---
title: 'Prioritize Complex Examples'
docname: 'complex_examples'
---

## Overview

Choose more complex examples (longer reasoning or more steps) to improve model performance. When no examples exist, sample multiple responses, pick the most complex few, and aggregate answers. This is Complexity-Based Consistency.

## Example

```php
<?php
require 'examples/boot.php';

use Cognesy\Instructor\StructuredOutput;

class ReasoningStep {
    public int $step;
    public string $subquestion;
    public string $procedure;
    public string $result;
}

class QAResponse {
    /** @var ReasoningStep[] */
    public array $reasoning;
    public int $correct_answer;
}

class ComplexityBasedConsistency {
    public function __invoke(string $query, string $context, int $samples = 5, int $topK = 3) : array {
        $responses = [];
        for ($i = 0; $i < $samples; $i++) {
            $responses[] = $this->generate($query, $context);
        }
        usort($responses, fn($a, $b) => count($b->reasoning) <=> count($a->reasoning));
        return array_slice($responses, 0, $topK);
    }

    private function generate(string $query, string $context) : QAResponse {
        $system = "You are an expert Question Answering system. Output structured reasoning steps before the final answer.";
        return (new StructuredOutput)->with(
            messages: [
                ['role' => 'system', 'content' => $system . "\n\nContext:\n{$context}\n\nQuery:\n{$query}"],
            ],
            responseModel: QAResponse::class,
        )->get();
    }
}

$query = 'How many loaves of bread did they have left?';
$context = <<<'CTX'
The bakers at the Beverly Hills Bakery baked 200 loaves of bread on Monday morning.
They sold 93 loaves in the morning and 39 loaves in the afternoon. A grocery store returned 6 unsold loaves.
CTX;

$selector = new ComplexityBasedConsistency();
$top = $selector($query, $context, samples: 5, topK: 3);

$counts = [];
foreach ($top as $r) { $a = (string)$r->correct_answer; $counts[$a] = ($counts[$a] ?? 0) + 1; }
$max = max($counts);
$finals = array_keys(array_filter($counts, fn($c) => $c === $max));
$final = $finals[array_rand($finals)];
dump($final);
?>
```

### References

1) Complexity-based prompting for multi-step reasoning (https://arxiv.org/pdf/2210.00720)
