# Functionally Equivalent or Not? Graph-Grounded Differential Surrogate Execution for Code Equivalence

arXiv: https://arxiv.org/abs/2610.04371 · HTML: https://mlsanity.com/paper/2610.04371/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [GraphCodeBERT: Pre-training Code Representations with Data Flow](https://mlsanity.com/paper/2009.08366/) (2020)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [RepoGraph: Enhancing AI Software Engineering with Repository-level Code Graph](https://mlsanity.com/paper/2410.14684/) (2024)
- [CodexGraph: Bridging Large Language Models and Code Repositories via Code Graph Databases](https://mlsanity.com/paper/2408.03910/) (2024)
- [CodeMind: Evaluating Large Language Models for Code Reasoning](https://mlsanity.com/paper/2402.09664/) (2024)
- [EquiBench: Benchmarking Large Language Models' Reasoning about Program Semantics via Equivalence Checking](https://mlsanity.com/paper/2502.12466/) (2025)
- [What can Large Language Models Capture about Code Functional Equivalence?](https://mlsanity.com/paper/2408.11081/) (2024)

## Abstract (arXiv)

Determining whether two programs are functionally equivalent is central to code modernization, patch validation, refactoring, and code-generation evaluation. Yet the usual signals are incomplete: tests cover only finite inputs, textual similarity confuses implementation with behavior, and unconstrained LLM judgments are difficult to audit. Direct execution is often impossible when a program depends on an obsolete, licensed, unavailable, or unsafe environment. We introduce FEAgent, a selective equivalence assessor agent that combines typed program-graph evidence with differential surrogate execution. FEAgent first aligns public interfaces and behaviorally relevant graph anchors, then issues bounded queries over call-flow, control-flow, data-flow, type, import, and effect relations. Next, a branch-aware generator agent proposes discriminating inputs, and two blinded LLM surrogates independently predict source and target observables. Every claim and predicted divergence is recorded in an evidence ledger. A deterministic reconciler then returns EQUIVALENT, INEQUIVALENT, or UNCLEAR rather than forcing a verdict when paths are uncovered or evidence conflicts. We evaluate FEAgent on function-level equivalence and repository-level bug patches, where the existing oracle is a benchmark label or a passing test suite. Every disagreement with that oracle is adjudicated by direct execution, revealing errors in benchmark labels and behavioral divergences missed by unit-test-only scoring. On EquiBench, execution confirms FEAgent's disagreements with published labels on 216 of 1,200 evaluated pairs (18.0%); on SWE-bench Verified, 94 of 331 test-passing agent patches (28.4%) diverge from the reference patch. FEAgent thus serves as an audit layer between testing and formal verification, keeping its evidence reviewable and its uncertainty explicit without claiming a proof of equivalence.