# A Symbolic Neural CPU for Quantization-Simulated Writeback and Interpretable Program Execution

arXiv: https://arxiv.org/abs/2607.10021 · HTML: https://mlsanity.com/paper/2607.10021/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 61 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 30 of 30)

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- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Memory Networks](https://mlsanity.com/paper/1410.3916/) (2014)
- [Neural GPUs Learn Algorithms](https://mlsanity.com/paper/1511.08228/) (2015)
- [Learning to Execute](https://mlsanity.com/paper/1410.4615/) (2014)
- [Neural Programmer-Interpreters](https://mlsanity.com/paper/1511.06279/) (2015)
- [Neural Programmer: Inducing Latent Programs with Gradient Descent](https://mlsanity.com/paper/1511.04834/) (2015)
- [Neural Random-Access Machines](https://mlsanity.com/paper/1511.06392/) (2015)
- [Transformers meet Neural Algorithmic Reasoners](https://mlsanity.com/paper/2406.09308/) (2024)
- [Tropical Attention: Neural Algorithmic Reasoning for Combinatorial Algorithms](https://mlsanity.com/paper/2505.17190/) (2025)
- [MemMA: Coordinating the Memory Cycle through Multi-Agent Reasoning and In-Situ Self-Evolution](https://mlsanity.com/paper/2603.18718/) (2026)
- [When Continual Learning Moves to Memory: A Study of Experience Reuse in LLM Agents](https://mlsanity.com/paper/2604.27003/) (2026)
- [Primal-Dual Neural Algorithmic Reasoning](https://mlsanity.com/paper/2505.24067/) (2025)
- [Code Simulation as a Proxy for High-order Tasks in Large Language Models](https://mlsanity.com/paper/2502.03568/) (2025)
- [Gradient-Based Program Synthesis with Neurally Interpreted Languages](https://mlsanity.com/paper/2604.18907/) (2026)
- [Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers](https://mlsanity.com/paper/2501.10688/) (2025)
- [Open-Book Neural Algorithmic Reasoning](https://mlsanity.com/paper/2501.00072/) (2024)
- [Neural Computers](https://mlsanity.com/paper/2604.06425/) (2026)
- [FeNN: A RISC-V vector processor for Spiking Neural Network acceleration](https://mlsanity.com/paper/2506.11760/) (2025)
- [Constraint Guided Model Quantization of Neural Networks](https://mlsanity.com/paper/2409.20138/) (2024)
- [KNARsack: Teaching Neural Algorithmic Reasoners to Solve Pseudo-Polynomial Problems](https://mlsanity.com/paper/2509.15239/) (2025)
- [Rescaling-Aware Training for Efficient Deployment of Deep Learning Models on Full-Integer Hardware](https://mlsanity.com/paper/2510.11484/) (2025)
- [Transformers are Stateless Differentiable Neural Computers](https://mlsanity.com/paper/2603.19272/) (2026)

## Abstract (arXiv)

Neural networks can learn algorithmic input-output mappings, but trusting a learned executor requires more than a correct final answer because the state transitions that produce it are usually hidden. To make those transitions visible, we introduce a trace-supervised symbolic neural CPU, a factorized learned execution architecture that combines recurrent control, an explicit operation router over a fixed differentiable arithmetic-logic unit bank, destination-masked register writeback, complete trajectory supervision and matched fixed-point replay. The model exposes the selected operation, source and destination registers, register trajectory, memory signals and writeback semantics at every step. On the principal 16-wide benchmark, the non-quantized executor reproduces reference execution exactly, while the eight-bit quantization-simulated executor preserves the symbolic operation path through programs of 1,000 instructions. When the same execution is evaluated against a matched fixed-point replay, the residual numerical drift disappears, showing that it comes from a mismatch between continuous and low-precision reference semantics rather than from execution failure. We compare recurrent, Transformer, temporal-convolution, temporal graph-inspired and state-space controllers, and the ablations show that operation-gate supervision is necessary for an inspectable execution path. Hidden-opcode memory-pressure tasks expose the remaining limits in delayed state use and temporal binding. We also extend the interface with ValueMemory, hybrid adaptive leaky integrate-and-fire controllers, candidate-constrained symbolic control trained through behaviour cloning and actor-critic reinforcement learning, and an RV32I base-integer semantic bridge. Together, these results establish a trace-verifiable framework for interpretable, low-precision and controllable neural execution.