# Narcissus: Program Synthesis Using Context-Aware LLM Approximations

arXiv: https://arxiv.org/abs/2608.25657 · HTML: https://mlsanity.com/paper/2608.25657/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [DeepCoder: Learning to Write Programs](https://mlsanity.com/paper/1611.01989/) (2016)
- [Combining Induction and Transduction for Abstract Reasoning](https://mlsanity.com/paper/2411.02272/) (2024)
- [Self-Improving Language Models for Evolutionary Program Synthesis: A Case Study on ARC-AGI](https://mlsanity.com/paper/2507.14172/) (2025)
- [Graphs, Constraints, and Search for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2210.09880/) (2022)
- [BUSTLE: Bottom-Up Program Synthesis Through Learning-Guided Exploration](https://mlsanity.com/paper/2007.14381/) (2020)
- [Program Synthesis using Conflict-Driven Learning](https://mlsanity.com/paper/1711.08029/) (2017)
- [Just-in-Time Learning for Bottom-Up Enumerative Synthesis](https://mlsanity.com/paper/2010.08663/) (2020)
- [HYSYNTH: Context-Free LLM Approximation for Guiding Program Synthesis](https://mlsanity.com/paper/2405.15880/) (2024)
- [ConceptSearch: Towards Efficient Program Search Using LLMs for Abstraction and Reasoning Corpus (ARC)](https://mlsanity.com/paper/2412.07322/) (2024)
- [Program Synthesis with Best-First Bottom-Up Search](https://mlsanity.com/paper/2310.04327/) (2023)
- [ReaComp: Compiling LLM Reasoning into Symbolic Solvers for Efficient Program Synthesis](https://mlsanity.com/paper/2605.05485/) (2026)
- [Herb.jl: A Unifying Program Synthesis Library](https://mlsanity.com/paper/2510.09726/) (2025)

## Abstract (arXiv)

Large language models (LLMs) excel at programming, but not when the task fixes the target language: prompted with a grammar rare in their training data, their programs usually break the grammar or fail the given specification. Enumerative synthesizers search the space of syntactically correct programs systematically guided by LLMs; the state of the art guides them by approximating LLM proposals into rule frequencies, which loses where each construct belongs and prunes every rule the proposals miss, exactly when the proposals are wrong. We present Narcissus, a synthesizer that keeps the proposals as syntax trees and scores each expansion of a candidate program in its context: does a proposal with the same surrounding structure continue the same way, and does the expansion rebuild a fragment the proposals repeat? A regularization term keeps every rule reachable, so wrong proposals delay the solution but cannot hide it. Across five domains and two search backends, Narcissus beats static guidance at every budget and consistently outperforms re-prompting the LLM to fix its own proposals; it reaches proposal-like programs an order of magnitude sooner and solves 40% of ARC tasks where the raw proposals solve 13%, all without a single LLM call during search.