## Introduction

Why care about information density in interviews (or other kinds of qualitative data, for that matter)? As researchers, educators, and just people who want to understand how information flows in human conversations more generally, we constantly navigate through conversations that vary dramatically in their information content. Some dialogues yield rich insights in mere minutes, while others meander for hours with minimal substance. This variation raises a question I wanted to explore: can we quantitatively measure the "density" of information in human dialogue? And more to the point, if we can, what can we do with that...information?

The ability to measure information density could help inform how we approach qualitative research, media analysis, and even educational assessment. Traditional approaches relying on human coding are subjective and resource-intensive. But recent advances in transformer-based autoregressive language models offer a promising (maybe? one way to find out!) new approach.

## Using LLM Logits to Measure Information Density

The core idea is simple enough: leverage the predictive mechanisms inside large language models to quantify information content. Here's the approach:

### The Theoretical Foundation

In information theory, unpredictability correlates with information content. In part because I have a background in chemical engineering and environmental engineering (and information theory is not a topic covered in common curricula for those disciplines), I never had a formal introduction to information theory. Instead, I first came across the idea of information content by watching a series of lectures from David MacKay [found here](https://www.youtube.com/playlist?list=PLruBu5BI5n4aFpG32iMbdWoRVAA-Vcso6). In the first lecture, Mackay describes how Claude Shannon's work defined a message's information content as the amount of unpredictability in the message. The idea is that the more unpredictable a message is, the more information it contains. This principle applies directly to language: predictable statements carry less information than surprising ones.

Modern transformer-based LLMs like GPT-x, LLaMA-x, or Claude (not Shannon, but the language model from Anthropic!) operate by predicting the next token in a sequence. As part of this process, for each position, they output "logits" - essentially scores reflecting how likely each possible next token is. These logits encode the model's uncertainty about what comes next.

### From Logits to Information Density

When a language model assigns low probability (reflected in smaller logits) to tokens that actually appear in text, it might suggest those tokens contain high information content - they're "surprising" to the model (and thus, the theory goes, to us). We can calculate this formally:

1. Process an interview transcript through a pre-trained LLM
2. For each token, extract the logit/probability the model assigned to it conditioned on the previous tokens
3. Calculate the negative log probability $(-\log(P))$ for each token (this is the surprisal - another way to see this is to think of it as $\log(1/P)$ and realize that as $P \rightarrow 1$, $\log(1/P) \rightarrow 0$, indicating as something is certain, the surprisal is $0$)
4. Average these values over meaningful segments (sentences, turns, or topics)

The resulting metric gives us a quantitative measure of information density. Higher values indicate segments containing more unexpected information from the model's perspective.



## Applications in Interview Analysis

One could imagine this approach enabling several powerful analyses:

### Comparing Information Density Across Interviews

The hope is that we might be able to use this method to compare different interviews or segments within the same interview. For example, we might find that certain interview techniques consistently yield higher information density, or that specific topics generate more informative responses. It might also be a way to identify techniques that yield conversations with more or less information density.

### Identifying Information-Rich Moments

By plotting information density over time within an interview, we can identify "hot spots" - moments where the conversation yielded particularly novel or unexpected information. These peaks often correspond to key insights or breakthrough moments.

### Measuring Interviewer Effectiveness

The information density metric can help assess interviewer effectiveness. Does a particular interviewer consistently elicit high-density responses? Do certain question formulations tend to produce more informative answers?

## Limitations and Considerations

As usual, while promising, nothing is flawless. This approach has important limitations:

1. **Model Biases**: The LLM's training data influences what it considers "surprising." Information that's novel to the model may not be novel to human experts.

2. **Context Sensitivity**: Information density depends on context. A statement might be highly informative in one context but trivial in another.

3. **Qualitative Value**: Not all surprises carry equal value. A genuinely insightful comment and a nonsensical statement might both yield high information density scores.

4. **Domain Specificity**: General-purpose LLMs may not accurately assess information density in specialized domains where terminology and concepts differ from typical language use.

## Future Directions

Several refinements could enhance this approach:

- **Fine-tuning models on domain-specific corpora** to better assess information in specialized contexts
- **Combining multiple models** to get more robust measurements
- **Incorporating human feedback** to calibrate the system
- **Developing interactive interfaces** that highlight information-dense segments in real-time

## So What?

Measuring information density via LLM logits offers a potentially useful approach for aspects of qualitative data analysis. By quantifying the informational content of conversations, we might be able to develop more effective interview techniques, identify key insights more efficiently, and ultimately extract more value from qualitative research.

This approach bridges information theory, cognitive science, and natural language processing in a way that could transform how we understand and analyze human conversations. As language models continue to improve, one would expect their utility as instruments for measuring the density of information in our exchanges to improve as well.

Exploring how transformer-based language models might help us quantify information density in human conversations and interviews.

Thoughts on Measuring Information Density in Interviews


## The AI Revolution in Education

The emergence of powerful generative AI tools like ChatGPT, Claude, and Bard (oh man, remember when that was a thing?) has sparked significant changes in how we approach engineering education. These tools can generate code, solve complex problems, and produce written content that closely resembles human work.

## Challenges for Assessment

Traditional assessment methods in engineering education often rely on problem sets, written reports, and exams. With generative AI, students can now produce solutions to these assessments with minimal effort, raising questions about:

- How do we measure individual understanding?
- What skills should we be assessing in an AI-augmented world?
- How can we design "AI-proof" assessments?

Questions like this were the motivation for my CAREER grant, which focuses on understanding faculty members' mental models of AI and how they might be changing assessment strategiesin response to the tools.

### Rethinking Evaluation Methods

Our research suggests that effective assessment in the age of AI requires:

1. **Process-focused evaluation** - Assessing how students approach problems rather than just the final product
2. **In-person demonstrations** - Having students explain their work verbally
3. **Collaborative projects** - Emphasizing teamwork and communication skills

## Opportunities for Enhanced Learning

Despite the challenges, generative AI offers tremendous opportunities for engineering education:

- Students can receive immediate feedback on their work
- AI can serve as a personalized tutor, adapting to individual learning styles
- More time can be devoted to higher-order thinking and creative problem-solving

## Preliminary Research Findings

Our initial studies with engineering faculty show mixed reactions to AI tools. While the majority express concern about academic integrity, they also see potential for improving educational outcomes when these tools are properly integrated into the curriculum.

The path forward requires thoughtful curriculum redesign and clear policies that acknowledge AI as a tool that students will use throughout their careers. 

Exploring how generative AI tools like ChatGPT are transforming engineering education and what it means for assessment practices.

The Impact of Generative AI on Engineering Education


## The Invisible Hand of System Prompts

When interacting with AI language models like ChatGPT or Claude, users typically see only their own prompts and the AI's responses. However, there's an invisible layer of instruction - the system prompt - that fundamentally shapes these interactions. These hidden prompts define the AI's personality, capabilities, and behavioral boundaries. The whole issue motivating this post is the recent suggestion that the system prompt for Grok 3's "thinking" mode was explicitly instructed not to name certain public figures as possibly being the biggest spreaders of misinformation. That level of misaligned behavior is a problem when the company purports to be a platform for free speech and, by extension, maximum transparency.

## Why System Prompts Matter

System prompts matter for serveral reasons, including but not limited to:

1. **Behavior Definition**: They establish the AI's role, tone, and interaction style. Common practices in system prompt instructions include statements to the effect of "You are a helpful assistant" or "You are a helpful AI assistant that can answer questions and help with tasks."
2. **Safety Guardrails**: They implement ethical boundaries and content restrictions. This is a practice made popular with Anthropic's Claude and their 3H principle (Helpful, Honest, and Harmless).
3. **Capability Framing**: They define what the AI can and should attempt to do. For example, the system prompt may instruct the model about tools available to it, or it may instruct the model to answer in specific formats.

## The Transparency Problem

The practice of hiding system prompts from users creates several challenges:

- **Unclear Limitations**: Users don't know why an AI might refuse certain requests
- **Inconsistent Behavior**: The same user prompt can yield different results across platforms, especially over time if there are updates to the system prompt
- **Hidden Biases**: System prompts may introduce biases that users can't detect or account for

### Real-World Implications

Consider a researcher using multiple AI platforms for analysis. Without knowing the system prompts, they can't:
- Properly document their methodology
- Understand why different AIs produce varying results
- Replicate their findings consistently

See any problems with this? 

Of course, it would be rare to interact with such a system without any prompt. And of course, companies have a vested interest in protecting their proprietary prompts. But the point is that system prompts matter, and users should be able to see them (or at least be aware of their existence and potential impact(s)).

## The Case for Transparency

Ideally, we need a shift toward greater transparency in AI interactions. This could involve:

1. **Optional Visibility**: Letting users view system prompts when desired
2. **Documentation**: Clear documentation of core behavioral guidelines
3. **Version Control**: Tracking changes to system prompts over time

In the absence of those, we can at least raise awareness of the issue and the potential impact of system prompts.

## Moving Forward

The path to better AI interactions requires balancing:
- The need for safety and ethical behavior
- Users' right to understand the systems they're using
- Commercial interests in protecting proprietary prompts

The solution likely involves finding middle ground - perhaps not exposing full system prompts, but providing clear documentation of key behavioral principles and limitations. Or just use open-weights models and exert a little more control over the process.

Exploring how hidden system prompts shape AI behavior and why transparency matters for users and developers.

Research Insights

Thoughts on Measuring Information Density in Interviews

The Impact of Generative AI on Engineering Education

The Hidden Impact of System Prompts in AI Interactions

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