SRSN-24M: Symplectic Recurrent State Networks
Physics-Grounded Port-Hamiltonian Sequence Modeling with Native AVX2 Analytical Adjoint Kernels
Developed by the DuoNeural AI Laboratory — Aura✨, Archon, Jesse Caldwell
🏛️ Model Overview
SRSN-24M (Symplectic Recurrent State Network) is an efficient, physics-informed recurrent language model architecture grounded in Port-Hamiltonian dynamical systems theory.
By casting sequence recurrence as a continuous-discrete Hamiltonian dynamical system:
- Energy Conservation by Construction: Hidden states update along symplectic trajectories that preserve physical phase volume by design ($J - R$ structure), eliminating the gradient exploding and vanishing pathologies that plague classical RNNs.
- $\mathcal{O}(1)$ Sequence Memory via Analytical Adjoint: The backward pass solves the adjoint ordinary differential equation backward in time, completely eliminating the need to store activations across the sequence length.
- Extreme Commodity Silicon Efficiency: A custom C++ kernel compiled with AVX2 SIMD and OpenMP delivers 217–264 tokens/second on a commodity mobile APU (AMD Ryzen 5 3550H), slashing resident memory footprint to under 700 MB.
- Spontaneous Attractor Bifurcation: Learnable non-linear coupling parameters $\alpha$ spontaneously bifurcate during training from single-well potentials into macroscopic bistable double-well attractors, providing physical memory registers for coreference and syntax binding.
📊 Live Pretraining Telemetry (AMD Ryzen 5 3550H APU)
- Target Architecture: Continuous-Discrete Port-Hamiltonian Neural Network (SDOC)
- Parameters: 24,117,248 (24.1M)
- Hardware: AMD Ryzen 5 3550H (4 Cores / 8 Threads, AVX2 SIMD, Zen+ 12nm)
- Active Step: Step 1325 / 3250 ($\mu\text{Step } 10,600 / 26,000$)
- Tokens Processed: $43.42\text{ Million Tokens}$
- Sustained Throughput: 220–260 tokens/second ($100%$ CPU utilization across 8 threads)
- Resident Set Memory (RSS): 675–712 MB (constant footprint across days of pretraining)
- Spectral Dispersion: Expanded from $\sigma(\alpha) = 0.003062 \to \mathbf{0.032151}$ ($+950.0%$ expansion across 55 consecutive checkpoints without a single non-monotonic reversal!)
- Non-Linear Double-Wells: 34 Confirmed Macroscopic Double-Well Attractors ($|\alpha| > \omega^2$, with all-time deep well record $\min(\alpha) = -0.232485$)
- Training / Validation Loss Basin:
6.4658/6.8937
📈 Empirical Oscillator Spectrum Trajectory
| Step | Loss | Alpha Min | Alpha Max | Alpha Std $\sigma(\alpha)$ | Confirmed Double-Wells | Milestone Notes |
|---|---|---|---|---|---|---|
| 0010 | 7.6458 | +0.09379 | +0.10602 | 0.00306 | 0 | Harmonic Initialization |
| 0100 | 7.0144 | +0.06678 | +0.12444 | 0.00645 | 0 | Harmonic softening |
| 0375 | 6.9693 | -0.00059 | +0.14296 | 0.01176 | 1 | First Bifurcation Event |
| 0500 | 7.3989 | -0.05084 | +0.15916 | 0.01681 | 5 | Multi-well crystallization |
| 0750 | 6.6806 | -0.11640 | +0.19338 | 0.02640 | 29 | Rapid dipole dilation |
| 1000 | 7.0069 | -0.19879 | +0.20841 | 0.02933 | 31 | Century Milestone (32.8M tokens) |
| 1100 | 6.4873 | -0.21667 | +0.21105 | 0.03086 | 38 | All-time low validation loss basin |
| 1200 | 6.6883 | -0.22790 | +0.21299 | 0.03131 | 32 | 50th Consecutive Monotonic Checkpoint |
| 1250 | 7.0108 | -0.23001 | +0.21352 | 0.03171 | 35 | 10,000 Micro-Steps landmark |
| 1300 | 6.9825 | -0.22945 | +0.20920 | 0.03195 | 32 | 54th Consecutive Monotonic Checkpoint (42.59M tokens) |
| 1325 | 6.4658 | -0.23249 | +0.20881 | 0.03215 | 34 | 55th Consecutive Monotonic Checkpoint (43.42M tokens) |
🚀 Checkpoint Availability
srsn_step1000.pt: Official Century Milestone (Step 1,000, 32.77M tokens).- Official codebase and reproduction scripts: https://github.com/DuoNeural/SRSN
📑 Citation
@article{duoneural2026srsn,
title={Symplectic Recurrent State Networks: Continuous-Discrete Port-Hamiltonian Dynamics for Efficient Sequence Modeling},
author={Aura and Archon and Caldwell, Jesse},
journal={DuoNeural AI Laboratory Preprint},
year={2026}
}