Thank you for your additional comments. We acknowledge that there are some typos and unclear explanations in the equations presented in our paper. We will address them in this response and revise the manuscript accordingly.
**Response to 1 and 2. Notation $\odot$ and Dimension Mismatch in $\odot$ Operation**
As you suggested, we will explicitly state in the revised paper that the notation $\odot$ represents element-wise multiplication. Additionally, we want to clarify that we assume element-wise multiplication with broadcasting to a common shape, which functions exactly the same as in current deep learning frameworks. This means that in A $\odot$ B, the dimensions of A and B do not need to match exactly for the operation to proceed. For example, if A has dimensions $n \times m$ and B has dimensions $1 \times m$, B will be broadcasted to a common shape of $n \times m$ and then multiplied by A. Specifically, for the first dimension, the same value of B is multiplied by A. We will also clarify this broadcasting to a common shape in our revised paper.
**Response to 2 and 3. Clarification of Eq.(2)-(5)**
**Eq.(2):** This equation was adopted from the OneBit operation. To ensure compatibility with the subsequent equations, we will swap the row and column dimensions of $S_{in}$ and $S_{out}$. In the revised version, Eq. (2) will be expressed as $X [S_{in}^T \odot \text{Sign}(W^T_{FP}) \odot S_{out}] = [(X \odot S_{in})\text{Sign}(W^T_{FP})] \odot S_{out}$, where $S_{in}\in \mathbb{R}^{1 \times m}$, $S_{out}\in \mathbb{R}^{1 \times n}$.
**Eq.(3):** As you correctly pointed out, $W_R$ should have dimensions $m \times e$, but it was mistakenly written as $n \times e$. We will correct this in the revision.
**$S_{in}$ and $S_{out}$ of Eq.(4):** Given that $e$ scaling factors are used, the dimension of $S_{in}$ and $S_{out}$ should be $e \times m$ and $S_{out}$ as $e \times n$, respectively. We will clarify these dimensions in the revision. Meanwhile, as the dimension of $G$ is $k \times e$, the matrix multiplication in Eq. (4) between $G$ and $S_{in/out}$ is correct.
**Eq.(5):** As you mentioned, the transpose notation should be removed from $\hat{S_{in}}$ and $\hat{S_{out}}$. We will correct Eq. (5) in the revision to: $[(X \odot \hat{S_{in}})\text{Sign}(W^T_{FP})] \odot \hat{S_{out}}$.
We apologize for any confusion these equations may have caused. We will include clearer descriptions and correct typos in the final version of the paper.
Lastly, we would like to emphasize the major contribution of this work once again. We propose a new LLM binarization method called BinaryMoS. It introduces the concept of Mixture-of-Scale to adaptively generate scaling factors, thereby enhancing the representational power of binary models.
The accuracy evaluation results in our paper and the latency measurements provided in the global rebuttal demonstrate that the proposed method achieves state-of-the-art accuracy while maintaining the latency advantage of binary models.
We hope our response has clarified your concerns. Thank you again for your feedback.