# Differentiable Programs with Neural Libraries

arXiv: https://arxiv.org/abs/1611.02109 · HTML: https://mlsanity.com/paper/1611.02109/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2016.

## Built on by (most cited first, 30 of 30)

- [NExT: Teaching Large Language Models to Reason about Code Execution](https://mlsanity.com/paper/2404.14662/) (2024)
- [Learning to Synthesize Programs as Interpretable and Generalizable Policies](https://mlsanity.com/paper/2108.13643/) (2021)
- [How to Reuse and Compose Knowledge for a Lifetime of Tasks: A Survey on Continual Learning and Functional Composition](https://mlsanity.com/paper/2207.07730/) (2022)
- [Limits of Deep Learning: Sequence Modeling through the Lens of Complexity Theory](https://mlsanity.com/paper/2405.16674/) (2024)
- [From Perception to Programs: Regularize, Overparameterize, and Amortize](https://mlsanity.com/paper/2206.05922/) (2022)
- [Static Prediction of Runtime Errors by Learning to Execute Programs with External Resource Descriptions](https://mlsanity.com/paper/2203.03771/) (2022)
- [From explanation to synthesis: Compositional program induction for learning from demonstration](https://mlsanity.com/paper/1902.10657/) (2019)
- [Construction of Hierarchical Neural Architecture Search Spaces based on Context-free Grammars](https://mlsanity.com/paper/2211.01842/) (2022)
- [REFACTOR: Learning to Extract Theorems from Proofs](https://mlsanity.com/paper/2402.17032/) (2024)
- [Hierarchical Neural Program Synthesis](https://mlsanity.com/paper/2303.06018/) (2023)
- [Smoothing Methods for Automatic Differentiation Across Conditional Branches](https://mlsanity.com/paper/2310.03585/) (2023)
- [Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees](https://mlsanity.com/paper/2308.10487/) (2023)
- [Robot Program Parameter Inference via Differentiable Shadow Program Inversion](https://mlsanity.com/paper/2103.14452/) (2021)
- [Differentiable Logic Programming for Distant Supervision](https://mlsanity.com/paper/2408.12591/) (2024)
- [Deep Algorithmic Question Answering: Towards a Compositionally Hybrid AI for Algorithmic Reasoning](https://mlsanity.com/paper/2109.08006/) (2021)
- [Automated causal inference in application to randomized controlled clinical trials](https://mlsanity.com/paper/2201.05773/) (2022)
- [Compiling to linear neurons](https://mlsanity.com/paper/2511.13769/) (2025)
- [NESTER: An Adaptive Neurosymbolic Method for Causal Effect Estimation](https://mlsanity.com/paper/2211.04370/) (2022)
- [Neural Decision-Propagation for Answer Set Programming](https://mlsanity.com/paper/2605.01797/) (2026)
- [Understanding in Artificial Intelligence](https://mlsanity.com/paper/2101.06573/) (2021)
- [Procedures as Programs: Hierarchical Control of Situated Agents through Natural Language](https://mlsanity.com/paper/2109.08214/) (2021)
- [Synthesizing Machine Learning Programs with PAC Guarantees via Statistical Sketching](https://mlsanity.com/paper/2110.05390/) (2021)
- [Differentiable Quantum Programming with Unbounded Loops](https://mlsanity.com/paper/2211.04507/) (2022)
- [A Short Survey of Systematic Generalization](https://mlsanity.com/paper/2211.11956/) (2022)
- [Neural Feature-Adaptation for Symbolic Predictions Using Pre-Training and Semantic Loss](https://mlsanity.com/paper/2211.16047/) (2022)
- [A differentiable programming framework for spin models](https://mlsanity.com/paper/2304.01772/) (2023)
- [MetaLint: Easy-to-Hard Generalization for Code Linting](https://mlsanity.com/paper/2507.11687/) (2025)
- [Compiling to recurrent neurons](https://mlsanity.com/paper/2511.14953/) (2025)
- [Neural-Symbolic Integration with Evolvable Policies](https://mlsanity.com/paper/2601.04799/) (2026)
- [Differentiate the Evaluator, Not the Program: An Efficient Runtime Representation for Neuro-Symbolic Learning](https://mlsanity.com/paper/2607.03574/) (2026)

## Abstract (arXiv)

We develop a framework for combining differentiable programming languages with neural networks. Using this framework we create end-to-end trainable systems that learn to write interpretable algorithms with perceptual components. We explore the benefits of inductive biases for strong generalization and modularity that come from the program-like structure of our models. In particular, modularity allows us to learn a library of (neural) functions which grows and improves as more tasks are solved. Empirically, we show that this leads to lifelong learning systems that transfer knowledge to new tasks more effectively than baselines.