Merge pull request #304 from stalkermustang/latex-formula-fix

fix formula in RAG

pages/applications/synthetic_rag.en.mdx

@@ -73,7 +73,7 @@ Image Source: [Dai et al. (2022)](https://arxiv.org/abs/2209.11755)
 
 It's crucial to handle manual annotation of examples responsibly. It's better to prepare more (for instance, 20), and randomly pick 2-8 of them to the prompt. This increases the diversity of generated data without significant time costs in annotation. However, these examples should be representative, correctly formatted, and even detail specifics such as the target query length or its tone. The more precise the examples and instructions, the better the synthetic data will be for training Retriever. Low-quality few-shot examples can negatively impact the resulting quality of the trained model.
 
-In most cases, using a more affordable model like ChatGPT is sufficient, as it performs well with unusual domains and languages other than English. Let's say, a prompt with instructions and 4-5 examples typically takes up 700 tokens (assuming each passage is no longer than 128 tokens due to Retriever constraints) and generation is 25 tokens. Thus, generating a synthetic dataset for a corpus of 50,000 documents for local model fine-tuning would cost: 50,000 * (700 * 0.001 * $0.0015 + 25 * 0.001 * $0.002) = $55, where $0.0015 and $0.002 are the cost per 1,000 tokens in the GPT-3.5 Turbo API. It's even possible to generate 2-4 query examples for the same document. However, often the benefits of further training are worth it, especially if you're using Retriever not for a general domain (like news retrieval in English) but for a specific one (like Czech laws, as mentioned).
+In most cases, using a more affordable model like ChatGPT is sufficient, as it performs well with unusual domains and languages other than English. Let's say, a prompt with instructions and 4-5 examples typically takes up 700 tokens (assuming each passage is no longer than 128 tokens due to Retriever constraints) and generation is 25 tokens. Thus, generating a synthetic dataset for a corpus of 50,000 documents for local model fine-tuning would cost: `50,000 * (700 * 0.001 * $0.0015 + 25 * 0.001 * $0.002) = 55`, where `$0.0015` and `$0.002` are the cost per 1,000 tokens in the GPT-3.5 Turbo API. It's even possible to generate 2-4 query examples for the same document. However, often the benefits of further training are worth it, especially if you're using Retriever not for a general domain (like news retrieval in English) but for a specific one (like Czech laws, as mentioned).
 
 The figure of 50,000 isn't random. In the research by [Dai et al. (2022)](https://arxiv.org/abs/2209.11755), it's stated that this is approximately the number of manually labeled data needed for a model to match the quality of one trained on synthetic data. Imagine having to gather at least 10,000 examples before launching your product! It would take no less than a month, and the labor costs would surely exceed a thousand dollars, much more than generating synthetic data and training a local Retriever Model. Now, with the technique you learned today, you can achieve double-digit metric growth in just a couple of days!