"""Multi-step arithmetic — chained computation primitive. Tests the model's ability to perform sequential arithmetic operations, a prerequisite for GSM8k-style math reasoning. Categories: - two_step: "3 + 4, then multiply by 2" → "14" - three_step: "Start with 10, subtract 3, then multiply by 4" → "28" All operands and results are small positive integers (≤200) to keep the task about *chaining* rather than large-number arithmetic. Format (ICL): Input: 3 + 4, then multiply by 2 Output: 14 """ import random from typing import Dict, List, Any from tasks.base_task import BaseTask, TaskConfig class MultistepArithmeticTask(BaseTask): """Multi-step (chained) arithmetic task.""" TASK_NAME = "multistep_arithmetic" CATEGORY_DATA: Dict[str, List[Dict[str, str]]] = { "two_step": [ {"input": "3 + 4, then multiply by 2", "output": "14"}, {"input": "10 - 3, then add 5", "output": "12"}, {"input": "6 * 3, then subtract 8", "output": "10"}, {"input": "20 / 4, then add 7", "output": "12"}, {"input": "8 + 7, then divide by 3", "output": "5"}, {"input": "5 * 5, then subtract 10", "output": "15"}, {"input": "9 - 2, then multiply by 4", "output": "28"}, {"input": "12 / 3, then add 11", "output": "15"}, {"input": "7 + 8, then subtract 6", "output": "9"}, {"input": "4 * 6, then divide by 8", "output": "3"}, {"input": "15 - 9, then multiply by 5", "output": "30"}, {"input": "18 / 6, then add 9", "output": "12"}, {"input": "2 + 13, then divide by 5", "output": "3"}, {"input": "11 * 2, then subtract 14", "output": "8"}, {"input": "16 - 7, then multiply by 3", "output": "27"}, {"input": "30 / 5, then add 4", "output": "10"}, {"input": "8 + 2, then multiply by 7", "output": "70"}, {"input": "14 - 6, then divide by 2", "output": "4"}, {"input": "3 * 9, then subtract 17", "output": "10"}, {"input": "24 / 8, then add 6", "output": "9"}, ], "three_step": [ {"input": "Start with 10, subtract 3, then multiply by 4", "output": "28"}, {"input": "Start with 2, add 6, then divide by 4", "output": "2"}, {"input": "Start with 5, multiply by 3, then subtract 7", "output": "8"}, {"input": "Start with 20, divide by 5, then add 8", "output": "12"}, {"input": "Start with 3, add 9, then multiply by 2", "output": "24"}, {"input": "Start with 18, subtract 6, then divide by 3", "output": "4"}, {"input": "Start with 4, multiply by 5, then subtract 11", "output": "9"}, {"input": "Start with 15, divide by 3, then add 10", "output": "15"}, {"input": "Start with 7, add 5, then divide by 6", "output": "2"}, {"input": "Start with 8, multiply by 4, then subtract 20", "output": "12"}, {"input": "Start with 30, divide by 6, then multiply by 3", "output": "15"}, {"input": "Start with 1, add 11, then divide by 4", "output": "3"}, {"input": "Start with 9, subtract 4, then multiply by 6", "output": "30"}, {"input": "Start with 16, divide by 2, then add 7", "output": "15"}, {"input": "Start with 6, multiply by 7, then subtract 32", "output": "10"}, {"input": "Start with 25, subtract 10, then divide by 5", "output": "3"}, {"input": "Start with 11, add 4, then multiply by 2", "output": "30"}, {"input": "Start with 36, divide by 9, then add 5", "output": "9"}, {"input": "Start with 3, multiply by 8, then subtract 14", "output": "10"}, {"input": "Start with 14, subtract 8, then multiply by 5", "output": "30"}, ], } CATEGORY_DEMOS: Dict[str, List[str]] = { "two_step": [ "Input: 5 + 3, then multiply by 4\nOutput: 32", "Input: 12 - 4, then add 3\nOutput: 11", "Input: 7 * 2, then subtract 5\nOutput: 9", "Input: 20 / 5, then add 2\nOutput: 6", "Input: 9 + 1, then divide by 2\nOutput: 5", ], "three_step": [ "Input: Start with 6, add 4, then multiply by 3\nOutput: 30", "Input: Start with 12, subtract 2, then divide by 5\nOutput: 2", "Input: Start with 4, multiply by 3, then add 8\nOutput: 20", "Input: Start with 24, divide by 6, then subtract 1\nOutput: 3", "Input: Start with 7, add 3, then divide by 2\nOutput: 5", ], } def __init__(self, config: TaskConfig): super().__init__(config) def _load_data(self): import pandas as pd if self.config.in_memory_data: self.data = pd.DataFrame(self.config.in_memory_data) return rows: List[Dict[str, str]] = [] for category, examples in self.CATEGORY_DATA.items(): for ex in examples: rows.append({ "input": ex["input"], "output": ex["output"], "category_name": category, }) self.data = pd.DataFrame(rows) def build_prompt(self, instance: Dict[str, Any], num_shots: int = 5) -> str: category = instance.get("category_name", "two_step") demos = self.CATEGORY_DEMOS.get(category, []) inst_input = instance.get("input", "") demos = [d for d in demos if inst_input not in d][:num_shots] prompt = "" for d in demos: prompt += d + "\n\n" prompt += f"Input: {inst_input}\nOutput:" return prompt def _extract_number(self, text: str) -> str: """Extract the first number (integer) from model output.""" import re text = text.strip() match = re.search(r'-?\d+', text) return match.group() if match else text def evaluate(self, predictions: List[str], split: str = "test", **kwargs) -> Dict[str, float]: ground_truth = self.get_ground_truth(split) task_data = self.get_split(split) if len(predictions) != len(ground_truth): raise ValueError( f"Prediction count ({len(predictions)}) != ground truth ({len(ground_truth)})" ) processed = [self._extract_number(self.preprocess_prediction(p)) for p in predictions] correct = sum( 1 for p, g in zip(processed, ground_truth) if p.strip() == g.strip() ) results: Dict[str, Any] = { "accuracy": correct / len(ground_truth), "correct": correct, "total": len(ground_truth), } cat_stats: Dict[str, Dict[str, int]] = {} for p, g, item in zip(processed, ground_truth, task_data): cat = item.get("category_name", "unknown") cat_stats.setdefault(cat, {"correct": 0, "total": 0}) cat_stats[cat]["total"] += 1 if p.strip() == g.strip(): cat_stats[cat]["correct"] += 1 for cat, s in cat_stats.items(): results[f"accuracy_{cat}"] = s["correct"] / s["total"] return results def get_ground_truth(self, split: str = "test") -> List[str]: rows = self.get_split(split) return [str(r.get("output", "")) for r in rows] def create_multistep_arithmetic_task( category: str = None, name: str = "multistep_arithmetic", ) -> MultistepArithmeticTask: """Create a MultistepArithmeticTask, optionally filtered to one category.""" data = None if category and category in MultistepArithmeticTask.CATEGORY_DATA: data = [ {**ex, "category_name": category} for ex in MultistepArithmeticTask.CATEGORY_DATA[category] ] name = f"multistep_arithmetic:{category}" config = TaskConfig( name=name, description="Multi-step chained arithmetic", data_format="memory", in_memory_data=data, input_column="input", output_column="output", evaluation_metrics=["accuracy"], metadata={"task_type": "multistep_arithmetic", "category": category}, ) return MultistepArithmeticTask(config)