REVIEW 3 major objections 5 minor 30 references
Disentangled Interleaving Variational Encoding
T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read The paper claims that one evidence lower bound can carry a VAE's reconstruction, forecasting, and disentanglement objectives, with cross-entropy loss replacing the KL term on each disentangled dimension.
desk verdict The architecture is a genuinely new combination, but the paper's central theoretical claim — that the cross-entropy minimizer also minimizes the DKL upper bound — does not hold as proved, so the loss derivation is currently unsupported. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The carrying object is the evidence lower bound for the joint density of the input and forecast windows, written as forecast loss $+$ reconstruction loss $- D_{\mathrm{KL}}(q_\phi(a,b|x) \| p_\theta(a,b))$, with the latent vector split into conditional dimensions $a$ and marginal dimensions $b$. The load-bearing identity is the inequality of Proposition 4: the marginal KL $D_{\mathrm{KL}}(q_\phi(b|x) \| p_\theta(b))$ equals the negative conditional entropy of the encoder plus $\int q_\phi(b|x)\log\sum_k p_\theta(b,k)\,db$, which Jensen's inequality bounds by $\mathbb{E}_{b\sim q_\phi}[\sum_k Q(k)(-\log p_\theta(b,k)/Q(k))]$, with the bound tight at $Q(k)=p_\theta(k|b)$. Gaussian radial basis functions supply the mixture prior $p_\theta(b|k)=\psi_k(b)$, whose log-concavity lets the sufficiency corollary turn the shared stationary conditions of Propositions 5 and 6 into global optimality and links the upper bound to the cross-entropy loss. The architecture — an RBF layer, cross-attention fusion at the first decoder layer, and interleaved training that alternates between updating the conditional dimensions and the marginal classifiers — is chosen so that each piece of the theorem has a corresponding component.
What would settle it
On a two-class synthetic problem with Gaussian clusters, compute the exact minimizers of the cross-entropy loss $-\log p_\theta(j|b)$ and of the upper bound $\mathbb{E}_{b\sim q_\phi}[\sum_k Q(k)(-\log p_\theta(b,k)/Q(k))]$ as functions of the RBF center $\nu$ and scale $\tau$, for instance by fine grid search. If the minimizing $(\nu,\tau)$ differ between the two objectives, the corollary's equivalence is false and the claimed grounding of the training loss in the evidence lower bound fails; if they coincide, the claim survives this direct check.
Extended reading notes
Core claim
The paper claims that the log-likelihood of the joint distribution of an input window $x$ and a forecast window $y$ decomposes as $\log p_\theta(x,y) = \mathcal{L}(\theta,\phi;x,y) + D_{\mathrm{KL}}(q_\phi(a,b|x) \| p_\theta(a,b|x,y))$, so maximizing the evidence lower bound — forecast loss plus reconstruction loss minus a KL term — is a valid objective for both tasks at once. Under a naive-Bayes independence assumption, the KL term splits into a conditional part for the dimensions $a$ and a sum of per-dimension divergences for the marginal dimensions $b$, and each marginal divergence is shown to be upper bounded by an expectation involving the joint $p_\theta(b,k)$ over the class $k$. Choosing a Gaussian radial-basis-function mixture as the prior makes both this upper bound and the cross-entropy loss $-\log p_\theta(j|b)$ for the true class $j$ have stationary points satisfying the same derivative conditions on the RBF centers and scales; the sufficiency corollary adds log-concavity so those stationary points are global minima. The paper therefore concludes that the minimizer of the cross-entropy loss also minimizes the upper bound of the KL divergence on each marginal dimension, and designs DeepDIVE — an RBF layer, cross-attention fusion, and interleaved training that freezes the marginal dimensions while updating the conditional ones — to implement this loss. Empirically, DeepDIVE reports lower root relative squared error than the plain VAE and $\beta$-TCVAE baselines on the gait and electricity datasets, and forecast accuracy comparable to dedicated forecasting baselines on the electricity data.
Load-bearing premise
The theoretical foundation rests on the corollary to Proposition 6 (Section 3.1; proof in Appendix A.2.7), which asserts that a minimizer of the cross-entropy loss also minimizes the upper bound on the marginal KL divergence; the proof shows only that both objectives have stationary points (where the derivative is zero) satisfying the same condition, not that the two objectives share a minimizer, and the paper's own remark concedes that the companion naive-independence assumption does not generally hold.
Editorial extensions
If this is right
- Because every objective term descends from one log-likelihood, the paper's loss needs no gradient-balancing or conflict-resolution step before each update, unlike other multi-task schemes.
- Labeled categorical variables can be encoded as individual latent dimensions, so the learned representation separates into univariate factors that can be plotted and inspected directly.
- The mixture prior's centers and scales are learned rather than fixed, so no hand-crafted prior or pre-specified clustering is needed.
- On the two datasets tested, the full model beats the plain VAE and $\beta$-TCVAE in reconstruction and forecast error, and matches dedicated forecasting models on the electricity benchmark.
- The same derivation justifies semi-supervised VAE training in general: classifying a sequence as a whole can improve reconstruction and forecasting of that sequence within one shared encoder.
Reading between the lines
- The paper's own remark that its naive independence assumption fails on the gait dataset while results still improve suggests the per-dimension cross-entropy decomposition may be robust to correlation; a controlled experiment that varies the correlation among marginal dimensions would show whether accuracy degrades gracefully or the summed per-dimension losses start to aggregate errors.
- If the corollary's stationarity argument is sound, the same substitution of cross-entropy for an intractable KL term should work for any log-concave mixture prior, not just Gaussian RBFs, and for any labeled auxiliary task, so the derivation plausibly extends beyond time-series forecasting to other semi-supervised generative settings.
- A direct comparison the paper does not report — training with the true marginal KL computed against the learned mixture prior versus training with the cross-entropy surrogate — would separate the contribution of the surrogate loss from the benefit of the interleaving scheme and the RBF architecture.
Formalized claims in Lean
-
Claim #1: The paper claims that the log-likelihood of the joint distribution of an input window $x$ and a forecast window $y$ decomposes as $\log p_\theta(x,y) = \mathcal{L}(\theta,\phi;x,y) + D_{\mathrm{KL}}(q_\phi(a,b|x) \| p_\theta(a,b|x,y))$, so maximizing the evidence lower bound — forecast loss plus reconstruction loss minus a KL term — is a valid objective for both tasks at once. Under a naive-Bayes
/-- @claim 1 The paper claims that the log-likelihood of the joint distribution of an input window $x$ and a forecast window $y$ decomposes as $\log p_\theta(x,y) = \mathcal{L}(\theta,\phi;x,y) + D_{\mathrm{KL}}(q_\phi(a,b|x) \| p_\theta(a,b|x,y))$, so maximizing the evidence lower bound — forecast loss plus reconstruction loss minus a KL term — is a valid objective for both tasks at once. Under a naive-Bayes -/ def central_claim : Prop :=
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes DeepDIVE, a variational autoencoder architecture for joint reconstruction, forecasting, and classification on time-series data. The authors derive an ELBO for the joint log-likelihood log p(x,y), decompose the KL term into conditional and marginal components under a naive-Bayes independence assumption, and then propose to replace the KL divergence on each marginal latent dimension with a cross-entropy classification loss. The justification is a chain of propositions (1-6) culminating in Theorem 1, which claims that the minimizer of the cross-entropy loss also minimizes an upper bound on the marginal KL, thereby making the multi-task objective conflict-free and principled. The architecture uses RBF units for the latent classes, cross-attention fusion, and interleaved training. Experiments on a gait dataset and an electricity dataset report lower RRSE than VAE-based baselines and are claimed to be comparable to state-of-the-art forecasting methods.
Significance. If the theoretical derivation were sound, the paper would make a valuable contribution: a semi-supervised VAE with a principled, conflict-free objective for reconstruction and forecasting, with interpretable disentangled dimensions. The paper also ships a concrete architecture and experiments, which is a strength. However, the central theoretical bridge from cross-entropy minimization to KL-divergence minimization is not established. The claimed equivalence between the minimizers of the two objectives conflates a conditional log-likelihood with a joint-distribution bound and omits the required convexity properties for the RBF parameterization actually used. Because this bridge is the load-bearing justification for the proposed loss function and the ``no conflict'' claim, the paper's main theoretical contribution fails. The empirical results are limited to two datasets and do not compensate for the unsupported core claim.
major comments (3)
- [Appendix A.2.6 (sufficiency corollary) and Section 3.1] The corollary asserts that a minimizer of the cross-entropy loss L_CE(phi, theta; j) = -log p_theta(j|b) also minimizes the upper bound in Eq. (22), E_{b~q}[sum_k Q(k)(-log p_theta(b,k)/Q(k))]. Proposition 6 only shows that a point minimizing L_CE satisfies the stationarity conditions partial psi/partial nu = partial psi/partial tau = 0 (Eqs. 29-30), which are the same equations as those in Proposition 5 (Eqs. 25-26). But the two objectives are different functions: the upper bound is a weighted average over all classes k of -log p_theta(b,k), whereas the cross-entropy loss is a single conditional log-likelihood -log p_theta(j|b) for the true class j. The derivative of -log p_theta(j|b) involves the softmax denominator over all classes, while the derivative of the upper bound involves p_theta(k)/p_theta(b,k) times partial psi_k. Showing that partial psi = 0 is a common stationary point does not imply that the global minimizers of the two objectives coincide. Furthermore, the proof of Proposition 6 in Appendix A.2.7 explicitly treats only the two-class case with p_theta(j|b) = sigma(f(psi(b))), and the extension to K > 2 classes is asserted without proof. The corollary is therefore unproved, and Theorem 1's substitution of L_CE for the marginal DKL terms is not justified.
- [Appendix A.2.6; Eq. (23)-(24)] The sufficiency corollary claims that if p_theta(b|k) is log-concave in its parameters, the upper bound in Eq. (71)-(73) is convex and any stationary point is a global minimum. However, the Gaussian RBF cell psi_k(b) = (2 pi tau_k^2)^(-1/2) exp(-(b-nu_k)^2/(2 tau_k^2)) is not jointly log-concave in (nu_k, tau_k): the negative log-likelihood -log psi_k(b) = (b-nu_k)^2/(2 tau_k^2) + log tau_k + const is not convex in (nu_k, tau_k) jointly (the Hessian is indefinite in the tau direction for b != nu_k). Thus the sufficiency condition stated in the main-text corollary does not hold for the RBF prior that DeepDIVE actually employs. The appendix even notes that the Gaussian in sigma has only a stationary-point property, not log-concavity, yet the main text requires log-concavity. Consequently, Eqs. (25)-(26) are not sufficient for global optimality of the upper bound, breaking the necessity-sufficiency chain that the paper relies on.
- [Section 3.3, Theorem 1 (Eqs. 31-33) and the concluding paragraph] The final loss in Theorem 1 replaces the marginal DKL terms with cross-entropy losses L_CE(phi, theta; j_i) for each label i. Since the equivalence between the minimizers of L_CE and the minimizers of the DKL upper bound is unproved (see the first major comment), the resulting objective is not actually derived from the ELBO as claimed. The statement that ``these objectives exhibit no mutual conflict'' because the constituent terms arise from the log-likelihood of a pre-existing data point is therefore unsupported. The paper provides no analysis of the gradient directions of the MSE terms and the CE terms, so the central claim of conflict-free multi-task learning is not established. This is the paper's headline theoretical contribution, and it fails.
minor comments (5)
- [Section 4, paragraph on interleaving training] The text contains a duplicated article: ``with the the objective function.'' Please correct the typo.
- [Table 3 (Appendix A.1)] The DeepDIVE row reports an RRSE of 1.0000 at the 24-th horizon, which is an order of magnitude larger than the other horizons and contradicts the claim of performance comparable to state-of-the-art baselines. This appears to be a typo (likely 0.1000), but as printed it is a serious inconsistency that must be fixed.
- [Appendix A.2.6] The statement ``eg. N(mu, sigma^2) in mu, Exp(lambda) in lambda'' is correct, but the follow-up ``or have the stationary point where likelihood is maximum (eg. N(mu, sigma^2) in sigma)'' does not satisfy the log-concavity requirement stated in the main-text sufficiency corollary. The distinction should be made explicit to avoid the impression that the Gaussian in sigma qualifies.
- [Section 3.1, around Eq. (22)] The notation Q(k) is introduced as an arbitrary distribution, but later Theorem 1 sets Q(k) = p_{theta_t}(k|b). The subscript t and the distinction between the old parameters theta_t and the optimized theta are not defined in the main text; please define these in Section 3.1.
- [Abstract and Section 5] The claim that DeepDIVE is ``comparable to existing state-of-the-art baselines'' is only supported by Table 3, where DeepDIVE is consistently worse than all listed SOTA baselines at all horizons (after correcting the apparent 24-th typo). Please qualify the claim with the actual relative differences, and consider adding statistical significance tests over the 30 runs.
Circularity Check
No circularity: the DeepDIVE loss derivation is self-contained, and the CE-to-KL bridge is an asserted theorem, not a rename of its inputs.
full rationale
The paper's derivation chain starts from the standard VAE ELBO (Kingma & Welling), extends it to the joint log-likelihood log p(x,y) in Proposition 1, and then decomposes the KL term via the chain rule and a naive-Bayes independence assumption (Propositions 2 and 3). The replacement of the marginal-dimension KL with cross-entropy is justified by an upper bound (Proposition 4) followed by stationary-point comparisons (Proposition 5, Proposition 6, and the Corollary). None of these steps fits a parameter to the quantity that is later reported as a prediction; the CE loss is not obtained by fitting the DKL upper bound to data, and the paper contains no load-bearing self-citations. The architecture choices (RBF units, CE on marginal dimensions, interleaving) are presented as consequences of the derivations, not as inputs that are then relabeled as results. The Corollary to Proposition 6 is mathematically questionable—it infers global minimality of the upper bound from shared stationary conditions and appears to require convexity that the Gaussian RBF does not satisfy jointly in (nu,tau)—but that is a proof-soundness issue, not a circularity. A failed or overreaching proof is not the same as a derivation that reduces to its own assumptions by construction. The empirical disentanglement evaluation is also not circular in the derivation-chain sense: the auxiliary classification loss does encourage label-aligned clustering, which makes the qualitative cluster plots unsurprising, but the paper does not present those plots as a test of the CE-to-KL theorem. Overall, no step in the claimed chain is equivalent to its input by definition.
Assumptions & free parameters
free parameters (3)
- RBF centroids nu_k =
learned (not reported)
- RBF scales tau_k =
learned (not reported)
- Latent split (n1, n2) =
n2=2 (gait), n2=3 (electricity); n1 not specified
assumptions (6)
- domain assumption Prior p(a,b) = p(a)p(b) (independent latent dimensions)
- domain assumption q(b_i,b_j|x) = q(b_i|x)q(b_j|x) for all i != j (naive conditional independence)
- domain assumption Prior p(b|k) is a Gaussian RBF, psi_k(b)
- domain assumption p(k) approx n_k/n (empirical class frequencies)
- ad hoc to paper p(b|k) is log-concave in its parameters
- ad hoc to paper A minimizer of L_CE also minimizes the DKL upper bound
Cite this review
Pith. "Pith review of Disentangled Interleaving Variational Encoding." pith.science (2026). https://pith.science/paper/NNBBZPXA
@misc{pith2026250108710,
author = {Pith},
title = {Pith review of: Disentangled Interleaving Variational Encoding},
year = {2026},
howpublished = {\url{https://pith.science/paper/NNBBZPXA}},
note = {Machine review of arXiv:2501.08710}
}
read the original abstract
Conflicting objectives present a considerable challenge in interleaving multi-task learning, necessitating the need for meticulous design and balance to ensure effective learning of a representative latent data space across all tasks without mutual negative impact. Drawing inspiration from the concept of marginal and conditional probability distributions in probability theory, we design a principled and well-founded approach to disentangle the original input into marginal and conditional probability distributions in the latent space of a variational autoencoder. Our proposed model, Deep Disentangled Interleaving Variational Encoding (DeepDIVE) learns disentangled features from the original input to form clusters in the embedding space and unifies these features via the cross-attention mechanism in the fusion stage. We theoretically prove that combining the objectives for reconstruction and forecasting fully captures the lower bound and mathematically derive a loss function for disentanglement using Na\"ive Bayes. Under the assumption that the prior is a mixture of log-concave distributions, we also establish that the Kullback-Leibler divergence between the prior and the posterior is upper bounded by a function minimized by the minimizer of the cross entropy loss, informing our adoption of radial basis functions (RBF) and cross entropy with interleaving training for DeepDIVE to provide a justified basis for convergence. Experiments on two public datasets show that DeepDIVE disentangles the original input and yields forecast accuracies better than the original VAE and comparable to existing state-of-the-art baselines.
Figures
Figures from the paper (2 more)
Reference graph
Works this paper leans on
-
[1]
write newline
" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...
-
[2]
Zhang, Michael Ruan, Eric Wang, So Hasegawa, Jimmy Ba, and Roger Baker Grosse
Juhan Bae, Michael R. Zhang, Michael Ruan, Eric Wang, So Hasegawa, Jimmy Ba, and Roger Baker Grosse. Multi-rate VAE : Train once, get the full rate-distortion curve. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=OJ8aSjCaMNK
work page 2023
-
[3]
Understanding disentangling in \( \)-vae
Christopher P Burgess, Irina Higgins, Arka Pal, Loic Matthey, Nick Watters, Guillaume Desjardins, and Alexander Lerchner. Understanding disentangling in \( \)-vae. arXiv preprint arXiv:1804.03599, 2018
arXiv 2018
-
[4]
Isolating sources of disentanglement in variational autoencoders
Ricky TQ Chen, Xuechen Li, Roger B Grosse, and David K Duvenaud. Isolating sources of disentanglement in variational autoencoders. Advances in neural information processing systems, 31, 2018
2018
-
[5]
A bayesian approach to state space multivariate time series modeling
Jeffrey H Dorfman and Arthur M Havenner. A bayesian approach to state space multivariate time series modeling. Journal of Econometrics, 52 0 (3): 0 315--346, 1992
work page 1992
-
[6]
Neural architecture search: A survey
Thomas Elsken, Jan Hendrik Metzen, and Frank Hutter. Neural architecture search: A survey. Journal of Machine Learning Research, 20 0 (55): 0 1--21, 2019
2019
-
[7]
beta-vae: Learning basic visual concepts with a constrained variational framework
Irina Higgins, Loic Matthey, Arka Pal, Christopher P Burgess, Xavier Glorot, Matthew M Botvinick, Shakir Mohamed, and Alexander Lerchner. beta-vae: Learning basic visual concepts with a constrained variational framework. ICLR (Poster), 3, 2017
2017
-
[8]
Elbo surgery: yet another way to carve up the variational evidence lower bound
Matthew D Hoffman and Matthew J Johnson. Elbo surgery: yet another way to carve up the variational evidence lower bound. In Workshop in Advances in Approximate Bayesian Inference, NIPS, volume 1, 2016
work page 2016
Show all 30 references
-
[9]
Dsanet: Dual self-attention network for multivariate time series forecasting
Siteng Huang, Donglin Wang, Xuehan Wu, and Ao Tang. Dsanet: Dual self-attention network for multivariate time series forecasting. In Proceedings of the 28th ACM international conference on information and knowledge management, pp.\ 2129--2132, 2019
2019
-
[10]
Kingma and Max Welling
Diederik P. Kingma and Max Welling. Auto-Encoding Variational Bayes . In 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings , 2014
2014
-
[11]
Modeling long-and short-term temporal patterns with deep neural networks
Guokun Lai, Wei-Cheng Chang, Yiming Yang, and Hanxiao Liu. Modeling long-and short-term temporal patterns with deep neural networks. In The 41st international ACM SIGIR conference on research & development in information retrieval, pp.\ 95--104, 2018
2018
-
[12]
Lightcts: A lightweight framework for correlated time series forecasting
Zhichen Lai, Dalin Zhang, Huan Li, Christian S Jensen, Hua Lu, and Yan Zhao. Lightcts: A lightweight framework for correlated time series forecasting. Proceedings of the ACM on Management of Data, 1 0 (2): 0 1--26, 2023
2023
-
[13]
Conflict-averse gradient descent for multi-task learning
Bo Liu, Xingchao Liu, Xiaojie Jin, Peter Stone, and Qiang Liu. Conflict-averse gradient descent for multi-task learning. Advances in Neural Information Processing Systems, 34: 0 18878--18890, 2021
2021
-
[14]
Machine learning: a probabilistic perspective
Kevin P Murphy. Machine learning: a probabilistic perspective. MIT press, 2012
2012
-
[15]
Temporal latent auto-encoder: A method for probabilistic multivariate time series forecasting
Nam Nguyen and Brian Quanz. Temporal latent auto-encoder: A method for probabilistic multivariate time series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pp.\ 9117--9125, 2021
2021
-
[16]
Multivariate bayesian structural time series model
Jinwen Qiu, S Rao Jammalamadaka, and Ning Ning. Multivariate bayesian structural time series model. Journal of Machine Learning Research, 19 0 (68): 0 1--33, 2018
2018
-
[17]
Deep state space models for time series forecasting
Syama Sundar Rangapuram, Matthias W Seeger, Jan Gasthaus, Lorenzo Stella, Yuyang Wang, and Tim Januschowski. Deep state space models for time series forecasting. Advances in neural information processing systems, 31, 2018
2018
-
[18]
Deepar: Probabilistic forecasting with autoregressive recurrent networks
David Salinas, Valentin Flunkert, Jan Gasthaus, and Tim Januschowski. Deepar: Probabilistic forecasting with autoregressive recurrent networks. International journal of forecasting, 36 0 (3): 0 1181--1191, 2020
2020
-
[19]
\( \)-annealed variational autoencoder for glitches
Sivaramakrishnan Sankarapandian and Brian Kulis. \( \)-annealed variational autoencoder for glitches. arXiv preprint arXiv:2107.10667, 2021
2021 arXiv
-
[20]
Think globally, act locally: A deep neural network approach to high-dimensional time series forecasting
Rajat Sen, Hsiang-Fu Yu, and Inderjit S Dhillon. Think globally, act locally: A deep neural network approach to high-dimensional time series forecasting. Advances in neural information processing systems, 32, 2019
2019
-
[21]
Multi-task learning as multi-objective optimization
Ozan Sener and Vladlen Koltun. Multi-task learning as multi-objective optimization. Advances in neural information processing systems, 31, 2018
2018
-
[22]
Electricityloaddiagrams20112014 data set, Dec 2015
Artur Trindade. Electricityloaddiagrams20112014 data set, Dec 2015. URL https://archive.ics.uci.edu/ml/datasets/ElectricityLoadDiagrams20112014
2015
-
[23]
Attention is all you need
A Vaswani. Attention is all you need. Advances in Neural Information Processing Systems, 2017
2017
-
[24]
Autocts: Automated correlated time series forecasting
Xinle Wu, Dalin Zhang, Chenjuan Guo, Chaoyang He, Bin Yang, and Christian S Jensen. Autocts: Automated correlated time series forecasting. Proceedings of the VLDB Endowment, 15 0 (4): 0 971--983, 2021
2021
-
[25]
Gradient surgery for multi-task learning
Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine, Karol Hausman, and Chelsea Finn. Gradient surgery for multi-task learning. Advances in Neural Information Processing Systems, 33: 0 5824--5836, 2020
2020
-
[26]
Alternating least-squares for low-rank matrix reconstruction
Dave Zachariah, Martin Sundin, Magnus Jansson, and Saikat Chatterjee. Alternating least-squares for low-rank matrix reconstruction. IEEE Signal Processing Letters, 19 0 (4): 0 231--234, 2012
2012
-
[27]
GaitMotion: A Multitask Dataset for Pathological Gait Forecasting , 2023
Wenwen Zhang, Hao Zhang, Zenan Jiang, Jing Wang, Amir Servati, Calvin Kuo, and Peyman Servati. GaitMotion: A Multitask Dataset for Pathological Gait Forecasting , 2023. URL https://doi.org/10.5683/SP3/V6C59O
2023 doi
-
[28]
@esa (Ref
\@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should ...
-
[29]
\@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@firs...
-
[30]
M A^Uxi UX F !3' ] (|w 3 Z jkIS EMxYav+ZO dBfAĦZ>8 z1*-.@Vf6*ۏS* > ' n/|-8( W 1ؙ? Qos މG^x .YBK56o
@open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibset...
Reviewed August 10, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.