SAAC-JEPA / project page / arXiv 2609.16071

Source machine, latent state, target machine Animated schematic: a left panel labelled THWS source shows seventeen scrolling teal sensor traces and four amber step-shaped command traces; a violet latent state in the middle pulses when a prediction is emitted, with signal packets travelling from the source panel into it and out to the target; a right panel labelled JOANNEUM target, whose header reads 10 SHARED and 7 ABSENT, shows the same traces entering, where ten keep flowing in teal and seven fade to grey dashed flat lines. THWS SOURCE · SPINNER U5-620 17 CH + 4 CMD · 1 Hz LATENT STATE z PREDICTION EMITTED JOANNEUM TARGET · SEALED 10 SHARED · 7 ABSENT

Scroll sideways to read the figure

World Models for Cross-Machine CNC Transfer under Partial Sensor Overlap

A command-conditioned latent world model, trained on a CNC machine with 17 sensors, selected and locked on that machine alone, then evaluated once on a machine it has never seen, which measures only 10 of them.

Ayoub Louaye BouazizUniversité de Bretagne Occidentale Matthieu OstertagMines Nancy, Université de Lorraine Anton DemaslesMines Nancy, Université de Lorraine

Key findings

Three questions, three answers. Lower RMSE is better; all numbers are in z units of the source normalizer.

  1. Q1Does latent pretraining help on the source machine?

    No. Matched training from scratch does as well as a pretrained body, five seeds each (p = 0.76).

  2. Q2Does it transfer to an unseen machine with 7 sensors missing?

    Yes, above persistence. Locked on source data, evaluated once on the target: R² = 0.012, a small margin.

  3. Q3Why do PatchTST and iTransformer do better?

    Input normalization is enough to explain it. In a post-lock ablation the same model with RevIN matches them, but the target NLL of the paired arms jumps from 0.89 to 20.6.

Abstract

Industrial world models must move between machines whose dynamics, sensing interfaces and command conventions differ. This study asks whether a command-conditioned latent world model—trained to predict future representations of the process rather than to reconstruct future samples—keeps its value on a machine it has never seen: a source CNC machine exposes 17 sensor channels, the target sharing 10 of those. All model selection uses source data only, and the locked configuration is evaluated on the target once. Two findings follow. First, latent-predictive pretraining brings no in-domain forecasting gain over matched training from scratch, so source accuracy alone cannot show what such a representation is worth. Second, the transferred model beats persistence on the unseen machine (with R² ≈ 0.01 against the target mean) but trails official forecasters that normalize each input window by its own statistics; a post-lock ablation, declared before it ran, shows that this input normalization alone closes the gap, and closing it costs predictive calibration. Cross-machine transfer under partial sensor overlap is therefore a distinct evaluation axis for command-conditioned world models.

Two machines, one set of weights

The same process runs on two machines that do not measure the same things. Under domain shift the channels are the same but the signals differ; under schema shift the list of channels itself changes. The target machine has both.

FIG. 1Sensor schemas and commands of the two machinespaper Table 1

THWS · sourceSpinner U5-620 · 62 sessions · 17 channels

  • spindle current
  • spindle torque
  • spindle power
  • X current
  • X torque
  • Y current
  • Y torque
  • Z current
  • Z torque
  • Z power
  • spindle motor temp.
  • X motor temp.
  • Y motor temp.
  • Z motor temp.
  • spindle DC-link voltage
  • spindle modulation depth
  • ambient temp.

JOANNEUM · target7 independent runs · 10 of 17 channels

  • spindle current
  • spindle torque
  • spindle power
  • X current
  • X torque
  • Y current
  • Y torque
  • Z current
  • Z torque
  • Z power
  • spindle motor temp. absent
  • X motor temp. absent
  • Y motor temp. absent
  • Z motor temp. absent
  • spindle DC-link voltage absent
  • spindle modulation depth absent
  • ambient temp. absent

Commands · both machinessetpoints issued by the numerical controller, units aligned

  • spindle speed
  • feed X
  • feed Y
  • feed Z

Each chip is one canonical channel. Teal: measured sensors, solid if the target machine also has the channel, dashed if only the source does. Grey, struck through: the seven source channels absent on the target, which the model reads as absent rather than zero. Amber: the four command channels, present on both machines after unit alignment. Native column names: docs/data.md.

An absent channel is not a zero. Each channel is one token with a presence bit; tokens marked absent are dropped before attention and pooling, so the seven source-only channels simply do not exist for the model on the target, and the same weights read both machines without imputation or retraining.

Context
K = 32 s @ 1 Hz
Horizons
1 2 4 8 16 s
Rollout
direct, one pass
Source windows
18,267 / 3,423 / 5,189
Target windows
2,457 · sealed
Normalizer
source train only

The world model

A forecaster answers “what happens next”. A world model answers “what happens next if the controller issues these commands”. The commands are an input given in advance; nothing here is closed loop.

FIG. 2 Command-conditioned simulation of candidate futures schematic · not dataafter paper Fig. 2
Command-conditioned simulation of candidate futures Animated schematic: a 32-second context window of observed sensor traces is encoded into a latent state; two candidate spindle-speed command sequences, up and down, then produce two diverging multi-horizon predictions with widening uncertainty bands at 1, 2, 4, 8 and 16 seconds. Conceptual, not measured, and not a closed-loop result.

Scroll sideways to read the figure

The same context and latent state are predicted forward at each horizon, directly rather than autoregressively, under two candidate spindle commands; the head emits a mean and a variance per channel. The divergence of the branches and the width of the bands illustrate the mechanism and are not taken from data; the measured command sensitivity is in Fig. 7. Teal: observed sensors; violet: latent state and predictions, solid under candidate A and dashed under candidate B, bands ±1σ; amber: the spindle-speed command, dashed for A and dotted for B.

FIG. 3 Training graph of the command-conditioned latent dynamics after paper Figs. 1(b) and 3
Training graph of the command-conditioned latent dynamics Animated schematic of the world model's training graph. Sensors pass through a schema mask and enter the context encoder together with the presence mask and past commands, producing a context latent. Mean future commands and that latent enter the predictor, which emits predicted latents at horizons of 1, 2, 4, 8 and 16 seconds in one pass. The five future rows are encoded jointly, with zero commands, by an EMA target encoder to give target latents, compared to the predictions through a stop-gradient by the latent loss. Two partial schema views drive the schema-consistency loss, a variance-covariance term regularises the context latent, and a command-recovery head regresses the mean future command from the context and target latents. In the post-lock RevIN variant, shown as dashed green blocks, both windows are first normalised with per-channel statistics of the context window and the physical head output is de-normalised before any loss or metric; the locked model does not include this step. SENSORS xt−K+1:t · 17 ch PAST COMMANDS at−K+1:t SCHEMA MASK m presence bits RevIN variant view A view B Lschema reduced view pulled to the fuller one CONTEXT ENCODER fθe · two passes EMA τ = 0.996 zct context latent PREDICTOR gφ · 5 slots, one pass FUTURE COMMANDS āh = mean at+1:t+h ẑ h = 1 s ẑ h = 2 s ẑ h = 4 s ẑ h = 8 s ẑ h = 16 s FUTURE ROWS xt+h, h ∈ ℋ RevIN same (c, s) TARGET ENCODER fθ̄e · EMA, sg z̄t+h target latent sg[ · ] L lat V(zcpool) variance–covariance, anti-collapse Lact · command recovery rω(zc, z̄t+h) → āh

Scroll sideways to read the figure

One training step. The context encoder reads the present sensors, their presence mask and the past commands; the predictor fills five horizon slots in one pass from the context latent and the mean future command of each horizon; an EMA target encoder, behind a stop-gradient, gives the latents the predictions must match. Three auxiliary terms hold the representation in place. Colours: teal sensors, amber commands, violet latents, red training terms, grey dashed the EMA copy of the encoder, green dashed the post-lock RevIN variant (paper Sec. 4.4 and App. H), not part of the locked model. Symbols: x sensor rows, m presence mask, a commands, āh mean command over (t, t+h], zc context latent, ẑ predicted latent, z̄ target latent, sg stop-gradient (a frozen argument in the Training row below), ℋ = {1, 2, 4, 8, 16} s.

What is modelled, and how it is trained

Object

pθ(xt+1:t+H∣xt−K+1:t,mt−K+1:t,at−K+1:t+H)

Future sensor rows given the last K = 32 rows, their presence mask m and the commands a, past and planned. This is the object of interest; pretraining does not fit it, fine-tuning does.

Model

pθ(xt+ℋ∣·)=∏h∈ℋ𝒩(xt+h;μψ(z^t+h),diagσψ2(z^t+h)) z^t+ℋ=gφ(ztc,(a¯h)h∈ℋ) ztc=fθe(xt−K+1:t,mt−K+1:t,at−K+1:t)

A Gaussian head ψ on each predicted latent, over the grid ℋ = {1, 2, 4, 8, 16} s, with θ = (θe, φ, ψ). The future commands enter through their means āh = mean(at+1:t+h), nested over the five horizons.

Training

𝒥k(ϑ)=ℒlat(ϑ;θ¯k)+0.052V(zpoolc)+0.10ℒschema(ϑ;ϑk)+0.05ℒact(ϑ;θ¯k) ϑk+1=AdamW(ϑk,∇𝒥k(ϑk)) θ¯k+1=τθ¯k+(1−τ)θe,k+1

Pretraining is this iteration, not the minimization of one function. Each step is one AdamW step on 𝒥k (gradient norm clipped to 1) with its second arguments held fixed: the EMA weights θ̄k of the encoder, or a frozen copy ϑk of the current weights (the stop-gradients of the code). ℒlat and ℒschema regress toward, and ℒact reads, quantities computed by the network itself; they are fixed during the step but move with ϑ across steps, so the update is a partial gradient, in general the gradient of no single function: a semi-gradient iteration, as in BYOL or TD learning. It does not by itself exclude collapse: with shared weights and no stop-gradient, ℒlat would be zero for any constant encoder, and the plain JEPA control, trained on ℒlat alone, collapsed on all four seeds.

  • ℒlat smooth-L1 between each predicted latent ẑt+h, computed with ϑ, and the target latent z̄t+h that the EMA encoder computes with θ̄, averaged over horizons.
  • V variance hinge and covariance penalty (α = 25, β = 1) on the pooled context latent. Without an invariance term it is a variance–covariance regularizer, not VICReg (the search labels below still call it VICReg). Its weight is halved because the logged term averages it with the same statistics on the target latents, which depend on θ̄ only and carry no gradient.
  • ℒschema the prediction from a further random channel subset (κ = 0.65), computed with ϑ, is pulled toward the prediction of the fuller view computed with the frozen copy ϑk; with a whole-window channel dropout of 0.15, a channel is missing from the reduced view with probability ≈ 0.45, close to the 7/17 ≈ 0.41 the target lacks.
  • ℒact a small head rω regresses the mean command āh from the context latent, computed with ϑ, and the target latent, computed with θ̄: a weak, multi-step inverse-dynamics term.

Here ϑ = (θe, φ, ω) are the weights trained in pretraining: the command head ω is trained there, the physical head ψ of θ receives no gradient. A low value of 𝒥k is not by itself evidence of a useful representation; collapse is monitored separately. The only loss on the object is the Gaussian negative log-likelihood of the head, added in fine-tuning, where the schema term moves to the physical output; that stage keeps the frozen-argument terms, so it is the same kind of iteration. The weight of ℒlat is 1 by normalization: a common rescaling of the four weights rescales ∇𝒥k, which AdamW's normalized update absorbs (up to its ε and the gradient clip), so three weights are free.

Read the equations carefully

  • Pretraining is only a surrogate for fitting the object, not a bound on its likelihood: during pretraining the head receives no gradient. Whether it helps is an empirical question, and on the source machine it does not (Q1).
  • The model is a product of per-horizon marginals: horizons and channels are treated as conditionally independent given the context and commands, so it does not model their correlations.
  • All horizons come from one pass with a causal slot mask; no predicted latent is fed back, so there is no autoregressive rollout, and the future commands enter only as nested means, not as a step-by-step profile.
Latent
d = 256
Attention
8 heads · 6 temporal layers
EMA
τ = 0.996
Channel dropout
p = 0.15
Schema view
κ = 0.65
Weights λ
1 · 0.05 · 0.10 · 0.05

Where it sits among JEPA world models

As summarized in the paper’s Related Work (Sec. 2); “not discussed” means that summary does not cover it, a dash that the method does without the component. The distinguishing axis here is the shift: the observation space itself changes between training and test.
AspectPLDMEB-JEPALeWorldModelThis work
Inverse dynamicsone-step, at from (zt, zt+1)one-step; in its Two Rooms ablation, removing it collapses the representation—multi-step, mean command from (zct, z̄t+h), λ = 0.05
Anti-collapsevariance, covariance, temporal smoothnesssame familySIGReg, trained end-to-end from pixels, no EMA or stop-gradientvariance, covariance; EMA target, stop-gradient
Useplanning (MPPI)planningnot discussedmulti-horizon prediction under given commands; no planning
Train → test shiftheld-out maze layouts, same physics and observation spacenot discussednot discussednew machine: dynamics change and 7 of 17 channels disappear

Selection without looking at the target

Twenty candidates were written down before any ran and ranked on source validation only. The target machine enters no decision before the lock.

The composite score weights clean, schema-drop, masked and long-horizon RMSE, calibration and the SSL validation score, each z-scored within the pool, and penalizes collapsed seeds and weak command use (RMSE with shuffled commands less than 1.02 times RMSE with true ones). When the provisional winner changed under confirmation, locking was refused and seeds were added. Two candidates collapsed: the plain JEPA control without anti-collapse regularization on all four seeds, and the largest model (d = 512, eight layers) on three of four.

FIG. 4 Leakage-free selection pipeline paper Fig. 4
Leakage-free selection pipeline Animated schematic of the model-selection pipeline: twenty candidate chips are each run with four seeds, ranked by a composite source-validation score; the top five receive a fifth seed, at which point the provisional winner changes — per-horizon VICReg drops from first place and the schema-consistency plus command-recovery variant rises to first. Seven seeds confirm it, the configuration is locked with a SHA-256 hash, and a single arrow leads to the sealed JOANNEUM target test. Target data enters no arrow before the lock. 20 CANDIDATES × 4 seeds each · source only 2 collapsed — plain control 4/4 seeds, d = 512 3/4 COMPOSITE SCORE .30 clean · .25 schema-drop .15 masked · .10 long-h .10 calib penalty · .10 SSL collapse +3 · weak cmd +1 TOP-5 + a 5th seed confirmation stage LEADER CHANGES lock refused extra seeds added to the leaders RANK AFTER 7 SEEDS composite score, lower is better #1 #2 schema + command recovery −0.83 per-horizon VICReg +0.09 the 4-seed leader is not the winner 7 SEEDS stability confirmed 0.822 ± 0.009 RMSE source validation LOCK · SHA-256 config · code normalizer · ckpt JOANNEUM · ONE PASS 0.546 zero-shot RMSE R² = 0.012 · NLL = 0.52 Selection runs on THWS source validation only — the target machine enters no arrow before the lock.

Scroll sideways to read the figure

Four seeds per candidate, a fifth for the top five, a leader change, a refused lock, seven seeds to settle it, and only then one arrow to the sealed target. Scores are composite source-validation scores, z-normalized within the pool, lower is better; RMSE in z units. Red: the refused lock; violet: the lock; teal: candidates, red chips the two that collapsed. A pre-lock model had also been evaluated on the target; those reads entered neither the ranking nor the lock.

Results on the unseen machine

Same 2,457 target windows, same 10 shared channels, no target-side selection for any method.

FIG. 5Zero-shot RMSE on the target machinepaper Table 3

JOANNEUM target, 10 shared channels, 2,457 windows, all horizons pooled; no method is selected on the target. Red dashed line: persistence, the trivial floor; points left of it beat it. Violet: the locked world model, one declared pass. Grey: official baselines, one seed each, no hyperparameter search. Green dashed: the same world model with RevIN, post-lock, mean of three seeds with ± SD as whiskers.

FIG. 6Explained variance by horizon, locked modelpaper Sec. 6.5

Target R² of the locked model at each horizon of ℋ, computed against the pooled target mean, so 0 means “as good as predicting the mean”. Violet: above that reference; grey dashed: below it. The model explains a small share of variance up to 4 s and falls below the mean predictor at 8 and 16 s.

FIG. 7Does it use the commands? Is it calibrated?paper Secs. 4.2, 6.6, 8

Command sensitivity, source

1.058

RMSE with shuffled future commands over RMSE with the true ones, source validation, 7 seeds. The matched candidate without command recovery reaches 1.044 (4 seeds); this is a comparison of candidates, not an ablation.

Command sensitivity, target

not yet shown

On the pre-lock model, shuffling future commands moved target RMSE by less than 0.005. It has not been re-measured on the locked model: the first test to run.

Coverage at nominal 90 %, target

0.953 → 0.874

Paired ablation, three seeds per arm: without RevIN, then with it. NLL 0.89 → 20.6. The locked seed alone has NLL 0.52; the pre-lock model covered 67 %.

Command sensitivity is the ratio of RMSE under shuffled future commands to RMSE under the true ones: 1 means the commands are ignored, and below 1.02 a candidate is flagged during selection. Coverage is the share of targets inside the nominal 90 % predictive interval. Violet: the locked model; grey: the matched candidate without command recovery.

  1. RevIN gains most on the channels whose level shifts across machines (Z-axis current RMSE 0.84 → 0.20). It costs calibration because a stationary context window (spindle stopped, constant power) shrinks the instance scale to √ε ≈ 3 × 10−3; the variance is de-normalized with that scale, so a start-up within the horizon costs hundreds of nats. The mean is de-normalized with the same scale, so RMSE is protected.
  2. The target windows have been read by the pre-lock model (several diagnostic reads, outside selection), once by the locked model, and once by the declared RevIN ablation. No further target evaluation of this pipeline can be called sealed.
  3. On the source machine ordinary supervised models are stronger (RSSM 0.759, MLP 0.771, locked candidate 0.822 on source validation). The claim is transfer under partial sensor overlap, not source forecasting.
Full results table · paper Tables 2(a) and 3
RMSE in z units, lower is better. Source column: the official baselines are scored on the source test split (5,189 windows, 17 sensors); the world model is the seven-seed mean ± SD on source validation, and the scratch and pretrained rows are five-seed source validation, so the source column does not compare like with like. Target column: the 10 shared JOANNEUM channels (2,457 windows); the locked row is the single confirmatory pass, the RevIN row a second, declared read of three seeds with no selection on the target.
SettingSource RMSETarget zero-shot RMSENotes
Does pretraining help on the source machine?
Scratch0.811 ± 0.022—five matched seeds
Pretrained body + fresh head0.813 ± 0.022—p = 0.76 vs scratch
Complete pretrained checkpoint0.812 ± 0.012—third matched control
Does it transfer to an unseen machine?
Persistence1.1350.654trivial floor; 1.135 on source validation, 1.128 on the source test split
Linear drift0.928—trivial reference
PatchTST (official, RevIN)0.8040.503deterministic
iTransformer (official, RevIN)0.8220.498deterministic
World model (locked, M03)0.822 ± 0.0090.546probabilistic (mean and log-variance head); NLL 0.52; single declared pass
World model + RevIN (post-lock)0.766 ± 0.0010.495 ± 0.004same model, instance normalization on; NLL 20.6; three seeds, diagnostic

Adaptation and scope

A few target windows help, on the pre-lock model. That curve is a diagnostic, not a confirmatory result.

FIG. 8 THWS → JOANNEUM few-shot adaptation (pre-lock model) paper Fig. 6(b)
THWS to JOANNEUM few-shot adaptation curve Animated line chart. Horizontal axis: target support fraction of 0, 5, 10 and 20 percent. Vertical axis: RMSE on the JOANNEUM target in z units. The line runs 0.612 at zero support, 0.611 at five percent, 0.540 at ten percent and 0.520 at twenty percent. A dashed reference line marks persistence at 0.654. The curve was measured on the pre-lock model and is diagnostic, not confirmatory. 0.50 0.54 0.58 0.62 0.66 0 5% 10% 20% target support RMSE on JOANNEUM (z units) persistence, sealed pass — 0.654 0.612 0.611 0.540 0.520 no complete 48-step support window at 5% — this point is effectively zero-shot, not an adaptation failure Pre-lock model, evaluated on the query windows left after the support fraction is removed. Diagnostic, not confirmatory. The persistence reference comes from the separate sealed 2,457-window pass.

Scroll sideways to read the figure

Support is the leading fraction of each target run; the predictor and head are updated for 50 steps and evaluated on the later, disjoint windows. Zero-shot on this model: MAE 0.401, R² = −0.244; at 10 %, R² = 0.046; at 20 %, MAE 0.299, R² = 0.167. RMSE in z units on the 10 shared channels, lower is better; red dashed: persistence from the sealed pass.

What the numbers support today

  • One transfer pair. One source machine, one target machine, seven independent target runs. Broader invariance claims wait for more machines.
  • One locked checkpoint, evaluated once. The target number is a single seed; run-level confidence intervals and the few-shot curve on the locked model are still to compute.
  • The latent terms are not isolated on the target. Every arm, scratch included, trains with the latent terms, so no target arm measures their contribution.
  • Predictive, not decision-theoretic. No policy, no planning, no closed loop: the commands are inputs, and downstream control is future work.

Cite

BibTeX 
@misc{bouaziz2026worldmodelscrossmachinecnc,
  title         = {World Models for Cross-Machine CNC Transfer under Partial Sensor Overlap},
  author        = {Ayoub Louaye Bouaziz and Matthieu Ostertag and Anton Demasles},
  year          = {2026},
  eprint        = {2609.16071},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  doi           = {10.48550/arXiv.2609.16071},
  url           = {https://arxiv.org/abs/2609.16071}
}

https://doi.org/10.48550/arXiv.2609.16071