✗ Failed on benchmark 2026

Disturbance-Augmented Neural State Space

Implementation & benchmark of arXiv:2607.20939 — Interaction Dynamics Modeling and Predictive Control for Safe Steerable Catheter--Tissue Interaction

Usefulness7/10

Difficulty5/10

Novelty6/10

Dynamics Stability Accuracy Generalization Rnn Ssm World model Training dynamics Control theory Dynamical systems Stochastic processes Linear algebra

Source paper: Interaction Dynamics Modeling and Predictive Control for Safe Steerable Catheter--Tissue Interaction arXiv:2607.20939 ⓘ · analyzed Aug 30, 2026

AI-generated research hypothesis, automatically tested. Not peer-reviewed.

Idea description

Augment a neural recurrent or state-space model with an explicit slowly varying disturbance state that absorbs contact effects, friction, hysteresis, actuator mismatch, and other systematic residuals. The network predicts nominal dynamics, while the disturbance channel provides offset-free correction without forcing the main model to memorize every operating-condition-dependent bias.

Formulas

$$M(\kappa)\ddot{\kappa}+C(\kappa,\dot{\kappa})\dot{\kappa}+K(\kappa)=u+d_{\mathrm{cat}}$$

$$x_{t+1}=f_\theta(x_t,u_t)+E d_t,\qquad d_{t+1}=\rho d_t+w_t,\qquad y_t=g_\theta(x_t)+v_t$$

$$z_{t+1}=\begin{bmatrix}f_\theta(x_t,u_t)+E d_t\\ \rho d_t\end{bmatrix}+\begin{bmatrix}0\\w_t\end{bmatrix},\qquad z_t=\begin{bmatrix}x_t\\d_t\end{bmatrix}$$

$$\lim_{t\to\infty}\|y_t-y_t^{\mathrm{target}}\|\approx 0\quad\text{under a constant unknown bias, provided the augmented pair is observable and the observer is stable}$$

Mathematical statement

The paper starts from the mechanical decomposition $M(\kappa)\ddot{\kappa}+C(\kappa,\dot{\kappa})\dot{\kappa}+K(\kappa)=u+d_{\mathrm{cat}}$, where $\kappa$ is curvature, $u$ is tendon input, $M$ is effective inertia, $C$ is damping, $K$ is stiffness, and $d_{\mathrm{cat}}$ aggregates contact, friction, backlash, and hysteresis. Transfer this decomposition to a learned discrete-time model $x_{t+1}=f_\theta(x_t,u_t)+E d_t$, $y_t=g_\theta(x_t)$, with disturbance evolution $d_{t+1}=\rho d_t+w_t$. Here $x_t$ is the learned latent state, $u_t$ is the input, $y_t$ is the observed output, $E$ maps disturbance into state dynamics, $\rho\in[0,1]$ controls disturbance persistence, and $w_t$ is process noise. An augmented Kalman filter or differentiable recurrent observer estimates $[x_t,d_t]$ from observations. For $\rho$ close to one, persistent modeling bias is represented as a state rather than repeatedly injected prediction error. The measurable signature is offset decay: after a constant unknown bias is introduced, the steady-state output error should approach zero, whereas the unaugmented model retains a nonzero residual.

Implementation notes

1. Integration point: use a small GRU, MLP state-space model, or diagonal SSM as the nominal predictor $f_\theta$. Add a disturbance vector $d_t\in\mathbb{R}^r$, initially with $r=1$ or $r=4$, injected through a learned matrix $E$ into the latent transition or output head. Maintain the augmented state $z_t=[x_t;d_t]$ with an observer update after each measurement. 2. Pseudocode: predict $x^-_{t+1}=f_\theta(x_t,u_t)+Ed_t$ and $d^-_{t+1}=\rho d_t$; compute $y^-_{t+1}=g_\theta(x^-_{t+1})$; form innovation $e=y_{t+1}-y^-_{t+1}$; update $[x_{t+1},d_{t+1}]=[x^-_{t+1},d^-_{t+1}]+Le$, where $L$ is a learned or Kalman-style gain. Train with multi-step prediction loss plus $\lambda_d\|d_{t+1}-\rho d_t\|^2$ and constrain the observer transition spectral radius below one. 3. Computed versus estimated: the disturbance decomposition and persistence mechanism are taken from the paper; $E$, $L$, $\rho$, and the neural dynamics are estimated from data. 4. First cheap experiment: train a GRU on Pendulum, CartPole, or a one-dimensional mass-spring dataset, then add an unobserved constant force and slowly varying sinusoidal force at test time. Compare a standard GRU, an augmented model with $\rho=0.99$, and one with learned $\rho$. The quantitative prediction is that the augmented model's post-perturbation mean output bias will fall by at least 80%, and with observer correction its residual will converge near sensor-noise level. With correction disabled, disturbance magnitude should decay approximately as $\rho^t$. Sweep observer gain and report divergence when the estimated augmented-transition spectral radius reaches one.

Verification

Failed on benchmark

Stage 1 · Toy mechanism gate: Passed ✓

Stage 2 · Mechanism transferred to benchmark: Not reproduced ✗

Stage 2 · Practical benchmark result: Inconclusive

Methodology: 8 paired seeds, permutation test (p<0.05) against a learning-rate-tuned baseline. How verification works

Stage 1 — Mechanism check agent confidence 9/10

Built a scalar disturbance-augmented state-space observer and verified the mechanism numerically. The three predicted behaviors manifested: disturbance decay matched rho^t exactly, the observed stability boundary was lx≈2.22 versus the analytic 1+1/a≈2.22, and rho=0.99 reduced constant-bias RMSE by 95.8% versus the nominal observer. This is a clear toy-level win, though not yet evidence for a learned neural model.

Agent confidence: 9/10

Baseline: Nominal observer post-transient RMSE 0.1989; persistent final error about 0.199.
Idea: Augmented observer at rho=0.99 post-transient RMSE 0.00828, 95.84% reduction, final absolute error 0.00791; rho^t persistence max absolute verification error 0.0.

Limitations: Only a scalar, known nominal linear system was tested; there was no trained GRU/MLP, learned rho, multidimensional disturbance, slowly varying sinusoidal disturbance, FLOP/speed comparison, or broad gain/noise sweep. The persistence verification is an exact recurrence check rather than an independently simulated noisy observer trajectory.

How to run: python3 experiment.py

Stage 2 — Benchmark vs. tuned baseline (arXiv:2607.20939) Aug 31, 2026

No significant difference vs. the tuned baseline (+10.1%, p=0.2879, wins 4 / 8 paired seeds).

Benchmark: Dynamics forecasting
Model: rnn_small
Paired seeds: 8
Baseline mean: 0.0001
Idea mean: 0.0001
Effect (Δ): 0 (+10.1%; negative = idea better)
Wins: 4 / 8 paired seeds
p-value: 0.2879 (permutation test, 20 000 shuffles)
Smallest detectable effect: ±18.4%
Mechanism: Not confirmed ✗
Practical effect: Inconclusive
Baseline tuning: swept over 3 configs

Limitations:

Only the built-in controlled-pendulum dynamics track was tested. The intervention used a scalar output disturbance initialized from the final observation rather than a full latent Kalman observer, did not learn rho, and did not test sinusoidal disturbances, multidimensional disturbance ranks, observer-gain sweeps, rollout horizons beyond the benchmark target, FLOPs, or wall-clock speed.

How to run: python3 bench_experiment.py

Verdict computed by deterministic test code from paired-seed statistics — not by the language model.

Stage 2 — Benchmark Aug 31, 2026 latest Failed ✗

Agent confidence: 9/10

Implemented an end-to-end disturbance-augmented GRU on the structurally matched controlled-pendulum dynamics track, with identical learning-rate sweep values and eight paired seeds against the standard rnn_small baseline. The idea was slightly worse: baseline MSE 5.3983e-05 versus idea MSE 5.9412e-05, paired delta +5.4291e-06, permutation p=0.2879. The trained-model constant-bias signature was also not confirmed, showing a 1.09% increase rather than the predicted 80% reduction.

Baseline: rnn_small, best lr=0.01, full 8-seed mean MSE=5.398313965088164e-05, std=3.768574167715651e-05
Idea: disturbance GRU, rho=0.99 and lr=0.01, full 8-seed mean MSE=5.941226436334546e-05, std=3.632683313745886e-05
Math sanity: rho persistence max absolute error <=1.11e-16; scalar stability boundary analytic 2.43902439 versus grid observed 2.439
Mechanism signature: constant test bias 0.25: baseline MAE 0.2497041, idea MAE 0.2524243, reduction fraction -0.01089, confirmed=false
Paired delta: idea-baseline = +5.4291247124638176e-06; idea wins 4/8; permutation p=0.2879

Benchmark result