When Dynamics Models Read the Wrong Time Steps: Label-Free Event Credit Re-Anchoring for Robust Global Readouts

Abstract: Learned dynamics models often answer global physical questions, such as fault severity or impact stiffness, by pooling a per-step feature sequence into one readout vector. This sequence-to-global interface creates an under-studied temporal credit problem: with only trajectory-level supervision, a model can predict accurately in training conditions while reading from abundant smooth correlates rather than the brief physical events that determine the target. We call this failure temporal credit dilution. It is not exposed by the training loss and is not removed by standard physics-informed residuals, because the error lies in where the global readout assigns functional credit. We introduce Credit-in-Event, an interface-level probe for measuring how much pooled credit lands on event steps, and prove in closed form that a pooled linear reader routes credit to a spurious background channel as the event fraction shrinks. We then propose CREST, a training-free and label-free readout that estimates a transient event core from learned features and re-anchors the pooled representation through event-versus-rest contrast. Across simulated gear and impact systems, recurrent and attention encoders, and public bearing vibration data, CREST reduces out-of-distribution error while restoring event credit. Ablations show that stable-step selection and receptive-field shrinking fail, confirming that the gain comes from event-core credit re-anchoring rather than a generic locality or stability prior.

• The study introduces the concept of 'temporal credit dilution' as a failure mode in sequence-to-global dynamics models, where the model relies on non-causal correlates instead and not the decisive content itself
• The proposed CREST (Credit RE-anchoring through Sparse Transients) method improves upon this greatly by leveraging transient events and event credits. It offers training-free, label-free readout replacement
• Creates normalized, low pass residuals for each feature channel and average across channels for a calculated transience score.

The problem: pooled readouts that read the wrong steps

Learned dynamics models frequently answer global physical questions—fault severity, impact stiffness, stability margins—by encoding a trajectory into a per-step feature sequence, pooling that sequence into a single vector, and applying a linear readout. The paper under review identifies a failure mode specific to this interface: because supervision is one label per trajectory, the training loss never specifies which time steps should determine the answer. When the physically decisive content is concentrated in brief events while a smooth global statistic correlates with the label during data collection, a pooled reader can minimize training error by placing its functional credit on the smooth statistic. The authors term this temporal credit dilution: the sparse events that determine the target receive negligible credit in the pooled representation, and the prediction rests on a non-causal correlate.

The failure is invisible to standard diagnostics. In-distribution validation error decreases smoothly; physics-informed residuals constrain local state evolution but leave the global aggregation free to summarize whatever is predictive rather than what is decisive. Only a distribution shift that breaks the smooth correlate exposes the problem, at which point the model has already committed to reading the wrong steps.

A closed-form account of dilution

The theoretical core is a two-channel generative model: an invariant event channel observed only on an event set of fraction $\varepsilon$, and a spurious background channel occupying the remaining $(1-\varepsilon)T$ steps with cue strength $\gamma$. A pooled linear reader sees only global means. Because averaging shrinks the event amplitude by $\varepsilon$, its pooled signal-to-noise ratio scales as $S_E = \varepsilon^2 T / s_0^2$, while the background cue retains order-one signal power. Proposition 1 shows that the population least-squares reader assigns event credit share $\rho_E = \Theta(\varepsilon^2)$: as the event fraction shrinks, in-distribution risk approaches $1/(1+S_B)$ while out-of-distribution risk (with the cue removed) exceeds that of predicting the mean. Notably, this is not an optimization pathology—the failure is the population-optimal pooled solution in the sparse-event regime.

A corollary establishes an interface-measurement principle with practical consequence for attribution methods: the input-gradient sensitivity ratio between event and background steps is order one and can exceed one, so gradient-based saliency can flag event steps as locally sensitive while their aggregate contribution to the pooled vector remains negligible. Input-level shortcut detection therefore cannot see this failure class.

Training-dynamics experiments on a gear simulator corroborate the theory: in-distribution error falls by nearly an order of magnitude while out-of-distribution error stalls and event credit rises briefly then decays below the chance line. Two-factor isolation experiments show that an event-localized auxiliary loss (a positive control requiring labels) restores credit and halves out-of-distribution error, whereas shrinking the aggregation window—a locality prior—does not move credit onto events and hurts both errors.

CREST: label-free re-anchoring via transient cores

The proposed remedy, CREST (Credit RE-anchoring through Sparse Transients), is a training-free, label-free readout replacement. It computes a normalized low-pass residual per feature channel—deviation from a Gaussian-smoothed temporal profile—and averages across channels to obtain a transience score. From the concentration of this profile (an inverse participation width), it estimates the event budget $\hat\varepsilon$ by blending a sharp-core estimate with an Otsu-thresholded tail estimate, and sets a contrast weight $\alpha$ that strengthens event-versus-rest contrast for sharp cores. Per channel, it selects top transience entries, dilates them into a mask, and forms the pooled vector as a weighted combination of the selected-minus-rest contrast and the global mean:

$$p=\alpha\big(\bar F_{\mathrm{sel}}-\bar F_{\mathrm{rest}}\big)+(1-\alpha)\,\bar F_{\mathrm{global}}.$$

Selection is non-differentiable with stop-gradients through the mask. All constants are fixed before evaluation and shared across systems; no event labels, out-of-distribution labels, or per-system test tuning are used. A recovery proposition shows the anchored event signal-to-noise ratio scales linearly in the selected support $(1-\varepsilon)T$0 (versus quadratically in $(1-\varepsilon)T$1 under pooling), and a budget-law theorem establishes that risk is U-shaped in $(1-\varepsilon)T$2 with its minimum at the true event-core size—at $(1-\varepsilon)T$3 the anchored selector degenerates to the same dilution as global averaging.

Empirical evidence

Experiments span two simulators (SG-Drive torsional gear system with faulty-tooth engagement events; a wall-contact impact oscillator targeting log stiffness), recurrent and attention encoders, and the public CWRU bearing vibration benchmark under a held-load split. Headline results over ten seeds:

System	Method	ID RMSE	OOD RMSE	ΔOOD	CiE@1	ECM
SG-Drive	attention	0.052	0.404 ± 0.055	—	0.27	0.26
SG-Drive	CREST	0.072	0.286 ± 0.045	−29%	0.62	0.62
Impact	attention	0.173	1.377 ± 0.087	—	0.02	0.04
Impact	CREST	0.160	0.683 ± 0.105	−50%	0.80	0.86

Paired one-sided signed-rank tests give $(1-\varepsilon)T$4 on both systems. On CWRU, CREST reduces held-load error from 0.874 to 0.589 over five seeds. Stronger baselines fail: last-state pooling, ERM, and group DRO using quartiles of the known spurious speed proxy all reach OOD error near 1.46 on the gear system versus CREST's 0.96—group robustness over the spurious factor does not repair temporal credit.

Three ablation results are particularly informative. First, the budget sweep confirms the U-shaped law, with the empirical minimum tracking the event core. Second, selecting stable rather than transient steps is the worst configuration in the study, ruling out an interpretation of CREST as a generic stability or locality prior transferred from visual-token repair. Third, causal masking validates the restored credit: removing attention's highest-credit steps barely changes its error, while removing CREST's selected steps is catastrophic. Strikingly, on the impact system the label-free adaptive core estimator reaches 0.683, below even the supervised dilated event-window reference—the annotated diagnostic window contains non-informative halo steps, and the informative contact core is narrower than the annotation.

Limitations and open questions

The paper is candid about scope. CREST presupposes that decisive evidence is sparse and transient; if the target is determined by diffuse slow dynamics, or if the spurious cue is itself transient and co-located with the event, the transience prior cannot separate causal from non-causal content. Real-data evidence covers a single public bearing benchmark under a single held-load protocol, which the authors explicitly frame as public evidence rather than field validation. The recovery theorem assumes a noise-independent selector, but CREST reads learned features; a sample-splitting variant mitigates but does not eliminate this dependence. Open questions include whether the budget estimator generalizes to systems with multiple event scales, and whether interface-level probes like Credit-in-Event can be integrated as diagnostics during training rather than post hoc analysis.

Conclusion

This paper formalizes temporal credit dilution as a population-optimal failure of sequence-to-global readouts, proves why global pooling routes credit away from sparse physical events at rate $(1-\varepsilon)T$5, and demonstrates that a training-free transient-core re-anchoring rule restores both out-of-distribution accuracy and event credit across simulated and real systems. Its central claim—that where a global readout reads from deserves scrutiny equal to the loss—is supported by falsification-style ablations showing that locality, stability, and group-robustness remedies all fail where event re-anchoring succeeds.