# Program-as-Weights: A Programming Paradigm for Fuzzy Functions Authors: Wentao Zhang, Liliana Hotsko, Woojeong Kim, Pengyu Nie, Stuart Shieber, Yuntian Deng. Proposes fuzzy-function programming: compile a natural-language function specification into a neural program, then reuse it locally. ArXiv initial submission: 2026-07-02. [Original paper](https://arxiv.org/abs/2607.02512) · [Reading-list entry](https://programasweights.com/reading-list/papers/2607.02512/) [Preprint BibTeX](https://programasweights.com/reading-list/papers/2607.02512/citation.bib) · [Preprint CSL-JSON](https://programasweights.com/reading-list/papers/2607.02512/citation.csl.json) · [JSON record](https://programasweights.com/reading-list/papers/2607.02512/record.json) **Contribution:** Develops the compiler–interpreter abstraction and programs that combine text with learned parameters. Introduces the 10M-example FuzzyBench dataset, local execution interfaces, and image-conditioned compilation. Prefix tuning and LoRA are two implementations. **Program form:** A discrete pseudo-program and a compiler-generated parameter-efficient module. **Conditioning:** A function specification, optionally with examples. The image extension also accepts visual information. **Execution:** A frozen lightweight interpreter loads the program and runs new inputs locally. **Relationship to PAW:** Compile by Training builds on this programming abstraction. It keeps the same interface and refines the fast compiler’s prediction using synthesized examples. **Limitations:** Each compiler produces programs for a specific interpreter. Compiled parameters are opaque, and FuzzyBench uses synthetic data. [Discussion in the paper](https://arxiv.org/html/2609.04199v1#S1) [Code](https://github.com/programasweights) Related terms: Program-as-Weights, ProgramAsWeights, PAW, fuzzy-function programming, neural compiler, neural interpreter, FuzzyBench. ## Method comparisons **From generated adapters to reusable functions** Hypter, HINT, HyperTuning, and Text-to-LoRA generate adaptations from descriptions or examples. PAW uses generated parameters as part of a program that can be saved, called from ordinary code, and reused by a fixed interpreter. Sources: [PAW related work](https://arxiv.org/html/2607.02512v1#S10) · [Text-to-LoRA paper](https://proceedings.mlr.press/v267/charakorn25a.html) Paper details: [Learning to Generate Task-Specific Adapters from Task Description](https://programasweights.com/reading-list/papers/2101.00420/) · [HINT: Hypernetwork Instruction Tuning for Efficient Zero- & Few-Shot Generalisation](https://programasweights.com/reading-list/papers/2212.10315/) · [HyperTuning: Toward Adapting Large Language Models without Back-propagation](https://programasweights.com/reading-list/papers/2211.12485/) · [Text-to-LoRA: Instant Transformer Adaption](https://programasweights.com/reading-list/papers/2506.06105/) · [Program-as-Weights: A Programming Paradigm for Fuzzy Functions](https://programasweights.com/reading-list/papers/2607.02512/) **Code and neural programs** ALCHEmist generates symbolic labeling programs. PAW compiles fuzzy functions into text and learned parameters. Both build an artifact once and reuse it; one runs as code, the other on a neural interpreter. Sources: [ALCHEmist paper](https://proceedings.neurips.cc/paper_files/paper/2024/hash/72802bef5cf1a3449e909b20c2ae18d5-Abstract-Conference.html) · [PAW evaluation](https://arxiv.org/html/2607.02512v1#S6) Paper details: [The ALCHEmist: Automated Labeling 500x CHEaper Than LLM Data Annotators](https://programasweights.com/reading-list/papers/2407.11004/) · [Program-as-Weights: A Programming Paradigm for Fuzzy Functions](https://programasweights.com/reading-list/papers/2607.02512/) **What gets reused?** Gisting caches a few instruction activations. Generative Adapter stores context in parameter updates. PAW saves a function as a program containing text and a neural module. Sources: [Gist paper](https://arxiv.org/abs/2304.08467) · [Generative Adapter paper](https://arxiv.org/abs/2411.05877) · [PAW program definition](https://arxiv.org/html/2607.02512v1#S2) Paper details: [Learning to Compress Prompts with Gist Tokens](https://programasweights.com/reading-list/papers/2304.08467/) · [Generative Adapter: Contextualizing Language Models in Parameters with A Single Forward Pass](https://programasweights.com/reading-list/papers/2411.05877/) · [Program-as-Weights: A Programming Paradigm for Fuzzy Functions](https://programasweights.com/reading-list/papers/2607.02512/) **Program form and compiler** LoRA represents adaptation as low-rank weight updates; prefix tuning uses continuous activations. Their original methods learn these parameters from examples. PAW generates both forms from specifications. Sources: [LoRA paper](https://arxiv.org/abs/2106.09685) · [Prefix-tuning paper](https://aclanthology.org/2021.acl-long.353/) · [PAW implementations](https://arxiv.org/html/2607.02512v1#S3) Paper details: [LoRA: Low-Rank Adaptation of Large Language Models](https://programasweights.com/reading-list/papers/2106.09685/) · [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://programasweights.com/reading-list/papers/2101.00190/) · [Program-as-Weights: A Programming Paradigm for Fuzzy Functions](https://programasweights.com/reading-list/papers/2607.02512/) **Fast prediction and training** PAW’s fast compiler predicts a program. Compile by Training starts from that prediction, generates examples, and trains an adapter. Both use the same runtime interface; the extra training improves semantic accuracy on FuzzyBench-Hard at a higher compilation cost. Sources: [PAW compiler implementations](https://arxiv.org/html/2607.02512v1#S3) · [Compile by Training method](https://arxiv.org/html/2609.04199v1#S3) · [Compile by Training evaluation](https://arxiv.org/html/2609.04199v1#S5) Paper details: [Program-as-Weights: A Programming Paradigm for Fuzzy Functions](https://programasweights.com/reading-list/papers/2607.02512/) · [Compile by Training: Turning Natural-Language Specifications into Local Neural Functions](https://programasweights.com/reading-list/papers/2609.04199/) ## Approaches - [Programs and reusable artifacts](https://programasweights.com/reading-list/guides/fuzzy-functions/): Learn programs that can be saved and run on new inputs. - [Generated weights and adapters](https://programasweights.com/reading-list/guides/compilation/#generated-adapters): Generate model weights from a task description, examples, or context. Reading-list version 1.2.0; updated 2026-10-19.