udgamlabs/udgam-probes

UDGAM LABS · Evaluation set · 2,000 exact-answer questions in 7 types

Udgam Probe Suite

2,000 short questions with one correct answer each, made by a program: addition, multiplication, unit conversion, number sequences, word problems, comparing two numbers, and syllogisms about made-up words. They separate language models of 90M to 400M parameters, where many public benchmarks sit close to chance. Because the items come from a generator, they were in nobody's training data before release, and new items or harder levels can be made at any time. The generator is included. Scoring a 100–400M-parameter model takes a few minutes on an Apple-silicon Mac.

Code: github.com/udgamlabs/udgam-evals · Companion test: Fresh Text, October 2026 · udgamlabs.com

Quick start

git clone https://github.com/udgamlabs/udgam-evals && cd udgam-evals
pip install -r requirements.txt
python probes/score.py HuggingFaceTB/SmolLM2-135M --out results/SmolLM2-135M.json

from datasets import load_dataset
ds = load_dataset("udgamlabs/udgam-probes", split="test")
print(ds[0])   # id, type, level, prompt, answer, choices

What is in it

Seven question types, three levels each (the levels describe how items are built, for example the number of digits), up to 100 items per level (a few easy levels have fewer distinct questions). Every prompt has the form Question: ...\nAnswer:.

Type	Items	Choices	Level 1 example	Level 3 example
add	300	4	What is 25 + 50?	What is 110,730 + 778,957?
mul	264	4	What is 8 × 7?	What is 62 × 90?
units	300	4	How many minutes are in 5 hours?	How many metres are in 12.2 kilometres?
sequence	236	4	What number comes next: 15, 21, 27, 33, 39, ?	What number comes next: 5, 8, 13, 20, 29, ?
word_problem	300	4	Chen has 12 apples and buys 6 more. How many apples does Chen have now?	Pens cost 4 dollars each. Kai buys 5 pens and pays with 35 dollars. How much change does Kai get, in dollars?
compare	300	2	Which number is larger, 22 or 37?	Which number is larger, 0.8 or 0.66?
syllogism	300	2	All blicks are wugs. All wugs are quams. Is every blick a quam? Answer Yes or No.	All zorps are snerks. All snerks are toves. All toves are daxs. Is every zorp a dax? Answer Yes or No.

For the five numeric types, the wrong choices are close to the right answer (off by 1, 2, 9, 10 or 100) or double it, so a model cannot pass by ruling out an implausible number.

How it is scored

For each item, the model computes the log-probability of each choice (written after a space) following the prompt, starting from its start-of-text (BOS) token when its tokenizer defines one. The choice with the highest summed log-probability is the model's answer. The score is the percentage of the 2,000 items answered correctly. Higher is better; chance is 32.5% (25% for the four-choice types, 50% for compare and syllogism).

Results

Accuracy (%), higher is better. Measured on 17 October 2026 on an Apple-silicon Mac (PyTorch, MPS, float32). Re-running probes/score.py on this dataset on 21 October 2026 gave SmolLM2-135M the same score.

Model	Parameters	All	add	mul	units	sequence	word problem	compare	syllogism
Falcon-H1-Tiny-90M-Base	90M	74.4	90.0	93.9	95.7	56.8	60.0	72.0	51.0
SmolLM2-360M	360M	71.2	81.3	85.6	90.3	80.9	57.0	49.3	57.3
Gargi-Base (Udgam Labs)	384M	69.2	80.0	84.8	90.0	57.2	50.7	67.0	54.0
Udgam-384M-Base-4K (Udgam Labs)	384M	61.9	65.7	75.4	88.7	41.5	41.7	57.3	60.3
SmolLM2-135M	135M	44.4	21.0	58.0	83.0	34.7	29.7	52.3	31.7
Chance		32.5	25	25	25	25	25	50	50

In a paired bootstrap over items, 95% intervals are about ±2 to ±3 points, and 9 of the 10 pairs of models differ significantly. The exception is SmolLM2-360M and Gargi-Base: 1.95 points apart, 95% interval [−0.35, +4.15]. The smallest model tested, Falcon-H1-Tiny-90M-Base, scores highest. Exact model revisions are listed in the GitHub README.

Why the two Udgam tests rank models differently. Falcon-H1-Tiny-90M-Base scores highest here but predicts fresh text worst of the five (0.981 bits per byte). The tests measure different things: bits per byte reflects how well a model predicts ordinary English prose, while these probes test a few numeric and logical skills, which need not go together. Falcon leads on five of the seven types (all but sequences, where SmolLM2-360M leads, and syllogisms, where Udgam-384M-Base-4K leads). We do not know Falcon's training data, so we do not claim a cause. Read the probe score as a measure of these skills, not of general ability.

How well each type separates models

Spread is the gap between the best and worst of the five models; noise is the average 95% interval half-width of one model's score on that type (from the number of items). A ratio well above 1 means the type separates these models reliably.

Type	Items	Spread (points)	Noise (± points)	Ratio
All	2,000	30.0	2.0	14.7
add	300	69.0	4.5	15.5
mul	264	36.0	4.5	8.0
sequence	236	46.2	6.0	7.7
word_problem	300	30.3	5.5	5.5
syllogism	300	28.7	5.5	5.2
compare	300	22.7	5.5	4.2
units	300	12.7	3.4	3.8

Levels are not a difficulty scale. Averaged over the five models, level 3 was harder than level 1 for multiplication (88.4% → 70.2%), sequences (58.8% → 39.4%), word problems (71.4% → 38.2%), syllogisms (68.0% → 49.6%) and comparison (60.8% → 56.4%), and the middle level often broke the order: geometric sequences (level 2, 82.8%) were the easiest sequence items and syllogisms of level 2, whose answer is always "No", the hardest (35.0%). For addition and unit conversion, level 3 was easier than level 1. Every model answered all 100 unit-conversion items of level 3 (kilometres to metres) correctly, so those items add no signal. We have not pinned down why; one guess is that the answer repeats the digits of the question (12.2 kilometres → 12,200), which a model can copy without converting. Report the overall score; use levels only to read where a model fails.

Where it falls short

• Narrow skills. Arithmetic, unit conversion, simple sequences, short word problems, comparisons and syllogisms of up to three steps. No world knowledge, reading comprehension, code or long reasoning.
• Likelihood, not generation. The test asks which of the given answers the model finds most likely. A model may pick the right choice and still fail to write it when asked to answer freely, or the reverse.
• Below-chance scores happen. SmolLM2-135M scores 21.0% on addition (chance 25%) and 31.7% on syllogisms (chance 50%): a model can systematically prefer some wrong answer strings. Read per-type scores with care and compare models on the overall score.
• Fixed phrasing. Each type uses one template. A model trained on text from this generator, or on similar templates, will score higher without being more capable. Now that the generator is public, be careful with models trained after October 2026, and make a fresh set with a new seed for important comparisons.
• Uneven levels and one saturated block. Levels do not reliably get harder, and unit conversion level 3 is solved by every model (see How well each type separates models). We kept the set as measured on 17 October 2026 so that published scores stay comparable; a future version can fix both.
• Number format. Numbers of 10,000 or more are written with commas and smaller ones without, so in a few items the choices differ in format as well as value (for example 5580 against 11,160).
• Two harder types are left out of the score. Weekday arithmetic ("If today is Monday, what day will it be in 30 days?") and ordering ("Ana is taller than Ben ... Who is the shortest?"): all five models we tested scored at or below chance on them (14.6% to 24.4% against 26.6%), so they cannot separate models of this size. The generator still makes them (--types frontier). A tenth type, letter counting, was dropped: small models' accuracy simply matched how often the right answer was "1".
• Measured on small models only. We have scored five models from 90M to 384M parameters. Larger models may come close to 100% on the easier levels; harder levels can be added to the generator.
• English only.

How it was made

generator/generate.py (in this repository and on GitHub) makes 10 question types × 3 levels × up to 100 items with a fixed random seed, removing duplicate prompts and any item whose answer also appears among the wrong choices. Some easy levels have fewer distinct questions (64 single-digit multiplications, 36 geometric sequences), which gives 2,000 items across the 7 types used for the score. The set was frozen on 17 October 2026. This command reproduces it exactly, including the order of the choices:

python generator/generate.py probes.jsonl --types core --per 100 --seed 2026

Fields

Field	Meaning
id	item id, pea-<type>-<level>-<index>
type	one of the 7 types above
level	difficulty, 1 to 3
prompt	the text given to the model, ending in Answer:
answer	the correct choice
choices	all choices, in a fixed shuffled order

Intended use

Comparing small pretrained (base) language models on basic numeric and logical skills; tracking a training run with a test on which small models are well above chance. Training on this set, or on the generator's output, would remove its value as a test.

Licence

The questions and answers are CC BY 4.0. The generator code is Apache-2.0.

Citation

@misc{udgamlabs2026probes,
  title        = {Udgam Probe Suite: procedurally generated exact-answer questions for small language models},
  author       = {Prasad, Jitesh K and {Udgam Labs}},
  year         = {2026},
  howpublished = {\url{https://huggingface.co/datasets/udgamlabs/udgam-probes}}
}

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About Udgam Labs. Udgam Labs is an independent AI research lab. We work from first principles: before we build, we understand why things work, whether we are training a model, fine-tuning one or applying AI to a new problem. Udgam (उद्गम) is Sanskrit for origin. udgamlabs.com