Channel Normalization for Time Series Channel Identification

Weakness 1. PCN’s CID capability

Reviewer: I am not fully convinced that PCN provides CID capability. ~ I believe PCN is more of an extension of CN (i.e., an effective channel normalization method that does not provide CID) and should be discussed in the appendix.

Thank you for pointing this out. We acknowledge that PCN indeed does not provide CID capability, as PCN does not assign an identity to “individual channels” but rather to “channel clusters”.

PCN is specifically designed for scenarios encountering new channels in new datasets (common settings for foundation models), where channel identification becomes infeasible. Our proposed PCN address this challenge by assigning “channel cluster” identification via learnable prototypes as affine transformation parameters after normalization.

While the current manuscript presents PCN as an extension of CN in that it also provides a form of identity (to either channels or channel clusters), we recognize the reviewer's concern that it may require a relaxed version of CID for channel clusters. We will clarify this distinction in the revision.

 

Weakness 2. Missing notations

Reviewer: The variables used in Section 4 are not introduced. What are $B$, $C$, $D$, and $K$? It is difficult to understand the methods without looking at the source code.

Thank you for pointing this out. We found some of these definitions were missing.

$B$ represents the batch size, $C$ denotes the number of channels, $D$ is the hidden dimension, and $K$ refers to the number of prototypes.

To improve clarity, we will explicitly define $B$, $C$, $D$, and $K$ in Section 4 and also include them in the algorithm pseudocode.

 

 

If there are any unresolved issues, please feel free to discuss them with us!

Weakness 1. Miscolored Figure 1

Reviewer: "Figure 1: ~ producing different outputs (green) even with same inputs (yellow)." Maybe the colors are mispositioned.

Thank you for pointing that out. We will fix it in the revised version.

 

 

Question 1. Details about the performance of CN, ACN, PCN

Reviewer: I have a concern about the performance of CN, ACN, PCN. The authors should provide some details about the performance.

[PCN vs. CN/ACN]
If your concern is the comparison between PCN and CN/ACN, please refer to Table 5. Although PCN extends CN, it underperforms CN in the ”single”-task model, as PCN is intended for scenarios where the number of channels is unknown. As shown in Table 3, PCN is tailored for zero-shot scenarios and does not allocate parameters per channel but rather shares them across channels. For example, only PCN is applied in Table 4, as CN and ACN are not applicable to zero-shot scenarios. L324–326 (Right column) We attribute this to the fact that, unlike CN and ACN which assign each channel a distinct parameter, PCN assigns each prototype a distinct parameter,

 

[CN vs. ACN]
If your concern is the comparison between CN and ACN, ACN extends CN by incorporating local parameters that dynamically adapt based on the input TS, considering its dynamic nature (L20--23 (Left column)). As seen in Table 8, this enhancement improves performance while introducing only a negligible increase in computational complexity.

 

[Others]
Alternatively, if your inquiry pertains to any of the following, we provide the relevant information:

• a) Performance results:
  • [CN/ACN] Tables 2, 6, 7
  • [PCN] Tables 4, 5
• b) Interpretation of results: Section 5.1
• c) Experimental details:
  • [Datasets] Appendix A.1
  • [Settings] Appendix A.2

If this response does not fully address your concern, we would appreciate any further clarification or specific details you could provide.

 

 

Question 2. Initialization of parameters of CN, ACN, PCN

Reviewer: How do authors initialize the parameters of CN, ACN, PCN? How do the different initialization methods affect the metrics?

The initialization of the parameters for CN, ACN, and PCN is designed to ensure that no normalization occurs when learning has not yet taken place:

• The scale parameter ($\alpha$) is initialized to 1.
• The shift parameter ($\beta$) is initialized to 0.

This aligns with the default initialization used in PyTorch normalization layers:

• (Pytorch) Layer normalization initialization: https://github.com/pytorch/pytorch/blob/1eba9b3aa3c43f86f4a2c807ac8e12c4a7767340/torch/nn/modules/normalization.py#L210
• (Pytorch) Batch normalization initialization: https://github.com/pytorch/pytorch/blob/1eba9b3aa3c43f86f4a2c807ac8e12c4a7767340/torch/nn/modules/batchnorm.py#L93

Therefore, the parameters for CN, ACN, and PCN are initialized as follows:

• CN: $\alpha=1, \beta=0$

• ACN: $\alpha^{\text{G}}=1, \alpha^{\text{L}}=0, \beta^{\text{G}}=1, \beta^{\text{L}}=0$, so that $\alpha=1, \beta=0$

• PCN: $\alpha^{\text{P}}=1, \beta^{\text{P}}=0$

This initialization is documented in the Python files within /layers in the attached anonymous GitHub link.

We acknowledge that the explanation of initialization was omitted in the paper. As the reviewer pointed out, we will include this explanation in the revised version. Thank you for your feedback.

 

Additionally, after testing on four ETT datasets and running experiments three times with different random initialization seeds (using PyTorch's default nn.Parameter initialization), the effect on the average across four horizons was negligible, differing only at the fourth decimal place.

 

 

If there are any unresolved issues, please feel free to discuss them with us!

Suggestions 1. Explanation of Legends in Figures

Reviewer: "It would be helpful for readers to provide what different legend in different figures represent. For example, LN in Figure 5? Is that layer normalization? This needs to be clarified

Thank you for your feedback. Due to space limitations, commonly used terms such as Channel Normalization (CN) and Layer Normalization (LN) were not explicitly labeled in the legends. To ensure clearer understanding, we will add these clarifications in the revised version.

 

 

Question 1. [Figure 1] Confusing descriptions & Miscolored

Reviewer: The description in Figure 1 is very confusing. The outputs are supposed to be yellow, and the inputs are supposed to be green. no?

[Confusing descriptions]

Regarding the description in the figure, "Figure 1: Channel Identifiability" is intended to motivate the necessity of CID.

To illustrate this, we present two cases: “with CID” and “without CID”. Specifically, in the left panel, when the local inputs are identical (green), non-CID models fail to distinguish between channels, producing identical outputs (yellow). In contrast, in the right panel, applying our proposed CN introduces CID, such that even if the local inputs are the same (green), CID models distinguish between channels, producing different outputs (yellow).

We will revise and clarify them in the updated version. If there are still any confusing aspects regarding the figure, please feel free to ask us; we are happy to provide additional clarification.

 

[Miscolored]

Regarding the coloring mistake, we will fix the colors (green & yellow) in the revised version. Thank you for pointing that out!

 

 

Question 2. Negative (approximated) entropy

Reviewer: Why is the entropy values negative in Figure 5?

As the Gaussian entropy is approximated based on the data samples, the negative entropy values in Figure 5 emerge. Previous studies ([1]--[5]) have also adopted this approximation (as mentioned in L369--374), and, as seen in [5] Sequence Complementor (AAAI 2025), negative values are observed in Figure 2-(c), Figure 5, and Figure S.6.

 

[1] Ma, et al. "Segmentation of multivariate mixed data via lossy data coding and compression." TPAMI (2007)

[2] Yu, et al. "Learning diverse and discriminative representations via the principle of maximal coding rate reduction." NeurIPS (2020)

[3] Chen, et al. "Learning on Bandwidth Constrained Multi-Source Data with MIMOinspired DPP MAP Inference." IEEE Transactions on Machine Learning in Communications and Networking (2024)

[4] Chen, et al. "Rd-dpp: Rate-distortion theory meets determinantal point process to diversify learning data samples." WACV (2025)

[5] Chen, et al. "Sequence Complementor: Complementing Transformers For Time Series Forecasting with Learnable Sequences." AAAI (2025)

 

 

Question 3. Is $\hat{\alpha}_{b, c}^{L}$, a vector or a scalar?

Reviewer: Is $\hat{\alpha}_{b, c}^{L}$ a value or a vector in $d$? what dimension does it lie in (For equation 6)?

In the Equation (6),

• $\hat{S}_{b, c, i}$ is a scalar and

• $\alpha_i^{\mathrm{L}}$ (or $\alpha_{i,:}^{\mathrm{L}}$) is a $D$-dimensional vector,

resulting in a $D$-dimensional vector.

Thanks to the reviewer’s feedback, we found typos in line 6 of Algorithm 2,3: $\alpha_{b,c,d}$ should be the vector $\alpha_{b,c,:}$, not a scalar, and this also applies to the bias term $\beta_{b,c,d}$ in line 7.

We agree that this might be difficult to understand with the explanation around Algorithm 2, we will provide a more detailed description of the dimensions in the main text and correct the error.

 

 

Question 4. Missing notations

Reviewer: What are $B$, $D$ in Algorithm 1, text before equation 4. This is never clarified which makes things confusing for the end user

Thank you for pointing that out. We found some of these definitions were missing. $B$ and $D$ represent the "batch size" and the "number of channels", respectively.

To improve clarity, we will explicitly define them in Section 4 and also include them in the algorithm pseudocode.

 

 

If there are any unresolved issues, please feel free to discuss them with us!