Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques

We would like to thank the reviewer for recognizing the strengths of our work with an acceptance rating.

Q1. Hyper-parameter Tuning.

We agree with the reviewer that hyperparameter tuning is important to achieve best performance. This is also true in the broader context of machine learning (ML). Most ML methods require some forms of hyperparameter tuning to achieve good performance. In our case, we adopt the hyperparameter tuning method from Design-Bench [1]. Specifically, we use the previously reported best hyperparameters for each baseline and only tune the additional hyperparameters introduced by the IGNITE regularizer. With a small set of hyperparameters, the tuning cost is not prohibitive.

[1] Gao, Chen, et al. "Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization." arXiv preprint arXiv:2202.08450 (2022).

Q2. Complexity Overhead of IGNITE.

To analyze the computational complexity of IGNITE, we break down the complexity of each step in Algorithm 1.

1. Initialization (Line 1):

   • Initializing $\omega^{(1)} \leftarrow \omega^{(0)}$ and $\lambda^{(1)} \leftarrow \lambda: O(1)$ each.

2. Main Loop (Line 2-12):

   • The loop runs for $T$ iterations. Thus, the complexity of the main loop will be multiplied by $T$.

3. Sampling (Line 3):

   • Sampling a batch $\mathcal{B} = \{(\mathbf{x}\_i, z\_i)\}\_{i=1}^m \sim \mathcal{D}$: $O(m)$.

4. Computing $\hat{z}_i$ (Line 4):

   • Evaluating the surrogate model $g(\mathbf{x}\_i; \omega^{(t)})$ for each $i \in [m]$. Assuming the surrogate model evaluation has a computational complexity of $C\_g = O(d)$ per sample where $d$ is the number of surrogate parameters, the total complexity is $O(m \cdot d)$.

5. Computing $g_1$ and $g_2$ (Line 5-6):

   • Computing gradients $\nabla\_\omega \ell (\hat{z}\_i, z\_i)$ and $\nabla\_\omega \hat{z}\_i$ have complexities $O(C\_\ell)$ and $O(C\_{\hat{z}})$ respectively per sample where $C\_\ell = C\_{\hat{z}} = O(d)$. Therefore, the total complexities are $O(m \cdot d)$.

6. Computing $\hat{\omega}$ (Line 7):

   • This involves simple vector operations with complexity $O(d)$, where $d$ is the dimensionality of $\omega$.

7. Computing $g_3$ (Line 8):

   • Similar to lines 4 and 6, involving evaluating the surrogate and gradient computations, with complexity $O(m \cdot C\_g + m \cdot C\_{\hat{z}}) = O(m \cdot d)$.

8. Computing $g^{(t)}$ (Line 9):

   • Vector operations involving addition and scalar multiplication with complexity $O(d)$.

9. Updating $\omega$ (Line 10):

   • Updating $\omega$ involves simple subtraction operations with complexity $O(d)$.

10. Updating $\lambda$ (Line 11):

    • Updating $\lambda$ is an $O(1)$ operation

Overall Complexity

Considering the above steps, the most computationally expensive parts are the gradient computations in lines 5, 6, and 8. Thus, the overall complexity per iteration is:

$O(2m \cdot C\_g + m \cdot C\_\ell + 2m \cdot C\_{\hat{z}})$

Since this loop runs for $T$ iterations, the total complexity is:

$O(T \cdot (2m \cdot C\_g + m \cdot C\_\ell + 2m \cdot C\_{\hat{z}}))$

Furthermore, we have the total complexity of the original baseline is:

$O(T \cdot (m \cdot C\_g + m \cdot C\_\ell))$

Thereby, IGNITE will include an additional complexity:

$O(T \cdot (m \cdot C\_g + 2m \cdot C\_{\hat{z}} )) = O(Tmd)$

where:

• $T$ is the number of iterations.

• $m$ is the batch size.

• $C\_g = O(d)$ is the complexity of evaluating the surrogate model.

• $C\_\ell = O(d)$ is the complexity of computing the loss gradient.

• $C\_{\hat{z}} = O(d)$ is the complexity of computing the gradient of the surrogate output with respect to its parameters.

• $d$ is the no. of surrogate parameters.

The empirical training time of the participating baselines with and without IGNITE is reported in the table below (see Table 1 in the PDF attached to our summary response). This is based on a NVIDIA RTX 3090 GPU with CUDA 11.8 system.

Q3. How to ensure convergence to an optima of the oracle?

We would like to emphasize that finding the optima of the oracle is an ill-posed task in the offline context since there might exist infinitely many functions that fit the offline data perfectly but will have different behaviors on the unseen input regions.

Instead, the ultimate goal of offline optimization is to focus the search on a safe region where the output prediction often does not change substantially across surrogate candidates. This can be achieved by finding surrogates with low sharpness. Their gradient will help shape a safe search region within which the surrogate optimum is close to the oracle’s local optimum (not necessarily a stationary point of the oracle). Our contribution here is to develop a rigorous framework to characterize and (provably) control the surrogate sharpness via a non-trivial adaptation of loss sharpness.

We would like to thank the reviewer for recognizing the strengths of our work with an acceptance rating.

Q1. How surrogate sharpness offers advantages over loss sharpness (SAM).

We will highlight below an important intuition on the key difference between a direct application of SAM and its non-trivial adaptation to control the surrogate sharpness (rather than its loss sharpness) in offline optimization.

The intuition is that minimizing the loss sharpness guarantees that on average, a single prediction at a randomly selected input in the OOD regime will have low error. However, such errors can accumulate along a gradient search process which results from multiple predictions on sequentially dependent inputs. Fortunately, our intuition in Figure 1 (as elaborated in lines 130-136) suggests that such error accumulation can be mitigated by controlling the surrogate sharpness. The idea is that with a sufficiently large perturbation radius, the oracle will be within the perturbation neighborhood. As surrogates with small sharpness will, by definition, not have their predictions changed substantially within its perturbation neighborhood (including the oracle), their optima will be close to those of the oracle.

As such, keeping the surrogate sharpness small while fitting it to the offline data will lessen the impact of error accumulation in the search phase. This is also verified via our empirical studies reported in Table 2 which compares the impact of using surrogate and loss sharpness on surrogate conditioning for offline optimization.

Q2. Is Assumption 2 strong?

We note that Assumption 2 can be satisfied for a class of surrogates established in Theorem 1 (see its proof in Appendix A). Since there exists an implementable surrogate formulation for which Assumption 2 holds, we believe it is not a strong assumption.

Q3. Complexity Overhead of IGNITE.

To analyze the computational complexity of IGNITE, we break down the complexity of each step in Algorithm 1.

1. Initialization (Line 1):

   • Initializing $\omega^{(1)} \leftarrow \omega^{(0)}$ and $\lambda^{(1)} \leftarrow \lambda: O(1)$ each.

2. Main Loop (Line 2-12):

   • The loop runs for $T$ iterations. Thus, the complexity of the main loop will be multiplied by $T$.

3. Sampling (Line 3):

   • Sampling a batch $\mathcal{B} = \{(\mathbf{x}\_i, z\_i)\}\_{i=1}^m \sim \mathcal{D}$: $O(m)$.

4. Computing $\hat{z}_i$ (Line 4):

   • Evaluating the surrogate model $g(\mathbf{x}\_i; \omega^{(t)})$ for each $i \in [m]$. Assuming the surrogate model evaluation has a computational complexity of $C\_g = O(d)$ per sample where $d$ is the number of surrogate parameters, the total complexity is $O(m \cdot d)$.

5. Computing $g_1$ and $g_2$ (Line 5-6):

   • Computing gradients $\nabla\_\omega \ell (\hat{z}\_i, z\_i)$ and $\nabla\_\omega \hat{z}\_i$ have complexities $O(C\_\ell)$ and $O(C\_{\hat{z}})$ respectively per sample where $C\_\ell = C\_{\hat{z}} = O(d)$. Therefore, the total complexities are $O(m \cdot d)$.

6. Computing $\hat{\omega}$ (Line 7):

   • This involves simple vector operations with complexity $O(d)$, where $d$ is the dimensionality of $\omega$.

7. Computing $g_3$ (Line 8):

   • Similar to lines 4 and 6, involving evaluating the surrogate and gradient computations, with complexity $O(m \cdot C\_g + m \cdot C\_{\hat{z}}) = O(m \cdot d)$.

8. Computing $g^{(t)}$ (Line 9):

   • Vector operations involving addition and scalar multiplication with complexity $O(d)$.

9. Updating $\omega$ (Line 10):

   • Updating $\omega$ involves simple subtraction operations with complexity $O(d)$.

10. Updating $\lambda$ (Line 11):

    • Updating $\lambda$ is an $O(1)$ operation

Overall Complexity

Considering the above steps, the most computationally expensive parts are the gradient computations in lines 5, 6, and 8. Thus, the overall complexity per iteration is:

$O(2m \cdot C\_g + m \cdot C\_\ell + 2m \cdot C\_{\hat{z}})$

Since this loop runs for $T$ iterations, the total complexity is:

$O(T \cdot (2m \cdot C\_g + m \cdot C\_\ell + 2m \cdot C\_{\hat{z}}))$

Furthermore, we have the total complexity of the original baseline is:

$O(T \cdot (m \cdot C\_g + m \cdot C\_\ell))$

Thereby, IGNITE will include an additional complexity:

$O(T \cdot (m \cdot C\_g + 2m \cdot C\_{\hat{z}} )) = O(Tmd)$

where:

• $T$ is the number of iterations.

• $m$ is the batch size.

• $C\_g = O(d)$ is the complexity of evaluating the surrogate model.

• $C\_\ell = O(d)$ is the complexity of computing the loss gradient.

• $C\_{\hat{z}} = O(d)$ is the complexity of computing the gradient of the surrogate output with respect to its parameters.

• $d$ is the no. of surrogate parameters.

The empirical training time of the participating baselines with and without IGNITE is reported in the table below (see Table 1 in the PDF attached to our summary response). This is based on a NVIDIA RTX 3090 GPU with CUDA 11.8 system.

Thank you for the rebuttal. all my concerns have been addressed by the authors. I've increased my score to support this paper to be accepted.

We would like to thank the reviewer for recognizing our contribution with an acceptance rating.

Q1.

A. More effective optimization techniques. We agree with the reviewer that an in-depth investigation of the specific structure of the objective could reveal a more effective optimization technique. We will explore this direction in a follow-up of the current work.

B. Convergence and effectiveness of optimization. According to our experiment, despite the use of a relatively simple BDMM to solve Eq. (12), we have achieved significant improvement in most cases. To demonstrate the convergence of the optimization algorithm, we have plotted the training loss and the sharpness value (plotting the $|| \nabla_\omega h(\omega) ||$ value) during the surrogate fitting process. This is based on an experiment using GA and REINFORCE baselines on Ant and Dkitty tasks. The results are illustrated in Figure 1 in the attached PDF of our summary response.

These results reveal that BDMM helps decrease both the training loss and sharpness value of the surrogate model during the training phase. This indicates that BDMM is effective and the optimization converges well in practice. Furthermore, our method, IGNITE, can be seamlessly integrated with other, more robust optimization techniques to solve Eq. (12).

Q2. Comparison in Table 1.

As explained in the paper, we excluded tasks known for their high inaccuracy and noise in oracle functions from prior works (ChEMBL, Hopper, and Superconductor), as well as those considered excessively expensive to evaluate (NAS). Nevertheless, for a more thorough comparison, we have conducted an experiment running the GA and REINFORCE baselines — with and without being regularized by IGNITE — in Superconductor and Chembl tasks. These results are shown in the table below (Table 3 in the attached PDF in our summary response)

The table illustrates that IGNITE also boosts the performance of baselines in noisy tasks. With more time and computation resources, we will conduct and include a thorough comparison of these tasks in the appendix.

Q3. Background Discussion.

We thank the reviewer for this suggestion. We will revise to include a more detailed description of the tasks and datasets. It will summarize the details of those datasets and tasks in Design-Bench [1]. We will include this information in the appendix.

[1] Gao, Chen, et al. "Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization." arXiv preprint arXiv:2202.08450 (2022).

We would like to thank the reviewer for recognizing the clarity and viability of our technical development. Your questions are addressed below.

Q1. Why the new notion of surrogate sharpness is better than loss sharpness?

To understand this, note that a surrogate that minimizes its loss sharpness might, on average, have a low prediction error for a single random input sampled from the OOD regime. However, offline optimization requires multiple predictions at consecutive inputs that occur during the gradient search process, where errors can accumulate and lead to suboptimal input candidates.

To mitigate such error accumulation, an alternative approach is to select a surrogate (from those that fit the offline data equally well) with low sharpness. We refer to this as surrogate sharpness. According to our intuition illustrated in Figure 1 and described in lines 130-136, the optima of surrogates with low sharpness tends to be closer to the oracle optima.

This means a well-controlled sharpness of the surrogate landscape (rather than its loss landscape) will help the corresponding gradient search accumulate less error. This is formalized in Eq. (5) which applies a low-sharpness constraint $\mathcal{R}\_\mathcal{X}(\omega) \leq \epsilon^{'}$ to the surrogate fitting loss. Solving Eq. (5) therefore requires upper-bounding $\mathcal{R}\_\mathcal{X}(\omega)$ with a tractable function — see Eq. (6) and Theorem 2.

Such insight is also confirmed via an empirical comparison between IGNITE and a direct application of SAM to minimize the loss sharpness of the surrogate. The reported results in Table 2 show a clear improvement of IGNITE over SAM, which confirms that controlling surrogate sharpness is more beneficial than minimizing loss sharpness.

Q2. More thorough comparison with SAM in Table 2.

We further run SAM with 2 other baselines BO-qEI and CbAS. In addition, we revise Table 2 by reporting the error interval as in the table below (see Table 4 in the PDF attached to our summary response):

The reported performance of the baselines in Table 2 shows that IGNITE surpasses SAM in terms of performance improvement over baselines across most tasks. It can also be observed that IGNITE in general has a smaller error interval than SAM.

Q3. Why does IGNITE still work on base optimizers with poor performance?

We note that each offline optimizer often comprises a predictor component (surrogate) and a search component that navigates the input space using the surrogate gradient to recommend a design candidate. The poor performance of an optimizer therefore does not mean its surrogate is not sufficiently proximal to the oracle. Instead, it is possible that the surrogate fits well on the offline data and is reasonably proximal to the oracle (though not perfect) but the search does not recognize well areas where the surrogate prediction is not reliable and gets misled into exploring more in those regions, resulting in sub-optimal performance. In such cases, our insight holds and IGNITE can still improve the surrogate by minimizing its surrogate sharpness. The improved surrogate is more reliable and will lessen the impact of the ineffective search as observed throughout Table 1.

We hope the reviewer would consider increasing the rating if our response above has sufficiently addressed all questions. We will be happy to discuss further if the reviewer has any follow-up questions. Thank you for the detailed feedback.

We would like to thank the reviewer for recognizing our contribution with an acceptance rating.

Q1. Introduction Improvement.

We would like to thank the reviewer for the suggestion. We will clearly emphasize the difference between surrogate sharpness and loss sharpness in the Introduction section. This will allow us to highlight an important intuition on the key difference between a direct application of SAM and its non-trivial adaptation to control the surrogate sharpness (rather than its loss sharpness) in offline optimization.

The intuition is that minimizing the loss sharpness guarantees that, on average, a single prediction at a randomly selected input in the OOD regime will have low error. However, such errors can accumulate along a gradient search process which results from multiple consecutive predictions. Fortunately, our intuition in Figure 1 (as elaborated in lines 130-136) suggests that such error accumulation can be mitigated by keeping the surrogate sharpness small during training. This is also verified via our empirical studies reported in Table 2. We will move Figure 1 to the Introduction to provide an earlier illustration of this insight.

Notation Clarification. We will also provide a more detailed explanation of $\delta$ and $\delta_\ast$ in the caption to avoid any confusion. Specifically, $\delta_\ast = \mathrm{argmax}_{||\delta||_2 \leq \rho} |\mathbb{E}[g(x; \omega + \delta)] - \mathbb{E}[g(x; \omega)]|$

Q2. More insightful discussion.

We will include a more insightful discussion in the revision. Concretely, we will emphasize the earlier intuition that instead of using a direct application of SAM to minimize the loss sharpness, we adapt SAM to select a surrogate (from those that fit the offline data equally well) with low sharpness.

According to our intuition illustrated in Figure 1 and described in lines 130-136, the optima of surrogates with low sharpness tends to be closer to the oracle optima. This means a well-controlled sharpness of the surrogate landscape (rather than its loss landscape) will help the corresponding gradient search accumulate less error.

This is formalized in Eq. (5) which applies a low-sharpness constraint $\mathcal{R}\_\mathcal{X} (\omega) \leq \epsilon^{'}$ to the surrogate fitting loss. Solving Eq. (5) therefore requires upper-bounding $\mathcal{R}_\mathcal{X}(\omega)$ with a tractable function — see Eq. (6) and Theorem 2.

As Theorem 2 depends on Assumptions 1 & 2, we put forward Theorem 1 to assert that both assumptions can be satisfied with implementable choices of the surrogate, indicating that those are not strong assumptions.

We will also improve the formatting of Eq. (16) for better readability.

Q3. Ablation studies.

Due to space constraints, we only presented ablation studies for a subset of the most important hyperparameters. We observed that the performance is less sensitive to changes in the others that were omitted from the ablation studies. In the revision, we will include a more comprehensive ablation study in the appendix and ensure that all previously unreferenced experimental results are appropriately referred to in the main text.

We would like to thank the reviewer for recognizing the strengths of our work with an acceptance rating.

Q1. Improving the introduction of SAM.

We appreciate the reviewer's insightful recommendation. We will cite the suggested works and discuss their impact on the development of SAM in our revision. We will also emphasize in the discussion that a key difference between such development and our work is that we provide a non-trivial adaptation of the proving technique in SAM to characterize and control the surrogate sharpness (rather than its loss sharpness). The intuition is that minimizing the loss sharpness guarantees that, on average, a single prediction at a randomly selected input in the OOD regime will have low error. However, such errors can accumulate along a gradient search process which results from multiple, consecutive predictions. Fortunately, our intuition in Figure 1 (as elaborated in lines 130-136) suggests that such error accumulation can be mitigated by controlling the surrogate sharpness. This is also verified via our empirical studies reported in Table 2 -- see also our response to Q1 of Reviewer xjU2.

Q2. Performance drop in Tables 4 and 5.

It is expected that the results for the 80th and 50th percentiles are less impressive than those for the 100th percentile. This is because the baseline methods are inevitably less effective at lower percentiles. As seen in Tables 4 and 5, the solutions for the 80th and 50th percentiles from the base methods often show minimal improvement over the empirical best.

Q3. Sharpness of objectives on unseen data before and after using IGNITE.

We conducted an experiment to compare the values of surrogate sharpness — $\rho || \nabla_\omega h(\omega) ||$ in Eq. (10) — with and without IGNITE. These surrogate sharpness values were computed on unseen data, which are design candidates found by the GA and REINFORCE baselines before and after being regularized with IGNITE. These are reported in the table below (Table 2 in the attached PDF in our summary response)

The reported results thus demonstrate that our method, IGNITE, helps decrease the sharpness of the surrogate model on unseen data (as expected).

We thank the reviewer for the detailed feedback. Your questions are addressed below.

Q1. Why not bounding $\mathcal{L}_\mathcal{X}(\omega)$ directly?

Bounding $\mathcal{L}\_\mathcal{X}(\omega)$ helps reduce the averaged prediction error in the OOD region but it does not guarantee such errors will not accumulate along consecutive predictions that guide the gradient-based optimization process. This could lead to substantial gaps between its recommended solutions and the true oracle optima.

To elaborate, $\mathcal{L}\_\mathcal{X}(\omega)$ can be bounded with a direct application of Sharpness-Aware Minimization (SAM) [1]. A surrogate that minimizes this bound might have on average a low (single) prediction error in OOD regions. However, offline optimization requires multiple predictions at consecutive inputs that occur during the gradient update process, where errors accumulate and mislead the gradient search toward suboptimal input candidates.

To mitigate this, our intuition in Fig. 1 (see lines 130-136) suggests that the optima of surrogates with low sharpness tend to be closer to the oracle optima. This means a low sharpness value of the surrogate landscape (rather than its loss landscape) will help the gradient search accumulate less error.

This is formulated in Eq. (5) which applies a low-sharpness constraint $\mathcal{R}\_\mathcal{X}(\omega) \leq \epsilon^{'}$ to the surrogate fitting loss. Solving Eq. (5) therefore requires upper-bounding $\mathcal{R}\_\mathcal{X}(\omega)$ with a tractable function — see Eq. (6). This insight is also supported by the empirical studies in Table 2.

[1] Sharpness-aware minimization for efficiently improving generalization. ArXiv:2010.01412.

Q2. Does the generalization over $\mathcal{R}\_\mathcal{X}(\omega)$ help to improve the generalization of $\mathcal{L}\_\mathcal{X}(\omega)$?

Following the response to Q1, bounding $\mathcal{L}\_\mathcal{X}(\omega)$ with SAM does not help mitigate the error accumulation along the gradient search. Hence, our approach does not aim to do this. Instead, we generalize over $\mathcal{R}\_\mathcal{X}(\omega)$ to solve Eq. (5) which is essential to prevent such error accumulation. Investigating whether generalizing over $\mathcal{R}\_\mathcal{X}(\omega)$ also improves generalization over $\mathcal{L}\_\mathcal{X}(\omega)$ is interesting but orthogonal to the scope of our work.

Q3. Is the bound tight?

Yes. When the no. of offline data points is sufficiently large, $\frac{\log n}{n}$ tends to zero and Eq. (6) or Eq. (16) in Theorem 2 reduces to $\frac{\mathcal{R}\_\mathcal{X}}{\mathcal{R}\_\mathcal{D}} \leq constant$. This depends only on properties of the surrogate, such as the boundedness of its gradient and the largest eigenvalue of its Hessian. Both can be made small via a theoretic choice of a surrogate whose gradient has a low Lipschitz constant (i.e., smooth).

Q3. Adding more details to proofs and Taylor’s remainder term in line 458.

We will present line 416 as a lemma in the revised paper. As for the question regarding the Taylor’s remainder in line 458: it is the second term in Eq. (65) which involves $\hat{\omega} = \omega + c\delta$, which is not eliminated. This is followed by the 1st-order Taylor expansion with an explicit characterization of the remainder term:

$h(\omega + \delta) - h(\omega) = \nabla\_\omega h(\omega)^T \delta + R\_1(\omega, \delta)$ where the remainder $R\_1 (\omega, \delta) = 1/2 \delta^T \nabla^2\_\omega h(\hat{\omega}) \delta$ with $\hat{\omega} = \omega + c\delta$.

For a quick reference, please refer to Eq. (4) in [1], and the 2nd equation in [2].

[1] https://sites.math.washington.edu/~folland/Math425/taylor2.pdf

[2] https://people.math.sc.edu/josephcf/Teaching/142/Files/Worksheets/Estimation%20of%20the%20Taylor%20Remainder.pdf

Q4. Is Assumption 2 strong?

Assumption 2 can be satisfied with a class of surrogates established in Theorem 1 (see its proof in Appendix A). Since there exists an implementable surrogate formulation for which Assumption 2 holds, we believe it is not a strong assumption.

Q5. Is the proposed method (IGNITE) robust?

The example that the reviewer pointed out – 6.5% gain over REINFORCE at the 100th percentile level, but a -4.6% at the 80th percentile level – does not pertain to our IGNITE method. Instead, it corresponds to a simpler version of our work (IGNITE-2) which is used to demonstrate the impact on performance if we use a manual choice for the Lagrangian parameter in Eq. (12). Our main method (IGNITE) uses BDMM to also optimize this Lagrangian parameter, leading to better and more stable performance than IGNITE-2. It can be observed that overall, IGNITE shows relatively high improvements over the baseline with very few cases of (very) slight performance decrease.

Q6. Complexity of IGNITE. According to Algorithm 1 and Appendix F on the effective computation of $\nabla\_\omega ||\nabla\_\omega h(\omega)||$, we provide a time complexity overhead for IGNITE below.

Complexity Analysis. Following our detailed complexity analysis in response to Reviewer qc6B, the complexity overhead of IGNITE is $O(Tmd)$ where:

• $T$ is the number of iterations.
• $m$ is the batch size.
• $d$ is the no. of surrogate parameters.

Running Time. We also report the running time of the participating baselines with and without IGNITE in Table 1 in the PDF attached to our summary response. This is based on a NVIDIA RTX 3090 GPU with CUDA 11.8 system. It can be observed that with IGNITE, the training time increases by 14.91% on average, which is an acceptable overhead in exchange for the significant performance gain. In terms of memory, we also observe that IGNITE incurs a negligible GPU memory overhead.

We hope the reviewer will consider increasing the rating if our response above has addressed all questions sufficiently. We are happy to discuss further if the reviewer has any follow-up questions for us.