Update README.md

README.md

@@ -11,6 +11,7 @@ size_categories:
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 # FineFineWeb: A Comprehensive Study on Fine-Grained Domain Web Corpus
 
+
 arXiv: Coming Soon
 
 Project Page: Coming Soon
@@ -143,19 +144,19 @@ The results above reveal the following observations:
 
 ## Domain-Domain Duplication
 
-Let \\(D_1,D_2,\dots,D_N)\\ represent $N$ distinct domains, where we select top-20 URLs for each domain $D_i$, denoted as $\{U_{i1}, U_{i2}, \dots, U_{i20}\}$,. The total set of URLs across all domains is represented as $\mathcal{U}$, and the total number of URLs is $M = |\mathcal{U}|$.
+Let \\(D_1, D_2, \dots, D_N\\) represent \\(N\\) distinct domains, where we select top-20 URLs for each domain \\(D_i\\), denoted as \\(\{U_{i1}, U_{i2}, \dots, U_{i20}\}\\),. The total set of URLs across all domains is represented as \\(\mathcal{U}\\), and the total number of URLs is \\(M = |\mathcal{U}|\\).
 
-For each URL $U_k \in \mathcal{U}$, the term frequency (TF) is defined as the proportion of $U_k$ in the total set of URLs:
+For each URL \\(U_k \in \mathcal{U}\\), the term frequency (TF) is defined as the proportion of \\(U_k\\) in the total set of URLs:
 
-$\text{TF}(U_k) = \frac{\text{count}(U_k)}{M}$
+\\(\text{TF}(U_k) = \frac{\text{count}(U_k)}{M}\\)
 
-where $\text{count}(U_k)$ is the number of times $U_k$ appears in $\mathcal{U}$. Additionally, the document frequency $K_k$ of $U_k$ is the number of domains in which $U_k$ appears. Based on this, the inverse document frequency (IDF) is calculated as:
+where \\(\text{count}(U_k)\\) is the number of times \\(U_k\\) appears in \\(\mathcal{U}\\). Additionally, the document frequency \\(K_k\\) of \\(U_k\\) is the number of domains in which \\(U_k\\) appears. Based on this, the inverse document frequency (IDF) is calculated as:
 
-$\text{IDF}(U_k) = \log(\frac{N}{K_k})$
+\\(\text{IDF}(U_k) = \log(\frac{N}{K_k})\\)
 
-The TF-IDF value for each URL $U_{ij}$ in a specific domain $D_i$ is then computed as:
+The TF-IDF value for each URL \\(U_{ij}\\) in a specific domain \\(D_i\\) is then computed as:
 
-$\text{TF-IDF}(U_{ij}) = \text{TF}(U_{ij}) \times \text{IDF}(U_{ij})$
+\\(\text{TF-IDF}(U_{ij}) = \text{TF}(U_{ij}) \times \text{IDF}(U_{ij})\\)
 
 ![domain-domain URL duplication](./assets/duplication.png)
 
@@ -165,7 +166,7 @@ As shown in the figure, most domains have low duplication rates, except for topi
 
 ## **Domain-Benchmark BPC-Acc Correlation**
 
-Experimental method: Using 28 models (see the paper), we first calculate BPC for all domains to obtain a model ranking $R_D$. Similarly, we compute scores across all benchmarks to obtain a model ranking $R_M$. We then calculate the Spearman correlation between $R_D$ and $R_M$.
+Experimental method: Using 28 models (see the paper), we first calculate BPC for all domains to obtain a model ranking \\(R_D\\). Similarly, we compute scores across all benchmarks to obtain a model ranking \\(R_M\\). We then calculate the Spearman correlation between \\(R_D\\) and \\(R_M\\).
 
 ![domain-benchmark BPC-Acc correlation](./assets/domain-benchmark%20correlation.png)
 
@@ -178,7 +179,7 @@ Experimental method: Using 28 models (see the paper), we first calculate BPC for
 @misc{
 title={FineFineWeb: A Comprehensive Study on Fine-grained Domain Web Corpus},
 url={[https://huggingface.co/datasets/m-a-p/FineFineWeb](https://huggingface.co/datasets/m-a-p/FineFineWeb)},
-author = {M-A-P, Ge Zhang*, Xinrun Du*, Zhimiao Yu*, Zili Wang*, Zekun Wang, Shuyue Guo, Tianyu Zheng, Kang Zhu, Jerry Liu, Shawn Yue, Binbin Liu, Zhongyuan Peng, Yifan Yao, Jack Yang, Ziming Li, Bingni Zhang, Wenhu Chen, Minghao Liu, Tianyu Liu, Xiaohuan Zhou, Yang Gao, Qian Liu, Taifeng Wang+, Wenhao Huang+},
+author = {M-A-P, Ge Zhang*, Xinrun Du*, Zhimiao Yu*, Zili Wang*, Zekun Wang, Shuyue Guo, Tianyu Zheng, Kang Zhu, Jerry Liu, Shawn Yue, Binbin Liu, Zhongyuan Peng, Yifan Yao, Jack Yang, Ziming Li, Bingni Zhang, Minghao Liu, Tianyu Liu, Yang Gao, Wenhu Chen, Xiaohuan Zhou, Qian Liu, Taifeng Wang+, Wenhao Huang+},
 publisher={huggingface},
 verision={v0.1.0},
 month={December},