On the Divergence of Accuracy and Mechanism Consistency in Time Series World Models

Haochen Zhang; Jiaheng Guo; Zhen Xu; Zachary Plotkin; Nicholas Konz; Zhen Tan; Tianlong Chen

cs.AIOct 1, 2026

On the Divergence of Accuracy and Mechanism Consistency in Time Series World Models

Authors: Haochen Zhang, Jiaheng Guo, Zhen Xu, Zachary Plotkin, Nicholas Konz, Zhen Tan, Tianlong Chen

Organizations: University of North Carolina at Chapel Hill · Foci Labs · Stevens Institute of Technology

Abstract

A time series world model (TSWM) predicts a controlled system's state from its observed history and planned actions and exogenous inputs. Current approaches build forecasters with actions as covariates, trained and evaluated on prediction error under the executed plan. Yet world models compare unexecuted plans, but their responses to changed plans remain untested. We ask which design choices matter and whether accurate forecasters respond to changed plans as real systems do. We address both with a formalization and benchmark. The formalization separates state, actions and exogenous inputs, distinguishes continuous, mode and event actions, and introduces mechanism consistency, a metric built on declared action-state relations with known directions, such as a vasopressor raising blood pressure: it checks whether shifting an action moves the forecast in the declared direction. The benchmark consolidates eight public datasets with real actions from engineered infrastructure and clinical care, varying prediction space, plan fusion and plan encoding across seven backbones and five seeds. First, a frozen latent prediction space lowers MAE by 9.9% over observation space and gated output fusion lowers it by 12.7% over input concatenation on average, with both improving all eight datasets; temporal plan encoding changes average MAE by at most 2.2%. Second, prediction error and mechanism consistency diverge: the lowest-error configuration is at or below chance in consistency on four of five datasets with declared mechanisms, and no design choice avoids this. Finally, directional supervision, a loss penalizing the wrong-signed part of the response to a shifted action, significantly raises consistency on penalized mechanisms with no change in MAE. Together they give TSWMs a recipe: a frozen latent space and output-side fusion for accuracy, and a training objective for mechanism consistency.

Figures & tables

Figure 1: Two plans from the same history. We sweep three design choices and score mechanism consistency.

Figure 2: Overview of the formalization and the model. Top: the channel roles, the window of history, plan and outcome, and the two metrics (Section 3.1 ). Bottom: the model and its three design choices (Section 3.2 ); the concatenation baseline conditions the backbone instead (Appendix B ).

			scale		series dim.		actions
Dataset	Domain	$\Delta t$	systems	windows	state	exog.	cont.	mode ( $K$ )	event
Greenhouse	horticulture	5 min	5/1	163	4	8	7	–	–
PleiaData	building HVAC	10 min	50/12	7,548	2	8	1	2 (2,6)	–
PREDIST	district heating	10 min	46/12	6,109	5	2	2	3 (2,3,2)	–
Wastewater	water treatment	2 min	1 plant	1,311	3	2	3	2 (2,2)	–
VitalDB	anesthesia	2 s	2,754/689	40,193	4	–	2	–	–

Table 1: The eight datasets, four engineered and four clinical. Systems are counted train/held-out; windows are held-out windows at

L\!=\!256

H\!=\!16

, stride

80

. The action columns are the three factors of

\mathcal{U}

d_{c}

continuous channels,

d_{m}

mode channels with their cardinalities

K_{j}

, and the number of event types

|\mathcal{A}|

Dataset	Action	State	Sign
Greenhouse	heating-pipe temp.	air temp.	$+$
	leeward vent	air temp.	$-$
	windward vent	air temp.	$-$
	CO 2 dosing	CO 2 level	$+$
VitalDB	propofol	BIS	$-$
	propofol	MAP	$-$

Table 2: The twenty-one declared mechanisms. A plus sign means that raising the action raises the state, a minus sign that it lowers it; the PleiaData mechanisms hold in the named mode. BIS, bispectral index; MAP, mean arterial pressure; FiO 2 , inspired oxygen fraction.

	Option	Greenhouse	PleiaData	PREDIST	Wastewater	VitalDB	CGMacros	Shanghai	MIMIC-Cardio	Rank
Space	Observation	.0821 ±.0269	.0476 ±.0306	.1866 ±.0099	.1718 ±.0116	.0377 ±.0090	.0131 ±.0054	.1330 ±.0132	.0562 ±.0029	2.52
	AE	.0761 ±.0200	.0337 ±.0252	.1821 ±.0047	.1695 ±.0123	.0329 ±.0026	.0114 ±.0049	.1249 ±.0096	.0552 ±.0021	1.93
	VAE	.0956 ±.0134	.0339 ±.0244	.1836 ±.0054	.1672 ±.0106	.0336 ±.0039	.0105 ±.0025	.1206 ±.0048	.0552 ±.0020	1.95
	JEPA	.1041 ±.0271	.0607 ±.0359	.2143 ±.0327	.1824 ±.0266	.0403 ±.0112	.0270 ±.0233	.1418 ±.0208	.0621 ±.0095	3.61
Fusion	None	.0751 ±.0364	.0292 ±.0172	.1858 ±.0219	.1928 ±.0085	.0396 ±.0187	.0174 ±.0187	.1257 ±.0155	.0608 ±.0174	4.89
	Concat	.0761 ±.0200	.0337 ±.0252	.1821 ±.0047	.1695 ±.0123	.0329 ±.0026	.0114 ±.0049	.1249 ±.0096	.0552 ±.0021	5.70

Table 3: Validation MAE of the three sweeps. Mean

\pm

std over the

35

backbone–seed runs of one dataset and one option (

70

for encoding, which pools Gate and FiLM-0 ); the std spans backbones. The fixed choices of each sweep are given in Section 4.2 . Bold is the lowest mean of each block, Rank is the mean rank over dataset–backbone cells, and the shaded row has the best rank of its block. Lower is better.

Figure 3: Mechanism consistency of the three sweeps. $\mathrm{MC}$ at $\delta=\pm 0.1$ , averaged over both directions, the declared mechanisms and the runs of Table 3 . White is chance, green agrees with the declared sign, red opposes it. Boxes mark the lowest-MAE choice of each row. None is omitted because its forecast does not move. Numbers are in Appendix E .

Figure 4: Directional supervision against the Gate control. Left: mechanism consistency (

\mathrm{MC}

\delta=+0.1

) on the penalized mechanisms, mean over the

35

backbone–seed runs of each dataset, with the paired gain. Right: change in validation MAE relative to Gate per run, with the median (diamond), a

90\%

interval (bar) and the

\pm 5\%

band (shaded).

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Adjusted forecast ${\bm{z}}^{\prime}_{t+k}$	Details
None	$\widehat{\bm{z}}_{t+k}$	Plan discarded.
Concat	$\widehat{\bm{z}}_{t+k}$ , backbone input $[{\bm{z}}_{s};\widetilde{\bm{a}}_{s}]$	The history plan enters with the latent history; the future plan $\widetilde{\bm{a}}_{t+k}$ enters through the native covariate interface of TimeXer and TiDE, and through $\mathrm{MLP}([\widehat{\bm{z}}_{t+k};\widetilde{\bm{a}}_{t+k}])$ otherwise.
Res	$\widehat{\bm{z}}_{t+k}+g(\bm{\phi}_{k})$	Standard initialization.
Res-0	$\widehat{\bm{z}}_{t+k}+g(\bm{\phi}_{k})$	Output layer of $g$ zero-initialized.
FiLM-0	$(1+\bm{\gamma}_{k})\odot\widehat{\bm{z}}_{t+k}+\bm{\beta}_{k}$	$[\bm{\gamma}_{k};\bm{\beta}_{k}]=g(\bm{\phi}_{k})$ , output layer zero-initialized.
Gate	$\widehat{\bm{z}}_{t+k}+\bm{\alpha}_{k}\odot\sigma({\bm{b}}_{k})$	$[\bm{\alpha}_{k};{\bm{b}}_{k}]=g([\bm{\phi}_{k};\widehat{\bm{z}}_{t+k}])$ , $\sigma$ the logistic function.

Appendix

Table 4: Plan-fusion methods.

\widehat{\bm{z}}_{t+k}

is the plan-blind forecast of the backbone at horizon step

t+k

and

{\bm{z}}^{\prime}_{t+k}

the adjusted forecast that is decoded;

\widetilde{\bm{a}}

is the encoded plan. Concat is the only method whose plan enters the backbone itself.

Encoder	Encoded plan $\widetilde{\bm{a}}_{s}$	Details
Instant	${\bm{a}}_{s}$	Identity.
Decay	${\bm{a}}_{s}+\bm{\eta}\odot({\bm{m}}_{s}-{\bm{a}}_{s})$	${\bm{m}}_{s}=(1-\bm{\alpha})\odot{\bm{a}}_{s}+\bm{\alpha}\odot{\bm{m}}_{s-1}$ with $\bm{\alpha}=\sigma(\bm{\theta})$ learned per channel; the gate $\bm{\eta}$ is zero-initialized.
Conv	${\bm{v}}^{(6)}_{s}$ , with ${\bm{v}}^{(0)}={\bm{a}}$	Six residual blocks ${{\bm{v}}^{(l)}_{s}={\bm{v}}^{(l-1)}_{s}+\mathrm{GELU}({\bm{c}}^{(l)}_{s})}$ with ${{\bm{c}}^{(l)}_{s}=\sum_{j=0}^{7}{\bm{w}}^{(l)}_{j}\odot{\bm{v}}^{(l-1)}_{s-2^{l-1}j}}$ : depthwise kernels of eight taps with dilation $2^{l-1}$ , zero-initialized; receptive field $442$ steps.
Attn	${\bm{a}}_{s}+W_{o}\,\mathrm{MHA}({\bm{o}}_{s},\,{\bm{o}}_{\leq s},\,{\bm{o}}_{\leq s})$	${\bm{o}}_{s}=W_{i}{\bm{a}}_{s}+{\bm{p}}^{\prime}_{s}$ with position embeddings ${\bm{p}}^{\prime}_{s}$ ; causal mask; four heads, width $64$ ; $W_{o}$ zero-initialized.

Appendix

Table 5: Plan encoders. Each maps the plan

{\bm{a}}_{t-L+1:t+H}

\widetilde{\bm{a}}_{t-L+1:t+H}

of the same width, causally and per channel unless stated otherwise; all parameters are per-channel vectors in

\mathbb{R}^{C}

except for Attn .

Forecasting protocol (Experiments 1–3, the diagnostic of Appendix G and Section 5 , whose added term is in Appendix F )
Window	context $L=256$ , horizon $H=16$ , stride $80$
Optimizer	Adam, learning rate $10^{-3}$ , no weight decay, batch size $128$
Schedule	halve the learning rate after $5$ epochs without held-out improvement
Stopping	at most $100$ epochs; stop after $20$ epochs without held-out improvement; the checkpoint with the lowest held-out loss is kept
Loss	MSE between the decoded forecast and the observed future states; gradients clipped at norm $1$
Seeds	training seeds $0$ – $4$ (initialization, minibatch order, dropout); the split is fixed at seed $0$ with a held-out fraction of $0.2$

Appendix

Table 6: Hyperparameters. Shared by every dataset, backbone, design choice and seed unless a row says otherwise.

L

H

and

d_{c}

are as in Section 3.1 ;

d

is the latent width;

\mathrm{MAD}

is the median absolute deviation.

Sweep	Method	Mean rank	$\Delta$ MAE vs. ref.	Params.
Prediction space	Observation	2.52	–	–
	AE	1.93	$-9.87\%$	–
	VAE	1.95	$-7.54\%$	–
	JEPA	3.61	$+20.21\%$	–
Plan fusion	None	4.89	$+5.73\%$	0
	Concat	5.70	–	–

Appendix

Table 7: Additional summaries of the three sweeps. References are observation space, Concat , and Instant , respectively. Relative MAE and ranks use seed-averaged paired cells. Parameter counts are dataset-averaged fusion-adapter or temporal-encoder sizes, excluding the backbone, codec, and shared embeddings.

Exp.	Contrast	$\Delta$ MAE	$95\%$ CI (bootstrap over datasets)	Datasets
1	AE vs. observation	$-9.87\%$	$[-17.71,-3.93]\%$	8/8
1	VAE vs. observation	$-7.54\%$	$[-16.35,+1.96]\%$	7/8
1	JEPA vs. observation	$+20.21\%$	$[+9.28,+37.40]\%$	0/8
1	VAE vs. AE	$+2.59\%$	$[-1.93,+9.75]\%$	3/8
2	Gate vs. Concat	$-12.73\%$	$[-19.03,-7.12]\%$	8/8
2	Gate vs. None	$-17.47\%$	$[-24.22,-10.90]\%$	8/8

Appendix

Table 8: Paired effects of the three sweeps.

\Delta

MAE is the geometric-mean change in validation MAE of the first method against the second, with its

95\%

bootstrap interval over datasets; Datasets counts the datasets on which the first method is better. Negative values favor the first method.

	Option	Greenhouse	PleiaData	PREDIST	VitalDB	MIMIC-Cardio	Mean
Space	Observation	.61 ±.13	.49 ±.10	.97 ±.03	.51 ±.10	.35 ±.14	.59
	AE	.55 ±.17	.51 ±.11	.92 ±.15	.55 ±.10	.33 ±.17	.57
	VAE	.47 ±.26	.53 ±.15	.98 ±.03	.47 ±.05	.33 ±.08	.55
	JEPA	.55 ±.15	.44 ±.16	.88 ±.13	.51 ±.11	.33 ±.10	.54
Fusion	Concat	.55 ±.17	.51 ±.11	.92 ±.15	.55 ±.10	.33 ±.17	.57
	Res	.49 ±.11	.46 ±.10	.97 ±.02	.35 ±.09	.48 ±.09	.55

Appendix

Table 10: Mechanism consistency of the three sweeps, the numbers behind Figure 3 . The

\mathrm{MC}

metric of Section 3.1 at

\delta=\pm 0.1

, averaged over both directions and over the mechanisms a dataset declares, as mean

\pm

std over the

35

backbone–seed runs of one dataset and one option, or

70

for encoding, which pools Gate and FiLM-0 . Chance is

0.5

and

1

is perfect agreement with the declared mechanism. None discards the plan, so its forecast does not move and it is omitted. Bold marks the highest unrounded mean of each block in each column; Mean averages the five datasets. Wastewater is set aside, see Appendix E.1 and Table 11 . Higher is better.

Dataset	Mechanism	Sign	Concat	Gate	FiLM-0	seed range
Greenhouse	Tpipe $\to$ Tair	$+$	.83	.97	.99	.03
	CO2dosing $\to$ CO2air	$+$	.48	.08	.17	.29
	VentLee $\to$ Tair	$-$	.61	.64	.36	.77
	VentWind $\to$ Tair	$-$	.28	.19	.22	.66
PleiaData	setpoint_norm@mode=1 $\to$ indoor_temp	$+$	.80	.60	.50	.75
PleiaData	setpoint_norm@mode=2 $\to$ indoor_temp	$-$	.21	.37	.42	.57

Appendix

Table 11: Mechanism consistency per declared relation under the three fusion methods that Section 4.3 discusses. Mean over

35

backbone–seed cells; the four engineered datasets first, then the two clinical ones. Sign is the declared direction. Seed range is the median over backbones of the spread of the five seeds of one cell configuration on that relation.

				$\delta=+0.1$		$\delta=-0.1$		lowest cell
Dataset	Action $\to$ State	Sign	Pen.	Gate	$+$ DS	Gate	$+$ DS	$+$ DS, $\delta=+0.1$
Greenhouse	heating-pipe temp. $\to$ air temp.	$+$	$\checkmark$	0.973	1.000	0.974	1.000	1.000
Greenhouse	leeward vent $\to$ air temp.	$-$	$\checkmark$	0.653	1.000	0.634	1.000	0.991
Greenhouse	windward vent $\to$ air temp.	$-$	$\checkmark$	0.196	1.000	0.181	1.000	1.000
Greenhouse	CO 2 dosing $\to$ CO 2 level	$+$		0.097	0.154	0.068	0.126	0.000
PleiaData	setpoint (heating) $\to$ indoor temp.	$+$	$\checkmark$	0.606	1.000	0.601	1.000	1.000

Appendix

Table 12: Mechanism consistency of every declared relation with and without directional supervision. Mean over the

35

backbone–seed runs of Gate and of Gate

+

directional supervision (

+

DS) under the upward and the downward shift; Pen. marks the twelve penalized mechanisms, the training shift is upward only. The last column is the lowest of the

35

runs of

+

DS under the upward shift. The last block holds the two relations that Section 4.1 sets aside; the on/off relation is categorical and has no downward shift.

Dataset	Pen.	Gate	$+$ DS	$\Delta$ MAE (median)	$90\%$ interval
Greenhouse	3	0.0632	0.0639	+0.03%	$[-0.24,+2.11]\%$
PleiaData	1	0.0205	0.0198	$-$ 1.54%	$[-9.60,+3.34]\%$
PREDIST	2	0.1641	0.1641	+0.35%	$[-0.34,+0.38]\%$
VitalDB	2	0.0313	0.0312	$-$ 0.07%	$[-0.70,+0.33]\%$
MIMIC-Cardio	4	0.0543	0.0542	$-$ 0.15%	$[-0.26,-0.03]\%$
Wastewater	0	0.1500	0.1498	+0.00%	$[-0.59,+0.34]\%$

Appendix

Table 13: Validation MAE with and without directional supervision. Mean over the

35

backbone–seed runs of each dataset; Pen. is the number of penalized mechanisms.

\Delta

MAE is the median of the paired relative change and the interval is a

t

-based

90\%

interval on the paired log ratios, as in Figure 4 . The pooled row pairs all

210

runs. Wastewater has no penalized mechanism and is the null control.

Dataset	$\lambda\!=\!0$	$\lambda\!=\!0.1$	$\lambda\!=\!0.3$
MAE (fused, $H\!=\!16$ )
Greenhouse	0.0632 ±.0005	0.0651 ±.0004	0.0658 ±.0009
VitalDB	0.0313 ±.0002	0.0312 ±.0001	0.0312 ±.0001
CGMacros	0.0086 ±.0001	0.0095 ±.0001	0.0098 ±.0002
Shanghai	0.1165 ±.0010	0.1174 ±.0010	0.1177 ±.0007
MIMIC-Cardio	0.0543 ±.0001	0.0545 ±.0001	0.0545 ±.0001

Appendix

Table 14: Auxiliary-loss results by dataset. The first two blocks report

16

-step full-model and pre-fusion MAE over seven backbones and five seeds. Rollout error is for steps

49

–

64

, not the cumulative horizon. It uses

273

matched triples:

35

per dataset except VitalDB (

28

; all TimeXer runs and two TimeKAN seeds missing). Subscripts are SDs over five seed means of available backbones; VitalDB coverage varies by seed. Bold marks the lowest unrounded mean of each row. Relative changes use seed-averaged cells in the first two blocks and matched backbone–seed triples for rollout.

Backbone dropped	$\Delta$ MAE		$\Delta$ MAE bypass
	$\lambda\!=\!0.1$	$\lambda\!=\!0.3$	$\lambda\!=\!0.1$	$\lambda\!=\!0.3$
none (full set)	$+1.75\%$	$+2.78\%$	$-44.73\%$	$-47.83\%$
TimeXer	$+2.35\%$	$+3.73\%$	$-45.24\%$	$-48.53\%$
TiDE	$+2.16\%$	$+3.37\%$	$-45.90\%$	$-49.20\%$
DUET	$+2.05\%$	$+2.90\%$	$-45.85\%$	$-48.87\%$
PatchTST	$+1.95\%$	$+3.26\%$	$-45.70\%$	$-48.63\%$

Appendix

Table 15: Sensitivity to backbone inclusion. Each row removes one backbone and recomputes the geometric-mean change relative to

\lambda=0

. Negative values indicate lower MAE. Removing CrossLinear changes the average full-model effect to approximately zero while retaining a large bypass gain, showing where the observed cost is concentrated.

Dataset	Backbone	Observation	AE	VAE	JEPA
Greenhouse	TimeXer	0.0627 ±.0008	0.0604 ±.0006	0.1051 ±.0009	0.0882 ±.0206
	TiDE	0.0635 ±.0026	0.0658 ±.0027	0.1094 ±.0007	0.1158 ±.0152
	DUET	0.0920 ±.0084	0.0709 ±.0016	0.0962 ±.0134	0.1453 ±.0261
	PatchTST	0.0986 ±.0334	0.0924 ±.0334	0.0921 ±.0025	0.1019 ±.0152
	TimeKAN	0.0620 ±.0007	0.0642 ±.0011	0.0770 ±.0022	0.0894 ±.0282
	CrossLinear	0.1147 ±.0327	0.1066 ±.0024	0.0996 ±.0142	0.0827 ±.0065

Appendix

Table 16: Experiment 1, prediction space: the complete grid. Validation MAE, mean and SD over five training seeds.

Dataset	Backbone	None	Concat	Res	Res-0	FiLM-0	Gate	X-attn
Greenhouse	TimeXer	0.0587 ±.0006	0.0604 ±.0006	0.0625 ±.0019	0.0621 ±.0013	0.0617 ±.0008	0.0608 ±.0012	0.0651 ±.0021
	TiDE	0.0609 ±.0005	0.0658 ±.0027	0.0636 ±.0017	0.0635 ±.0020	0.0629 ±.0012	0.0615 ±.0006	0.0641 ±.0011
	DUET	0.0657 ±.0006	0.0709 ±.0016	0.0670 ±.0013	0.0678 ±.0013	0.0642 ±.0006	0.0649 ±.0017	0.0694 ±.0014
	PatchTST	0.0563 ±.0008	0.0924 ±.0334	0.0606 ±.0013	0.0612 ±.0013	0.0605 ±.0026	0.0590 ±.0014	0.0694 ±.0039
	TimeKAN	0.0587 ±.0004	0.0642 ±.0011	0.0656 ±.0020	0.0650 ±.0022	0.0645 ±.0014	0.0636 ±.0017	0.0659 ±.0026
	CrossLinear	0.1626 ±.0056	0.1066 ±.0024	0.0731 ±.0009	0.0732 ±.0016	0.0721 ±.0039	0.0703 ±.0019	0.1310 ±.0060

Appendix

Table 17: Experiment 2, plan fusion: the complete grid. The Concat entries reuse the AE results from Table 16 .

Dataset	Backbone	Instant	Decay	Conv	Attn
Greenhouse	TimeXer	0.0608 ±.0012	0.0610 ±.0017	0.0611 ±.0018	0.0608 ±.0010
	TiDE	0.0615 ±.0006	0.0614 ±.0007	0.0616 ±.0009	0.0614 ±.0011
	DUET	0.0649 ±.0017	0.0657 ±.0011	0.0656 ±.0017	0.0646 ±.0009
	PatchTST	0.0590 ±.0014	0.0586 ±.0016	0.0596 ±.0009	0.0589 ±.0018
	TimeKAN	0.0636 ±.0017	0.0637 ±.0016	0.0635 ±.0018	0.0634 ±.0015
	CrossLinear	0.0703 ±.0019	0.0706 ±.0028	0.0705 ±.0013	0.0713 ±.0007

Appendix

Table 18: Experiment 3, plan encoding with Gate : the complete grid. The Instant entries reuse the Gate results from Table 17 .

Dataset	Backbone	Instant	Decay	Conv	Attn
Greenhouse	TimeXer	0.0617 ±.0008	0.0613 ±.0007	0.0623 ±.0013	0.0618 ±.0011
	TiDE	0.0629 ±.0012	0.0629 ±.0012	0.0631 ±.0013	0.0627 ±.0015
	DUET	0.0642 ±.0006	0.0642 ±.0014	0.0649 ±.0005	0.0655 ±.0014
	PatchTST	0.0605 ±.0026	0.0596 ±.0009	0.0609 ±.0024	0.0598 ±.0010
	TimeKAN	0.0645 ±.0014	0.0654 ±.0026	0.0648 ±.0015	0.0637 ±.0013
	CrossLinear	0.0721 ±.0039	0.0724 ±.0038	0.0722 ±.0033	0.0720 ±.0029

Appendix

Table 19: Experiment 3, plan encoding with FiLM-0 : the complete grid. The Instant entries reuse the FiLM-0 results from Table 17 ; Table 18 gives the same grid with Gate .

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