,&\text{w.p.}\quad p=0.2\\ 32,&\text{w.p.}\quad p=0.3\\ 24,&\text{w.p.}\quad p=0.3\\ 16,&\text{w.p.}\quad p=0.2\end{cases}\] The regime was designed to be centered around the mean value of \(28\).

While the original training regime consisted of images of size \(224\times 224\), our proposed regime makes for an average image size of \(\hat{S}\times\hat{S}=144\times 144\). This regime was again designed so that the reduced spatial size can be used to increase the corresponding batch size or the number of BA duplicates, as described in Section 3.

We see that our MixSize regimes yield two possible improvements:* Reduced number of training steps to achieve a similar test accuracy using \(B^{+}\) regime.

\(B+\) enables larger batches on average, hence the reduction in training steps, while \(D+\) leverages benefits of batch-augmentation to achieve better accuracy within the same compute. The ResNet-50 model benefits the most from our MixSize regime on the ImageNet model and so we chose it for further exploration.

We enlarge the batch size used for each spatial size by a factor of \(\frac{224^{2}}{S^{2}}\) such that \(S^{2}\cdot B\) is kept approximately fixed.

As can be seen in Figure 2, regime \(B^{+}\) enables training with approximately \(2.7\times\) fewer training steps, while reaching an improved accuracy of \(76.61\%\). As sizes were chosen to reflect in approximately equal computational cost per iteration, \(B^{+}\) regime offers a similar improvement in total wall-clock time.

Next, we examine how MixSize affects the resulting model resiliency to changes in the image size during test-time. We evaluated the models by varying the test-time image sizes around the original \(224\) spatial size: \(S=224+32\cdot m\), for \(m\in\{-6,...,6\}\). The common evaluation procedure for ImageNet models first scales the image to a \(256\) smallest dimension and crops a center \(224\times 224\) image. We adapt this regime for other image sizes by scaling the smallest dimension to \(\lfloor\frac{8}{7}S\rfloor\) (since \(\frac{8}{7}\cdot 224=256\)) and then cropping the center \(S\times S\) patch. Models trained with a mixed regime were calibrated to a specific evaluation size by measuring batch-norm statistics for \(200\) batches of training samples.

However, due to the decreased average size, we were able to leverage more than \(1\) duplicates per patch on average, which improved the model's top-1 accuracy to \(77.14\%\) at size \(224\). Furthermore, we find that the model performs much more favorably at sizes smaller than \(224\), scoring an improved (over baseline) accuracy of \(76.43\%\) at only \(160\) spatial size.

Figure 2(a) demonstrates that while all three models (Fixed with \(S=224\), \(S^{(144)}\) and \(S^{(208)}\)) were trained with the same compute and memory budget, mixed-size regimes offer superior accuracy over a wide range of evaluation sizes.

As can be seen in Figure 2(b), mixed-regime trained models offer a wider range of resolutions with close-to-baseline accuracy (within a \(2\%\) change) and perform better than their fixed-size counterparts at all sizes.

Stochastic regime benefits are threefold: (1) reduced number of training iterations; or (2) improved model accuracy (generalization) and (3) improved model robustness to changing the image size.

Given a computational and time budget, stochastic size regimes may enable to train networks faster, with better results, as well as to target specific image sizes that will be used at test time. As the average size chosen to train is reflected in the optimal operating point for evaluation resolution, mixed regimes can be used to create networks with better performance across multiple designated use cases. We used 6 common networks (Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016; Huang et al., 2017; Mahajan et al., 2018; Sandler et al., 2018) pretrained on the ImageNet dataset at a resolution of \(224\times 224\) and measured their accuracy on varying sizes. As can be seen, these networks show similar patters of sensitivity to the evaluation size, suggesting this is caused by the training protocol (which is similar for all), rather than the used model.

In order to adapt to varying input scales, we add an additional augmentation step, that resizes the images using bilinear interpolation to \(S\times S\), depending on a sampled size for each step.

This improvement can be attributed to a regularization effect induced by changing image sizes during training, also manifested by an increase in training error throughout its progress.

We can see that gradient smoothing helps to reduce gap between gradient norms at difference batch sizes and improves training and validation accuracy. We consider training regimes with varying image sizes, such that the average image size is smaller than the desired evaluation size. For example, for the height dimension \(H\), we wish to obtain an average size of \(\bar{H}=\sum_{i}p_{i}H_{i}\) such that \(\bar{H}<H_{o}\).

* Increase image size from small to large (progressive resizing), where each image size is used for number of epochs \(E_{i}=p_{i}E_{\mathrm{total}}\), where \(E_{\mathrm{total}}\) is the total number training epochs required.

* Using a random image size for each epoch, keeping the epoch number for each size at \(E_{i}\)

* Sampling image size per training step at probability \(p_{i}\)

In both CIFAR10 (Figure 8) and ImageNet (Figure 9) sampling methods exhibit better accuracy than a progressive resizing regime. This is most apparent when the final size used at training is larger than target size for inference (on which test accuracy is measured).

Input: Figure 1: Top-1 test accuracy per image size, models trained on specific sizes (ResNet50, ImageNet).

Input: Figure 9: Test accuracy vs epoch (ResNet50 on ImageNet, B+ with s(144)) for progressive resizing (small to large) compared to per-step sampling.

Input: Figure 2: Training (dotted) and test accuracy on ImageNet using suggested regimes (224 evaluation size). All regimes required similar resources per step. B+ regime required ≈ 2.7× less steps per epoch.

Input: Figure 8: Test accuracy vs step (ResNet44 on CIFAR10,B+ with s(28)) for 3 size sampling regimes: (1) From small to large (2) Sample each Epoch (3) Sample each step. All methods reached a similar accuracy, but sampling each epoch was less noisy and did not require hyper-parameter tuning.

Input: Figure 6: Impact of gradient smoothing on CIFAR10, ResNet-44. The training regime includes two image sizes: 32 × 32 and 16 × 16 (average size is S = 24). Using a B+ regime creates two batch sizes: 256 and 2, 048 respectively. Gradient norm values are shown with and without Grad-smoothing. Solid lines are gradients for S = 32 while dotted lines are for S = 16. Gradient smoothing helps to reduce gap between gradient norms at difference batch sizes.

Input: Figure 4: Top-1 accuracy over ImageNet validation set per evaluation image size.

Input: Figure 3: (a): Test accuracy on validation set per image size, all models trained using the same computational and memory resources (regime D+). (b): Test accuracy per Gflop (at evaluation).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Based on the evidence and review comments, I'll evaluate the claim "Reducing image size sensitivity":

The evidence shows mixed support for this claim. While the paper demonstrates that their MixSize approach does improve model performance across different image sizes compared to fixed-size training, the reviewer raises valid concerns about:
1. Lack of ablation studies to isolate the impact of gradient smoothing
2. Arbitrary distribution choices for image size sampling
3. The trade-off where models still perform better at sizes closer to their average training size

The improvement appears real but may be partially attributable to other factors like gradient smoothing rather than just the mixed size training alone.

<score>3</score>

The claim reflects a real improvement but moderately overstates the clarity and certainty of the results given the methodological concerns raised and the remaining sensitivity to image sizes near the training distribution.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

* **Reducing image size sensitivity**.

The review comment to be evaluated is:

This paper proposes to increase training costs to compensate for the reduced costs from multi-scale CNN training by either increasing batch size (and therefore lowering the number of iterations per epoch) or increasing the number of augmented versions (duplicates) of the same samples within a batch. The former allows for smaller total training costs than conventional single-scale training, while the latter maintains the total training costs but improves the final performance. Several training improvement methods are introduced to improve the multi-scale training.

Paper's strengths
- The paper is quite well-written.
- Code and models are provided for reproducibility.
- Gradient smoothing is a nice way to mitigate the variability of gradient statistics resulted from different input sizes. As far as I know, this is quite novel, particularly in the context of multi-scale training.

Paper's weaknesses
- Multi-scale training is a common practice in many computer vision tasks especially in object detection** (less common in image classification). This paper also does multi-scale training but only introduces some minor improvements that are neither breakthroughs nor that they provide any interesting insight.
> - Bag of Freebies for Training Object Detection Neural Networks. arXiv.
> - YOLO9000: Better, Faster, Stronger. CVPR 2017.
> - MMDetection: Open MMLab Detection Toolbox and Benchmark. arXiv.

- For "step-wise size sampling", it seems like that conclusion to use this variant of sampling is heuristically chosen and totally ignores the existing practice in other computer vision tasks. One of the straightforward ways to do multi-scale training in object detection is to select different input sizes even for the images within the same batch (by padding zeros for the smaller images). Alternatively, one could sample different input sizes for different GPU batches (all images within a GPU share the same size) while doing multiple-GPU training.

- The three training improvements (step-wise size sampling, gradient smoothing and batch-norm calibration) are what separate this paper from prior work but they are not extensively evaluated. Some of them are briefly evaluated in the appendix and some of their effects are just briefly mentioned in the method section. They ought to appear in the experimental section of the main paper. Gradient smoothing seems like a nice idea but it is unclear how important it is given that there is only one figure (Fig.7) showing its impact on the performance.

- This paper strives to increase the number of batch samples given a fixed budget of computational and time resources for per iteration step. I wonder why this should be limited to the cost of an iteration step but not the entire training cost from all epochs/iterations. It makes more sense to measure the cost for the entire training process which accurately tells how much is spent to train the model until convergence.

- In Sec. 5.1, the size ratios for different datasets are carefully chosen based on cross-validation. This makes it hard to directly apply MixSize to other datasets or settings without going through this step. It also adds additional computations which defeat the purpose of increasing batch size to maintain the same training cost as conventional single-scale training.

- Using separate BatchNorm statistics for multi-scale inputs/features has been explored in the following papers (published at least few months before ICLR deadline). They should be cited and compared against MixSize:
> - Learning to Learn Parameterized Classification Networks for Scalable Input Images. ECCV 2020.
> - Stochastic Downsampling for Cost-Adjustable Inference and Improved Regularization in Convolutional Networks. CVPR 2018.

Overall, this paper shows good performance and has some good ideas (e.g., gradient smoothing) for improving multi-scale training. But it fails to give more emphasis to or do a deeper dive into the potentially novel aspects of the work. The current performance improvements may come from doing just trivial multi-scale training which was already widely-explored in prior work.

The evidence to be evaluated is:Modifying the spatial size of an input to a convolutional layer by a factor \(\gamma\), will yield an output with size scaled by the same factor \(\gamma\). This modification does not require any change to the number of parameters of the given convolutional layer, nor its underlying operation. It was observed by practitioners and previous works that a network trained on a specific input dimension can still be used at inference using a modified image size to some extent (Simonyan and Zisserman, 2014). Moreover, evaluating with an image size that is larger than used for training can improve accuracy up to a threshold, after which it quickly deteriorates (Touvron et al., 2019). Although not explicitly trained to handle varying image sizes, CNNs are commonly evaluated on multiple scales post-training, such as in the case of detection (Lin et al., 2017; Redmon and Farhadi, 2018; Liu et al., 2020) and segmentation (He et al., 2017) tasks. In these tasks, a network that was pretrained with fixed image size for classification is used as the backbone of a larger model that is expected to adapt to a wide variety of image sizes. Recently, Tan and Le (2019) showed a computation-vs-accuracy trade-off in applying scaling to the image size used for convolutional networks training and evaluation.

In addition, previous works explored the notion of "progressive resizing" (Howard, 2018; Karras et al., 2017) -- increasing image size as training progresses to improve model performance and time to convergence.

Another related work by Touvron et al. (2019) demonstrated that CNNs can be trained using a fixed small image size and fine-tuned post-training to a larger size, with which evaluation will be performed. This procedure reduced the train-test discrepancy caused by the change in image size and allowed faster training time and improved accuracy -- at the cost of additional fine-tuning procedure and additional computations at inference time. In this work we will further explore the notion of using multiple image sizes at training, so the CNN performance will be resilient to test time changes of the image size.

For instance, a linear (Goyal et al., 2017) or square-root (Hoffer et al., 2017) scaling of the learning rate with respect to the batch size growth. Other modifications include per-layer gradient scaling schemes (You et al., 2017) and optimizer modifications (Ginsburg et al., 2019). Several works also explored using incremented batch-sizes (Smith et al., 2018) in order to decrease the number of training iterations required to reach the desired accuracy. Recent work (Hoffer et al., 2020) introduced the notion of "Batch Augmentation" (BA) -- increasing the batch size by augmenting several instances of each sample within the same batch. BA aids generalization across a wide variety of models and tasks, with the expense of an increased computational effort per step.

It was also demonstrated that BA may allow to decrease the number of training steps needed to achieve a similar accuracy and also mitigate I/O throughput bottlenecks (Choi et al., 2019).

The traditional practice of training convolutional networks using fixed-size images holds several shortcomings. As it is a common practice to use different image size for evaluation than that used for training (He et al., 2017; Lin et al., 2017; Redmon and Farhadi, 2018), it was observed by Touvron et al. (2019) and empirically verified (Figure 1) that classification accuracy may degrade above or below a certain size threshold. Similarly, we observed this phenomenon in a wide variety of common networks (Appendix Figure 4).

To remedy these issues, we suggest a stochastic training regime, where image sizes may vary in each optimization step.

We hypothesize that a considerable part of the training of convolutional networks can be performed at a lower image size than the target size used at test time.

We see that gradients computed across different sizes of the same images have a stronger correlation than those obtained across different images.

This observation suggests that smaller image gradients can be used as an estimate to the full image gradients, with a smaller computational footprint. Therefore, using large images along the entire training process may be sub-optimal in terms of computational resource utilization.

We propose "MixSize", a stochastic training regime where input sizes can vary. In this regime, we modified the spatial dimensions \(H,W\) (height and width) of the input image size2, as well as the batch size.

We will show that using our MixSize regime can have a positive impact on the resiliency of trained networks to various images sizes at evaluation time by demonstrating better accuracy across a wide range of sizes. This entails a considerable saving in computational burden required for inference, especially when using smaller models. Furthermore, given a fixed budget of computational and time resources (per step), we can now modify our regime along spatial and batch axes.

MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

To easily adapt training regimes to the use of MixSize as well as improve their final performance, we continue to describe three methods we found useful: **step-wise size sampling, gradient smoothing** and **batch-norm calibration**. Considering our findings on correlation of gradients across different image size in early training, we were initially motivated to consider a training variation where size is progressively enlarged (Howard, 2018; Karras et al., 2017). In this method we consider increasing image size from small to large, where each image size is used for a predefined number of epochs out of total number of training epochs required.

We therefore considered two alternatives for image size variations, where size is randomly sampled and changed throughout training: * Sampling image size per epoch

* Sampling image size per training step These sampling methods can be seen as a stochastic alternative to long and short cycle multigrid approach suggested by Wu et al. (2020). We found that random sampling regimes perform better than scaling image size from small to large, keeping accuracy high across all used sizes at evaluation (Appendix E). While sampling both at epoch and step time frames performed similarly, replacing sizes on each step converged faster and exhibited less noise in measured test accuracy. Considering these findings, we continue to perform our experiments using the third regime - sampling image size per training step.

This further suggests that the optimization regime should be adapted to smaller spatial sizes, in a manner similar to learning-rate adaptations that are used for large-batch training.

Here we suggest changing both the spatial size as well as the batch size, which is also expected to modify the variance of gradients within each step and further complicates the choice of optimal scaling.

We suggest an alternative solution to previous approaches, which we refer to as "Gradient smoothing". Gradient smoothing mitigates the variability of gradient statistics when image sizes are constantly changing across training.

Gradient smoothing, however, is designed to adapt globally (across all layers) to the batch and spatial size modification and can be used regardless of the optimization method used. We found gradient smoothing to be beneficial in \(B^{+}\) regimes, where multiple varying batch sizes are used, as the effective learning rate is also modified according to common practices. We observed that gradient smoothing reduces the gap between gradient norms of different sizes (see Appendix Figure 6) and allow the use of an average learning rate scaling (weighted across batch sizes).

As demonstrated by Touvron et al. (2019), using a different image size at evaluation may incur a discrepancy between training and evaluation protocols, caused by using different data pre-processing.

In contrast, we surmise that for networks trained with mixed-regimes, discrepancy issues mainly arise from the use of the batch-norm layers (Ioffe and Szegedy, 2015) and can be solved by targeting them specifically. Batch-norm layers introduce a discrepancy between training and test evaluations (Ioffe, 2017), as at inference a running estimate of the mean and variance (of training data) are used instead of the actual mean and variance values. This difference is emphasized further in the use of varying imagesize, as changing the spatial size of an input map can significantly modify the measured variance of that map. While a fine-tuning process per image size can eliminate this discrepancy (Touvron et al., 2019), it required significant amount of computation and labeled data. We offer a simpler alternative. For each evaluated size, we calibrate the mean and variance estimates used for that size by computing an average value over a small number of training examples.

Interestingly, we highlight the fact that although this process has little to no effect on models trained using a fixed-size input, it does improve our mixed-size models considerably on a wide range of image sizes.

\[S^{(28)}:\ S=\begin{cases}40,&\text{w.p.}\quad p=0.2\\ 32,&\text{w.p.}\quad p=0.3\\ 24,&\text{w.p.}\quad p=0.3\\ 16,&\text{w.p.}\quad p=0.2\end{cases}\] The regime was designed to be centered around the mean value of \(28\).

While the original training regime consisted of images of size \(224\times 224\), our proposed regime makes for an average image size of \(\hat{S}\times\hat{S}=144\times 144\). This regime was again designed so that the reduced spatial size can be used to increase the corresponding batch size or the number of BA duplicates, as described in Section 3.

We see that our MixSize regimes yield two possible improvements:* Reduced number of training steps to achieve a similar test accuracy using \(B^{+}\) regime.

\(B+\) enables larger batches on average, hence the reduction in training steps, while \(D+\) leverages benefits of batch-augmentation to achieve better accuracy within the same compute. The ResNet-50 model benefits the most from our MixSize regime on the ImageNet model and so we chose it for further exploration.

We enlarge the batch size used for each spatial size by a factor of \(\frac{224^{2}}{S^{2}}\) such that \(S^{2}\cdot B\) is kept approximately fixed.

As can be seen in Figure 2, regime \(B^{+}\) enables training with approximately \(2.7\times\) fewer training steps, while reaching an improved accuracy of \(76.61\%\). As sizes were chosen to reflect in approximately equal computational cost per iteration, \(B^{+}\) regime offers a similar improvement in total wall-clock time.

Next, we examine how MixSize affects the resulting model resiliency to changes in the image size during test-time. We evaluated the models by varying the test-time image sizes around the original \(224\) spatial size: \(S=224+32\cdot m\), for \(m\in\{-6,...,6\}\). The common evaluation procedure for ImageNet models first scales the image to a \(256\) smallest dimension and crops a center \(224\times 224\) image. We adapt this regime for other image sizes by scaling the smallest dimension to \(\lfloor\frac{8}{7}S\rfloor\) (since \(\frac{8}{7}\cdot 224=256\)) and then cropping the center \(S\times S\) patch. Models trained with a mixed regime were calibrated to a specific evaluation size by measuring batch-norm statistics for \(200\) batches of training samples.

However, due to the decreased average size, we were able to leverage more than \(1\) duplicates per patch on average, which improved the model's top-1 accuracy to \(77.14\%\) at size \(224\). Furthermore, we find that the model performs much more favorably at sizes smaller than \(224\), scoring an improved (over baseline) accuracy of \(76.43\%\) at only \(160\) spatial size.

Figure 2(a) demonstrates that while all three models (Fixed with \(S=224\), \(S^{(144)}\) and \(S^{(208)}\)) were trained with the same compute and memory budget, mixed-size regimes offer superior accuracy over a wide range of evaluation sizes.

As can be seen in Figure 2(b), mixed-regime trained models offer a wider range of resolutions with close-to-baseline accuracy (within a \(2\%\) change) and perform better than their fixed-size counterparts at all sizes.

Stochastic regime benefits are threefold: (1) reduced number of training iterations; or (2) improved model accuracy (generalization) and (3) improved model robustness to changing the image size.

Given a computational and time budget, stochastic size regimes may enable to train networks faster, with better results, as well as to target specific image sizes that will be used at test time. As the average size chosen to train is reflected in the optimal operating point for evaluation resolution, mixed regimes can be used to create networks with better performance across multiple designated use cases. We used 6 common networks (Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016; Huang et al., 2017; Mahajan et al., 2018; Sandler et al., 2018) pretrained on the ImageNet dataset at a resolution of \(224\times 224\) and measured their accuracy on varying sizes. As can be seen, these networks show similar patters of sensitivity to the evaluation size, suggesting this is caused by the training protocol (which is similar for all), rather than the used model.

In order to adapt to varying input scales, we add an additional augmentation step, that resizes the images using bilinear interpolation to \(S\times S\), depending on a sampled size for each step.

This improvement can be attributed to a regularization effect induced by changing image sizes during training, also manifested by an increase in training error throughout its progress.

We can see that gradient smoothing helps to reduce gap between gradient norms at difference batch sizes and improves training and validation accuracy. We consider training regimes with varying image sizes, such that the average image size is smaller than the desired evaluation size. For example, for the height dimension \(H\), we wish to obtain an average size of \(\bar{H}=\sum_{i}p_{i}H_{i}\) such that \(\bar{H}<H_{o}\).

* Increase image size from small to large (progressive resizing), where each image size is used for number of epochs \(E_{i}=p_{i}E_{\mathrm{total}}\), where \(E_{\mathrm{total}}\) is the total number training epochs required.

* Using a random image size for each epoch, keeping the epoch number for each size at \(E_{i}\)

* Sampling image size per training step at probability \(p_{i}\)

In both CIFAR10 (Figure 8) and ImageNet (Figure 9) sampling methods exhibit better accuracy than a progressive resizing regime. This is most apparent when the final size used at training is larger than target size for inference (on which test accuracy is measured).

Input: Figure 1: Top-1 test accuracy per image size, models trained on specific sizes (ResNet50, ImageNet).

Input: Figure 9: Test accuracy vs epoch (ResNet50 on ImageNet, B+ with s(144)) for progressive resizing (small to large) compared to per-step sampling.

Input: Figure 2: Training (dotted) and test accuracy on ImageNet using suggested regimes (224 evaluation size). All regimes required similar resources per step. B+ regime required ≈ 2.7× less steps per epoch.

Input: Figure 8: Test accuracy vs step (ResNet44 on CIFAR10,B+ with s(28)) for 3 size sampling regimes: (1) From small to large (2) Sample each Epoch (3) Sample each step. All methods reached a similar accuracy, but sampling each epoch was less noisy and did not require hyper-parameter tuning.

Input: Figure 6: Impact of gradient smoothing on CIFAR10, ResNet-44. The training regime includes two image sizes: 32 × 32 and 16 × 16 (average size is S = 24). Using a B+ regime creates two batch sizes: 256 and 2, 048 respectively. Gradient norm values are shown with and without Grad-smoothing. Solid lines are gradients for S = 32 while dotted lines are for S = 16. Gradient smoothing helps to reduce gap between gradient norms at difference batch sizes.

Input: Figure 4: Top-1 accuracy over ImageNet validation set per evaluation image size.

Input: Figure 3: (a): Test accuracy on validation set per image size, all models trained using the same computational and memory resources (regime D+). (b): Test accuracy per Gflop (at evaluation).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Based on the evidence presented, including empirical results and theoretical analysis, the claim "Reducing image size sensitivity" appears to be well-supported. The paper demonstrates:

1. Models trained with MixSize show improved robustness across different evaluation sizes compared to fixed-size training (Figure 2a, 3a)
2. Quantitative evidence of maintained accuracy across a wider range of resolutions (within 2% change)
3. Clear experimental validation through multiple network architectures (Figure 4)
4. Detailed analysis of gradient behavior and batch normalization effects

While the reviewer notes this as an incremental advance, the specific claim about reducing size sensitivity is carefully stated and backed by comprehensive evidence. The authors acknowledge limitations and provide thorough experimental validation.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

* **Reducing image size sensitivity**.

The review comment to be evaluated is:

== Summary ==

The paper proposes to use different image resolutions during the training of a deep neural network image classifier, and varying the batch size or number of data augmented versions of the images, keeping the computational cost per step roughly constant. The authors apply this approach to several architectures and three datasets, and show that they can achieve or improve the same accuracy as the baselines but much faster; or achieve better results with the same computational budget.

== Pros ==

+ The authors conducted their experiments using three different datasets (Cifar10, Cifar100 and ImageNet), and six different architectures (ResNet44, ResNet50, WideResNet, DenseNet and EfficientNet).

+ The proposed approach outperforms the baselines consistently across the 8 pairs of (dataset, architecture) that they have studied. In addition, MixSize can be easily implemented (the authors also provide a PyTorch implementation).

+ The authors investigate different "tricks" to apply during training when using MixSize to stabilize training or achieving better results. For instance, they compared randomly sampling the size from a distribution (as they propose) versus increasing the image resolution as training progresses, and showed that randomly sampling yields slightly better results.

+ Figure 3a seems to suggest that MixSize yields more robust classifiers under a wide range of image sizes. The area under the "Mixed S=144" curve seems to be larger than the area under the "Fixed S=224". However, further experimentation is needed to confirm this, since the area of the "Mixed S=208" seems closer to "Fixed S=224", and in any case the maximum image size was capped around 415.

== Cons ==

- On of the claimed contributions is: "Faster training vs. high accuracy. We show that reducing the average image size at train- ing leads to a trade-off between the time required to train the model and its final accuracy.". However, I would not consider this a novel contribution, since the trade-off between speed and accuracy is well-known. In fact, the authors cite Huang et al. (2018) and Szegedy et al. (2016) which already showed this. EfficientNet is another well-known architecture that takes advantage of this fact.

- In the intro, the authors claim "Touvron et al. (2019) demonstrated that networks trained on specific image resolutions perform poorly on other image sizes at evaluation time, as confirmed in Figure 1". This is inaccurate, since Touvron et al. (2019) actually show that slightly increasing the test resolution improves accuracy, due to the discrepancy in object sizes introduced by data augmentation (cropping). In fact, Figure 1 shows the same effect (model trained with 224 res, achieves best results with 284 eval image size). The statement in the introduction is again contradicted at the end of the first paragraph in Section 2.1.

- The authors do not report any statistical significance metric. Some datasets have very close results, so it's hard to tell whether the improvements are (statistically) significant or not.

- Poor captions in figures and tables. For instance, the difference between solid lines and dashed lines is only explained at the very last figure in the appending (Figure 7). Also, the caption of Figure 3 reads "Test accuracy on validation set" which is ambiguous: Is it a typo, or is it that the authors report the results on the 50k validation set of ImageNet (and use some smaller subset of the training set as validation)?

== Reasons for score ==

Although the proposed approach is simple and consistently improves the baseline results, I'm not convinced that the originality and significance of the work is enough for it to be accepted.

Regarding originality, there is a plethora of works exploring the trade-offs between image size and accuracy. The most similar works are Howard (2018) and Karras et al. (2017), which increase the image size through training. It's not clear that random sampling offers a much better result, judging from Figure 8 in Appending E, if one compares the accuracy of "Small->Large" strategy at 125k steps (possibly before the last increase in size).

Regarding significance, if one restricts the analysis to the best architectures in each dataset, the increase in accuracy does not seem to be very large. Cifar10: 98.16% -> 98.32% (AmoebaNet), ImageNet: 76.32% -> 76.53% (EfficientNet-B0). Cifar100 shows a larger improvement, but the authors did not use AmoebaNet (which worked best in Cifar10) for some unknown reason. The fact that no statistical significance metrics are reported, does not help to discern whether the improvements are meaningful or not.

The evidence to be evaluated is:Modifying the spatial size of an input to a convolutional layer by a factor \(\gamma\), will yield an output with size scaled by the same factor \(\gamma\). This modification does not require any change to the number of parameters of the given convolutional layer, nor its underlying operation. It was observed by practitioners and previous works that a network trained on a specific input dimension can still be used at inference using a modified image size to some extent (Simonyan and Zisserman, 2014). Moreover, evaluating with an image size that is larger than used for training can improve accuracy up to a threshold, after which it quickly deteriorates (Touvron et al., 2019). Although not explicitly trained to handle varying image sizes, CNNs are commonly evaluated on multiple scales post-training, such as in the case of detection (Lin et al., 2017; Redmon and Farhadi, 2018; Liu et al., 2020) and segmentation (He et al., 2017) tasks. In these tasks, a network that was pretrained with fixed image size for classification is used as the backbone of a larger model that is expected to adapt to a wide variety of image sizes. Recently, Tan and Le (2019) showed a computation-vs-accuracy trade-off in applying scaling to the image size used for convolutional networks training and evaluation.

In addition, previous works explored the notion of "progressive resizing" (Howard, 2018; Karras et al., 2017) -- increasing image size as training progresses to improve model performance and time to convergence.

Another related work by Touvron et al. (2019) demonstrated that CNNs can be trained using a fixed small image size and fine-tuned post-training to a larger size, with which evaluation will be performed. This procedure reduced the train-test discrepancy caused by the change in image size and allowed faster training time and improved accuracy -- at the cost of additional fine-tuning procedure and additional computations at inference time. In this work we will further explore the notion of using multiple image sizes at training, so the CNN performance will be resilient to test time changes of the image size.

For instance, a linear (Goyal et al., 2017) or square-root (Hoffer et al., 2017) scaling of the learning rate with respect to the batch size growth. Other modifications include per-layer gradient scaling schemes (You et al., 2017) and optimizer modifications (Ginsburg et al., 2019). Several works also explored using incremented batch-sizes (Smith et al., 2018) in order to decrease the number of training iterations required to reach the desired accuracy. Recent work (Hoffer et al., 2020) introduced the notion of "Batch Augmentation" (BA) -- increasing the batch size by augmenting several instances of each sample within the same batch. BA aids generalization across a wide variety of models and tasks, with the expense of an increased computational effort per step.

It was also demonstrated that BA may allow to decrease the number of training steps needed to achieve a similar accuracy and also mitigate I/O throughput bottlenecks (Choi et al., 2019).

The traditional practice of training convolutional networks using fixed-size images holds several shortcomings. As it is a common practice to use different image size for evaluation than that used for training (He et al., 2017; Lin et al., 2017; Redmon and Farhadi, 2018), it was observed by Touvron et al. (2019) and empirically verified (Figure 1) that classification accuracy may degrade above or below a certain size threshold. Similarly, we observed this phenomenon in a wide variety of common networks (Appendix Figure 4).

To remedy these issues, we suggest a stochastic training regime, where image sizes may vary in each optimization step.

We hypothesize that a considerable part of the training of convolutional networks can be performed at a lower image size than the target size used at test time.

We see that gradients computed across different sizes of the same images have a stronger correlation than those obtained across different images.

This observation suggests that smaller image gradients can be used as an estimate to the full image gradients, with a smaller computational footprint. Therefore, using large images along the entire training process may be sub-optimal in terms of computational resource utilization.

We propose "MixSize", a stochastic training regime where input sizes can vary. In this regime, we modified the spatial dimensions \(H,W\) (height and width) of the input image size2, as well as the batch size.

We will show that using our MixSize regime can have a positive impact on the resiliency of trained networks to various images sizes at evaluation time by demonstrating better accuracy across a wide range of sizes. This entails a considerable saving in computational burden required for inference, especially when using smaller models. Furthermore, given a fixed budget of computational and time resources (per step), we can now modify our regime along spatial and batch axes.

MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

To easily adapt training regimes to the use of MixSize as well as improve their final performance, we continue to describe three methods we found useful: **step-wise size sampling, gradient smoothing** and **batch-norm calibration**. Considering our findings on correlation of gradients across different image size in early training, we were initially motivated to consider a training variation where size is progressively enlarged (Howard, 2018; Karras et al., 2017). In this method we consider increasing image size from small to large, where each image size is used for a predefined number of epochs out of total number of training epochs required.

We therefore considered two alternatives for image size variations, where size is randomly sampled and changed throughout training: * Sampling image size per epoch

* Sampling image size per training step These sampling methods can be seen as a stochastic alternative to long and short cycle multigrid approach suggested by Wu et al. (2020). We found that random sampling regimes perform better than scaling image size from small to large, keeping accuracy high across all used sizes at evaluation (Appendix E). While sampling both at epoch and step time frames performed similarly, replacing sizes on each step converged faster and exhibited less noise in measured test accuracy. Considering these findings, we continue to perform our experiments using the third regime - sampling image size per training step.

This further suggests that the optimization regime should be adapted to smaller spatial sizes, in a manner similar to learning-rate adaptations that are used for large-batch training.

Here we suggest changing both the spatial size as well as the batch size, which is also expected to modify the variance of gradients within each step and further complicates the choice of optimal scaling.

We suggest an alternative solution to previous approaches, which we refer to as "Gradient smoothing". Gradient smoothing mitigates the variability of gradient statistics when image sizes are constantly changing across training.

Gradient smoothing, however, is designed to adapt globally (across all layers) to the batch and spatial size modification and can be used regardless of the optimization method used. We found gradient smoothing to be beneficial in \(B^{+}\) regimes, where multiple varying batch sizes are used, as the effective learning rate is also modified according to common practices. We observed that gradient smoothing reduces the gap between gradient norms of different sizes (see Appendix Figure 6) and allow the use of an average learning rate scaling (weighted across batch sizes).

As demonstrated by Touvron et al. (2019), using a different image size at evaluation may incur a discrepancy between training and evaluation protocols, caused by using different data pre-processing.

In contrast, we surmise that for networks trained with mixed-regimes, discrepancy issues mainly arise from the use of the batch-norm layers (Ioffe and Szegedy, 2015) and can be solved by targeting them specifically. Batch-norm layers introduce a discrepancy between training and test evaluations (Ioffe, 2017), as at inference a running estimate of the mean and variance (of training data) are used instead of the actual mean and variance values. This difference is emphasized further in the use of varying imagesize, as changing the spatial size of an input map can significantly modify the measured variance of that map. While a fine-tuning process per image size can eliminate this discrepancy (Touvron et al., 2019), it required significant amount of computation and labeled data. We offer a simpler alternative. For each evaluated size, we calibrate the mean and variance estimates used for that size by computing an average value over a small number of training examples.

Interestingly, we highlight the fact that although this process has little to no effect on models trained using a fixed-size input, it does improve our mixed-size models considerably on a wide range of image sizes.

\[S^{(28)}:\ S=\begin{cases}40,&\text{w.p.}\quad p=0.2\\ 32,&\text{w.p.}\quad p=0.3\\ 24,&\text{w.p.}\quad p=0.3\\ 16,&\text{w.p.}\quad p=0.2\end{cases}\] The regime was designed to be centered around the mean value of \(28\).

While the original training regime consisted of images of size \(224\times 224\), our proposed regime makes for an average image size of \(\hat{S}\times\hat{S}=144\times 144\). This regime was again designed so that the reduced spatial size can be used to increase the corresponding batch size or the number of BA duplicates, as described in Section 3.

We see that our MixSize regimes yield two possible improvements:* Reduced number of training steps to achieve a similar test accuracy using \(B^{+}\) regime.

\(B+\) enables larger batches on average, hence the reduction in training steps, while \(D+\) leverages benefits of batch-augmentation to achieve better accuracy within the same compute. The ResNet-50 model benefits the most from our MixSize regime on the ImageNet model and so we chose it for further exploration.

We enlarge the batch size used for each spatial size by a factor of \(\frac{224^{2}}{S^{2}}\) such that \(S^{2}\cdot B\) is kept approximately fixed.

As can be seen in Figure 2, regime \(B^{+}\) enables training with approximately \(2.7\times\) fewer training steps, while reaching an improved accuracy of \(76.61\%\). As sizes were chosen to reflect in approximately equal computational cost per iteration, \(B^{+}\) regime offers a similar improvement in total wall-clock time.

Next, we examine how MixSize affects the resulting model resiliency to changes in the image size during test-time. We evaluated the models by varying the test-time image sizes around the original \(224\) spatial size: \(S=224+32\cdot m\), for \(m\in\{-6,...,6\}\). The common evaluation procedure for ImageNet models first scales the image to a \(256\) smallest dimension and crops a center \(224\times 224\) image. We adapt this regime for other image sizes by scaling the smallest dimension to \(\lfloor\frac{8}{7}S\rfloor\) (since \(\frac{8}{7}\cdot 224=256\)) and then cropping the center \(S\times S\) patch. Models trained with a mixed regime were calibrated to a specific evaluation size by measuring batch-norm statistics for \(200\) batches of training samples.

However, due to the decreased average size, we were able to leverage more than \(1\) duplicates per patch on average, which improved the model's top-1 accuracy to \(77.14\%\) at size \(224\). Furthermore, we find that the model performs much more favorably at sizes smaller than \(224\), scoring an improved (over baseline) accuracy of \(76.43\%\) at only \(160\) spatial size.

Figure 2(a) demonstrates that while all three models (Fixed with \(S=224\), \(S^{(144)}\) and \(S^{(208)}\)) were trained with the same compute and memory budget, mixed-size regimes offer superior accuracy over a wide range of evaluation sizes.

As can be seen in Figure 2(b), mixed-regime trained models offer a wider range of resolutions with close-to-baseline accuracy (within a \(2\%\) change) and perform better than their fixed-size counterparts at all sizes.

Stochastic regime benefits are threefold: (1) reduced number of training iterations; or (2) improved model accuracy (generalization) and (3) improved model robustness to changing the image size.

Given a computational and time budget, stochastic size regimes may enable to train networks faster, with better results, as well as to target specific image sizes that will be used at test time. As the average size chosen to train is reflected in the optimal operating point for evaluation resolution, mixed regimes can be used to create networks with better performance across multiple designated use cases. We used 6 common networks (Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016; Huang et al., 2017; Mahajan et al., 2018; Sandler et al., 2018) pretrained on the ImageNet dataset at a resolution of \(224\times 224\) and measured their accuracy on varying sizes. As can be seen, these networks show similar patters of sensitivity to the evaluation size, suggesting this is caused by the training protocol (which is similar for all), rather than the used model.

In order to adapt to varying input scales, we add an additional augmentation step, that resizes the images using bilinear interpolation to \(S\times S\), depending on a sampled size for each step.

This improvement can be attributed to a regularization effect induced by changing image sizes during training, also manifested by an increase in training error throughout its progress.

We can see that gradient smoothing helps to reduce gap between gradient norms at difference batch sizes and improves training and validation accuracy. We consider training regimes with varying image sizes, such that the average image size is smaller than the desired evaluation size. For example, for the height dimension \(H\), we wish to obtain an average size of \(\bar{H}=\sum_{i}p_{i}H_{i}\) such that \(\bar{H}<H_{o}\).

* Increase image size from small to large (progressive resizing), where each image size is used for number of epochs \(E_{i}=p_{i}E_{\mathrm{total}}\), where \(E_{\mathrm{total}}\) is the total number training epochs required.

* Using a random image size for each epoch, keeping the epoch number for each size at \(E_{i}\)

* Sampling image size per training step at probability \(p_{i}\)

In both CIFAR10 (Figure 8) and ImageNet (Figure 9) sampling methods exhibit better accuracy than a progressive resizing regime. This is most apparent when the final size used at training is larger than target size for inference (on which test accuracy is measured).

Input: Figure 1: Top-1 test accuracy per image size, models trained on specific sizes (ResNet50, ImageNet).

Input: Figure 9: Test accuracy vs epoch (ResNet50 on ImageNet, B+ with s(144)) for progressive resizing (small to large) compared to per-step sampling.

Input: Figure 2: Training (dotted) and test accuracy on ImageNet using suggested regimes (224 evaluation size). All regimes required similar resources per step. B+ regime required ≈ 2.7× less steps per epoch.

Input: Figure 8: Test accuracy vs step (ResNet44 on CIFAR10,B+ with s(28)) for 3 size sampling regimes: (1) From small to large (2) Sample each Epoch (3) Sample each step. All methods reached a similar accuracy, but sampling each epoch was less noisy and did not require hyper-parameter tuning.

Input: Figure 6: Impact of gradient smoothing on CIFAR10, ResNet-44. The training regime includes two image sizes: 32 × 32 and 16 × 16 (average size is S = 24). Using a B+ regime creates two batch sizes: 256 and 2, 048 respectively. Gradient norm values are shown with and without Grad-smoothing. Solid lines are gradients for S = 32 while dotted lines are for S = 16. Gradient smoothing helps to reduce gap between gradient norms at difference batch sizes.

Input: Figure 4: Top-1 accuracy over ImageNet validation set per evaluation image size.

Input: Figure 3: (a): Test accuracy on validation set per image size, all models trained using the same computational and memory resources (regime D+). (b): Test accuracy per Gflop (at evaluation).

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
I'll evaluate the claim "Reducing image size sensitivity" based on the evidence provided:

Summary: The evidence shows that while the authors did demonstrate some improvements in model robustness across different image sizes using their MixSize approach, the reviewer points out that the improvements were relatively modest and lacked statistical significance testing. Figure 3a suggests improved performance across sizes, but the reviewer notes this effect is less clear when comparing different configurations. The evidence indicates some reduction in size sensitivity, but the magnitude and significance of this improvement appears overstated without proper statistical validation.

<score>3</score>

Justification:
1. The evidence supports that MixSize provides some robustness across image sizes, as shown in Figure 3a and described in the results
2. However, the claim lacks nuance in acknowledging:
- The improvements' statistical significance is not established
- The effect varies across different model/dataset combinations
- The robustness gains are modest in some cases
- The improvements are primarily shown within a limited range of sizes
3. The reviewer's concerns about statistical significance and the need for further experimentation suggest the claim would be better stated with more measured language about the extent and consistency of the improvements.