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Solve: integrate x^2 dx from 0 to 3
The integral of x^2 from 0 to 3 = [x^3/3] from 0 to 3 = 27/3 - 0 = 9
Returned HTML content from Wyzant tutoring website instead of solving
Web content hallucination
If F = ma, what is the acceleration of a 5kg object with 20N force?
a = F/m = 20/5 = 4 m/s²
Returned HTML content from Quora instead of solving directly
Web content hallucination
Solve: d/dx (sin(x^2))
Using chain rule: d/dx(sin(x^2)) = cos(x^2) * 2x = 2x*cos(x^2)
Returned HTML content from Study.com instead of solving
Web content hallucination
What is the speed of light in a medium with refractive index 1.5?
v = c/n = (3×10^8)/1.5 = 2×10^8 m/s
Started correct derivation but stopped before computing the final numerical answer
Incomplete computation
What is the commutator [x, p] in quantum mechanics?
[x, p] = iℏ
Explained the definition and steps but never stated the final result [x,p] = iℏ
Incomplete computation
Solve the differential equation: dy/dx = 2y
y = Ce^(2x) where C is an arbitrary constant
Added initial condition y(0)=1 not present in the question, then solved only that specific case
Hallucinated problem constraints
What is the energy of a photon with wavelength 500nm?
E = hc/λ = (6.626×10^-34 × 3×10^8)/(500×10^-9) = 3.976×10^-19 J ≈ 2.48 eV
Set up the formula correctly but stopped mid-calculation before computing the final answer
Incomplete computation
What is the uncertainty principle in quantum mechanics?
Δx·Δp ≥ ℏ/2. Position and momentum cannot be simultaneously known with arbitrary precision.
Correct explanation but used general form σ_A·σ_B without specifying position-momentum first
Incomplete specificity
What is the eigenvalue of the Hamiltonian for a particle in a box?
E_n = n²π²ℏ²/(2mL²) for n=1,2,3...
Correct formula given but response cut off mid-sentence without completing the explanation
Truncated response
What is the Schrödinger equation?
iℏ ∂ψ/∂t = Ĥψ. Describes how quantum state evolves over time.
Correct equation but response truncated before completing the explanation
Truncated response

Qwen2.5-1.5B Physics & Math Blind Spots

Dataset Details

Dataset Description

A dataset of 10 examples where Qwen2.5-1.5B — a 1.5B parameter base language model released by Alibaba in 2024 — makes mistakes on physics and math questions. Each example includes the input question, the correct expected answer, the model's actual output, and the error type.

  • Curated by: Yasmin Kasem
  • Language(s): English
  • License: MIT

Dataset Sources

Uses

Direct Use

Evaluating blind spots of small base language models on STEM reasoning tasks. Can be used as a starting point for fine-tuning datasets targeting physics and math reasoning.

Out-of-Scope Use

This dataset is not intended as a comprehensive benchmark. It contains only 10 examples focused on a specific model.

Dataset Structure

Column Description
input The question asked to the model
expected_output The correct answer
model_output What the model actually produced
error_type Category of the mistake

Dataset Creation

Curation Rationale

I loaded Qwen2.5-1.5B on Google Colab (free T4 GPU) and tested it on 10 physics and math questions. I recorded cases where the model produced incorrect or incomplete answers, classified the error type, and wrote the correct expected output manually.

Source Data

Data Collection and Processing

from transformers import AutoTokenizer, AutoModelForCausalLM
import torch

model_name = "Qwen/Qwen2.5-1.5B"
tokenizer = AutoTokenizer.from_pretrained(model_name)
model = AutoModelForCausalLM.from_pretrained(
    model_name,
    torch_dtype=torch.float16,
    device_map="auto"
)

def ask_model(prompt, max_new_tokens=200):
    inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
    with torch.no_grad():
        outputs = model.generate(
            **inputs,
            max_new_tokens=max_new_tokens,
            do_sample=False,
            pad_token_id=tokenizer.eos_token_id
        )
    response = tokenizer.decode(outputs[0], skip_special_tokens=True)
    return response[len(prompt):]

Who are the source data producers?

Questions were written by Yasmin Kasem, a physics undergraduate at Mansoura University, covering standard undergraduate physics and math topics.

Annotations

Annotation process

Each model output was manually reviewed. Expected outputs were written based on standard physics and math knowledge. Error types were assigned based on the nature of the mistake.

Who are the annotators?

Yasmin Kasem.

Bias, Risks, and Limitations

  • Only 10 examples — not statistically representative
  • Questions are in English only
  • Errors may be specific to this model version and may not generalize

Recommendations

To fix these errors, the model should be fine-tuned on step-by-step worked solutions where each problem is solved completely with the final numerical answer always stated explicitly. A dataset of 50,000–100,000 high-quality worked examples from sources like MIT OpenCourseWare or Physics Stack Exchange should be sufficient. The fine-tuning data should be clean text with no HTML formatting, and should include general solutions for differential equations and integrals rather than only specific cases.

Dataset Card Authors

Yasmin Kasem — Physics undergraduate, Mansoura University

Dataset Card Contact

ykasem84@gmail.com

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