💬 NLP

Verbal Confidence Saturation in 3-9B Open-Weight Instruction-Tuned LLMs: A Pre-Registered Psychometric Validity Screen

This study demonstrates that instruction-tuned open-weight LLMs in the 3-9B parameter range fail psychometric validity tests for verbalized confidence, showing extreme ceiling effects and a lack of correlation between verbalized certainty and actual accuracy or token-level logprobabilities.

Original authors: Jon-Paul Cacioli

Published 2026-04-27

📖 3 min read☕ Coffee break read

CC BY 4.0

Original authors: Jon-Paul Cacioli

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The "Overconfident Student" Problem: Why Your AI is Lying to You About How Sure It Is

Imagine you are a teacher grading a class of students. You ask them a series of difficult trivia questions. After each answer, you ask them: "On a scale of 1 to 100, how sure are you that you're right?"

You expect some students to say, "I'm 90% sure," and others to say, "I'm only 20% sure, I'm just guessing." This allows you to see who actually knows the material and who is just throwing darts in the dark.

This paper is about a group of "students" (small AI models) who have a very strange habit: No matter how hard the question is, they all shout, "I AM 100% SURE!"

The Core Discovery: The "Broken Thermometer"

The researcher, Jon-Paul Cacioli, tested seven different small AI models (the "students"). He wanted to see if their "confidence scores" actually meant anything. In science, if a tool can't tell the difference between a "hot" and "cold" situation, we call it invalid.

The results were startling:

The Ceiling Effect (The Broken Thermometer): Almost every model the researcher tested gave a confidence score of 95% or higher, regardless of whether they got the answer right or wrong. It’s like having a thermometer that only ever reads "100 degrees." It doesn't matter if you're in a freezer or a sauna; the thermometer just says "Hot!" This makes the score useless for telling if the AI is actually correct.
The "Multiple Choice" Disaster: The researcher tried to fix this by giving the AI a different way to express confidence (like a multiple-choice scale: No chance, Maybe, Almost certain). Instead of helping, this actually broke the AI's brain. The models became so confused by the new way of answering that they stopped answering the trivia questions correctly altogether.
The "Thinking Too Much" Paradox: In one specific model that "thinks" before it speaks (a reasoning model), the researcher found that the longer the AI spent "thinking," the less confident it sounded. It’s like a student who mumbles and hesitates for five minutes before finally saying, "I'm 100% sure!"

Why Does This Matter? (The "Safety" Problem)

You might think, "So what? If the AI is always confident, just look at its answer."

But in the real world, we want to use AI for important things—like medical advice, legal research, or driving cars. In those cases, we need the AI to say: "I don't know, I'm not sure, please ask a human."

If an AI is programmed to always sound 100% confident, it will never "abstain" or ask for help. It will confidently drive a car into a ditch or confidently give you the wrong dosage of medicine.

The Takeaway

The paper concludes that small AI models are currently "verbal liars." They might actually know they are wrong deep down in their digital "brains," but when you ask them how they feel, they can't communicate that uncertainty to you. They are stuck in a loop of extreme overconfidence.

The Lesson: Before we trust an AI to make big decisions based on its "confidence," we need to make sure it actually has a working "uncertainty sensor"—and right now, for these models, that sensor is broken.

Technical Summary: Verbal Confidence Saturation in 3–9B Open-Weight LLMs

Title: Verbal Confidence Saturation in 3–9B Open-Weight Instruction-Tuned LLMs: A Pre-Registered Psychometric Validity Screen
Author: Jon-Paul Cacioli
Date: April 2026

1. The Problem: The "Readout" Failure

While Large Language Models (LLMs) are frequently asked to verbalize their confidence (e.g., "I am 90% sure") to estimate uncertainty, there is a growing concern that this verbal signal does not accurately reflect the model's internal state. Current research suggests a "readout problem": even if a model "knows" it is wrong internally, the interface used to extract that information (the verbal output) may be broken.

Specifically, this paper investigates confidence saturation—a phenomenon where models provide near-ceiling confidence scores (e.g., 95–100%) regardless of whether their answer is correct or incorrect. If a signal is saturated, it cannot be used for downstream tasks like safety filtering, routing, or abstention, because it lacks the ability to discriminate between correct and incorrect responses.

2. Methodology

The study employed a rigorous, pre-registered psychometric approach to determine if verbal confidence meets the minimal requirements for Type-2 discrimination (the ability to distinguish correct from incorrect items).

Scope: Seven instruction-tuned open-weight models ranging from 3B to 9B parameters (including Llama 3, Mistral, Qwen 2.5, Gemma 2, and DeepSeek-R1-Distill).
Dataset: 524 items from the TriviaQA dataset, resulting in 8,384 deterministic trials.
Elicitation Formats:
- Numeric (NUM): Models were asked to provide a percentage from 0–100.
- Categorical (CAT): Models were asked to classify confidence into a 10-class ordinal scale.
Inference Settings: Greedy decoding (temperature = 0) on consumer-grade hardware to isolate the model's maximum-likelihood behavior.
Psychometric Validity Screen: Instead of simply measuring calibration (how close the number is to accuracy), the author applied a clinical-style validity protocol. This involves checking for degeneracy (where almost all responses fall into one category) and calculating indices like $L$ (probability of high confidence given an incorrect answer) and $F_p$ (probability of low confidence given a correct answer).

3. Key Results

The study confirmed several critical hypotheses:

Universal Saturation (H1 & H2): All seven instruction-tuned models failed the validity screen under numeric elicitation. The mean proportion of trials with confidence $\ge 95\%$ was 91.7%. Most models were classified as Invalid due to degeneracy (the signal was essentially a constant).
Failure of Categorical Rescue (H4): Switching to a categorical scale did not fix the problem. Instead, it caused an interaction failure: the categorical prompt disrupted the models' ability to answer the questions themselves, causing accuracy to plummet (in some cases to below 5%).
Independence from Logprobs (H5): Token-level log-probabilities (a common proxy for uncertainty) showed no usable predictive relationship with the verbalized confidence ( $R^2 < 0.01$ ).
Reasoning Contamination (E5): In the reasoning-distilled model (DeepSeek-R1), longer reasoning traces were strongly correlated with lower verbal confidence ( $\rho = -0.36$ ), suggesting that as the model "struggles" through a thought process, its verbalized confidence drops.
Internal vs. External Signal: Crucially, the study found that item difficulty did correlate with confidence ( $\rho = 0.50$ ), meaning the models do possess internal information about their uncertainty, but this information fails to survive the transition to the verbal output interface.

4. Key Contributions

Shift in Perspective: The paper argues that saturation should be treated as a validity failure (the signal is uninformative) rather than a calibration failure (the signal is just biased). You cannot "re-calibrate" a signal that has lost all variance.
Psychometric Framework: It introduces a formal, reproducible screening protocol (Appendix A) that researchers can use to validate uncertainty signals before deploying them in production.
Identification of the "Readout Problem": It provides empirical evidence that for the 3–9B parameter regime, the default interface for uncertainty (verbalization) is fundamentally broken under minimal prompting.

5. Significance and Implications

The findings serve as a warning for the AI deployment community. Any system that relies on an LLM's "self-reported" confidence to make high-stakes decisions (such as deciding whether to ask a human for help or whether a response is safe) is likely using a degenerate signal if the model is in the 3–9B parameter range.

The study concludes that psychometric screening must precede the use of verbal confidence signals. Researchers should not assume that because a model can say "I am 50% sure," it is actually capable of expressing nuanced uncertainty.