Introduction to Content Entropy in Q&A Systems #ContentEntropy

In a previous blog post, we discussed the notion of entropy in the context of the 19th and 20th centuries.

In the 21st century, the concept of entropy has found its way into the realm of AI, Retrieval-Augmented Generation (RAG) systems, and Knowledge Bases.

As AI systems become increasingly complex and less deterministic, it has become necessary to treat them as intricate physical processes. This means that Content Entropy can be used to measure and quantify the relationship between content quality and RAG performance.

In this blog post, we introduce the concept of Content Entropy, a novel metric designed to quantify the quality of content for Retrieval-Augmented Generation services as well as for human users of Knowledge Bases.

The performance of RAG systems heavily depends on the quality of the input data, a concept often referred to as “Garbage In, Garbage Out” (GIGO). We use the concept of Content Entropy to formalize the notion of “garbage.”

Let’s examine some concrete examples to understand what Content Entropy is.

Both Information and Embedding entropy are not directly related to the quality of the content in the context of the RAG system.

This can happen for several reasons:

• Information and Embedding entropies do not take into account question-answer pairs.
• A question is a piece of information that is external to the content itself.
• Only by having questions is it possible to assess whether or not the content is fit to answer them.
• Content is messy only at the point you start to interact with it.
• Content changes over time.
• Content that used to be accurate can become outdated.
• Content can be edited and updated incorrectly.
• Content can be removed or archived.
• Questions change over time.
• With new challenges for businesses, new questions must be answered with Q/A systems.
• Knowledge bases are not always updated as soon as new types of questions arise.
• Answers change over time.
• What used to be the correct answer a year ago can be wrong today.
• What used to be acceptable in the 80s can expose oneself to legal liability today.

All of the above points to the necessity of evaluating the entropy of the content by measuring the performance of the RAG system built on top of it.

Note: By issues with the content in this context, the author means those issues that cannot be fixed by even an ideal Retriever and LLM in the RAG. A good example of this is outdated content. No matter how smart your LLM is, if you put information that is no longer true into its context — there is no way it will give you the correct answer. (Source)

Content starts to be good or bad only when you actually use it. In the case of RAG systems, the most obvious way to measure content quality is via Q/A pairs.

Let’s assume that:

• A|Q — a question-answer pair, where A is the answer for a given question Q.
• P(A|Q) — the probability of getting the correct answer for a given question.

Then we can define the entropy of the content as follows:

H(A|Q) = — Σ (P(A|Q) * log(P(A|Q)))

for all Q-A pairs

Where:

• H(A|Q) is the entropy of the answers given the questions.
• Σ denotes the sum over all Q-A pairs.
• P(A|Q) is the probability of getting the correct answer A for a given question Q.
• log(P(A|Q)) is the logarithm (usually base 2) of the probability P(A|Q).

This formula of entropy takes into account the performance of the RAG system by considering the probability of getting the correct answer for each question. The entropy will be:

• High when the probabilities of getting correct answers are low and evenly distributed across all Q-A pairs.
• Low when the probabilities of getting correct answers are high and concentrated on a few Q-A pairs.

In other words, a RAG system with high entropy indicates that it is struggling to provide correct answers consistently across different questions, while a RAG system with low entropy suggests that it is performing well and providing accurate answers for most questions.

By measuring the entropy of the Q/A system, we can assess the quality of the content in the context of its actual use case, which is more informative than relying on Information or Embedding entropy alone.

To give some intuition to Content Entropy, let’s investigate the following scenario:

Company XYZ is a delivery company that has a RAG-driven chatbot that answers users’ questions. All questions can be grouped by specific topics, such as:

• Delivery Schedule Questions: Well-established in the knowledge base and easy to find answers to related questions
• Reimbursement Questions: Same as above.
• New Offer Questions: This category represents questions related to a new business service that is not well-documented.

All the answers can be grouped by how correct they are:

• Correct: Answers that fully satisfy users.
• Partially Correct: Answers that somewhat satisfy users but lack some aspects.
• Wrong: Misleading answers that are simply incorrect.
• Can’t Answer: Answers that the chatbot is programmed to return for non-related questions, e.g., “I can’t answer your question since it’s out of the scope of my knowledge.”

Let’s first examine the most desired state of the content — when it’s in near-perfect order for the RAG system to produce correct answers for most of the questions.

Both question categories have high chances of being answered correctly.

If we check the graph, we see that the distribution of Q/A pairs is heavily skewed towards the Correct category. The entropy value is 1.66, which should be close to the minimal possible entropy value. This is how our RAG system should perform — most Answers for most of the Questions are correct.

To calculate the entropy for this case:

• Delivery Schedule: H(A|Q) = — (0.9 *log2(0.9) + 0.04 * log2(0.04) + 0.04 * log2(0.04) + 0.02 * log2(0.02)) ≈ 0.62
• Reimbursement: H(A|Q) = — (0.8 * log2(0.8) + 0.07 * log2(0.07) + 0.07 * log2(0.07) + 0.06 * log2(0.06)) ≈ 1.04

The sum entropy for both categories combined is: 0.62 + 1.04 ≈ 1.66

This low average entropy indicates that the RAG system is performing well, with a high probability of providing correct answers for both question categories.

In an ideal scenario, the entropy would be even lower, with the “Correct” category approaching 1 and the other categories approaching 0. However, in real-world applications, it is difficult to achieve perfect performance, and a low entropy value, as demonstrated in this case, is indicative of a well-functioning RAG system.

Let’s consider the situation when a company expands its business and provides a new offer to users but forgets to update the knowledge base with relevant information.

A new category of questions appears from a content perspective seemingly out of nowhere.

Most of the questions from the New Offer Questions category are either not answered or answered incorrectly.

In this case, we expect the entropy to rise and to see a significant number of questions in the “Can’t Answer” and “Wrong” categories on the graph.

The sum entropy for all three categories combined is: H=3.49

Indeed, after calculating the entropy for this case, it is higher than in the first ideal RAG setup (3.49 vs 1.66).

The higher entropy value indicates that the RAG system is struggling to provide accurate answers, particularly for the new question category. This suggests that the knowledge base needs to be updated with relevant information to improve the system’s performance.

The presence of a significant proportion of questions in the “Can’t Answer” and “Wrong” categories for the New Offer Questions category highlights the need for the company to invest in updating its content to better serve users’ inquiries related to the new business offering.

Next, let’s assume that some time has passed and the content related to Delivery Schedule Questions and Reimbursement Questions has become outdated.

On the chart, we can observe that the distribution of questions across answer groups has become more even.

This increase in entropy indicates that the RAG system’s performance has deteriorated due to outdated content. The higher entropy value suggests that the system is providing less accurate answers and is more uncertain about its responses across all question categories.

The more even distribution of questions across answer groups, as observed in the chart, is a visual representation of the increased entropy. This distribution implies that the system is struggling to provide correct answers consistently, and there is a higher proportion of partially correct, wrong, and unanswered questions.

Let’s push entropy to its maximum value and see what it means for RAG performance. This is equivalent to a real-world situation where the knowledge base of an organization does not receive any improvements and only becomes more and more messy over time. Imagine the organization pushes more and more new content, does not update or remove old, outdated content, and still can’t provide all the required content for new types of questions.

Theoretically, maximum entropy can be achieved if every category of question has the same probability of ending up in any of the answer categories.

When you ask a question, you can’t even understand if the answer is wrong because they all look the same.

On the chart, we’ll see a uniform distribution of questions across answer groups. This will correspond to the maximum entropy H = 6.

This maximum entropy case represents the worst-case scenario for a RAG system. The uniform distribution of questions across answer groups indicates that the system is unable to provide accurate answers consistently, and the quality of responses is essentially random.

In this situation, users would find it difficult to trust the RAG system’s answers, as they would be unable to distinguish between correct, partially correct, wrong, and unanswered questions. The system’s performance would be highly unreliable, and its usefulness would be severely diminished.

One downside of content entropy is that it can have a low value for a RAG system that returns incorrect answers. This can happen when the knowledge base has very little content, and most of the answers the chatbot gives end up in the “Can’t Answer” category.

Think of a rigid and small FAQ content that is able to answer only a very narrow and specific set of questions.

Since most of the answers are in the “Can’t Answer” category, entropy will also be low.

On the chart, it is represented by the distribution of Q/A pairs being heavily skewed towards the “Can’t Answer” category, and the entropy being similar to the optimal case (1.64 vs 1.66).

This low entropy negative case highlights a limitation of using content entropy as a sole measure of RAG system performance. While a low entropy value typically indicates good performance, it can also be misleading in situations where the system primarily responds with “Can’t Answer” due to limited content in the knowledge base.

In such cases, the RAG system may appear to perform well based on the low entropy value, but in reality, it fails to provide satisfactory answers to a large proportion of user questions.

To sum up, the RAG system with maximum entropy corresponds to the state of the content where it is the most unorganized, messy, confusing, and misleading.

Minimum entropy in the general case corresponds to the state of the content that is most organized and best fitted to be used in the Q/A RAG system.

As a corner case, it is possible to have low entropy content with bad RAG performance. This points to either:

• A very rigid Q/A system, or
• A lack of content

The maximum entropy state is what Knowledge Bases tend to collapse to — a state where the answer to every question is “It depends.”

Keeping entropy low means:

• Constantly updating content.
• Expanding content according to user questions.

To maintain a well-performing RAG system, it is crucial to:

• Regularly review and update existing content.
• Add new content based on the types of questions users are asking.
• Remove outdated or irrelevant information.

By actively managing the knowledge base and keeping entropy low, organizations can ensure that their RAG systems provide accurate, helpful, and timely answers to user queries. This improves user satisfaction and trust in the system, leading to better overall performance and a more successful implementation of the RAG system.

Content entropy is a fresh concept that presents a set of challenges that must be overcome before it can be effectively utilized in practice.

1. Large amount of Q/A pairs in reality

• Filtering out noise can be difficult
• Not all Q/A pairs are relevant or useful for measuring content entropy
• Identifying and removing irrelevant or low-quality Q/A pairs requires sophisticated techniques
• Classifying Q/A pairs into groups is challenging
• Developing a consistent and meaningful categorization scheme for Q/A pairs can be complex
• Automated classification methods may struggle with ambiguity and context-dependent questions
• Scalability issues arise when dealing with large datasets
• Processing and analyzing vast amounts of Q/A pairs can be computationally expensive
• Efficient algorithms and data structures are needed to handle real-world datasets

2. Multi-step conversations

• Some questions require follow-up interactions
• Initial questions may not provide enough information to generate a complete answer
• Follow-up questions and clarifications are necessary for a satisfactory user experience
• Measuring content entropy becomes more complex in multi-step conversations
• Entropy calculations need to consider the entire conversation flow
• The impact of follow-up questions on the overall entropy must be accounted for
• Designing evaluation metrics for multi-step conversations is challenging
• Traditional metrics like accuracy and F1 score may not capture the nuances of multi-step interactions
• New evaluation frameworks that consider the quality and coherence of the entire conversation are needed

3. Difficulty in assessing the correctness of questions and answers

• Evaluating the correctness of all answers is resource-intensive
• Manually reviewing every answer generated by the RAG system is time-consuming and expensive
• Automated evaluation methods may not always capture the nuances and context of the answers
• Human verification for all chatbot answers is impractical
• Scaling human verification to cover all generated answers is infeasible
• The cost and time required for human verification can be prohibitive
• Lack of reliable ground truth data makes evaluation challenging
• Obtaining high-quality, annotated datasets for evaluating answer correctness can be difficult
• Inconsistencies and disagreements among human annotators can introduce noise and ambiguity

4. Relative nature of content entropy

• A baseline is needed to interpret the meaning of content entropy values
• Content entropy values are relative and depend on the specific dataset and domain
• Establishing a reference point or benchmark is necessary to understand if a given entropy value is good or bad
• A single content entropy number provides limited insights
• Content entropy alone does not give a complete picture of the RAG system’s performance
• Additional metrics, such as accuracy, coverage, and user satisfaction, should be considered alongside entropy
• Monitoring changes in content entropy over time is crucial
• Tracking the evolution of content entropy can reveal trends and identify areas for improvement
• Regular monitoring allows for proactive management of the knowledge base and early detection of potential issues

Addressing these challenges requires a combination of advanced technical approaches, such as:

• Robust data preprocessing and filtering techniques
• Efficient algorithms for handling large-scale datasets
• Sophisticated evaluation frameworks that capture the nuances of multi-step conversations
• Hybrid evaluation approaches that combine automated metrics with human feedback
• Establishing domain-specific benchmarks and baselines for interpreting content entropy values
• Integrating content entropy with other performance metrics for a holistic view of the RAG system’s effectiveness

Content Entropy is a valuable and promising metric for evaluating the quality and effectiveness of content in Knowledge Bases and Retrieval-Augmented Generation (RAG) systems. By considering the interactions between questions and answers, Content Entropy provides unique insights into the state and performance of these systems that go beyond traditional metrics focused solely on the content itself.

One of the key strengths of Content Entropy is its applicability to both human-readable content and AI-driven question-answering systems. For Knowledge Base curators, Content Entropy offers a powerful tool to understand the overall health and organization of their content, identify areas for improvement, and track the impact of updates over time.

In the context of RAG systems, Content Entropy enables engineers to quantify the relationship between content quality and system performance, facilitating data-driven optimizations and enhancing the user experience.

Importantly, Content Entropy is intrinsically linked to the interactions with the content, namely the question-answer pairs. This focus on actual usage sets Content Entropy apart from metrics that attempt to evaluate content quality in isolation. By grounding the analysis in real-world interactions, Content Entropy captures the dynamic nature of knowledge and the evolving needs of users, providing a more meaningful and actionable assessment of content effectiveness.

While there are several challenges to overcome in the practical implementation of Content Entropy, such as handling large datasets, dealing with multi-step conversations, and establishing reliable evaluation frameworks, these challenges also represent significant opportunities for further research and development. As we continue to refine and expand the Content Entropy methodology, we can expect to gain an even deeper understanding of the complex dynamics between content, questions, and answers.

The potential impact of Content Entropy is vast, spanning across various domains where knowledge management and question-answering play a crucial role. From enhancing customer support chatbots to optimizing educational resources and improving search engine results, the insights provided by Content Entropy can drive innovation and shape the future of AI-driven information systems.

In conclusion, Content Entropy is a powerful and promising concept that opens up new avenues for evaluating and improving the quality of content in Knowledge Bases and RAG systems. By embracing the challenges and opportunities associated with this metric, we can unlock its full potential and pave the way for more effective, user-centric, and knowledge-driven systems. As we continue to explore and refine Content Entropy, we can look forward to a future where the quality and relevance of information are consistently high, empowering users and fostering innovation across industries.