ArithMark 2.0 is a procedurally generated benchmark for evaluating integer arithmetic ability in language models. Each item is formatted as a continuation-style multiple-choice problem: the model sees an arithmetic expression ending in = and must assign the highest likelihood to the correct numeric continuation.

The benchmark is designed for base-model log-likelihood scoring. It does not require instruction following, chain-of-thought, or generated explanations. Random chance is 25%.

The included script benchmark_arithmark-2.0.py can be used to run the benchmark.

Baseline Results

The following results use raw continuation log-likelihood scoring on the 2,500-example ArithMark 2.0 set. Random chance is 25%.

Model	Parameters	Overall	1 Op	2 Ops	3 Ops
Qwen/Qwen2.5-Math-1.5B	1.54B	82.08%	97.44%	77.87%	50.00%
Qwen/Qwen2.5-3B	3.09B	78.44%	95.52%	71.47%	46.20%
Qwen/Qwen2.5-1.5B	1.54B	77.72%	97.12%	69.47%	41.60%
Qwen/Qwen2.5-Coder-1.5B	1.54B	74.88%	94.96%	65.73%	38.40%
HuggingFaceTB/SmolLM2-1.7B	1.71B	66.12%	89.36%	49.33%	33.20%
Qwen/Qwen2.5-0.5B	494M	63.04%	82.96%	49.87%	33.00%
facebook/MobileLLM-R1-140M-base	140M	53.88%	62.16%	51.47%	36.80%
EleutherAI/pythia-2.8b	2.78B	36.72%	34.48%	44.93%	30.00%
HuggingFaceTB/SmolLM2-135M	135M	33.48%	36.32%	33.87%	25.80%
AxiomicLabs/GPT-X2-125M	125M	30.72%	28.88%	36.00%	27.40%
AxiomicLabs/GPT-X-125M	125M	30.16%	27.92%	35.20%	28.20%
openai-community/gpt2-xl	1.56B	29.92%	29.84%	35.20%	22.20%
HuggingFaceTB/SmolLM-135M	135M	28.96%	28.40%	31.47%	26.60%
AxiomicLabs/GPT-S-5M	5.2M	27.24%	26.32%	30.00%	25.40%
SupraLabs/Supra-50M-Base	52M	27.12%	26.08%	31.60%	23.00%
EleutherAI/pythia-31m	30M	27.04%	26.16%	31.60%	22.40%
EleutherAI/pythia-14m	14M	27.04%	25.04%	31.87%	24.80%
CompactAI-O/Shard-1	55M	26.92%	26.00%	29.20%	25.80%
google/gemma-3-270m	268M	26.84%	25.76%	30.40%	24.20%
openai-community/gpt2	124M	26.52%	24.80%	31.33%	23.60%
openai-community/gpt2-medium	355M	26.48%	24.96%	30.67%	24.00%
EleutherAI/gpt-neo-125m	125M	26.36%	27.28%	27.87%	21.80%
HuggingFaceTB/nanowhale-100m-base	110M	25.52%	23.68%	27.20%	27.60%
EleutherAI/pythia-70m	70M	25.40%	24.48%	26.80%	25.60%
EleutherAI/pythia-160m	162M	25.32%	25.44%	26.93%	22.60%
LH-Tech-AI/Spark-5M-Base-v4	5.0M	25.04%	25.04%	27.33%	21.60%
Harley-ml/Dillion-1.2M	1.3M	24.92%	24.56%	27.47%	22.00%
facebook/opt-125m	125M	24.68%	24.56%	26.67%	22.00%
CompactAI-O/Glint-1.3	982k	24.68%	24.48%	24.13%	26.00%
SupraLabs/Supra-Mini-v5-8M	7.9M	24.40%	24.48%	25.73%	22.20%
SupraLabs/Supra-Mini-v4-2M	2.6M	24.08%	23.04%	27.47%	21.60%

Task Format

Each example contains a context and four possible continuations:

(16 / 4) + 44 =

{
  "ctx": "(16 / 4) + 44 =",
  "endings": [" 52", " 53", " 68", " 48"],
  "label": "3"
}

The endings include leading spaces and no trailing punctuation. Evaluation should score the raw log-likelihood of each full continuation and select the highest-scoring option.

Dataset

File:

arithmark_2.0.jsonl

Size:

2,500 examples

Answer labels are exactly balanced:

Label	Count
0	625
1	625
2	625
3	625

Difficulty Mix

Difficulty	Count
easy	1,250
medium	750
hard	500

By operator count:

Operator Count	Count
1	1,250
2	750
3	500

Topic Mix

Topic	Count
addition	538
subtraction	438
mixed_two_ops	395
parentheses_two_ops	355
parentheses_three_ops	258
mixed_three_ops	242
multiplication	144
division	130

Parentheses:

Has Parentheses	Count
false	1,887
true	613

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Total file size:

1.77 MB