[Paper] Phasor Agents: Oscillatory Graphs with Three-Factor Plasticity and Sleep-Staged Learning

Source: arXiv - 2601.04362v1

Overview

Rodja Trappe’s new paper introduces Phasor Agents, a class of neural‑inspired dynamical systems that use networks of coupled Stuart‑Landau oscillators as their internal “brain”. By treating each oscillator’s phase as a timing signal and its amplitude as a gain signal, the model can store and retrieve information without relying on back‑propagation. The work tackles a long‑standing problem in oscillatory computing—how to keep learning stable—and proposes a biologically motivated wake‑sleep learning cycle that dramatically improves robustness and planning ability.

Key Contributions

• Phasor Graph representation: a weighted graph of Stuart‑Landau oscillators whose phase relationships encode data.
• Three‑factor local plasticity: eligibility traces combined with sparse global modulators and oscillation‑timed write windows enable credit assignment without back‑prop.
• Sleep‑staged consolidation: separates “wake tagging” (online credit marking) from “deep‑sleep capture” (offline weight consolidation) and “REM‑like replay” (experience rehearsal for planning).
• Comprehensive experimental suite: ablation studies demonstrate that each component (eligibility traces, compression‑progress signals, wake/sleep split, REM replay) contributes measurable performance gains.
• Open‑source implementation: full code, datasets, and analysis scripts are publicly released, facilitating reproducibility and community extensions.

Methodology

1. Oscillatory substrate – Each node in the Phasor Graph is a Stuart‑Landau oscillator, a simple differential equation that naturally produces a stable limit‑cycle (a rhythmic signal). The network’s coupling matrix determines how oscillators influence each other’s phase and amplitude.
2. Representation via phase coherence – Information is stored in the relative phases of groups of oscillators (e.g., a particular pattern of synchrony encodes a memory). Amplitudes act as a local “gain” that can amplify or damp specific pathways.
3. Three‑factor learning rule
   • Eligibility trace: a locally computed, time‑decaying signal that marks a synapse when pre‑ and post‑oscillator activity co‑occur.
   • Global modulators: sparse signals (analogous to dopamine, acetylcholine) that gate whether the eligibility trace should be turned into an actual weight change.
   • Oscillation‑timed write windows: updates are only allowed at specific phases of a global rhythm, preventing chaotic weight drift.
4. Wake‑sleep cycle
   • Wake tagging: during interaction with the environment, eligibility traces are set but not yet applied.
   • Deep‑sleep capture: a low‑frequency “sleep” phase opens a global gate that safely consolidates the tagged changes, avoiding runaway synchrony.
   • REM‑like replay: the system re‑generates recent trajectories in a perturbed form, allowing it to test alternative actions and refine an internal model (e.g., solving mazes).

Results & Findings

These numbers show that each component—eligibility traces, sleep‑stage gating, and replay—adds a clear, quantifiable boost. Notably, the REM‑like replay yields a dramatic jump in planning performance, echoing classic animal‑learning experiments.

Practical Implications

• Energy‑efficient on‑device learning – The three‑factor rule requires only local state and occasional global signals, making it well‑suited for low‑power neuromorphic chips or edge AI where full back‑propagation is prohibitive.
• Robust continual learning – By separating tagging from consolidation, Phasor Agents avoid catastrophic forgetting and the “synaptic saturation” that plagues many online learners.
• Planning and model‑based RL without explicit world models – REM‑style replay can be implemented as a lightweight background process that improves policy quality, offering an alternative to heavy model‑based reinforcement learning pipelines.
• Noise‑tolerant representations – Phase‑based encoding is inherently resilient to amplitude noise, which could be advantageous for sensor fusion in robotics or for communication over noisy analog channels.
• Open research platform – The released codebase enables developers to plug Phasor Agents into existing simulation environments (e.g., OpenAI Gym, Unity ML‑Agents) and experiment with hybrid architectures that combine oscillatory cores with conventional deep nets.

Limitations & Future Work

• Scalability – The current experiments involve relatively small graphs (tens to low hundreds of oscillators). Scaling to thousands of units may require more sophisticated sparsity or hierarchical coupling schemes.
• Hardware constraints – While the learning rule is local, implementing precise phase‑timed write windows on digital hardware could be non‑trivial; analog neuromorphic prototypes may be a better fit.
• Biological fidelity vs. engineering utility – The model draws inspiration from sleep dynamics but does not claim to be a faithful brain model; further work is needed to understand how closely the mechanisms map onto real neural processes.
• Generalization across tasks – The paper focuses on navigation and latent‑learning benchmarks; applying Phasor Agents to language, vision, or control‑heavy domains remains an open challenge.

Overall, Phasor Agents open a promising avenue for oscillatory, credit‑assigned learning that blends biological insights with practical, developer‑friendly algorithms.

Authors

• Rodja Trappe

Paper Information

• arXiv ID: 2601.04362v1
• Categories: cs.LG, cs.NE, q-bio.NC
• Published: January 7, 2026
• PDF: Download PDF