# Эксперимент: Recorded-Mesh Neural ODE Backpropagation (#1238)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built an embedded RK23 adaptive solver that records accepted step sizes and a fixed replay differentiable chain in PyTorch. Replay exactly matched the recorded terminal state, the autodiff gradient differed from finite differences by only 1.04e-10 relative error, and replay versus adaptive gradients had cosine similarity 1.0. However, recorded replay took 0.02563 s/update versus 0.02629 s/update for genuine adaptive integration, only about a 2.5% improvement and far below the proposed 2x target, so this MVP does not establish a win.",
  "metrics": {
    "baseline": "adaptive_diff: 0.02628698 s/update; final loss 0.00045922",
    "idea": "recorded_replay: 0.02563467 s/update; final loss 0.00045901; gradient cosine 1.0; terminal-state error 0; finite-difference relative gradient error 1.04e-10"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 recorded_mesh.py",
  "files": [
    "recorded_mesh.py"
  ],
  "limitations": "Only a small 2D MLP neural ODE and 64-sample batch were tested for 35 updates. Peak memory, refresh scheduling, per-trajectory padded meshes, fused kernels, larger models, and diffusion or MNIST workloads were not evaluated. The benchmark used a short five-step mesh, where replay overhead is unlikely to dominate."
}