cs.ROMar 22, 2026

Evaluating Factor-Wise Auxiliary Dynamics Supervision for Latent Structure and Robustness in Simulated Humanoid Locomotion

Authors: Chayanin Chamachot

Organizations: Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

We evaluate whether factor-wise auxiliary dynamics supervision produces useful latent structure or improved robustness in simulated humanoid locomotion. DynaMITE -- a transformer encoder with a factored 24-d latent trained by per-factor auxiliary losses during proximal policy optimization (PPO) -- is compared against Long Short-Term Memory (LSTM), plain Transformer, and Multilayer Perceptron (MLP) baselines on a Unitree G1 humanoid across four Isaac Lab tasks. The supervised latent shows no evidence of decodable or functionally separable factor structure: probe R^2 ~ 0 for all five dynamics factors, clamping any subspace changes reward by < 0.05, and standard disentanglement metrics (MIG, DCI, SAP) are near zero. An unsupervised LSTM hidden state achieves higher probe R^2 (up to 0.10). A 2x2 factorial ablation (n = 10 seeds) isolates the contributions of the tanh bottleneck and auxiliary losses: the auxiliary losses show no measurable effect on either in-distribution (ID) reward (+0.03, p = 0.732) or severe out-of-distribution (OOD) reward (+0.03, p = 0.669), while the bottleneck shows a small, consistent advantage in both regimes (ID: +0.16, p = 0.207; OOD: +0.10, p = 0.208). The bottleneck advantage persists under severe combined perturbation but does not amplify, indicating a training-time representation benefit rather than a robustness mechanism. LSTM achieves the best nominal reward on all four tasks (p < 0.03); DynaMITE degrades less under combined-shift stress (2.3% vs. 16.7%), but this difference is attributable to the bottleneck compression, not the auxiliary supervision. For locomotion practitioners: auxiliary dynamics supervision does not produce an interpretable estimator and does not measurably improve reward or robustness beyond what the bottleneck alone provides; recurrent baselines remain the stronger choice for nominal performance.

Figures & tables

Figure 1: Overview of the DynaMITE architecture. A two-layer transformer encoder processes an 8-step (160 ms) observation–action history to produce a 24-dimensional factored latent vector z∈R24\bm{z}\in\mathbb{R}^{24} , decomposed into five factor subspaces (friction, mass, motor strength, contact stiffness, action delay). Each subspace is trained with a dedicated auxiliary dynamics-prediction loss during PPO training. The latent is concatenated with the current observation and fed to the policy π(a∣s,z)\pi(a\mid s,\bm{z}) and value V(s,z)V(s,\bm{z}) heads. Auxiliary losses are active only during training.
ModelHistoryLatentAux LossParams
MLPNoneNoNo266–362k
LSTMHidden stateNoNo176–215k
Transformer8 stepsNoNo330–342k
DynaMITE8 steps24-d factoredYes342–392k
Table 1: Model architecture summary. Parameter counts vary by task due to different observation dimensions.
MethodFlatPushRand.Terrain
MLP−4.83-4.83−5.01-5.01−5.32-5.32−4.82-4.82
LSTM−4.01\mathbf{-4.01}−4.30\mathbf{-4.30}−4.18\mathbf{-4.18}−4.06\mathbf{-4.06}
Transf.−5.02-5.02−4.83-4.83−4.77-4.77−4.46-4.46
DynaMITE−4.88-4.88−4.60-4.60−4.48-4.48−4.49-4.49
Table 2: In-distribution reward comparison (5 seeds, deterministic eval). Bold indicates best per task. All LSTM vs. DynaMITE paired tt -tests are significant ( p<0.03p<0.03 ).
Figure 2: In-distribution reward (5 seeds, deterministic evaluation). LSTM achieves the best reward on all tasks; DynaMITE ranks second on three of four tasks but is significantly worse than LSTM on all.
TaskMean Diffttpp
Flat+0.870+0.8708.490.0011
Push+0.305+0.3054.690.0094
Randomized+0.303+0.3033.340.029
Terrain+0.435+0.4358.550.0010
Table 3: Paired tt -tests: LSTM vs. DynaMITE (matched training seeds, n=5n=5 ).
MethodL0 (ID)L1L2L4
DynaMITE−4.38-4.38−4.47-4.47−4.50-4.50−4.63\mathbf{-4.63}
LSTM−3.56\mathbf{-3.56}−4.23\mathbf{-4.23}−4.40\mathbf{-4.40}−5.12-5.12
Transf.−4.67-4.67−4.73-4.73−4.72-4.72−4.86-4.86
MLP−5.68-5.68−5.61-5.61−5.55-5.55−5.64-5.64
Table 4: Combined-shift reward across severity levels (randomized task, 5 seeds, 50-episode deterministic eval per level). Bold indicates best at each level.
MethodL0L1L2L3L4
DynaMITE2.152.152.562.563.183.184.234.236.136.13
LSTM1.31\mathbf{1.31}2.19\mathbf{2.19}3.01\mathbf{3.01}4.594.596.946.94
Transf.2.082.082.582.583.173.174.354.356.486.48
MLP2.242.242.762.763.403.404.474.476.306.30
Table 5: Combined-shift tracking error across severity levels (randomized task, 5 seeds, 50-episode deterministic eval per level).
Figure 3: Combined-shift stress test (randomized task, 5 seeds). LSTM achieves the best reward at low severity but degrades steeply; DynaMITE’s reward is lower at baseline but more stable. The crossover occurs at severity level 3. Neither model dominates across all levels.
ModelIDSevereWorstDegrad.
DynaMITE−4.48-4.48−4.58-4.58−4.63-4.632.3%\mathbf{2.3\%}
LSTM−4.18-4.18−4.88-4.88−5.12-5.1216.7%16.7\%
Transf.−4.77-4.77−4.81-4.81−4.86-4.860.8%0.8\%
MLP−5.32-5.32−5.66-5.66−5.68-5.686.4%6.4\%
Table 6: Severe OOD degradation (combined-shift sweep, randomized task, 5 seeds, deterministic eval). Degradation =∣Severe−ID∣=|\text{Severe}-\text{ID}| ; percentages relative to ∣ID∣|\text{ID}| .
Figure 4: Pareto front: in-distribution reward vs. severe OOD reward. No model dominates both axes. LSTM achieves the best ID reward; DynaMITE has the highest mean severe OOD reward.
ModelIDSevere OODWorst
DynaMITE−4.61-4.61−4.58\mathbf{-4.58}−4.78\mathbf{-4.78}
LSTM−4.14\mathbf{-4.14}−4.67-4.67−5.12-5.12
Transf.−4.77-4.77−4.85-4.85−5.08-5.08
MLP−5.00-5.00−5.76-5.76−5.97-5.97
Table 7: Pareto analysis (5 seeds, deterministic eval): ID reward == 4-task mean; Severe OOD Mean == average across three randomized-task sweeps.
PushDynaMITELSTMTransf.MLP
1.05.6\mathbf{5.6}9.29.26.76.76.36.3
2.05.9\mathbf{5.9}15.915.98.18.17.67.6
3.06.0\mathbf{6.0}20.620.68.38.37.87.8
4.06.0\mathbf{6.0}19.719.78.38.38.18.1
5.06.1\mathbf{6.1}19.819.88.08.08.28.2
6.06.1\mathbf{6.1}19.519.58.18.18.78.7
Table 8: Steps to recover command tracking after push (flat task, 5 seeds ×\times 50 episodes per magnitude). Bold indicates fastest.
Push (m/s)DynaMITELSTM
1.03.96±0.533.96\pm 0.533.05±0.14\mathbf{3.05\pm 0.14}
2.04.03±0.374.03\pm 0.373.32±0.08\mathbf{3.32\pm 0.08}
3.04.36±0.394.36\pm 0.393.78±0.08\mathbf{3.78\pm 0.08}
4.05.01±0.265.01\pm 0.264.62±0.07\mathbf{4.62\pm 0.07}
5.05.76±0.225.76\pm 0.225.50±0.11\mathbf{5.50\pm 0.11}
6.06.74±0.176.74\pm 0.176.41±0.08\mathbf{6.41\pm 0.08}
Table 9: Peak tracking error after push (flat task, 5 seeds ×\times 50 episodes). Bold indicates lower peak error.
Method00.5–11–22–33–55–8S.
DynaMITE−4.37-4.37−4.44-4.44−4.50-4.50−4.56-4.56−4.63\mathbf{-4.63}−4.78\mathbf{-4.78}0.41
LSTM−3.58\mathbf{-3.58}−4.05\mathbf{-4.05}−4.23\mathbf{-4.23}−4.45\mathbf{-4.45}−4.70-4.70−5.09-5.091.52
Transf.−4.65-4.65−4.72-4.72−4.76-4.76−4.81-4.81−4.94-4.94−5.08-5.080.42
MLP−5.65-5.65−5.64-5.64−5.79-5.79−5.75-5.75−5.89-5.89−5.97-5.970.33\mathbf{0.33}
Table 10: Push magnitude sweep (randomized task, 5 seeds, 50-ep eval per level). Bold indicates best.
SweepTaskDynaMITELSTMCross.
Combinedrand.2.3%\mathbf{2.3\%}16.7%L3
Push mag.rand.5.1%\mathbf{5.1\%}17.1%L4
Push mag.push4.4%\mathbf{4.4\%}12.2%L5
Push mag.terrain6.6%\mathbf{6.6\%}21.5%L5
Frictionrand.−0.4%-0.4\% *1.5%None
Table 11: Severe OOD degradation across all sweep types and tasks (5 seeds). DynaMITE degrades less than LSTM on all push-related sweeps; crossover == level where DynaMITE first matches or exceeds LSTM.
Figure 5: OOD sweep comparison across four models and five seeds. LSTM degrades more steeply than DynaMITE under push magnitude perturbation across all three tasks.
Figure 6: Latent correlation heatmap showing the Pearson correlation between each factor subspace dimension and the corresponding ground-truth dynamics parameter.
Factor (dims)Avg ∣ΔReward∣|\Delta\text{Reward}|Interpretation
Friction (0–3)0.007Negligible
Mass (4–9)0.012Negligible
Motor (10–15)0.021Negligible
Contact (16–19)0.020Negligible
Delay (20–23)0.020Negligible
Table 12: Latent intervention analysis: average absolute reward change per factor subspace (3 seeds ×\times 5 factors ×\times 3 DR levels == 90 conditions, 50-ep eval).
FactorDM Lin.DM MLPLSTM Lin.LSTM MLP
Friction−0.000-0.000−0.001-0.0010.0260.0260.101\mathbf{0.101}
Mass0.0000.000−0.002-0.0020.0120.0120.018\mathbf{0.018}
Motor0.0000.000−0.002-0.0020.0100.0100.015\mathbf{0.015}
Contact0.0000.000−0.000-0.0000.0060.0060.045\mathbf{0.045}
Delay0.0000.000−0.000-0.0000.0110.0110.041\mathbf{0.041}
Overall0.000−- 0.0010.0130.044
Table 13: Latent probe R2R^{2} for DynaMITE vs. LSTM (5 seeds, 5-fold CV, ∼\sim 36k samples). Bold indicates best per factor.
VariantRewardΔ\DeltappWorse
Full−4.46\mathbf{-4.46}———
No Aux−4.51-4.51−0.05-0.050.6416/10
No Latent−4.64-4.64−0.18-0.180.2259/10
Single−4.69-4.69−0.23-0.230.048\mathbf{0.048}8/10
Aux Only−4.64-4.64−0.18-0.180.2517/10
Table 14: Ablation study on the randomized task (10 seeds, paired tt -test vs. full DynaMITE). Bold pp -value indicates p<0.05p<0.05 .
 No Aux LossAux Loss
Bottleneck−4.51±0.20-4.51\pm 0.20−4.46±0.25\mathbf{-4.46\pm 0.25}
No Bottleneck−4.64±0.36-4.64\pm 0.36−4.64±0.34-4.64\pm 0.34
Table 15: 2×22\times 2 factorial: bottleneck vs. auxiliary loss (10 seeds, randomized task). Each cell averages 10 paired seeds.
 No Aux LossAux Loss
Bottleneck−4.59±0.21-4.59\pm 0.21−4.55±0.22\mathbf{-4.55\pm 0.22}
No Bottleneck−4.68±0.28-4.68\pm 0.28−4.66±0.23-4.66\pm 0.23
Table 16: 2×22\times 2 factorial under severe combined-shift (avg. of Levels 3–4, 10 seeds, 50-ep eval per level).
VariantIDSevereΔ\DeltaDegrad.
Full (B+A)−4.46-4.46−4.55-4.55−0.09-0.092.1%2.1\%
No Aux (B)−4.51-4.51−4.59-4.59−0.08-0.081.9%1.9\%
No Latent−4.64-4.64−4.68-4.68−0.04-0.040.9%0.9\%
Aux Only (A)−4.64-4.64−4.66-4.66−0.02-0.020.5%0.5\%
Table 17: Factorial degradation analysis (10 seeds, randomized task). Degradation =∣Severe−ID∣/∣ID∣=|\text{Severe}-\text{ID}|/|\text{ID}| .
ClaimEvidenceStatus
Latent decodable?Probe R2≈0R^{2}\approx 0 ; MIG/DCI/SAP ≈0\approx 0No
Factor-specific effect?∣Δr∣<0.05|\Delta r|<0.05No evidence
Aux heads learn targets?MSE ≈3.7\approx 3.7 (48% drop)Not accurately
LSTM best ID?p<0.03p<0.03 , all 4 tasksYes
DynaMITE lower OOD sens.?0.25 vs. 1.57Directional
DynaMITE faster recovery?∼6{\sim}6 vs. 9–21 stepsDirectional
Table 18: Summary of key claims and evidence status.
FactorMean cos⁡(∇PPO,∇aux)\cos(\nabla_{\text{PPO}},\nabla_{\text{aux}})Std
Friction−0.001-0.0010.005
Mass−0.002-0.0020.010
Motor−0.005-0.0050.016
Contact−0.008-0.0080.026
Delay−0.002-0.0020.009
Table 19: Cosine similarity between PPO and auxiliary gradients (3 seeds, averaged over training).
Figure 7: Cosine similarity between PPO and auxiliary gradients over training (3 seeds). All five factor-specific auxiliary gradients remain orthogonal to the PPO gradient ( ∣cos⁡∣<0.01|\cos|<0.01 ) throughout the entire training run.
MetricDynaMITE (24-d)LSTM (128-d)
Effective rank4.78±0.72\mathbf{4.78\pm 0.72}32.20±3.8532.20\pm 3.85
Participation ratio2.27±0.15\mathbf{2.27\pm 0.15}4.96±1.524.96\pm 1.52
Condition number315.9±204.1315.9\pm 204.1108.4±19.9\mathbf{108.4\pm 19.9}
Table 20: Representation geometry comparison (5 seeds, SVD on ∼\sim 36k representations per model).
Figure 8: Representation geometry. DynaMITE’s 24-d latent collapses to effective rank ∼5{\sim}5 ; LSTM’s 128-d hidden state uses ∼32{\sim}32 effective dimensions.
FactorDynaMITE (nats)LSTM (nats)
Overall0.233±0.052\mathbf{0.233\pm 0.052}0.028±0.0330.028\pm 0.033
Friction0.054±0.021\mathbf{0.054\pm 0.021}0.024±0.0200.024\pm 0.020
Mass0.091±0.010\mathbf{0.091\pm 0.010}0.011±0.0130.011\pm 0.013
Motor0.037±0.031\mathbf{0.037\pm 0.031}0.013±0.0150.013\pm 0.015
Contact0.026±0.011\mathbf{0.026\pm 0.011}0.010±0.0150.010\pm 0.015
Delay0.007±0.0040.007\pm 0.0040.005±0.0030.005\pm 0.003
Table 21: Mutual information between representations and dynamics factors (5 seeds, KNN estimation k=5k=5 , ∼\sim 36k samples, nats).
Figure 9: Mutual information between learned representations and ground-truth dynamics factors (KNN estimation). DynaMITE retains more MI with dynamics parameters than LSTM (0.233 vs. 0.028 nats), but absolute values for both models are low.
MetricDynaMITELSTM
MIG0.00130.00130.00130.0013
DCI Disent.0.01950.01950.0929\mathbf{0.0929}
DCI Complete0.01680.01680.0542\mathbf{0.0542}
DCI Info.0.0846\mathbf{0.0846}0.13970.1397
SAP0.00010.00010.00060.0006
Table 22: Standard disentanglement metrics (5 seeds). Lower DCI-I is better (prediction error).
ScenarioFavoredEvidence
Nominal ID rewardLSTMConfirmed
Moderate mismatchLSTMDirectional
Severe mismatchDynaMITEDirectional
Fast re-adaptationDynaMITEDirectional
Inspect latentNeitherConfirmed
Table 23: Observed patterns under our simulation protocol.
More in this topic

Latent Dynamics Modeling

Latent dynamics modeling learns compact hidden-state representations and transition rules to predict, explain, and control evolving systems.

See all 253 papers

Explore similar work

CardsList

  1. Dynamics Are Learned, Not Told: Semi-Supervised Discovery of Latent Dynamics Geometries For Zero-Shot Policy Adaptation

    Jun 1, 2026Zhiming Xu, Weitao Zhou, Xianghui Pan +4Robot Policy AdaptationLatent Dynamics Modeling

    School of Computer Science and Engineering, Tongji University, Shanghai, China · School of Vehicle and Mobility, Tsinghua University, Beijing, China · Simple AI, Beijing, China +1

  2. ADP: Adversarial Dynamics Priors for Physically Grounded Humanoid Locomotion

    Jul 3, 2026Seokju Lee, Jeongtae Lee, Jeonghyeok Lim +6Adversarial TrainingHumanoid Robot Locomotion

    Mechatronics, Systems and Control Lab (MSC Lab), Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Yuseong-gu, Daejeon 34141, Republic of Korea · Samsung Electronics, Future Robotics AI Group, Seoul, Republic of Korea · School of Electrical Engineering, Hanyang University, Ansan 15588, Republic of Korea +1

  3. Spectral-Target Physical Latent Structuring for JEPA-Style World Models

    Sep 2, 2026Penghao Zhu, Salvatore Penachio, Kaustav Mukherjee +1World Model LearningWorld Model-Based Planning

    Kaliber Labs San Francisco, CA 94103, USA