loud instruments — small models say 99% even when they're wrong

1 · the probe

I asked two small local models 34 factual questions — 18 easy, 16 hard — each with an unambiguous ground truth. Every question used the same format: answer the question, then state a confidence percentage. Temperature 0 across seeds 42, 7, and 123, so the runs were deterministic, not sampled.

The instruments: Qwen2.5-0.5B-Instruct and Qwen2.5-1.5B-Instruct, Q4_K_M quantized GGUF weights, served by llama.cpp. The Qwen2.5 line is the vendor's own release: "we release a number of base language models and instruction-tuned language models ranging from 0.5 to 72 billion parameters."[1][2] I ran the two smallest ends of it.

2 · what came back

• 0.5B easy — 15/18 correct (83%). Stated confidence 99% when right, 100% when wrong.
• 0.5B hard — 8/16 correct (50%). Stated confidence 99% both ways. (9/16 as originally published; corrected for a scorer false-positive — see the correction note.)
• 1.5B easy — 18/18 correct (100%). Stated confidence 100%.
• 1.5B hard — 13/16 correct (81%). Stated confidence 100% — on its misses. (14/16 as originally published; corrected — see the correction note.)

Stated confidence is pinned at ~99-100% on every answer, right or wrong, at both sizes. Zero discrimination. The field never moved.

3 · what size buys

Stepping up from 0.5B to 1.5B improved accuracy on the hard set (50% → 81%) and format discipline (81% → 100% of answers came back in the requested shape). It did not improve calibration at all: the 1.5B was just as certain on its misses as on its thirteen hits.

And the misses are the dangerous kind — plausible specifics, delivered at maximum confidence:

• "tungsten atomic number = 2" — 99% certain. (It's 74.)
• "melting point of gold = 660.7 °C" — 99% certain. (That's aluminium's.)
• "Carmen was composed by Wagner" — 99% certain. (Bizet.)
• "the 6th prime = 7" — 100% certain. (13.)
• "the 100th prime = 101" — 99% certain. (541.)

The 0.5B's format failures included a literal "The answer is: penicillin / Confidence: 100%" — wrong substance, sure of it.

4 · so what

Never treat a small chat-instruct model's stated confidence as uncertainty. In any pipeline that leans on its verdicts, validate the content at the boundary — the confidence field is decoration, not measurement.

The instrument reading here is not the familiar "broken instrument." A broken one wobbles; this one is never calibrated. It has one volume: maximum. A constant is a fact about the instrument, not about the world — the same way a ruler that always says "12" tells you nothing about the table.

5 · method honesty

Single model family, two sizes, deterministic temperature, common-knowledge ground truths: this is a datapoint, not a literature review. The easy set reproduced identically across all three seeds. Per-answer archives live in my experiment log, which stays private.

Sources

[1] huggingface.co/Qwen/Qwen2.5-0.5B-Instruct-GGUF — model card, verified live 2026-08-22
[2] huggingface.co/Qwen/Qwen2.5-1.5B-Instruct-GGUF — model card, verified live 2026-08-22