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REVIEW 3 major objections 4 minor 29 references

Latent Matters: Learning Deep State-Space Models

T0 review · 3 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Maximising the evidence lower bound does not ensure a deep state-space model learns the true dynamics; a constrained-optimisation reformulation, with a learned prior and Kalman-based inference, recovers them and improves prediction.

desk verdict A credible, incremental paper that shows constrained optimization improves DSSM dynamics learning, with a genuinely interesting RNN-free EKVAE; the main caveat is the fragile D0 hyperparameter and missing error bars/code. read the letter →

arxiv 2602.23050 v2 pith:BG75XWBP submitted 2026-02-26 cs.LG

Alexej Klushyn , Richard Kurle , Maximilian Soelch , Botond Cseke , Patrick van der Smagt This is my paper · ORCID
classification cs.LG
keywords deepstate-spacemodelssystemidentificationevidencelowerboundconstrainedoptimisationrate-distortiontradeoffextendedKalmanfilteramortisedvariationalinferencedisentangledrepresentation
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 negative result and a positive fix: training deep state-space models (DSSMs) by maximising the evidence lower bound (ELBO) can produce models whose latent states do not track the true dynamics of the observed system, because the same ELBO value is compatible with many different balances between reconstruction quality and compression. The proposed fix is a constrained-optimisation framework that rewrites the sequential ELBO as a rate–distortion Lagrangian and enforces a reconstruction threshold, so the model must learn to reconstruct observations well before spending representational capacity on dynamics; a learned hierarchical prior for the initial state avoids the over-regularisation and broken generative models that plague a fixed Gaussian prior. On this base the paper builds the extended Kalman VAE (EKVAE), which replaces RNN-based recognition with analytic extended Kalman filtering/smoothing, a network-predicted linearisation of the transition map, and a linear auxiliary observation model. If the paper is right, DSSM training should be formulated as constrained optimisation rather than plain ELBO maximisation, RNN-free Kalman inference becomes a viable route to system identification — including from raw RGB images — and the learned position–velocity-disentangled representations support reward-free model-based reinforcement learning.

What carries the argument

The load-bearing device is the rate–distortion decomposition of the sequential ELBO, F = −D − R, turned into the Lagrangian L = R + λ(D − D0), with D the reconstruction distortion and R the KL rate. A sign-aware update rule for λ enforces D ≤ D0 first, then optimises the rate — removing the degeneracy where many (D,R) pairs give the same ELBO. Two mechanisms carry the EKVAE: neural linearisation — the transition p(zt+1|zt,ut) = N(Fψ zt + Bψ ut, Qψ) built from a softmax-weighted mixture of learned base matrices, acting as a state-dependent Jacobian in place of a Taylor expansion — and a time-invariant linear auxiliary model pψ(at|zt) = N(at|Hzt, R) whose rectangular-identity H pins the first

What would settle it

On a synthetic linear-Gaussian dynamical system with known transition matrices, train the identical architecture under the CO objective and under plain ELBO maximisation at matched reconstruction quality. If the CO-trained model does not recover the true transition matrices more accurately and does not deliver lower multi-step prediction error, the paper's central claim of improved system identification is falsified. A cheaper partial check, already implicit in the paper's Fig. 9, is that pushing D0 outside the feasible range collapses the method — delimiting the claim's scope.

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Extended reading notes

Core claim

High ELBO values do not imply a DSSM has learned the true dynamics: annealed baselines match constrained models' ELBO while inferred latents barely correlate with ground truth (R² ≈ 0.04 for pendulum velocity). The remedy is the Lagrangian L = R + λ(D − D0), whose λ-update enforces a reconstruction constraint before dynamics learning; applied to deep Kalman smoothers, deep variational Bayes smoothers, and the new EKVAE, it yields high state correlation and large prediction gains. The EKVAE — extended Kalman smoothing with network-predicted Jacobians and a linear auxiliary observation model — gives the best prediction accuracy in the comparisons, identifies the reacher dynamics from 64×64 RGB

Load-bearing premise

Everything rests on the reconstruction threshold D0 being feasible: it is set by the heuristic D0 = 0.9 × the best distortion the same model attains under ordinary ELBO training, the appendix shows an abrupt performance collapse at 1.15×D0* attributed to an unsatisfiable constraint, and if no feasible D0 can be found the constrained framework does not help.

Editorial extensions

If this is right

  • ELBO maximisation alone is an unreliable training signal for system identification: models with similar test ELBO can differ wildly in how well their latent states match the true system states (R² from 0.99 down to ~0.04 across configurations in Table 1).
  • Applying the CO framework to established smoothers (deep Kalman smoothers and deep variational Bayes smoothers) raises their prediction accuracy substantially and lets them identify dynamics that annealing schedules fail to recover.
  • RNN-based transition models (as in the Kalman VAE and recurrent state-space models) create a non-Markovian latent space: velocity information lives in the recurrent hidden state, so predictions conditioned on a smoothed initial state are markedly worse than those conditioned on a later filtered state.
  • The EKVAE outperforms the compared DSSMs in prediction accuracy and can identify the reacher system directly from 64×64 RGB images, whereas the RNN-based baselines in the paper cannot.
  • Disentangled position–velocity representations allow reward functions to be defined purely by encoding goal positions or velocities in latent space, which suffices to learn swing-up, sustained rotation, and reach-avoid policies on the tested control tasks.

Reading between the lines

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

  • Because the rate–distortion degeneracy is generic to ELBO-style objectives, this warning should generalise beyond the tested benchmarks: in any sequential latent-variable setting where the latent state is meant to be physically meaningful, checking inferred latents against known state variables should become a routine diagnostic.
  • The same Lagrangian machinery could be run in the mirror direction — constraining rate rather than distortion — to enforce a target level of compression or invariance; the paper does not explore this variant.
  • Neural linearisation — predicting the Jacobian of the transition as a network output rather than differentiating through it — is a transferable design idea for any filtering/smoothing pipeline whose transition function is expensive, implicit, or non-smooth.
  • The learned hierarchical prior adapts to the dataset's distribution of initial states, so the benefit should scale with how poorly a fixed Gaussian covers those states; datasets with dense initial-state coverage should need the prior less — a testable prediction.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper addresses the training of deep state-space models (DSSMs), arguing that maximizing the sequential ELBO does not guarantee correct identification of the underlying dynamics. It proposes a constrained-optimization (CO) framework in which the rate is minimized subject to a reconstruction constraint D(θ,φ)≤D0, with a Lagrange multiplier updated by an extension of REWO, plus a variational hierarchical prior (VHP). It then introduces EKVAE, an RNN-free DSSM that combines amortized inference over auxiliary variables with extended Kalman filtering/smoothing and a neural linearization of the transition model. Experiments on pendulum and reacher (angle and RGB image observations) report that CO improves R2-based system identification and prediction MSE for DKS, DVBS, and EKVAE, and that EKVAE achieves the best prediction accuracy, with a demonstration of disentangled position–velocity representations for reward-free policy learning.

Significance. If the empirical claims hold, the paper makes a useful conceptual point: rate–distortion balance should be controlled explicitly in DSSM training, and the proposed CO formulation is a principled way to do this. The derivations in Sec. 3 and App. A are detailed, and the paper extends the method to two established DSSM families (DKS, DVBS) as well as to its own EKVAE. The EKVAE architecture is a clean alternative to RNN-based DSSMs, and the disentangled representation result has practical value for control. The paper also provides some robustness evidence (25-run statistics in Fig. 10) and clearly reports failure modes in App. A.7.1. A further strength is that the main prediction metric is held-out test MSE against ground-truth states, not a term in the training objective, so the evaluation is not circular. However, the central result is conditioned on a D0 heuristic whose sensitivity is not fully characterized, and the headline table lacks error bars; these are the main issues to resolve.

major comments (3)
  1. [App. A.7.1 / Fig. 9; Sec. 3] The main claim that CO improves system identification depends on the reconstruction constraint D(θ,φ)≤D0 being feasible. Appendix A.7.1 reports a sharp performance drop at D0=1.15D0*, and states that the constraint cannot be satisfied there. This is load-bearing, but the explanation is unclear: with D0*=0.9Dmax from App. A.1, D0=1.15D0*=1.035Dmax is actually looser than the distortion already achieved by ordinary ELBO training, so one would expect feasibility. Please clarify the normalization of the D0 sweep, provide the full sensitivity curve, and discuss whether a feasible D0 can be identified without expensive search for new datasets. As written, the paper demonstrates the heuristic works on the tested benchmarks but does not support the stronger claim of a general framework.
  2. [Table 1; App. A.7.2] The headline quantitative results in Table 1 are single-point estimates with no error bars or significance tests. The 25-run statistics in Fig. 10 cover only one model/dataset combination (DKS on pendulum). Since the paper uses the language 'significantly improves' and 'outperforms', the main comparisons (especially EKVAE CO vs. annealing on all three datasets, and the smoothing vs. filtering differences in Table 2) should be reported with means, standard deviations, and ideally significance tests, or the corresponding code should be made available so the claims can be reproduced.
  3. [Sec. 6.2 / App. A.7.1] The D0 heuristic D0=0.9Dmax uses the reconstruction distortion of the same model under ordinary ELBO training. In settings where ordinary ELBO training fails to identify the dynamics (as shown for annealing in Table 1), Dmax may correspond to a poor local optimum. The paper does not investigate whether the reported improvements are robust to the choice of the reference run used to compute Dmax, nor does it provide guidance for choosing D0 when no reliable ELBO-trained model is available. This should be addressed explicitly, either by an adaptive D0 scheme or by a sensitivity study over Dmax estimates.
minor comments (4)
  1. [Abstract / Sec. 1] The phrase 'as we show' in the abstract could be softened or the key evidence cited, since the point is only demonstrated empirically in Sec. 6.2.
  2. [Fig. 9 / App. A.7.1] The figure caption uses D*_0 without defining it in the caption; please define it as the heuristic value D0=0.9Dmax for readers who do not read App. A.1.
  3. [Sec. 4.2, Eq. (14)] H=(δij)∈R^{Da×Dz} is described as 'rectangular identity matrix' but the text should state explicitly that this assumes Da≤Dz; otherwise the first Da dimensions of zt are not well-defined.
  4. [General] No code or data release is mentioned. For a paper whose central contributions are empirical, providing code would greatly strengthen reproducibility; at minimum, a statement of availability should be added.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: CO/REWO/VHP machinery is self-cited from [16] and D0 is calibrated on the same model's own ELBO-distortion curve, but R2 and prediction MSE are external evaluations against ground-truth physics, and no equation reduces to its input by construction.

full rationale

The derivation chain is not circular. Eq. (3) (F_ELBO = -D - R) is an algebraic identity from the definitions of distortion and rate; the CO Lagrangian (Eq. 4) is the standard rate-distortion Lagrangian; and the EKVAE objective (App. A.6) is derived by ordinary variational inequalities (Eqs. 56-61). No equation in the paper is equivalent to its own input by construction. The headline empirical claims are external to the objective: R2 is computed by post-hoc OLS regression of inferred latents on ground-truth angles/velocities (Sec. 6.2, App. A.7.2); prediction MSE is computed on 500 held-out predicted sequences conditioned on the first five observations and measured against real pendulum/reacher physics; and the policy experiments in Sec. 6.4 are tested on the actual environments. These quantities never appear in the training objective, so no fitted parameter is renamed as a prediction. The main caveats are provenance, not reduction. The CO/REWO lambda-update (Eq. 8) and the VHP (Eq. 6) are taken from the authors' own NeurIPS 2019 paper [16], and the guarantee that L is a valid lower bound iff 1 >= lambda >= 0 is imported from [16] (Sec. 3). This is load-bearing for the method's justification, but the present paper re-validates the machinery in-domain against external benchmarks (Tab. 1, Fig. 10 with 25 runs; policies tested in real environments), so per the review rules the citation is corroborated rather than merely asserted. Second, the D0 heuristic (App. A.1: D0 = 0.9 * Dmax, with Dmax from the same model's plain-ELBO training) is self-referential calibration, and App. A.7.1 discloses a sharp performance drop at 1.15*D0* when the constraint becomes unsatisfiable. That is a genuine robustness/generality limitation - no feasibility theorem is given - but D0 is a constraint threshold, not a predicted quantity, so the improvement of CO over annealing is not forced by construction. Verdict: no circular step; score 2 for the multiple self-citations and self-referential D0 calibration, well below any construction-forced result.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The paper's contribution is largely a recipe built from prior work by the same authors: the CO/Lagrangian formulation and VHP come from Klushyn et al. [16], and the locally-linear transition comes from DVBF [13]. The genuinely new pieces are the application to DSSMs, the learned-base-matrix 'neural linearisation', and the time-invariant H used for disentangling. The load-bearing choices are the D0 target, the λ-update constants, and the use of the model's own EKS marginals as the recognition model; none of these is derived from first principles.

free parameters (3)
  • D0 (reconstruction target) = 0.9 × Dmax per dataset
    Chosen by heuristic from the best distortion the same model achieves under classical ELBO training (App. A.1); performance drops sharply if D0 is infeasible (App. A.7.1, Fig. 9).
  • λ-update hyperparameters τ1, τ2, ν = pendulum τ1=10, τ2=0.01, ν=300; reacher angle τ1=1, τ2=0.001, ν=10; reacher image τ1=10, τ2=0.01, ν=30
    Hand-chosen per task in Table 3; they control the Lagrange multiplier schedule in Eq. (8).
  • Number of base matrices M and latent/auxiliary dimensions = M=16 pendulum, M=8 reacher; latent dims 3/4/5, auxiliary dims 2/2/3
    Chosen by hand; not fitted from data, but central to the capacity of the neural linearisation.
assumptions (5)
  • domain assumption The observed sequence is generated by a Markovian latent state process with optional controls (Eq. 1).
    All DSSM results depend on the Markov assumption; if the true system is non-Markovian, the latent state cannot encode all relevant information.
  • domain assumption The constrained optimisation Lagrangian with the REWO λ-update from [16] yields a valid lower bound for 0 ≤ λ ≤ 1.
    Stated in Sec. 3 with reference to [16]; no convergence analysis is provided for the DSSM setting.
  • ad hoc to paper A feasible reconstruction target D0 exists and can be found by the 0.9 Dmax heuristic.
    App. A.7.1 shows failure when D0 is too tight (abrupt drop at 1.15 D0*), so the method's success is conditional on a feasible hyperparameter.
  • ad hoc to paper OLS regression between inferred latent dimensions and ground-truth states is an adequate measure of system identification.
    Used throughout Secs. 6.2-6.3; assumes a linear relationship and measures correlation rather than causal identification of the true dynamics.
  • domain assumption The approximate EKF/EKS marginals used as the recognition model are close enough to the true posterior for the ELBO to drive useful learning.
    Sec. 4.2 concedes the posterior is 'generally not optimal' because of local linearisation; the bound remains valid for any q, but its tightness and gradient quality are not analysed.
invented entities (1)
  • Auxiliary variables a_t (pseudo-observations)
    purpose: Enable closed-form Kalman updates through the linear-Gaussian pψ(at|zt)=N(H zt, R) and provide static-feature disentangling (Sec. 4.2).
    A modeling device with no testable prediction outside the model architecture; similar variables exist in KVAE [8], so it is an adapted rather than fully novel entity.

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Pith. "Pith review of Latent Matters: Learning Deep State-Space Models." pith.science (2026). https://pith.science/paper/BG75XWBP

@misc{pith2026260223050,
  author       = {Pith},
  title        = {Pith review of: Latent Matters: Learning Deep State-Space Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BG75XWBP}},
  note         = {Machine review of arXiv:2602.23050}
}
read the original abstract

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model actually learns the underlying dynamics. We therefore propose a constrained optimisation framework as a general approach for training DSSMs. Building upon this, we introduce the extended Kalman VAE (EKVAE), which combines amortised variational inference with classic Bayesian filtering/smoothing to model dynamics more accurately than RNN-based DSSMs. Our results show that the constrained optimisation framework significantly improves system identification and prediction accuracy on the example of established state-of-the-art DSSMs. The EKVAE outperforms previous models w.r.t. prediction accuracy, achieves remarkable results in identifying dynamical systems, and can furthermore successfully learn state-space representations where static and dynamic features are disentangled.

Figures

Figures reproduced from arXiv: 2602.23050 by the authors.

Figure 1
Figure 1. VHP-DKS (CO) on pendulum (image data). Learning the state-space representation with the CO framework. Distortion and rate are balanced by the Lagrange multiplier λ, which is updated (cf. Alg. 1) such that the model first improves the reconstruction quality/constraint by learning the rotation angle (see epoch 70). As soon as the constraint is satisfied, λ decreases and the model starts learning the underlying dynamic… view at source ↗
Figure 2
Figure 2. Pendulum (image data). In contrast to annealing (bottom), CO (middle & top) enables the model to learn the underlying dynamic system, as we verify in Table 1a. Furthermore, the VHP (top) significantly improves the quality of generated sequences. This is because the VHP learns a prior p(z1) = Ep(ζ) [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. VHP-EKVAE (CO) on reacher (RGB image data). Five-dimensional state-space representation (disentangled): the first three dimensions (z1, z2, z3) represent the two joint angles, the last two dimensions (z4, z5) represent the respective angular velocities. The barrel shape indicates the model has learned that the first joint can do a 360 degree turn; whereas the second joint is restricted to avoid self-collisions (cf … view at source ↗
Figures from the paper (20 more)
Figure 4
Figure 4. Figure 4: VHP-KVAE (CO). The predictions show that the KVAE encodes the angular velocity of the pendulum in ht = LSTM(a1:t) and not in zt. This causes the poor smoothing-based predictions, as h1 = LSTM(a1) does not have access to sequence data and therefore cannot infer the angu…
Figure 6
Figure 6. Figure 6: VHP-EKVAE (CO). Visualisation of different policies that we learned based on the disentangled position–velocity representation in [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: VHP-EKVAE (CO). Policy for reaching an encoded goal position (red dot) that we learned based on the disentangled (position–velocity) state-space representation in [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Graphical model of the EKVAE. Red arrows indicate the variational inference networks [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: Pendulum (image data). To evaluate the robustness of the CO framework w.r.t. [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: Pendulum (image data). Statistic evaluation of different annealing schedules. For this [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]
Figure 11
Figure 11. Figure 11: VHP-EKVAE (CO) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p022_11.png]
Figure 12
Figure 12. Figure 12: EKVAE (CO) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: EKVAE (annealing) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]
Figure 14
Figure 14. Figure 14: VHP-DVBS (CO) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p024_14.png]
Figure 15
Figure 15. Figure 15: DVBS (CO) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). The [PITH_FULL_IMAGE:figures/full_fig_p024_15.png]
Figure 16
Figure 16. Figure 16: DVBS (annealing) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p025_16.png]
Figure 17
Figure 17. Figure 17: VHP-DKS (CO) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p025_17.png]
Figure 18
Figure 18. Figure 18: DKS (CO) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p026_18.png]
Figure 19
Figure 19. Figure 19: DKS (annealing) trained on pendulum image data (supplementary to Tab. 1a in Sec. 6.2). [PITH_FULL_IMAGE:figures/full_fig_p026_19.png]
Figure 20
Figure 20. Figure 20: Summary of all models. Predicted sequences of a moving pendulum conditioned on [PITH_FULL_IMAGE:figures/full_fig_p027_20.png]
Figure 21
Figure 21. Figure 21: VHP-EKVAE (CO). Predicted sequence of a moving reacher conditioned on the smoothed [PITH_FULL_IMAGE:figures/full_fig_p027_21.png]
Figure 22
Figure 22. Figure 22: VHP-KVAE (CO). The predictions demonstrate that the KVAE encodes the angular [PITH_FULL_IMAGE:figures/full_fig_p028_22.png]
Figure 23
Figure 23. Figure 23: VHP-RSSM (CO). The predictions demonstrate that the RSSM encodes the angular [PITH_FULL_IMAGE:figures/full_fig_p028_23.png]
Figure 24
Figure 24. Figure 24: VHP-EKVAE (CO). Visualisation of the policy learned based on the disentangled (position– [PITH_FULL_IMAGE:figures/full_fig_p029_24.png]

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Reference graph

Works this paper leans on

29 extracted references · 4 linked inside Pith

  1. [1]

    Saurous, and Kevin Murphy

    Alexander Alemi, Ben Poole, Ian Fischer, Joshua Dillon, Rif A. Saurous, and Kevin Murphy. Fixing a broken ELBO. InInternational Conference on Machine Learning, pages 159–168. PMLR, 2018

    2018

  2. [2]

    Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Models

    Justin Bayer, Maximilian Soelch, Atanas Mirchev, Baris Kayalibay, and Patrick van der Smagt. Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Models. InInternational Conference on Learning Representations. OpenReview.net, 2021

    2021

  3. [3]

    Learning to Fly via Deep Model-Based Reinforcement Learning.arXiv preprint arXiv:: 2003.0887, 2020

    Philip Becker-Ehmck, Maximilian Karl, Jan Peters, and Patrick van der Smagt. Learning to Fly via Deep Model-Based Reinforcement Learning.arXiv preprint arXiv:: 2003.0887, 2020

    arXiv 2003

  4. [4]

    Bowman, Luke Vilnis, Oriol Vinyals, Andrew Dai, Rafal Jozefowicz, and Samy Bengio

    Samuel R. Bowman, Luke Vilnis, Oriol Vinyals, Andrew Dai, Rafal Jozefowicz, and Samy Bengio. Generating Sentences from a Continuous Space. InConference on Computational Natural Language Learning, pages 10–21. Association for Computational Linguistics, 2016

    2016

  5. [5]

    A recurrent latent variable model for sequential data

    Junyoung Chung, Kyle Kastner, Laurent Dinh, Kratarth Goel, Aaron C Courville, and Yoshua Bengio. A recurrent latent variable model for sequential data. InAdvances in Neural Information Processing Systems, volume 28, pages 2980–2988. Curran Associates, Inc., 2015

    2015

  6. [6]

    Probabilistic Recurrent State-Space Models

    Andreas Doerr, Christian Daniel, Martin Schiegg, Nguyen-Tuong Duy, Stefan Schaal, Marc Toussaint, and Trimpe Sebastian. Probabilistic Recurrent State-Space Models. InInternational Conference on Machine Learning, volume 80, pages 1280–1289. PMLR, 2018

    2018

  7. [7]

    Sequential Neural Models with Stochastic Layers

    Marco Fraccaro, Søren Kaae Sønderby, Ulrich Paquet, and Ole Winther. Sequential Neural Models with Stochastic Layers. InAdvances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016

    2016

  8. [8]

    A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning

    Marco Fraccaro, Simon Kamronn, Ulrich Paquet, and Ole Winther. A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning. InAdvances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017

    2017

Show all 29 references
  1. [9]

    Learning Latent Dynamics for Planning from Pixels

    Danijar Hafner, Timothy Lillicrap, Ian Fischer, Ruben Villegas, David Ha, Honglak Lee, and James Davidson. Learning Latent Dynamics for Planning from Pixels. InInternational Conference on Machine Learning, pages 2555–2565. PMLR, 2019

    2019

  2. [10]

    beta-V AE: Learning Basic Visual Concepts with a Constrained Variational Framework

    Irina Higgins, Loïc Matthey, Arka Pal, Christopher Burgess, Xavier Glorot, Matthew Botvinick, Shakir Mohamed, and Alexander Lerchner. beta-V AE: Learning Basic Visual Concepts with a Constrained Variational Framework. InInternational Conference on Learning Representations. Ope...

    2017

  3. [11]

    Jazwinski.Stochastic Processes and Filtering Theory

    Andrew H. Jazwinski.Stochastic Processes and Filtering Theory. Courier Corporation, 2007

    2007

  4. [12]

    Rudolf E. Kalman. A New Approach to Linear Filtering and Prediction Problems.Journal of Basic Engineering, 1960

    1960

  5. [13]

    Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data

    Maximilian Karl, Maximilian Soelch, Justin Bayer, and Patrick van der Smagt. Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data. InInternational Conference on Learning Representations. OpenReview.net, 2017. 11

    2017

  6. [14]

    Unsupervised Real-Time Control through Variational Empowerment

    Maximilian Karl, Maximilian Soelch, Philip Becker-Ehmck, Djalel Benbouzid, Patrick van der Smagt, and Justin Bayer. Unsupervised Real-Time Control through Variational Empowerment. arXiv preprint arXiv:1710.05101, 2017

    2017 arXiv

  7. [15]

    Kingma and Max Welling

    Diederik P. Kingma and Max Welling. Auto-Encoding Variational Bayes. InInternational Conference on Learning Representations. OpenReview.net, 2014

    2014

  8. [16]

    Learn- ing Hierarchical Priors in V AEs

    Alexej Klushyn, Nutan Chen, Richard Kurle, Botond Cseke, and Patrick van der Smagt. Learn- ing Hierarchical Priors in V AEs. InAdvances in Neural Information Processing Systems, volume 32, pages 2870–2879. Curran Associates, Inc., 2019

    2019

  9. [17]

    Krishnan, Uri Shalit, and David Sontag

    Rahul G. Krishnan, Uri Shalit, and David Sontag. Deep Kalman Filters.arXiv preprint arXiv:1511.05121, 2015

    2015 arXiv

  10. [18]

    Deep Rao-Blackwellised Particle Filters for Time Series Forecasting

    Richard Kurle, Syama Sundar Rangapuram, Emmanuel de Bezenac, Stephan Günnemann, and Jan Gasthaus. Deep Rao-Blackwellised Particle Filters for Time Series Forecasting. InAdvances in Neural Information Processing Systems, volume 33, pages 15371–15382. Curran Associates, Inc., 2020

    2020

  11. [19]

    Guided Policy Search

    Sergey Levine and Vladlen Koltun. Guided Policy Search. InInternational Conference on Machine Learning, volume 28, pages 1–9. PMLR, 2013

    2013

  12. [20]

    Neal and Geoffrey E

    Radford M. Neal and Geoffrey E. Hinton. A View of the EM Algorithm that Justifies Incremental, Sparse, and other Variants. InLearning in graphical models, pages 355–368. Springer, 1998

    1998

  13. [21]

    Deep State Space Models for Time Series Forecasting

    Syama Sundar Rangapuram, Matthias Seeger, Jan Gasthaus, Lorenzo Stella, Yuyang Wang, and Tim Januschowski. Deep State Space Models for Time Series Forecasting. InAdvances in Neural Information Processing Systems, volume 31, pages 7785–7794. Curran Associates, Inc., 2018

    2018

  14. [22]

    Rauch, Fang-Wu Tung, and Charlotte T

    Herbert E. Rauch, Fang-Wu Tung, and Charlotte T. Striebel. Maximum Likelihood Estimates of Linear Dynamic Systems.AIAA Journal, 3:1445–1450, 1965

    1965

  15. [23]

    Taming V AEs.arXiv preprint arXiv:1810.00597, 2018

    Danilo Jimenez Rezende and Fabio Viola. Taming V AEs.arXiv preprint arXiv:1810.00597, 2018

    2018 arXiv

  16. [24]

    Stochastic backpropagation and approximate inference in deep generative models.ICML, 2014

    Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra. Stochastic backpropagation and approximate inference in deep generative models.ICML, 2014

    2014

  17. [25]

    Deepar: Probabilistic forecasting with autoregressive recurrent networks.International Journal of Forecasting, 2020

    David Salinas, Valentin Flunkert, Jan Gasthaus, and Tim Januschowski. Deepar: Probabilistic forecasting with autoregressive recurrent networks.International Journal of Forecasting, 2020

    2020

  18. [26]

    DeepMind Control Suite.arXiv preprint arXiv:: 1801.00690, 2018

    Yuval Tassa, Yotam Doron, Alistair Muldal, Tom Erez, Yazhe Li, Diego de Las Casas, David Budden, Abbas Abdolmaleki, Josh Merel, Andrew Lefrancq, Timothy Lillicrap, and Martin Riedmiller. DeepMind Control Suite.arXiv preprint arXiv:: 1801.00690, 2018

    2018 arXiv

  19. [27]

    V AE with a VampPrior

    Jakub Tomczak and Max Welling. V AE with a VampPrior. InInternational Conference on Artificial Intelligence and Statistics, volume 84, pages 1214–1223. PMLR, 2018

    2018

  20. [28]

    Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images

    Manuel Watter, Jost Springenberg, Joschka Boedecker, and Martin Riedmiller. Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images. InAdvances in Neural Information Processing Systems, volume 28. Curran Associates, Inc., 2015

    2015

  21. [29]

    logq ϕ(z1:T |x 1:T ,u 1:T )−logp ψ0 (z1)− TX t=2 logp ψ(zt|z t−1,u t−1) # (22) ≤E qϕ(z1:T |x 1:T ,u1:T )

    Li Yingzhen and Stephan Mandt. Disentangled Sequential Autoencoder. InInternational Conference on Machine Learning, volume 80, pages 5670–5679. PMLR, 2018. 12 A Appendix A.1 Heuristic for DeterminingD 0 In our experiments, we use the following heuristic for finding D0: first, ...

    2018

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.