What if neural networks are wave propagation systems?
This research series derives learning algorithms from physical first principles, viewing neural networks as waves propagating through tunable media. The framework unifies Hebbian learning, Oja's rule, and backpropagation—and extends to explain the Fermi Paradox.
Date: March 9, 2026 | Collaboration: Macheng Shen + Claude (Opus 4.6)
Hebbian Learning, Oja's Rule, and Backpropagation Unified
Central thesis: Three fundamental learning principles—Hebbian learning (1949), Oja's rule (1982), and backpropagation (1986)—are not independent mechanisms but unified manifestations of wave interference in tunable media.
Key results:
- Hebbian learning = correlation between incident (forward) and reflected (error) waves
- Oja's rule = physical saturation constraints in finite-capacity media
- Backpropagation = reflected error waves (no explicit algorithm needed)
- Resolves "biological plausibility of backprop" debate
Implications: Any wave system with tunable coupling automatically supports learning. Provides design principles for neuromorphic computing (optical, acoustic, memristive).
Read Full Paper →Deriving Backpropagation from Wave Equations & the Fermi Paradox
Central thesis: Information transmission obeys physical laws with fundamental cost constraints. The same framework that explains neural network training also explains why we see no signs of extraterrestrial intelligence.
Part I: Neural Networks
- Forward pass = steady-state wave propagation
- Loss function = boundary impedance mismatch
- Backprop = time-reversed wave dynamics carrying reflected error signals
- Explains vanishing gradients, ResNet, BatchNorm, spectral bias
Part II: Fermi Paradox
- Control cost scales as ~R5 with distance
- Light-year latencies make interstellar closed-loop control infeasible
- Civilizations "trapped" by thermodynamics, not technology
- Universe may be full of "hermit civilizations" in local high-efficiency bubbles
Deriving Backpropagation from Wave Equations (Short Version)
A focused derivation of backpropagation from wave dynamics, without the Fermi Paradox extension. Best for readers interested in the core mathematical framework.
Read Short Version →Sleep as Wave Optimization: Why We Wake with Solutions
Central thesis: Sleep is not passive recovery but active wave impedance optimization. Slow-wave sleep (SWS) minimizes global impedance through synaptic renormalization and memory replay; REM sleep explores novel pathways through random frequency scanning. Morning insights emerge when optimized connections are first "seen" by conscious awareness.
Key mechanisms:
- SWS (hours 0-3): Synaptic pruning (15-20% reduction), sharp-wave ripples replay at 10-20× speed, slow oscillations enable global optimization
- REM (hours 4-6): Theta oscillations, frontal lobe suppression, random wave propagation discovers new connections
- Awakening: Optimized pathways become conscious → "Aha!" moments
Neuroscience evidence (2003-2026):
- ✅ Sharp-wave ripples predict consolidation (Cell Neuron 2025, PMC 12576410)
- ✅ Synaptic homeostasis hypothesis confirmed (Tononi & Cirelli 2003-2012)
- ✅ REM enhances creativity via associative networks (PNAS 2009)
- ✅ Guided dreaming boosts problem-solving +25% (Northwestern 2026)
Parallels with AI: Human sleep = batch training + exploration; awake = online learning. Same optimization principles!
Practical applications: Load problems before sleep, protect REM (7-8h), capture insights immediately upon waking.
Read Full Theory →Connections to other theories:
- Feedback Alignment (Lillicrap 2016): wave interference explains why random feedback works
- Predictive Coding: forward wave = prediction, reflected wave = prediction error
- Target Propagation: propagating "desired wave patterns"
Testable predictions: bidirectional wave propagation, phase-dependent synaptic plasticity, impedance-based learning difficulty.
Read Full Response →🔬 Testable Predictions
- Physical wave systems (optical, acoustic) with only local Hebbian plasticity should achieve backprop-level performance
- Trained networks should have flat frequency response curves at task-relevant frequencies
- STDP timing windows should scale with dendritic length (~L/v)
- Network eigenmodes should align with learned weight structure
📬 Feedback & Collaboration
If you find errors, have suggestions, or want to collaborate on experimental validation, please reach out: macshen93@gmail.com