Pith. sign in

REVIEW 4 major objections 6 minor 69 references

Tracking control of latent dynamic systems with application to spacecraft attitude control

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that a continuous-time latent dynamic system can be identified up to an invertible componentwise transformation and tracked asymptotically by feedback linearization built on the learned model, including when…

desk verdict A promising combination of identifiable representation learning and feedback linearization, but the main identifiability theorem is stated too broadly and needs a fix before the tracking guarantees hold. read the letter →

arxiv 2412.06342 v1 pith:EYUSFSU2 submitted 2024-12-09 eess.SY cs.LGcs.SY

Congxi Zhang , Yongchun Xie This is my paper · ORCID
classification eess.SYcs.LGcs.SY MSC 93B1893C1093D1593B30
keywords latentdynamicsystemsidentifiablerepresentationlearningfeedbacklinearizationasymptotictrackingspacecraftattitudecontrolaffinenonlinearuncontrollableenvironmentallatentscontinuous-time
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish a full pipeline from high-dimensional observations to asymptotic tracking for a class of latent dynamic systems, where an unknown smooth injective map $x=g(z)$ hides a low-dimensional state whose dynamics are affine in an available control $u$. The authors show that minimizing a latent-velocity prediction error recovers the true controllable latent $q$ up to an invertible componentwise transformation, making the composition $\tau=h\circ g$ a diffeomorphism. On the identified model they build a feedback linearization controller and prove that the real tracking error $e=z-z_d$ converges to zero as $t\to\infty$ whenever the chosen gains make $A$ Hurwitz. The same guarantee extends to settings with uncontrollable environmental latents by training in several environments whose uncontrollable dynamics differ. If correct, the result offers a training procedure that does not depend on goals or reference trajectories, in contrast to reinforcement learning approaches for controlling spacecraft or robots from images or neural-network outputs.

What carries the argument

The load-bearing object is the pair of learned modules $(h,\hat F,\hat B)$ that minimizes the velocity-matching objective (5), together with the Jacobian of the composition $\tau=h\circ g$. The proof's central step is differentiating the matched dynamics with respect to $u$: this forces the upper-right $n\times n$ blocks of the Jacobian to vanish and the diagonal blocks to equal $\hat B(\hat z)B^{-1}(z)$, giving a lower triangular Jacobian. Recursion over the derivative levels then shows $\hat q_0$ depends only on $q$ and the Jacobian is nonsingular, so $\tau$ is a diffeomorphism and identification is componentwise invertible. The controller is a feedback linearization law, i.e., a control that uses the estimated model to cancel the estimated nonlinearity and impose the linear error dynamics $\dot{\hat e}=A\hat e$; choosing the gain matrices $K_i$ so that $A$ is Hurwitz turns asymptotic tracking for the estimated coordinates into asymptotic tracking for the real coordinates.

What would settle it

Train the model on a finite dataset from a concrete system in the assumed class and record both the achieved value of (5) and the closed-loop tracking error $e(t)$ under (19). If the empirical loss stays strictly positive while $e(t)$ still converges to zero, the zero-loss premise is stronger than needed; if the error fails to decay whenever the loss is positive, the premise is doing the load-bearing work. A cleaner check is to compute, for a smooth injective $g$, whether the infimum of (5) over the chosen function class is zero; a positive infimum leaves Theorem 3.1 with no case to apply.

Watch

Extended reading notes

Core claim

The central claim is Theorem 3.1 plus Theorem 3.3: for a continuous-time affine nonlinear latent dynamic system with injective mixing $g$, solving the learning objective (5) gives an exact fitted model $\dot{\hat z}=\hat F(\hat z,u)$, identifies the true $q$ up to an invertible componentwise transformation $\hat q_0=\tau_q(q)$, and makes $\tau=h\circ g$ a diffeomorphism. With that model, the feedback linearizing controller (19) makes the estimated tracking error obey $\dot{\hat e}=A\hat e$, so if all eigenvalues of $A$ have negative real parts, the real tracking error $e=z-z_d$ goes to zero as $t\to\infty$. For linear constant-$B$ systems, Corollary 3.2 sharpens identification to scaling and translation, and to exact coefficients when the dynamics are linear. Theorem 3.4 extends the same guarantees to the presence of uncontrollable environmental latents: training in $l+1$ environments with nonsingular differences among the latent-environment dynamics makes $\tau_{zs}$ depend only on $z$, so tracking still holds in an unseen stable test environment.

Load-bearing premise

The proofs assume the learning objective (5) reaches a global minimum of exactly zero, so the learned model satisfies $\dot{\hat z}=\hat F(\hat z,u)$ perfectly on the training states and inputs; no finite-sample, capacity, or approximation-error bound is provided, and the tracking guarantee rests on that exact fit.

Editorial extensions

If this is right

  • The learned model can track any reference trajectory $x_d=g(z_d)$ without retraining or online planning, provided the chosen gains make $A$ Hurwitz.
  • Controller design reduces to selecting the coefficient matrices $K_0,\dots,K_{k-1}$; no reward shaping or policy search is needed.
  • When $B$ is constant and the dynamics are linear, the latent state is identified up to scaling and translation and the system matrix is identified exactly, making the learned model interpretable for model-based design.
  • With uncontrollable environmental latents, training in $l+1$ environments whose latent-environment dynamics differ by a nonsingular matrix isolates the controllable latents, so tracking succeeds in a stable unseen test environment.
  • In the spacecraft attitude experiments, the closed-loop tracking errors reach the $10^{-3}$ rad level within a few seconds in the noise-free case, and limited control deviations degrade but do not destabilize the response.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The zero-loss premise is stronger than any finite neural network can meet on a continuum; a perturbation analysis that tracks a positive residual in (5) into the closed-loop error would turn the guarantee into a practical bound, and the paper does not supply it.
  • The identifiability argument differentiates the matched dynamics with respect to $u$, so the affine-in-control structure is doing real work: a system nonlinear in $u$ would break the step that isolates $\hat B$, and the approach would need a different identification route.
  • The multi-environment result suggests a concrete recipe for image-based control: collect data under several different environmental dynamics (for instance, different disturbance or lighting regimes), train on the same objective (5), and the controllable latents should be decorrelated automatically; this can be tested in simulation before spacecraft deployment.
  • The forward-difference approximation (6) used to estimate $\dot{\hat z}$ introduces a bias the theory does not model; replacing it with a differentiable ODE solver or a trajectory-level loss would reduce that bias and may be necessary when the sampling period is large.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This paper studies continuous-time latent dynamic systems of the form (1)-(2), where the true latent state z is observed through an unknown injective mixing function g. The authors propose to train a decoder h and a model (Fhat, Bhat) by minimizing the latent predictive loss (5), then to use the feedback-linearizing controller (19) on the learned coordinates. The main theoretical results are Theorem 3.1 (identifiability of q up to a componentwise transformation and diffeomorphism tau = h composed with g), Theorem 3.3 (asymptotic tracking e -> 0), and Theorem 3.4 (extension to uncontrollable environmental latents using multiple training environments). The claims are tested in simulation on a rigid-body spacecraft attitude model with high-dimensional observations produced by a random multilayer perceptron.

Significance. The contribution is potentially valuable: it connects identifiable representation learning with a stability-certified feedback controller, offering an alternative to RL for latent-space control. The proof strategy is transparent, and the simulations include observation noise and control deviation studies. However, the central theoretical premise, namely the existence of a zero-loss differentiable model, is not a consequence of the stated assumptions, and the proof of the global diffeomorphism property is incomplete. The significance is therefore conditional on strengthening the assumptions and closing the proof gaps; under those strengthened assumptions the framework would be a useful step for safety-relevant latent-space control.

major comments (4)
  1. [§3.1.1, proof of Theorem 3.1] The assertion that solving (5) gives \dot{\hat z} = \hat F(\hat z,u) assumes a zero-loss model exists, but this is not guaranteed by the stated assumptions. The proof cites 'the actual model' as h = g^{-1}; however, g is only assumed injective and C^k, so g^{-1} need not be differentiable. Concrete counterexample: k=1, n=1, F=0, B=1, x = g(q) = q^3. For any differentiable h, equality in (5) forces \hat B(h(q^3)) u = 3q^2 h'(q^3) u for all q,u; at q=0 this gives \hat B(h(0)) = 0, contradicting \hat B \ge \hat b_h > 0. The theorem needs an explicit realizability assumption, e.g., that g is an injective immersion with a C^k left inverse on its image, or that a C^k h attaining zero loss exists. This is load-bearing because Theorem 3.3 transfers its conclusion through Theorem 3.1.
  2. [§3.1.1, final paragraph of the proof of Theorem 3.1] Nonsingularity of J(z) for all z only establishes that tau = h composed with g is a local diffeomorphism by the inverse function theorem; it does not establish that tau is a global diffeomorphism on R^{nk}. Global injectivity and surjectivity need separate arguments, for example properness or an induction exploiting the triangular structure. Since Theorem 3.3 uses invertibility of tau to convert convergence of \hat e into convergence of the real tracking error e, this gap should be closed, or the statement weakened to a version where injectivity plus continuity is shown to suffice for the tracking error transfer.
  3. [§3.1.2, proof of Theorem 3.3] The statement 'Theorem 3.1 ensures ... \forall i = 0,...,k-2, \dot{\hat q}_{d,i} = \hat q_{d,i+1}' is asserted without proof. For arbitrary desired trajectories z_d(t), this identity is not automatic; it requires the triangular structure of tau to imply that the components \hat q_{d,i} form a prolonged jet, i.e., that \hat q_{d,i+1} equals the total time derivative of \hat q_{d,i} along any smooth curve. Please add the missing argument or a lemma establishing this derivative identity, because equation (21) for \hat e depends on it.
  4. [§3.1.1, objective (5)] Even under a realizability assumption, the paper does not analyze the effect of the nonzero training loss that any finite-capacity or finite-sample learner will have. Theorems 3.1 and 3.3 require the exact equality \dot{\hat z} = \hat F(\hat z,u) for all z,u; no approximation-error, generalization, or perturbation bound is given. As a result, the asymptotic tracking theorem does not apply to the trained models in the experiments, which have positive loss (Figure 2). Please either add a robustness result for the closed loop under a bounded model error \|\dot{\hat z} - \hat F(\hat z,u)\| \le \varepsilon, or explicitly restrict the claims to the idealized zero-loss setting and revise the experimental discussion accordingly.
minor comments (6)
  1. [§3.1.1, Eqs. (12)-(15)] The block index convention is easy to misread; with the natural convention J^{i,j} = \partial \hat q_{i-1}/\partial q^{(j-1)}, the recursion after Eq. (15) is consistent. I recommend defining the block index explicitly to remove ambiguity.
  2. [§3.2, proof of Theorem 3.4] In the sentence containing Eq. (28), 'G_{k+1}(s)' should read 'G_{l+1}(s)'.
  3. [§3.1.2, controller (19)] The text says '\hat z (and hence \hat q_i) is inferred from \hat x', but \hat x is not defined; it should say 'inferred from x'.
  4. [§3.1.1, Eq. (16)] The displayed chain in Eq. (16) is garbled; it should read \hat q_{k-1} = \Delta B q^{(k-1)} rather than the repeated equalities shown.
  5. [§4.2.1, Figure 1] The subplot labels in Figure 1 are inconsistent: panels (a), (c), (e) should label the angles as \theta_x, \theta_y, \theta_z rather than 'x(rad)', 'y(rad)', 'z(rad)', and panels (b), (d), (f) should label angular rates as \omega_x, \omega_y, \omega_z.
  6. [References] Reference [51] is an unpublished self-citation with no preprint identifier; please provide an arXiv number or publication status, or remove the reliance on it if the relevant results are proved in this manuscript.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: tracking guarantee follows from explicit zero-loss and structural assumptions, not from fitted tracking outcomes.

full rationale

The derivation chain is: (i) assume objective (5) reaches a global minimum (an explicit premise; for the theorem the paper posits existence of a zero-loss model), (ii) algebraically compare (7), (8), (9) to conclude componentwise identifiability of q and a triangular nonsingular Jacobian, and (iii) design the feedback-linearizing controller (19) with manually chosen Hurwitz gains so that the estimated error satisfies \dot{\hat e}=A\hat e; convergence of \hat e then transfers to the true error through the claimed diffeomorphism. At no point is a parameter fitted to the tracking error and then reported as a prediction: the controller gains K0 and K1 are selected a priori and any Hurwitz choice satisfies the theorem, while the tracking errors in Section 4 are simulation outputs produced after training. The only self-citation, [51], is cited for inspiration and for the discrete-time analogue; the proofs here are self-contained and do not import the result of [51] as a load-bearing premise. The main weaknesses are mathematical gaps, not circularity: zero-loss differentiability of an inverse of an injective-but-not-immersive g is not guaranteed, and nonsingular Jacobian alone does not prove global diffeomorphism. Those are correctness risks and do not make the derivation circular. Consequently no circular step meeting the quoted-evidence standard is present.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The theoretical claims rest on a small set of structural assumptions: affine diagonal dynamics, injective mixing, exact zero-loss optimization, and environment diversity for the uncontrollable-latent extension. No invented entities are introduced. The experimental validation introduces manual controller gains and network hyperparameters, but these do not enter the theorems.

free parameters (3)
  • Controller gains K0, K1 = 50 I_3
    Manually chosen in Section 4.1.3; the theorem requires only Hurwitz A, so this choice does not affect the theoretical claim but affects experimental transient behavior.
  • Sampling period Delta t = 0.01 s
    Used for finite-difference approximation of ˙zhat in training and control; the theorem assumes exact derivatives, so this is an implementation parameter.
  • Network hyperparameters = 3-layer MLP, LeakyReLU(0.2), ReLU bias 0.1
    Section 4.1.2; architecture choices affect the finite-sample fit quality but do not enter the theorems.
assumptions (5)
  • domain assumption The latent dynamics are affine nonlinear of known order k: q^{(k)} = F(z)+B(z)u with F bounded, B diagonal and bi(z) >= bh > 0.
    Equation (1), Section 2.1. This is the model class for which all theorems are proved; the authors note in Discussion it is a key limitation.
  • domain assumption The mixing function g is injective and k times differentiable.
    Equation (2), Section 2.1; injectivity is needed for existence of a left-inverse h and for identifiability.
  • domain assumption The learning objective (5) attains its global minimum with zero loss using the chosen model class.
    Proof of Theorem 3.1, Section 3.1.1. The theorem assumes a global minimizer exists and is found; no finite-sample or approximation-error bound is given.
  • domain assumption For Theorem 3.4, the matrix [G2(s)-G1(s),...,G_{l+1}(s)-G1(s)] is nonsingular for all s, and the test environment s-dynamics are stable.
    Theorem 3.4, Section 3.2. This diversity condition is needed to guarantee the learned representation is independent of s.
  • domain assumption The desired observation trajectory satisfies x_d = g(z_d) with z_d in the domain.
    Section 2.2 and controller (19). If x_d is not in the image of g, the controller cannot recover a valid latent reference.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tracking control of latent dynamic systems with application to spacecraft attitude control." pith.science (2026). https://pith.science/paper/EYUSFSU2

@misc{pith2026241206342,
  author       = {Pith},
  title        = {Pith review of: Tracking control of latent dynamic systems with application to spacecraft attitude control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EYUSFSU2}},
  note         = {Machine review of arXiv:2412.06342}
}
read the original abstract

When intelligent spacecraft or space robots perform tasks in a complex environment, the controllable variables are usually not directly available and have to be inferred from high-dimensional observable variables, such as outputs of neural networks or images. While the dynamics of these observations are highly complex, the mechanisms behind them may be simple, which makes it possible to regard them as latent dynamic systems. For control of latent dynamic systems, methods based on reinforcement learning suffer from sample inefficiency and generalization problems. In this work, we propose an asymptotic tracking controller for latent dynamic systems. The latent variables are related to the high-dimensional observations through an unknown nonlinear function. The dynamics are unknown but assumed to be affine nonlinear. To realize asymptotic tracking, an identifiable latent dynamic model is learned to recover the latents and estimate the dynamics. This training process does not depend on the goals or reference trajectories. Based on the learned model, we use a manually designed feedback linearization controller to ensure the asymptotic tracking property of the closed-loop system. After considering fully controllable systems, the results are extended to the case that uncontrollable environmental latents exist. As an application, simulation experiments on a latent spacecraft attitude dynamic model are conducted to verify the proposed methods, and the observation noise and control deviation are taken into consideration.

Figures

Figures reproduced from arXiv: 2412.06342 by the authors.

Figure 1
Figure 1. Tracking property for the fully controllable system. Time evolution of: (a) [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. loss function curve The convergence time is 5.0 (s), and there is almost no overshoot. We report the tracking errors based on the infinite norm of the error signal in the period t ∈ [10, 20] (s). The attitude tracking error is [0.0006, 0.0004, 0.0029] (rad), and the attitude angular velocity tracking error is [0.0007, 0.0009, 0.0034] (rad). The results show that the proposed controller ensures that the closed￾loop s… view at source ↗
Figure 3
Figure 3. Tracking property in the test environment after training in a single environment. Time [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Tracking property in the test environment after training in two environments. Time [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

69 extracted references · 62 canonical work pages

  1. [1]

    Rigid spacecraft attitude control using adaptive integral second order sliding mode,

    P. M. Tiwari, S. Janardhanan, and M. un Nabi, “Rigid spacecraft attitude control using adaptive integral second order sliding mode,” Aerospace Science and Technology, vol. 42, pp. 50–57, 2015

    work page 2015

  2. [2]

    Y. Miao, I. Hwang, M. Liu, and F. Wang, “Adaptive fast nonsingular terminal sliding mode 16 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 t(s) 0.0 0.2 0.4 0.6 0.8 1.0x(rad) rx x (a) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 t(s) 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 x(rad/s) rx x (b) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 t(s) 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1....

    work page

  3. [3]

    Spacecraft attitude control using explicit model predictive control,

    Ø. Hegrenæs, J. T. Gravdahl, and P. Tøndel, “Spacecraft attitude control using explicit model predictive control,” Automatica, vol. 41, no. 12, pp. 2107–2114, 2005

    work page 2005

  4. [4]

    Tube-based robust output feedback model predictive control for autonomous rendezvous and docking with a tumbling target,

    K. Dong, J. Luo, Z. Dang, and L. Wei, “Tube-based robust output feedback model predictive control for autonomous rendezvous and docking with a tumbling target,” Advances in Space Research, vol. 65, no. 4, pp. 1158–1181, 2020

    work page 2020

  5. [5]

    Characteristic model-based all-coefficient adaptive control method and its applications,

    H. Wu, J. Hu, and Y. Xie, “Characteristic model-based all-coefficient adaptive control method and its applications,” IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applica- tions and Reviews) , vol. 37, no. 2, pp. 213–221, 2007

    work page 2007

  6. [6]

    Intelligent fuzzy control in stabilizing solar sail with individually controllable elements,

    L. Chen, X. Fu, S. Ramil, and M. Xu, “Intelligent fuzzy control in stabilizing solar sail with individually controllable elements,” Space: Science & Technology, 2022. 17

    work page 2022

  7. [7]

    Satellite attitude identification and prediction based on neural network compensation,

    Z. Sun, J. Simo, and S. Gong, “Satellite attitude identification and prediction based on neural network compensation,” Space: Science & Technology, vol. 3, p. 0009, 2023

    work page 2023

  8. [8]

    On adaptive attitude tracking control of spacecraft: A reinforcement learning based gain tuning way with guaranteed performance,

    C. Wei, Y. Xiong, Q. Chen, and D. Xu, “On adaptive attitude tracking control of spacecraft: A reinforcement learning based gain tuning way with guaranteed performance,” Advances in Space Research, vol. 71, no. 11, pp. 4534–4548, 2023

    work page 2023

Show all 69 references
  1. [9]

    H. K. Khalil, Control of nonlinear systems . Prentice Hall, New York, NY, 2002

    2002

  2. [10]

    Applied nonlinear control,

    J.-J. E. Slotine, “Applied nonlinear control,” PRENTICE-HALL google schola, vol. 2, pp. 1123– 1131, 1991

    1991

  3. [11]

    Neural networks for control systems—a survey,

    K. J. Hunt, D. Sbarbaro, R. ˙Zbikowski, and P. J. Gawthrop, “Neural networks for control systems—a survey,” Automatica, vol. 28, no. 6, pp. 1083–1112, 1992

    1992

  4. [12]

    Safe learn- ing in robotics: From learning-based control to safe reinforcement learning,

    L. Brunke, M. Greeff, A. W. Hall, Z. Yuan, S. Zhou, J. Panerati, and A. P. Schoellig, “Safe learn- ing in robotics: From learning-based control to safe reinforcement learning,” Annual Review of Control, Robotics, and Autonomous Systems , vol. 5, pp. 411–444, 2022

    2022

  5. [13]

    Uniform error bounds for gaussian process regression with application to safe control,

    A. Lederer, J. Umlauft, and S. Hirche, “Uniform error bounds for gaussian process regression with application to safe control,” Advances in Neural Information Processing Systems , vol. 32, 2019

    2019

  6. [14]

    Neural lyapunov control,

    Y.-C. Chang, N. Roohi, and S. Gao, “Neural lyapunov control,” Advances in neural information processing systems, vol. 32, 2019

    2019

  7. [15]

    Learning certified control using contraction metric,

    D. Sun, S. Jha, and C. Fan, “Learning certified control using contraction metric,” in Conference on Robot Learning. PMLR, 2021, pp. 1519–1539

    2021

  8. [16]

    Learning control-oriented dynamical structure from data,

    S. M. Richards, J.-J. Slotine, N. Azizan, and M. Pavone, “Learning control-oriented dynamical structure from data,” in International Conference on Machine Learning . PMLR, 2023, pp. 29 051–29 062

    2023

  9. [17]

    Toward causal representation learning,

    B. Sch¨ olkopf, F. Locatello, S. Bauer, N. R. Ke, N. Kalchbrenner, A. Goyal, and Y. Bengio, “Toward causal representation learning,” Proceedings of the IEEE, vol. 109, no. 5, pp. 612–634, 2021

    2021

  10. [18]

    Learning representations for pixel-based control: What matters and why?

    M. Tomar, U. A. Mishra, A. Zhang, and M. E. Taylor, “Learning representations for pixel-based control: What matters and why?” Transactions on Machine Learning Research ,

  11. [19]

    Current trends of spacecraft intelligent autonomous control(in chi- nese),

    L. Yuan and H. Huang, “Current trends of spacecraft intelligent autonomous control(in chi- nese),” in Aerospace Contrd and Application, 2019, pp. 45(4): 7–18

    2019

  12. [20]

    Space robotic manipulation: a multi-task learning perspective(in chinese),

    L. Li and Y. Xie, “Space robotic manipulation: a multi-task learning perspective(in chinese),” in Chinese Space Science and Technology, 2022, pp. 42(03): 10–24. 18

    2022

  13. [21]

    Representation learning: A review and new perspec- tives,

    Y. Bengio, A. Courville, and P. Vincent, “Representation learning: A review and new perspec- tives,” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 35, no. 8, pp. 1798–1828, 2013

    2013

  14. [22]

    End-to-end robotic reinforcement learning without reward engineering,

    A. Singh, L. Yang, C. Finn, and S. Levine, “End-to-end robotic reinforcement learning without reward engineering,” Robotics: Science and Systems XV , 2019

    2019

  15. [23]

    Learning dexterous in-hand manipulation,

    O. M. Andrychowicz, B. Baker, M. Chociej, R. Jozefowicz, B. McGrew, J. Pachocki, A. Petron, M. Plappert, G. Powell, A. Ray et al., “Learning dexterous in-hand manipulation,” The Inter- national Journal of Robotics Research , vol. 39, no. 1, pp. 3–20, 2020

    2020

  16. [24]

    Rein- forcement learning, fast and slow,

    M. Botvinick, S. Ritter, J. X. Wang, Z. Kurth-Nelson, C. Blundell, and D. Hassabis, “Rein- forcement learning, fast and slow,” Trends in cognitive sciences , vol. 23, no. 5, pp. 408–422, 2019

    2019

  17. [25]

    Large sequence models for sequential decision-making: a survey,

    M. Wen, R. Lin, H. Wang, Y. Yang, Y. Wen, L. Mai, J. Wang, H. Zhang, and W. Zhang, “Large sequence models for sequential decision-making: a survey,” Frontiers of Computer Science , vol. 17, no. 6, p. 176349, 2023

    2023

  18. [26]

    A survey of zero-shot generalisation in deep reinforcement learning,

    R. Kirk, A. Zhang, E. Grefenstette, and T. Rockt¨ aschel, “A survey of zero-shot generalisation in deep reinforcement learning,” Journal of Artificial Intelligence Research , vol. 76, pp. 201–264, 2023

    2023

  19. [27]

    DeepMDP: Learning continuous latent space models for representation learning,

    C. Gelada, S. Kumar, J. Buckman, O. Nachum, and M. G. Bellemare, “DeepMDP: Learning continuous latent space models for representation learning,” in International Conference on Machine Learning. PMLR, 2019, pp. 2170–2179

    2019

  20. [28]

    DayDreamer: World models for physical robot learning,

    P. Wu, A. Escontrela, D. Hafner, P. Abbeel, and K. Goldberg, “DayDreamer: World models for physical robot learning,” in Conference on Robot Learning. PMLR, 2023, pp. 2226–2240

    2023

  21. [29]

    CURL: Contrastive unsupervised representations for reinforcement learning,

    M. Laskin, A. Srinivas, and P. Abbeel, “CURL: Contrastive unsupervised representations for reinforcement learning,” in International Conference on Machine Learning . PMLR, 2020, pp. 5639–5650

    2020

  22. [30]

    Data-efficient reinforcement learning with self-predictive representations,

    M. Schwarzer, A. Anand, R. Goel, R. D. Hjelm, A. Courville, and P. Bachman, “Data-efficient reinforcement learning with self-predictive representations,” in International Conference on Learning Representations, 2020

    2020

  23. [31]

    Learning invariant repre- sentations for reinforcement learning without reconstruction,

    A. Zhang, R. T. McAllister, R. Calandra, Y. Gal, and S. Levine, “Learning invariant repre- sentations for reinforcement learning without reconstruction,” in International Conference on Learning Representations, 2020

    2020

  24. [32]

    Embed to control: A locally linear latent dynamics model for control from raw images,

    M. Watter, J. Springenberg, J. Boedecker, and M. Riedmiller, “Embed to control: A locally linear latent dynamics model for control from raw images,” Advances in neural information processing systems, vol. 28, 2015. 19

    2015

  25. [33]

    Deepmpc: Learning deep latent features for model predictive control

    I. Lenz, R. A. Knepper, and A. Saxena, “Deepmpc: Learning deep latent features for model predictive control.” in Robotics: Science and Systems , vol. 10. Rome, Italy, 2015, p. 25

    2015

  26. [34]

    Dream to control: Learning behaviors by latent imagination,

    D. Hafner, T. Lillicrap, J. Ba, and M. Norouzi, “Dream to control: Learning behaviors by latent imagination,” arXiv preprint arXiv:1912.01603 , 2019

    1912 arXiv

  27. [35]

    Learning latent dynamics for planning from pixels,

    D. Hafner, T. Lillicrap, I. Fischer, R. Villegas, D. Ha, H. Lee, and J. Davidson, “Learning latent dynamics for planning from pixels,” in International Conference on Machine Learning . PMLR, 2019, pp. 2555–2565

    2019

  28. [36]

    Learning task informed abstractions,

    X. Fu, G. Yang, P. Agrawal, and T. Jaakkola, “Learning task informed abstractions,” in Inter- national Conference on Machine Learning . PMLR, 2021, pp. 3480–3491

    2021

  29. [37]

    Inverse dynamics pretraining learns good repre- sentations for multitask imitation,

    D. Brandfonbrener, O. Nachum, and J. Bruna, “Inverse dynamics pretraining learns good repre- sentations for multitask imitation,”Advances in Neural Information Processing Systems, vol. 36, 2024

    2024

  30. [38]

    Neural contractive dynamical systems,

    H. B. Mohammadi, S. Hauberg, G. Arvanitidis, N. Figueroa, G. Neumann, and L. Rozo, “Neural contractive dynamical systems,” in The Twelfth International Conference on Learning Repre- sentations, 2023

    2023

  31. [39]

    Learning neural contracting dynamics: Extended linearization and global guarantees,

    S. Jaffe, A. Davydov, D. Lapsekili, F. Bullo et al. , “Learning neural contracting dynamics: Extended linearization and global guarantees,” arXiv preprint arXiv:2402.08090 , 2024

    2024 arXiv

  32. [40]

    Denoised MDPs: Learning world models better than the world itself,

    T. Wang, S. Du, A. Torralba, P. Isola, A. Zhang, and Y. Tian, “Denoised MDPs: Learning world models better than the world itself,” in International Conference on Machine Learning . PMLR, 2022, pp. 22 591–22 612

    2022

  33. [41]

    Action-sufficient state representation learning for control with structural constraints,

    B. Huang, C. Lu, L. Leqi, J. M. Hern´ andez-Lobato, C. Glymour, B. Sch¨ olkopf, and K. Zhang, “Action-sufficient state representation learning for control with structural constraints,” in In- ternational Conference on Machine Learning . PMLR, 2022, pp. 9260–9279

    2022

  34. [42]

    Learning world models with identifiable factorization,

    Y. Liu, B. Huang, Z. Zhu, H. Tian, M. Gong, Y. Yu, and K. Zhang, “Learning world models with identifiable factorization,” Advances in Neural Information Processing Systems , vol. 36, 2024

    2024

  35. [43]

    Chal- lenging common assumptions in the unsupervised learning of disentangled representations,

    F. Locatello, S. Bauer, M. Lucic, G. Raetsch, S. Gelly, B. Sch¨ olkopf, and O. Bachem, “Chal- lenging common assumptions in the unsupervised learning of disentangled representations,” in International Conference on Machine Learning . PMLR, 2019, pp. 4114–4124

    2019

  36. [44]

    Variational autoencoders and non- linear ICA: A unifying framework,

    I. Khemakhem, D. Kingma, R. Monti, and A. Hyvarinen, “Variational autoencoders and non- linear ICA: A unifying framework,” in International Conference on Artificial Intelligence and Statistics. PMLR, 2020, pp. 2207–2217

    2020

  37. [45]

    Disentanglement via mechanism sparsity regularization: A new principle for nonlinear ICA,

    S. Lachapelle, P. Rodriguez, Y. Sharma, K. E. Everett, R. Le Priol, A. Lacoste, and S. Lacoste- Julien, “Disentanglement via mechanism sparsity regularization: A new principle for nonlinear ICA,” in Conference on Causal Learning and Reasoning . PMLR, 2022, pp. 428–484. 20

    2022

  38. [46]

    Properties from mechanisms: An equivariance perspec- tive on identifiable representation learning,

    K. Ahuja, J. Hartford, and Y. Bengio, “Properties from mechanisms: An equivariance perspec- tive on identifiable representation learning,” in International Conference on Learning Repre- sentations, 2021

    2021

  39. [47]

    Weakly supervised representation learning with sparse perturbations,

    K. Ahuja, J. S. Hartford, and Y. Bengio, “Weakly supervised representation learning with sparse perturbations,” Advances in Neural Information Processing Systems, vol. 35, pp. 15 516–15 528, 2022

    2022

  40. [48]

    Temporally disentangled representation learning,

    W. Yao, G. Chen, and K. Zhang, “Temporally disentangled representation learning,” Advances in Neural Information Processing Systems , vol. 35, pp. 26 492–26 503, 2022

    2022

  41. [49]

    CITRIS: Causal identifiability from temporal intervened sequences,

    P. Lippe, S. Magliacane, S. L¨ owe, Y. M. Asano, T. Cohen, and S. Gavves, “CITRIS: Causal identifiability from temporal intervened sequences,” in International Conference on Machine Learning. PMLR, 2022, pp. 13 557–13 603

    2022

  42. [50]

    Learning world models with identifiable factorization,

    Y.-R. Liu, B. Huang, Z. Zhu, H. Tian, M. Gong, Y. Yu, and K. Zhang, “Learning world models with identifiable factorization,” arXiv preprint arXiv:2306.06561 , 2023

    2023 arXiv

  43. [51]

    Identifiable representation and model learning for latent dynamic sys- tems

    C. Zhang and Y. Xie, “Identifiable representation and model learning for latent dynamic sys- tems.”

  44. [52]

    An analytic layer-wise deep learning framework with applications to robotics,

    H.-T. Nguyen, C. C. Cheah, and K.-A. Toh, “An analytic layer-wise deep learning framework with applications to robotics,” Automatica, vol. 135, p. 110007, 2022

    2022

  45. [53]

    A layer-wise theoretical framework for deep learning of convolutional neural networks,

    H.-T. Nguyen, S. Li, and C. C. Cheah, “A layer-wise theoretical framework for deep learning of convolutional neural networks,” IEEE Access, vol. 10, pp. 14 270–14 287, 2022

    2022

  46. [54]

    Multilayer feedforward networks are universal approximators,

    K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural networks, vol. 2, no. 5, pp. 359–366, 1989

    1989

  47. [55]

    Discovering governing equations from data by sparse identification of nonlinear dynamical systems,

    S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proceedings of the national academy of sciences, vol. 113, no. 15, pp. 3932–3937, 2016

    2016

  48. [56]

    Lasdi: Parametric latent space dynamics identification,

    W. D. Fries, X. He, and Y. Choi, “Lasdi: Parametric latent space dynamics identification,” Computer Methods in Applied Mechanics and Engineering , vol. 399, p. 115436, 2022

    2022

  49. [57]

    Gplasdi: Gaussian process-based inter- pretable latent space dynamics identification through deep autoencoder,

    C. Bonneville, Y. Choi, D. Ghosh, and J. L. Belof, “Gplasdi: Gaussian process-based inter- pretable latent space dynamics identification through deep autoencoder,” Computer Methods in Applied Mechanics and Engineering , vol. 418, p. 116535, 2024

    2024

  50. [58]

    tlasdi: Thermodynamics-informed latent space dynamics identification,

    J. S. R. Park, S. W. Cheung, Y. Choi, and Y. Shin, “tlasdi: Thermodynamics-informed latent space dynamics identification,” arXiv preprint arXiv:2403.05848 , 2024

    2024 arXiv

  51. [59]

    Isidori, Nonlinear control systems: an introduction

    A. Isidori, Nonlinear control systems: an introduction . Springer, 1985

    1985

  52. [60]

    An introduction to the use of neural networks in control systems,

    M. T. Hagan, H. B. Demuth, and O. D. Jes´ us, “An introduction to the use of neural networks in control systems,” International Journal of Robust and Nonlinear Control: IF AC-Affiliated Journal, vol. 12, no. 11, pp. 959–985, 2002. 21

    2002

  53. [61]

    Self-supervised learning with data augmentations provably isolates content from style,

    J. Von K¨ ugelgen, Y. Sharma, L. Gresele, W. Brendel, B. Sch¨ olkopf, M. Besserve, and F. Lo- catello, “Self-supervised learning with data augmentations provably isolates content from style,” Advances in neural information processing systems , vol. 34, pp. 16 451–16 467, 2021

    2021

  54. [62]

    Nonparametric identifiability of causal representations from unknown interven- tions,

    J. von K¨ ugelgen, M. Besserve, W. Liang, L. Gresele, A. Keki´ c, E. Bareinboim, D. M. Blei, and B. Sch¨ olkopf, “Nonparametric identifiability of causal representations from unknown interven- tions,” arXiv preprint arXiv:2306.00542 , 2023

    2023 arXiv

  55. [63]

    Multi-domain causal representation learning via weak distributional invariances,

    K. Ahuja, A. Mansouri, and Y. Wang, “Multi-domain causal representation learning via weak distributional invariances,” in International Conference on Artificial Intelligence and Statistics . PMLR, 2024, pp. 865–873

    2024

  56. [64]

    Provably filtering ex- ogenous distractors using multistep inverse dynamics,

    Y. Efroni, D. Misra, A. Krishnamurthy, A. Agarwal, and J. Langford, “Provably filtering ex- ogenous distractors using multistep inverse dynamics,” in International Conference on Learning Representations, 2021

    2021

  57. [65]

    Guaranteed discovery of control-endogenous latent states with multi-step inverse models,

    A. Lamb, R. Islam, Y. Efroni, A. R. Didolkar, D. Misra, D. J. Foster, L. P. Molu, R. Chari, A. Krishnamurthy, and J. Langford, “Guaranteed discovery of control-endogenous latent states with multi-step inverse models,” Transactions on Machine Learning Research, 2022

    2022

  58. [66]

    Multistep inverse is not all you need,

    A. Levine, P. Stone, and A. Zhang, “Multistep inverse is not all you need,” arXiv preprint arXiv:2403.11940, 2024

    2024 arXiv

  59. [67]

    Y. Xie, Y. Lei, J. Guo, and B. Meng, Spacecraft dynamics and control. Springer, 2022

    2022

  60. [68]

    Contrastive learning inverts the data generating process,

    R. S. Zimmermann, Y. Sharma, S. Schneider, M. Bethge, and W. Brendel, “Contrastive learning inverts the data generating process,” inInternational Conference on Machine Learning. PMLR, 2021, pp. 12 979–12 990. 22

    2021

  61. [2023]

    Available: https://openreview.net/forum?id=wIXHG8LZ2w

    [Online]. Available: https://openreview.net/forum?id=wIXHG8LZ2w

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.