📘 Overview

MultimodalMathGenerator is a data generation operator for automatically creating function plots (images) and corresponding math Question-Answer (QA) pairs.
It supports various function types (linear, quadratic, sine, exponential, etc.) and generates simple calculation problems or advanced conceptual problems based on the mode field (simple or complex) in the input data. This operator is suitable for educational applications, visual QA model training, and math reasoning evaluation.

---

🏗️ __init__ Function

def __init__(
    self,
    image_dir: str = "~/cache",
    seed: int | None = None
):
    ...

🧾 __init__ Parameters

Parameter	Type	Default	Description
image_dir	str	"~/cache"	Directory used to save the generated function plots
seed	int | None	None	Random seed to ensure reproducibility of generated results

---

⚡ run Function

def run(
    self,
    storage: DataFlowStorage,
    input_key: str = "mode",
):
    ...

The run function executes the main operator logic: it reads the data from storage, generates the corresponding function image and math QA pair based on the value in the input_key field for each row, and then horizontally concatenates the newly generated columns back to the original data.

---

🧾 run Parameters

Parameter	Type	Default	Description
storage	DataFlowStorage	-	Dataflow storage object (contains the rows to be processed)
input_key	str	"mode"	Field name for the mode column. Its value determines whether to generate a "simple" or "complex" problem.

---

🧠 Mode Description and Example Usage

📐 Mode Description

Mode	mode Column Value	Characteristics	Problem Type
Simple	"simple"	Basic function recognition and numerical substitution.	Given the function expression $f(x)$, find the function value $f(a)$ at $x=a$.
Complex	Other values (e.g., "complex")	Emphasizes mathematical analysis skills (derivatives, extrema, monotonicity).	Randomly generates questions on derivative sign, extreme points within an interval, or monotonicity judgment.

🧩 Example Usage (Requires an input file pre-populated with a mode column)

from dataflow.utils.storage import FileStorage
from dataflow.operators.core_math import MultimodalMathGenerator
import pandas as pd

# Step 1: Prepare an input file containing the 'mode' column (e.g., data/math_tasks.jsonl)
# Assuming data/math_tasks.jsonl contains:
# {"id": 1, "mode": "simple"}
# {"id": 2, "mode": "complex"}
# {"id": 3, "mode": "complex"}

storage = FileStorage(
    first_entry_file_name="data/math_tasks.jsonl",
    cache_path="./cache_local",
    file_name_prefix="math_out",
    cache_type="jsonl"
)
storage.step() # Load data

# Step 2: Initialize the operator
math_generator = MultimodalMathGenerator(
    image_dir="./math_plots",
    seed=42
)

# Step 3: Run the operator, generating problems based on the 'mode' column of each row
math_generator.run(
    storage=storage,
    input_key="mode" # Specify 'mode' column to control generation
)

---

🧾 Default Output Format

The operator will horizontally concatenate the following four fields onto the original input DataFrame:

Field	Type	Description
image_path	str	Local path where the function plot image is saved
question	str	Automatically generated mathematical question
answer	str	Answer
solution	str	Detailed solution steps and explanation

---

📥 Example Input

Note: The operator relies on the number of rows in the input storage and the value of the input_key column (defaults to mode) to generate data.

{"id": 1, "mode": "simple"}
{"id": 2, "mode": "complex"}

---

📤 Example Output (Simple Mode Row)

{
  "id": 1,
  "mode": "simple",
  "image_path": "./math_plots/plot_0.png",
  "question": "The function plot represents f(x) = x². What is the function value at x=3.5?",
  "answer": "12.25",
  "solution": "According to the function expression f(x) = x², substitute x=3.5 to get y=12.25."
}

---

📤 Example Output (Complex Mode Row)

{
  "id": 2,
  "mode": "complex",
  "image_path": "./math_plots/plot_1.png",
  "question": "The function plot represents f(x) = sin(x). Is the rate of change (derivative) at x=2.5 positive or negative?",
  "answer": "negative",
  "solution": "By observing the slope of the plot near x=2.5, the rate of change is negative."
}