# Hey Pentti, We Did (More of) It!: A Vector-Symbolic Lisp With Residue Arithmetic

arXiv: https://arxiv.org/abs/2511.08767 · HTML: https://mlsanity.com/paper/2511.08767/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [Scaling Scaling Laws with Board Games](https://mlsanity.com/paper/2104.03113/) (2021)
- [Generalized Holographic Reduced Representations](https://mlsanity.com/paper/2405.09689/) (2024)
- [Compositional Generalization Across Distributional Shifts with Sparse Tree Operations](https://mlsanity.com/paper/2412.14076/) (2024)
- [Hey Pentti, We Did It!: A Fully Vector-Symbolic Lisp](https://mlsanity.com/paper/2510.17889/) (2025)

## Abstract (arXiv)

Using Frequency-domain Holographic Reduced Representations (FHRRs), we extend a Vector-Symbolic Architecture (VSA) encoding of Lisp 1.5 with primitives for arithmetic operations using Residue Hyperdimensional Computing (RHC). Encoding a Turing-complete syntax over a high-dimensional vector space increases the expressivity of neural network states, enabling network states to contain arbitrarily structured representations that are inherently interpretable. We discuss the potential applications of the VSA encoding in machine learning tasks, as well as the importance of encoding structured representations and designing neural networks whose behavior is sensitive to the structure of their representations in virtue of attaining more general intelligent agents than exist at present.