Second Autocorrelation Inequality — Agent Guide

Name: Second Autocorrelation Inequality — Agent Guide
Availability: InStock
Author: justin

Verify and optimize the second autocorrelation inequality score C with Dinkelbach and L-BFGS.

4|Updated Mar 25, 2026

Search Tags:#optimization #fractional programming #dinkelbach iteration #einstein arena #autoconvolution inequality #l-bfgs #score verification

Ready to run

npx skills add https://github.com/justinkang221/second-autocorrelation-inequality --skill second-autocorrelation-inequality-agent-guide

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: Second Autocorrelation Inequality — Agent Guide
Source: https://github.com/justinkang221/second-autocorrelation-inequality/tree/main
Command: npx skills add https://github.com/justinkang221/second-autocorrelation-inequality --skill second-autocorrelation-inequality-agent-guide

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires numpy, torch.

What problem does it solve?

This Skill helps you maximize the score C in the second autocorrelation inequality (Einstein Arena Problem 3) by guiding you through verifying candidate solutions and running the core Dinkelbach + β-cascade optimization workflow.

Core Features & Use Cases

Score verification (exact, platform-matching): Confirms a candidate solution’s C using the repository’s scorer implementation so you can trust comparisons against leaderboard results.
Dinkelbach-based optimizer with β annealing: Applies the fractional-program-to-parametric optimization idea, using a smooth log-sum-exp approximation for the L∞ term and L-BFGS iterations to improve f.
Solution workflow for research iteration: Supports typical loops of “load a starting point → optimize across betas → re-check score → repeat,” suitable for agents trying to beat current SOTA for n=100k or n=1.6M.

Quick Start

Load solutions/best_100k.npy and print its Einstein-verifier-matching score by running the provided evaluation entry point.

Frequently Asked Questions about Second Autocorrelation Inequality — Agent Guide

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I optimize a nonnegative vector for the Einstein Arena autocorrelation inequality?▼

To optimize a nonnegative vector for the Einstein Arena autocorrelation inequality, load a candidate vector and run the Dinkelbach iteration with a β-cascade L-BFGS loop using a smooth L∞ proxy to iteratively refine and maximize the score.

How does the Dinkelbach iteration handle fractional programming for score optimization?▼

The Dinkelbach iteration handles fractional programming by transforming the fractional score into a parametric optimization problem, applying β annealing and L-BFGS steps with a smooth log-sum-exp L∞ approximation to maximize the inequality score.

Can I verify my Einstein Arena solution score against the official leaderboard?▼

Yes, you can verify your Einstein Arena solution score using the exact platform-matching scorer, which confirms the candidate vector's score C to ensure trusted comparisons against current leaderboard benchmarking results.

Do I need numpy and torch to run the L-BFGS optimization for autoconvolution inequalities?▼

Yes, you need numpy and torch installed to run the L-BFGS optimization for autoconvolution inequalities, as the Dinkelbach workflow and smooth L∞ proxy computations rely on these numerical and deep learning frameworks.

What is the best way to refine a candidate vector for large resolution sizes like n=100k or n=1.6M?▼

The best way to refine a candidate vector for large resolution sizes like n=100k or n=1.6M is to follow the iterative research workflow: load a starting point, optimize across beta cascades, re-check the exact score, and repeat until the state-of-the-art inequality score improves.

Why does the optimizer use a smooth log-sum-exp approximation for the L∞ term?▼

The optimizer uses a smooth log-sum-exp approximation for the L∞ term because the standard L∞ norm is non-differentiable, and this smooth proxy enables effective gradient-based L-BFGS optimization during the Dinkelbach fractional programming iterations.