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:

The main contributions of the MixSize regime are:

The evidence to be evaluated is:This finding is consistent with past findings, which demonstrated that training with a larger image size can result in a better classification accuracy (Huang et al., 2018; Szegedy et al., 2016). 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. A similar idea by Wu et al. (2020) was used to improve performance of training on video data, by balancing resolution with batch size. 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.

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). This hints the issue here is related more to the training procedure, rather than to a specific model. 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. As a first step to substantiate this claim, we evaluated the impact of various image sizes on the CNN training progress by examining gradient statistics during training. Specifically, we measured the correlation between weight gradients with respect to varying image sizes (Appendix Table 2).

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.

Formally, in the MixSize regime, these sizes can be described as random variables sharing a single discrete distribution \[(\hat{S},\hat{B},\hat{D})=\left\{(S,B,D)_{i}\;\;\text{w.p.}\;\;p_{i}\right\}, \tag{1}\] where \(\forall i:p_{i}\geq 0\) and \(\sum_{i}p_{i}=1\). As the computational cost of each training step is approximately proportional to \(S^{2}\cdot B\cdot D\), we choose these quantities to reflect a nearly fixed budget for any choice \(i\) such that \(S_{i}^{2}B_{i}D_{i}\approx Const\). Thus, in this regime, the computational and memory requirements for each step in remain fixed.

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.

* by enlarging \(B\) at the expense of \(S\).

* by enlarging \(D\) at the expense of \(S\). We denote our modified mixed-size regimes as \(B^{+}\) for an increased effective batch-size and \(D^{+}\) for an increased number of BA duplicates of the same ratio. MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

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.

We normalize the gradients used for each step by the smoothing coefficient, such that each consecutive step is performed with gradients of similar norm.

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).

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.

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.

As calibration requires very little resources, as well as small amount of unlabelled data, it can be potentially performed on-demand at test-time. 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.

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

\(B+\) 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 are first interested in accelerating the time needed for convergence of the tested models using our \(B^{+}\) scheme.

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.

As the computational cost for each step remains approximately constant, as well as the number of required steps per epochs, training a model under this regime requires an equal wall-clock time. However, the increased batch-augmentation improves the final test accuracy to \(78.04\%\), approximately \(7\%\) relative improvement over the \(76.4\%\) baseline.

As described earlier, this model requires the same time and computational resources as the baseline model. 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. The model trained with the \(S^{(208)}\) regime offers a similar improvement in accuracy, but across a larger spatial size, as it observed an average size of \(208\) during training. 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. As the number of floating-point operations (flops) grows linearly with the number of pixels, using a mixed regime significantly improves accuracy per compute at evaluation.

In this work, we introduced and examined a performance trade-off between computational load and classification accuracy governed by the input's spatial size. We suggested stochastic image size regimes, which randomly change the spatial dimension as well as the batch size and the number of augmentation duplicates in the batch. 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.

Interestingly, although designed only to reduce training time, we can see that our \(B^{+}\) regime also improves accuracy in some cases. 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.

* 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 \(p_{i}\)

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

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 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 assess whether the claim about MixSize regime's main contributions was overstated.

After reviewing the extensive evidence presented, the evidence strongly supports the core contributions claimed, with multiple figures demonstrating:
1. Figure 2 validates reduced training steps (~2.7x fewer) while maintaining/improving accuracy
2. Figure 3 shows improved accuracy and efficiency across different image sizes
3. Multiple experimental results demonstrate enhanced model robustness to varying image sizes
4. The computational trade-offs and benefits are thoroughly documented with empirical data

The evidence provides comprehensive experimental validation with clear metrics, limitations are acknowledged, and claims are carefully qualified. The contributions appear to be well-supported by the data presented without exaggeration.

<score>1</score>

The claim is considered well-stated (score of 1) as it accurately reflects the demonstrated evidence without overstating the findings. The benefits of MixSize are clearly substantiated through multiple experiments, statistical analyses, and comparative evaluations across different conditions.


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:

The main contributions of the MixSize regime are:

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:This finding is consistent with past findings, which demonstrated that training with a larger image size can result in a better classification accuracy (Huang et al., 2018; Szegedy et al., 2016). 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. A similar idea by Wu et al. (2020) was used to improve performance of training on video data, by balancing resolution with batch size. 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.

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). This hints the issue here is related more to the training procedure, rather than to a specific model. 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. As a first step to substantiate this claim, we evaluated the impact of various image sizes on the CNN training progress by examining gradient statistics during training. Specifically, we measured the correlation between weight gradients with respect to varying image sizes (Appendix Table 2).

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.

Formally, in the MixSize regime, these sizes can be described as random variables sharing a single discrete distribution \[(\hat{S},\hat{B},\hat{D})=\left\{(S,B,D)_{i}\;\;\text{w.p.}\;\;p_{i}\right\}, \tag{1}\] where \(\forall i:p_{i}\geq 0\) and \(\sum_{i}p_{i}=1\). As the computational cost of each training step is approximately proportional to \(S^{2}\cdot B\cdot D\), we choose these quantities to reflect a nearly fixed budget for any choice \(i\) such that \(S_{i}^{2}B_{i}D_{i}\approx Const\). Thus, in this regime, the computational and memory requirements for each step in remain fixed.

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.

* by enlarging \(B\) at the expense of \(S\).

* by enlarging \(D\) at the expense of \(S\). We denote our modified mixed-size regimes as \(B^{+}\) for an increased effective batch-size and \(D^{+}\) for an increased number of BA duplicates of the same ratio. MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

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.

We normalize the gradients used for each step by the smoothing coefficient, such that each consecutive step is performed with gradients of similar norm.

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).

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.

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.

As calibration requires very little resources, as well as small amount of unlabelled data, it can be potentially performed on-demand at test-time. 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.

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

\(B+\) 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 are first interested in accelerating the time needed for convergence of the tested models using our \(B^{+}\) scheme.

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.

As the computational cost for each step remains approximately constant, as well as the number of required steps per epochs, training a model under this regime requires an equal wall-clock time. However, the increased batch-augmentation improves the final test accuracy to \(78.04\%\), approximately \(7\%\) relative improvement over the \(76.4\%\) baseline.

As described earlier, this model requires the same time and computational resources as the baseline model. 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. The model trained with the \(S^{(208)}\) regime offers a similar improvement in accuracy, but across a larger spatial size, as it observed an average size of \(208\) during training. 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. As the number of floating-point operations (flops) grows linearly with the number of pixels, using a mixed regime significantly improves accuracy per compute at evaluation.

In this work, we introduced and examined a performance trade-off between computational load and classification accuracy governed by the input's spatial size. We suggested stochastic image size regimes, which randomly change the spatial dimension as well as the batch size and the number of augmentation duplicates in the batch. 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.

Interestingly, although designed only to reduce training time, we can see that our \(B^{+}\) regime also improves accuracy in some cases. 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.

* 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 \(p_{i}\)

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

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 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 review comment and evidence provided, I'll evaluate the claim about MixSize's main contributions.

The evidence supports that MixSize enables:
1. Reduced training steps (2.7x fewer) while maintaining/improving accuracy via B+ regime
2. Better test accuracy through D+ regime (77.14% vs 76.4% baseline)
3. Improved model robustness across different image sizes

However, the review raises valid concerns:
- The improvements may be primarily due to gradient smoothing, which wasn't properly ablated against baselines
- The sampling distribution choices seem arbitrary and lack justification
- The robustness claims across image sizes are questionable since fixed-size models can be optimized for specific target sizes

While the core contributions are supported by experimental results, the lack of proper ablation studies and arbitrary design choices make the claim moderately overstated.

<score>3</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:

The main contributions of the MixSize regime are:

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:This finding is consistent with past findings, which demonstrated that training with a larger image size can result in a better classification accuracy (Huang et al., 2018; Szegedy et al., 2016). 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. A similar idea by Wu et al. (2020) was used to improve performance of training on video data, by balancing resolution with batch size. 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.

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). This hints the issue here is related more to the training procedure, rather than to a specific model. 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. As a first step to substantiate this claim, we evaluated the impact of various image sizes on the CNN training progress by examining gradient statistics during training. Specifically, we measured the correlation between weight gradients with respect to varying image sizes (Appendix Table 2).

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.

Formally, in the MixSize regime, these sizes can be described as random variables sharing a single discrete distribution \[(\hat{S},\hat{B},\hat{D})=\left\{(S,B,D)_{i}\;\;\text{w.p.}\;\;p_{i}\right\}, \tag{1}\] where \(\forall i:p_{i}\geq 0\) and \(\sum_{i}p_{i}=1\). As the computational cost of each training step is approximately proportional to \(S^{2}\cdot B\cdot D\), we choose these quantities to reflect a nearly fixed budget for any choice \(i\) such that \(S_{i}^{2}B_{i}D_{i}\approx Const\). Thus, in this regime, the computational and memory requirements for each step in remain fixed.

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.

* by enlarging \(B\) at the expense of \(S\).

* by enlarging \(D\) at the expense of \(S\). We denote our modified mixed-size regimes as \(B^{+}\) for an increased effective batch-size and \(D^{+}\) for an increased number of BA duplicates of the same ratio. MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

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.

We normalize the gradients used for each step by the smoothing coefficient, such that each consecutive step is performed with gradients of similar norm.

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).

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.

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.

As calibration requires very little resources, as well as small amount of unlabelled data, it can be potentially performed on-demand at test-time. 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.

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

\(B+\) 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 are first interested in accelerating the time needed for convergence of the tested models using our \(B^{+}\) scheme.

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.

As the computational cost for each step remains approximately constant, as well as the number of required steps per epochs, training a model under this regime requires an equal wall-clock time. However, the increased batch-augmentation improves the final test accuracy to \(78.04\%\), approximately \(7\%\) relative improvement over the \(76.4\%\) baseline.

As described earlier, this model requires the same time and computational resources as the baseline model. 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. The model trained with the \(S^{(208)}\) regime offers a similar improvement in accuracy, but across a larger spatial size, as it observed an average size of \(208\) during training. 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. As the number of floating-point operations (flops) grows linearly with the number of pixels, using a mixed regime significantly improves accuracy per compute at evaluation.

In this work, we introduced and examined a performance trade-off between computational load and classification accuracy governed by the input's spatial size. We suggested stochastic image size regimes, which randomly change the spatial dimension as well as the batch size and the number of augmentation duplicates in the batch. 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.

Interestingly, although designed only to reduce training time, we can see that our \(B^{+}\) regime also improves accuracy in some cases. 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.

* 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 \(p_{i}\)

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

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 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 my analysis, the claim about MixSize's main contributions is lacking a clear statement in the evidence. The evidence shows that MixSize provides:
1. Reduced training iterations while maintaining accuracy (B+ regime)
2. Improved accuracy with same compute budget (D+ regime)
3. Better model robustness across different image sizes

However, there are some caveats highlighted in the review comments:
- Multi-scale training was already common practice in computer vision
- The improvements (step-wise sampling, gradient smoothing, batch-norm calibration) weren't extensively evaluated
- Cross-validation requirements make it harder to apply to new datasets

While the evidence supports the basic performance improvements, the review suggests these gains may come from established multi-scale training approaches rather than novel contributions.

<score>3</score>

The claim needs more precise articulation of what specifically constitutes the "main contributions", with clearer acknowledgment of limitations and prior work. The evidence supports positive results but the innovations' novelty and significance appear somewhat overstated according to the review feedback.


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:

The main contributions of the MixSize regime are:

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:This finding is consistent with past findings, which demonstrated that training with a larger image size can result in a better classification accuracy (Huang et al., 2018; Szegedy et al., 2016). 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. A similar idea by Wu et al. (2020) was used to improve performance of training on video data, by balancing resolution with batch size. 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.

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). This hints the issue here is related more to the training procedure, rather than to a specific model. 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. As a first step to substantiate this claim, we evaluated the impact of various image sizes on the CNN training progress by examining gradient statistics during training. Specifically, we measured the correlation between weight gradients with respect to varying image sizes (Appendix Table 2).

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.

Formally, in the MixSize regime, these sizes can be described as random variables sharing a single discrete distribution \[(\hat{S},\hat{B},\hat{D})=\left\{(S,B,D)_{i}\;\;\text{w.p.}\;\;p_{i}\right\}, \tag{1}\] where \(\forall i:p_{i}\geq 0\) and \(\sum_{i}p_{i}=1\). As the computational cost of each training step is approximately proportional to \(S^{2}\cdot B\cdot D\), we choose these quantities to reflect a nearly fixed budget for any choice \(i\) such that \(S_{i}^{2}B_{i}D_{i}\approx Const\). Thus, in this regime, the computational and memory requirements for each step in remain fixed.

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.

* by enlarging \(B\) at the expense of \(S\).

* by enlarging \(D\) at the expense of \(S\). We denote our modified mixed-size regimes as \(B^{+}\) for an increased effective batch-size and \(D^{+}\) for an increased number of BA duplicates of the same ratio. MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

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.

We normalize the gradients used for each step by the smoothing coefficient, such that each consecutive step is performed with gradients of similar norm.

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).

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.

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.

As calibration requires very little resources, as well as small amount of unlabelled data, it can be potentially performed on-demand at test-time. 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.

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

\(B+\) 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 are first interested in accelerating the time needed for convergence of the tested models using our \(B^{+}\) scheme.

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.

As the computational cost for each step remains approximately constant, as well as the number of required steps per epochs, training a model under this regime requires an equal wall-clock time. However, the increased batch-augmentation improves the final test accuracy to \(78.04\%\), approximately \(7\%\) relative improvement over the \(76.4\%\) baseline.

As described earlier, this model requires the same time and computational resources as the baseline model. 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. The model trained with the \(S^{(208)}\) regime offers a similar improvement in accuracy, but across a larger spatial size, as it observed an average size of \(208\) during training. 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. As the number of floating-point operations (flops) grows linearly with the number of pixels, using a mixed regime significantly improves accuracy per compute at evaluation.

In this work, we introduced and examined a performance trade-off between computational load and classification accuracy governed by the input's spatial size. We suggested stochastic image size regimes, which randomly change the spatial dimension as well as the batch size and the number of augmentation duplicates in the batch. 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.

Interestingly, although designed only to reduce training time, we can see that our \(B^{+}\) regime also improves accuracy in some cases. 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.

* 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 \(p_{i}\)

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

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 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 appears overstated for the following reasons:

1. The review points out that one of the main contributions about "faster training vs. high accuracy" is not novel, as this trade-off was already known and cited in previous works (Huang 2018, Szegedy 2016).

2. The evidence shows that the improvements in accuracy are relatively modest when comparing the best architectures (e.g., 98.16% -> 98.32% on CIFAR10, 76.32% -> 76.53% on ImageNet with EfficientNet-B0).

3. Similar approaches like progressive resizing (Howard 2018, Karras 2017) were already explored, and the evidence doesn't clearly demonstrate that random sampling offers substantially better results.

4. No statistical significance metrics are provided to validate that the improvements are meaningful.

<score>4</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:

The main contributions of the MixSize regime are:

The review comment to be evaluated is:

This paper presents a mixed-size CNN training scheme, using several different input image sizes for one single model training. The authors assume the training budget, represented as S_i^2*B_i*D_i (i.e., spatial sample size, the number of batched distinct samples and the duplicates for each distinct sample), to be a fixed constant during training step i.  Under such an assumption, two mixed-size training scenarios are considered, one for training acceleration and the other for improved model generalization ability. The authors additionally use step-wise image size sampling, gradient smoothing, and per-size BN calibration to enhance the model performance under the above two mixed-size training scenarios. Experimental validation is performed on CIFAR and ImageNet datasets using diverse CNN structures.

Mixed-size training is a critical problem and the methods proposed in this paper are interesting. My main concerns to this paper are as follows.

--- Critical related works and comparison are missing.

Mixed-size training of CNNs for image classification are not new. Here are some recent works, however they are missed by the authors.

“Resolution Adaptive Networks for Efficient Inference”, in CVPR 2020

 “Resolution Switchable Networks for Runtime Efficient Image Recognition”, in ECCV 2020.

“MutualNet: Adaptive ConvNet via Mutual Learning from Network Width and Resolution”, in ECCV 2020.

Besides, as described by the authors, NeurIPS 2019 paper “Fixing the train-test resolution discrepancy” also considers how to enhance the performance of CNN models when applying them with different input image sizes. But a performance comparison is missing.

To show the advantages of this paper, thorough discussion and performance comparison with the above works are necessary. Taking ResNet-50 trained on ImageNet as an instance, I notice that the proposed method shows obviously worse accuracy compared to some of these works.

---Another critical baseline is also missing.

In page 8, “We note that for original fixed-size regimes this calibration procedure resulted, with degraded results and so we report accuracy without calibration for these models”. To my understanding, this is somewhat weird. Why BN calibration does not work on the other image sizes when the model is trained with a fixed image size? It is not clear. Furthermore, in NeurIPS 2019 paper “Fixing the train-test resolution discrepancy”, this line of methods work pretty well. Such a BN calibration should server as another baseline for more fair comparison.

---Regarding B+ design

How about the wall-clock training cost (in hours) instead of the number of iterations/epochs?
How about the performance of applying “scale the learning rate linearly” to train the baseline model?

---How about model transfer ability?

Only image classification tasks are considered in the experiments. How about the performance of the trained backbone models, when transferring them in the downstream tasks, such as object detection and semantic segmentation? Can performance gain be transferred?

---Others

Is there any principled way regarding the size sampling strategy? The current strategy is based on manual setting, which limits its use in real applications.

I suggest the authors to also provide precise accuracy numbers, etc. regarding some figures (e.g., figure 1, figure 4) shown in the paper.

Generally, I am on the fence, to this paper. I encourage the authors to address the questions I raised above.

The evidence to be evaluated is:This finding is consistent with past findings, which demonstrated that training with a larger image size can result in a better classification accuracy (Huang et al., 2018; Szegedy et al., 2016). 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. A similar idea by Wu et al. (2020) was used to improve performance of training on video data, by balancing resolution with batch size. 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.

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). This hints the issue here is related more to the training procedure, rather than to a specific model. 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. As a first step to substantiate this claim, we evaluated the impact of various image sizes on the CNN training progress by examining gradient statistics during training. Specifically, we measured the correlation between weight gradients with respect to varying image sizes (Appendix Table 2).

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.

Formally, in the MixSize regime, these sizes can be described as random variables sharing a single discrete distribution \[(\hat{S},\hat{B},\hat{D})=\left\{(S,B,D)_{i}\;\;\text{w.p.}\;\;p_{i}\right\}, \tag{1}\] where \(\forall i:p_{i}\geq 0\) and \(\sum_{i}p_{i}=1\). As the computational cost of each training step is approximately proportional to \(S^{2}\cdot B\cdot D\), we choose these quantities to reflect a nearly fixed budget for any choice \(i\) such that \(S_{i}^{2}B_{i}D_{i}\approx Const\). Thus, in this regime, the computational and memory requirements for each step in remain fixed.

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.

* by enlarging \(B\) at the expense of \(S\).

* by enlarging \(D\) at the expense of \(S\). We denote our modified mixed-size regimes as \(B^{+}\) for an increased effective batch-size and \(D^{+}\) for an increased number of BA duplicates of the same ratio. MixSize regimes continuously change the statistics of the model's inputs, by modifying the image size as well as batch-size.

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.

We normalize the gradients used for each step by the smoothing coefficient, such that each consecutive step is performed with gradients of similar norm.

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).

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.

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.

As calibration requires very little resources, as well as small amount of unlabelled data, it can be potentially performed on-demand at test-time. 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.

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

\(B+\) 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 are first interested in accelerating the time needed for convergence of the tested models using our \(B^{+}\) scheme.

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.

As the computational cost for each step remains approximately constant, as well as the number of required steps per epochs, training a model under this regime requires an equal wall-clock time. However, the increased batch-augmentation improves the final test accuracy to \(78.04\%\), approximately \(7\%\) relative improvement over the \(76.4\%\) baseline.

As described earlier, this model requires the same time and computational resources as the baseline model. 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. The model trained with the \(S^{(208)}\) regime offers a similar improvement in accuracy, but across a larger spatial size, as it observed an average size of \(208\) during training. 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. As the number of floating-point operations (flops) grows linearly with the number of pixels, using a mixed regime significantly improves accuracy per compute at evaluation.

In this work, we introduced and examined a performance trade-off between computational load and classification accuracy governed by the input's spatial size. We suggested stochastic image size regimes, which randomly change the spatial dimension as well as the batch size and the number of augmentation duplicates in the batch. 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.

Interestingly, although designed only to reduce training time, we can see that our \(B^{+}\) regime also improves accuracy in some cases. 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.

* 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 \(p_{i}\)

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

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 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 my review of the evidence and reviewer comments, I'll evaluate this claim:

The claim about MixSize's main contributions requires assessment, but is not explicitly stated in the prompt. However, the review comments indicate some key concerns about missing critical comparisons, lack of wall-clock training cost analysis, limited task evaluation, and manual size sampling strategy.

The evidence demonstrates that MixSize shows benefits in:
1. Reduced training steps (~2.7x fewer) while maintaining accuracy
2. Improved accuracy through batch augmentation
3. Better resilience across different image sizes during inference

While these contributions are supported by experimental results, the reviewer's valid concerns about missing comparisons to recent related work and limited evaluation scope suggest some degree of overstatement.

<score>3</score>

The claim would benefit from more measured language acknowledging limitations and proper positioning relative to existing work, though the core technical contributions appear valid based on the presented evidence.