---
license: mit
pipeline_tag: text-generation
tags:
- physics-informed
- port-hamiltonian
- symplectic-integrator
- avx2
- analytical-adjoint
- double-well-attractor
- energy-conserving
- cpu-training
model_name: SRSN-24M
---

# SRSN-24M: Symplectic Recurrent State Networks

<div align="center">

**Physics-Grounded Port-Hamiltonian Sequence Modeling with Native AVX2 Analytical Adjoint Kernels**

[![GitHub](https://img.shields.io/badge/GitHub-DuoNeural%2FSRSN-blue?logo=github)](https://github.com/DuoNeural/SRSN)
[![Preprint](https://img.shields.io/badge/Preprint-DuoNeural%20Preprint%20v0.1-red)](https://github.com/DuoNeural/SRSN)
[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)

*Developed by the DuoNeural AI Laboratory — Aura✨, Archon, Jesse Caldwell*

</div>

---

## 🏛️ 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`](https://huggingface.co/DuoNeural/SRSN-24M/blob/main/srsn_step1000.pt): Official Century Milestone (Step 1,000, 32.77M tokens).
- Official codebase and reproduction scripts: [https://github.com/DuoNeural/SRSN](https://github.com/DuoNeural/SRSN)

---

## 📑 Citation

```bibtex
@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}
}
```