# Phasor Agents: Oscillatory Graphs with Three-Factor Plasticity and Sleep-Staged Learning

arXiv: https://arxiv.org/abs/2601.04362 · HTML: https://mlsanity.com/paper/2601.04362/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 74 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Artificial Kuramoto Oscillatory Neurons](https://mlsanity.com/paper/2410.13821/) (2024)
- [An Unsupervised STDP-based Spiking Neural Network Inspired By Biologically Plausible Learning Rules and Connections](https://mlsanity.com/paper/2207.02727/) (2022)
- [Deep Oscillatory Neural Network](https://mlsanity.com/paper/2405.03725/) (2024)
- [Stuart-Landau Oscillatory Graph Neural Network](https://mlsanity.com/paper/2511.08094/) (2025)
- [ElfCore: A 28nm Neural Processor Enabling Dynamic Structured Sparse Training and Online Self-Supervised Learning with Activity-Dependent Weight Update](https://mlsanity.com/paper/2512.21153/) (2025)
- [Holographic Transformers for Complex-Valued Signal Processing: Integrating Phase Interference into Self-Attention](https://mlsanity.com/paper/2509.19331/) (2025)
- [Personalized targeted memory reactivation enhances consolidation of challenging memories via slow wave and spindle dynamics](https://mlsanity.com/paper/2511.15013/) (2025)
- [Novel Kuramoto model with inhibition dynamics modeling scale-free avalanches and synchronization in neuronal cultures](https://mlsanity.com/paper/2512.17317/) (2025)
- [Benign nonconvexity of synchronization landscape induced by graph skeletons](https://mlsanity.com/paper/2512.21935/) (2025)

## Abstract (arXiv)

Phasor Agents are dynamical systems whose internal state is a Phasor Graph: a weighted graph of coupled Stuart-Landau oscillators. A Stuart-Landau oscillator is a minimal stable "rhythm generator" (the normal form near a Hopf bifurcation); each oscillator is treated as an abstract computational unit (inspired by, but not claiming to model, biological oscillatory populations). In this interpretation, oscillator phase tracks relative timing (coherence), while amplitude tracks local gain or activity. Relative phase structure serves as a representational medium; coupling weights are learned via three-factor local plasticity - eligibility traces gated by sparse global modulators and oscillation-timed write windows - without backpropagation. A central challenge in oscillatory substrates is stability: online weight updates can drive the network into unwanted regimes (e.g., global synchrony), collapsing representational diversity. We therefore separate wake tagging from offline consolidation, inspired by synaptic tagging-and-capture and sleep-stage dynamics: deep-sleep-like gated capture commits tagged changes safely, while REM-like replay reconstructs and perturbs experience for planning. A staged experiment suite validates each mechanism with ablations and falsifiers: eligibility traces preserve credit under delayed modulation; compression-progress signals pass timestamp-shuffle controls; phase-coherent retrieval reaches 4x diffusive baselines under noise; wake/sleep separation expands stable learning by 67 percent under matched weight-norm budgets; REM replay improves maze success rate by +45.5 percentage points; and a Tolman-style latent-learning signature - immediate competence and detour advantage after unrewarded exploration, consistent with an internal model - emerges from replay (Tolman, 1948). The codebase and all artifacts are open-source.