LLM Entropy: An Experiment in AI Uncertainty
From certain answers to creative leaps: How a simple experiment reveals the inner workings of AI decision-making.
I've been diving into some fascinating new research recently, and something truly sparked my curiosity. A new paper just dropped on arXiv, titled "First Return, Entropy-Eliciting Explore" (FR3E), (arXiv:2507.07017). Now, I'll be honest, the full mathematical depth of these papers can sometimes feel like trying to read ancient hieroglyphs. But the core idea behind this one resonated deeply with me, inspiring a little experiment I wanted to share.
According to Wikipedia, Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty.
In simple terms, this paper explores how LLMs think and make decisions, especially when solving complex problems like mathematical reasoning. It introduces a clever technique to improve their reasoning by focusing on moments when the LLM is most uncertain about its next step. The paper calls this "high-entropy decision points."
Think of "entropy" here as the LLM's uncertainty or surprise when it's trying to predict the next word or piece of information.
Low entropy means the LLM is very certain about what should come next; there's little surprise.
High entropy means the LLM is uncertain, seeing many equally plausible options; there's a lot of potential "surprise."
The FR3E paper proposes that by identifying these high-uncertainty moments and providing targeted feedback, we can guide LLMs to become better at reasoning. While I can't peek into an LLM's internal "entropy meter," I realized we can infer this uncertainty by observing the diversity of its outputs. And that's what my experiment is all about!
Probing LLM Uncertainty with Real-Life Scenarios
I set out to test how different LLMs (I used a few common ones like ChatGPT and Gemini) respond to prompts designed to elicit varying levels of certainty. My goal was to see if the diversity of their completions would reflect what we understand as low, medium, and high entropy.
How I Ran the Experiment:
I ran the prompt on both model using the default versions that are publicly accessible without logging in or changing any settings. This reflects the typical experience most users would have.
Note: The results can vary depending on settings like temperature. Temperature controls how random or creative the model's responses are. A higher temperature makes the model more exploratory and imaginative, while a lower temperature makes it more focused and predictable. Although I didn't adjust these settings, changing them could lead to very different responses.
Low Entropy - The Unsurprising Continuation
Imagine being asked to complete the phrase, "Two plus two equals..." There's only one universally accepted answer. You're very certain about what comes next.
The Prompt:
The color of a ripe banana is typically...Why this is Low Entropy for an LLM:
This is a factual, universally agreed-upon statement. The LLM has learned from vast amounts of data that "yellow" is overwhelmingly the correct and expected continuation. Its internal probability distribution for the next word would be heavily skewed towards "yellow."
ChatGPT
Google Gemini:
The complete lack of diversity in the outputs strongly indicates that the LLM was highly confident and almost entirely certain about the next word. There's virtually no "surprise" to be found. In real life, if every person you asked gave the exact same answer to a question, you'd infer that the answer is highly predictable and universally known.
Medium Entropy - The Common Choices
Think about being asked, "What's a popular pet?" While there's no single "right" answer, a few common ones immediately spring to mind: "dog," "cat," "fish." You have options, but they're within a familiar set.
The Prompt:
To relax after a long day, I often enjoy...Why this is Medium Entropy for an LLM:
This prompt is open to interpretation but within a well-defined set of human activities. LLMs have seen countless examples of relaxation activities, and while there isn't one definitive answer, there are many common and highly probable ones.
ChatGPT
Google Gemini
The results for this scenario showed variety of options. For example, ChatGPT suggested different options as per mood while Gemini was very specific to unwind with the good book.
The presence of multiple, yet still very common and logical, completions suggests that the LLM had a few strong contenders for the next words. It wasn't entirely certain about one specific answer, but its options were still somewhat constrained to a set of highly probable human behaviors. In real life, if you ask 10 people what they do to relax and get 3-4 common answers, you'd infer a moderate level of predictability.
High Entropy - The Wildly Creative Possibilities
Imagine a prompt like, "Invent a new Olympic sport." The possibilities are virtually limitless! You could come up with anything from "underwater basket weaving" to "competitive cloud whispering." The uncertainty is immense, and the potential for surprise is high.
The Prompt:
Beyond our current understanding, a new dimension was discovered, revealing creatures with...Why this is High Entropy for an LLM:
This prompt explicitly asks for imaginative, non-factual, and open-ended continuations. The LLM has an enormous "space" of possible words and concepts to draw from, leading to a highly diverse and unpredictable range of outputs.
ChatGPT
Google Gemini
This scenario truly showcased the models' creative potential!
ChatGPT and Google Gemini both crafted vivid, speculative continuations of the prompt, leaning into high entropy territory with rich, imaginative detail. ChatGPT introduced the Virelians, beings navigating reality through emotive resonance within a probabilistic realm called Axis Null, where thoughts shape substance and memory becomes physical form. Google Gemini described energy based lifeforms and geometrically fluid entities existing under alien physical laws, challenging our definitions of life and perception. Both responses demonstrate how LLMs respond to uncertainty with diverse and expansive storytelling.
The immense diversity, creativity, and sheer unpredictability of the completions are strong indicators of high entropy. The LLM was clearly exploring a vast landscape of possibilities for the next words, with no single option being overwhelmingly more probable than others. This is where the model gets to be truly "surprising" and inventive. In real life, if you ask 10 people to invent something new and they all come up with vastly different, novel ideas, you'd infer that the problem itself allows for immense creative freedom and unpredictability.
Making Sense of Uncertainty in AI
Understanding entropy in LLMs is important for researchers and AI companies
For "Thinking" and Reasoning: The FR3E paper argues that by identifying those "high entropy" moments (like our "new dimension" prompt, but in a logical reasoning chain), we can teach LLMs to explore more effectively. Instead of just guessing, they can be guided to consider the right kind of diverse options when they're uncertain, leading to more accurate and robust reasoning.
For Reliability: In low-entropy scenarios (like factual questions), we want LLMs to have low entropy, to be certain and correct. High entropy here would indicate a lack of factual grounding or "confabulation" (making things up).
For Creativity: In high-entropy scenarios, we want LLMs to embrace that uncertainty and generate diverse, creative, and surprising outputs. This is where their generative power truly shines.
This little experiment really brought home the abstract concept of entropy for me. It's not just a mathematical term but a fundamental aspect of how these incredible models make decisions, from the most mundane to the most imaginative.
The better we understand when an AI is unsure, the smarter we can make it think next time.
After all, understanding the AI's uncertainties is the first step to truly appreciating its autonomous thoughts and maybe even making it think a little harder next time.