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REVIEW 3 major objections 6 minor 58 references

From Digital to Physical Reservoir Computing: Co-Optimizing Soft Robotic Reservoirs via Dynamics Matching

T0 review · 3 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper claims that soft-robot physical reservoirs can be pretrained against a strong digital reservoir by co-optimizing the robot's parameters, an invertible coordinate map, and feedforward-feedback control, and that this lifts physical

desk verdict A clean, honest simulation proof of concept for co-optimizing soft robot reservoirs against digital reference dynamics, but the body's contribution is not isolated and the digital controller currently costs more than the digital reference. read the letter →

arxiv 2608.00484 v1 pith:2FNIVNF4 submitted 2026-08-01 cs.RO cs.LG

Nicola Visentin , Maximilian Stölzle , Mariano Ramírez Montero , Francesco Braghin , Daniela Rus , Cosimo Della Santina This is my paper
classification cs.ROcs.LG
keywords physicalreservoircomputingsoftroboticspretrainingdynamicsmatchingequation-errorobjectiveco-optimizationrandomoscillatorsnetworkdifferentiablesimulation
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 asks whether a physical reservoir—here, a simulated soft robot—can be pretrained the way digital reservoirs are, rather than being used as-is. The proposed answer is yes: jointly optimize the robot's physical parameters, an invertible coordinate map, and feedforward/feedback controllers so that the robot's dynamics match a well-tuned digital Random Oscillators Network. Matching is done at the acceleration level on randomly sampled states, avoiding expensive temporal rollouts. Across classification and forecasting tasks at four reservoir sizes, the optimized soft-robot reservoirs beat unoptimized physical reservoirs by 33.7% on average and retain 90.9% of digital reference performance. The result is a proof of concept in simulation, with morphology optimization as the key contributor over learning map and control alone.

What carries the argument

The central mechanism is the acceleration-level equation-error objective (Eqs. 5–6): for sampled reference states (y, y-dot, u), the target acceleration y-double-dot is compared with the acceleration obtained by mapping the state into the physical reservoir, propagating it through the differentiable soft-robot dynamics, and mapping the result back through the diffeomorphism. Because it compares instantaneous accelerations, the loss avoids temporal integration entirely. It is carried by three co-optimized components: the physical parameters of the piecewise-constant-strain soft robots, an affine diffeomorphic map parameterized through an SVD factorization, and two MLP controllers (feedforward

What would settle it

Take a pretrained reservoir with low acceleration test RMSE but high trajectory NRMSE, such as the reported sMNIST n_y=15 case with trajectory NRMSE 0.415, and measure whether downstream task accuracy tracks acceleration RMSE or trajectory NRMSE across the four seeds; if accuracy follows trajectory error rather than acceleration error, the equation-error objective is not sufficient as a pretraining signal. A hardware rollout of the same reservoir under sensor noise and unmodeled dynamics would settle whether the gain survives physical realization.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a physical reservoir does not have to be taken as given: for differentiable second-order physical systems, one can reproduce the vector field of a high-performing digital reference by jointly optimizing physical parameters, a diffeomorphic physical-to-reference state map, and feedforward-feedback controllers. The objective is an acceleration-level equation error—mean squared difference between the reference acceleration and the mapped physical acceleration—which requires no temporal integration during pretraining. In the simulated soft-robot instantiation, the pretrained reservoirs outperform unoptimized physical reservoirs by 33.7% on

Load-bearing premise

The method bets that making a physical model's instantaneous accelerations match the digital reference on random snapshots is enough to make its long-run behavior match when fed real task sequences; if small acceleration errors accumulate differently over time, the task-level gains may not transfer.

Editorial extensions

If this is right

  • Physical reservoir design no longer needs to be a task-level search: pretraining against a digital reference provides a task-independent way to shape the reservoir before the readout is trained.
  • Optimizing the physical morphology itself is the main driver of improvement: without it, map-and-controller-only optimization gives larger errors, higher variance, and occasional diverging rollouts.
  • The performance gap between the pretrained physical reservoir and the digital RON reference generally widens with reservoir dimension, while raw task performance still improves as the reservoir grows from 6 to 15 oscillators.
  • In the paper's cost analysis, absorbing the affine map into the readout makes the digital inference cost of the PRC pipeline scale linearly with reservoir dimension rather than quadratically, with the crossover where physical beats digital occurring near n_y ≈ 220 for the tested controller size.
  • Cross-task experiments in the supplementary material indicate that a reservoir pretrained on one task can be reused on another without reoptimizing morphology, with modest degradation on some tasks and larger degradation on others.

Reading between the lines

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

  • If acceleration-level matching is the right pretraining signal, the same recipe should transfer beyond RON references: a direct test is to swap in a differently structured second-order digital reservoir and check whether task gains persist.
  • The cost analysis points to a concrete lever the paper leaves implicit: smaller controllers than the fixed 64-neuron MLP would likely move the digital-inference crossover well below n_y ≈ 220, and the paper reports preliminary evidence that linear controllers remain effective.
  • Some reported trajectory NRMSEs are large (e.g., 0.415 for sMNIST at n_y = 15), which suggests the acceleration-only objective may under-penalize slow integration drift; a testable extension is to add a short rollout-consistency term while keeping the bulk of pretraining rollouts free.
  • The simulated-only evidence leaves the physical-world question open: a hardware demonstrator on any one of the four tasks, with unmodeled soft-body dynamics and sensor noise, would decide whether the 33.7% gain survives the sim-to-real gap.
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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 / 6 minor

Summary. The paper proposes a pretraining method for physical reservoir computing. Given a high-performing digital reference reservoir (a Random Oscillators Network), the authors jointly optimize the physical parameters of a simulated soft-robot reservoir, an affine diffeomorphic map between physical and reference coordinates, and feedforward/feedback MLP controllers. The training objective is an acceleration-level equation-error loss, Eq. (5), which avoids temporal integration. Experiments on sMNIST, ADIAC, Mackey-Glass, and Lorenz96, with reservoir dimensions n_y = 6, 9, 12, 15, show that the fully pretrained physical reservoir improves over an unoptimized PRC baseline by 33.7% on average, retains 90.9% of digital RON performance, and outperforms a partially pretrained baseline with fixed morphology. The supplementary material provides significance tests, a FLOP-based cost comparison, and cross-task reuse experiments. The mathematical derivations in Section 3 are clean, and the empirical results are internally consistent, but the paper's central 'physical reservoir' claim is weakened by the fully actuated setup and by the high digital cost of the learned controller at the tested scales.

Significance. If the result holds, the paper makes a useful methodological contribution: a task-independent, integration-free pretraining objective for co-designing soft robotic reservoirs against digital reference dynamics. The presentation is honest about the hybrid digital/physical nature of the pipeline, and the authors provide extensive supplementary analyses, including statistical tests, a FLOP comparison, and cross-task reuse. The use of machine-checked differentiable soft-robot simulation is a strength. The main significance caveat is that the experiments do not isolate how much of the reported improvement comes from the physical morphology versus from the high-capacity digital controller, and the cost analysis in Appendix G shows that at the tested n_y, the digital controller is more expensive than the digital RON itself. This limits the strength of the 'physical computation' narrative, though not necessarily the validity of the co-optimization method as a trajectory-matching tool.

major comments (3)
  1. [Sec. 4.1, Eq. (2)-(3); App. G] The physical reservoir is fully actuated (T has one generalized force per DOF) and the feedback controller is a two-layer 64-unit MLP. As the skeptic notes, for any invertible M(Q) the controller could in principle implement feedback linearization, making the mapped physical acceleration equal to f_ref independently of θ_phys. The θrob-fixed baseline in Table 2 does not resolve this: it still trains a high-capacity controller, so it only shows that optimizing morphology helps the optimization, not that the body is doing the computation. Appendix G compounds the issue: the controller costs K(382 n_y + 128 n_u + 16768) FLOPs, which exceeds the RON's K(2 n_y^2 + 9 n_y + 2 n_y n_u) for all tested n_y. The paper should include an explicit attribution analysis—e.g., ablating controller capacity, using underactuated or passive reservoirs, or measuring task performance with the controller remove
  2. [Sec. 4.2, Table 1] The paper concludes that the pretrained reservoirs 'closely approximate the target digital dynamics,' but several trajectory NRMSE values are large: 0.415 for sMNIST n_y=15, 0.432 for Lorenz96 n_y=12, and 0.443 for Lorenz96 n_y=15. These same reservoirs nevertheless perform well on downstream tasks (e.g., 71.3% sMNIST accuracy), which suggests that the acceleration-level equation-error objective may capture task-relevant dynamics despite poor trajectory-level matching. This is interesting but unexplained. The manuscript should either provide an analysis of where the trajectory error concentrates, show that the downstream task is insensitive to these modes, or soften the 'closely approximate' wording. Because Eq. (5) is the sole pretraining signal, this point bears directly on the method's validity.
  3. [Sec. 5.2 and App. F] The headline claim of 33.7% mean relative improvement is computed by averaging 16 task-dimension cases, but the aggregation mixes asymmetric metrics: accuracy gains are expressed as relative percentage increases, while forecasting gains are expressed as relative NRMSE reductions. These are not commensurable, and a single average over all cells can be dominated by tasks where the unoptimized baseline is particularly poor. The significance tests in App. F use only four runs per condition, so the minimum attainable p-value is 0.0143; the claim of '26 of 32 significant' is accurate but should be accompanied by effect sizes and per-task aggregates. I would ask the authors to report the per-task mean improvements separately and to justify the uniform averaging across mixed metrics.
minor comments (6)
  1. [Table 1] The column headers 'θrob fixed(↓)' and 'Full pretraining(↓)' are confusing; the arrows are unexplained. Clarify what the downward arrow denotes (presumably 'lower is better').
  2. [Figure 2] The text block contains garbled labels ('robotn-th roboti-th robot1st'), likely a rendering artifact. Please fix the figure.
  3. [Eq. (6)] The notation Dψ(Q_φ) is used in Eq. (6) before the Fréchet-derivative notation is fully introduced; a brief pointer to App. A would help.
  4. [Table 1 / Table 2 footnotes] The asterisk explanations differ: Table 1 says 'how many simulations were diverging' while Table 2 says 'one diverging trial.' Make the description consistent and state whether the treatment of diverged trials affects the reported means.
  5. [App. G] The FLOP count treats tanh/softmax evaluations as n FLOPs, which is an idealization. State this assumption prominently and note that wall-clock energy/latency are not captured.
  6. [Sec. 5.2] The 90.9% RON-retention figure is defined only implicitly via the mixed-metric normalization. Please give the exact formula in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dynamics-matching pretraining is a teacher–student distillation with external task benchmarks, and the cited RON/simulator are independently specified.

full rationale

The derivation chain is: (i) pick a digital RON teacher with explicit equations (Sec. 4.1, App. C); (ii) minimize the acceleration equation-error MSE between teacher labels and the mapped physical acceleration (Eqs. 5-6); (iii) freeze the optimized reservoir and train only a readout on downstream tasks (Sec. 5). Each claimed result is computed from this pipeline, not defined by it. The RON reference is reproduced in the paper and taken from a peer-reviewed publication (Ceni et al. 2024), which is not used to justify a premise uniquely; author overlap is present but the RON equations, initialization, and ACDS implementation are independently checkable, so the self-citation is not load-bearing. The manual per-task RON tuning (Table 3) does inject task-specific bias into the target dynamics, but the physical reservoir's task performance is not forced: the paper reports imperfect trajectory NRMSEs (e.g., 0.415 for sMNIST n_y=15) and the partially pretrained baseline shows that optimizing map/controller alone does not always match the teacher, so the benchmark outcomes are empirical rather than tautological. The fully actuated plus high-capacity-MLP concern is a real attribution confound - the controller could in principle feedback-linearize the soft robot to the RON independently of theta_phys (Eq. 6 with T = M[Dpsi f_ref - D2psi] + ...) - and the paper acknowledges this in Sec. 6. But a confound about causal attribution is not circularity: the prediction is not equivalent to its inputs by construction, and the paper's own fixed-morphology baseline is a controlled comparison rather than an identity. No circular step satisfying the quoted-reduction standard was found.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a small number of free parameters: the optimized physical parameters, the affine map, the MLP controller weights, and the per-task tuned RON reference. The axioms are mostly domain assumptions about simulator fidelity, the sufficiency of equation-error pretraining, reachability, and full actuation. No new physical entities are introduced.

free parameters (4)
  • soft robot physical parameters theta_phys = Final values not reported individually; sampled from ranges in Table 5 and optimized
    Length, damping, radius, density, Young's and shear modulus per PCS segment are optimized to match reference dynamics (Eq. 2, Sec 4.1).
  • affine map parameters theta_map (A, c) = Optimized values not reported
    The SVD-parametrized affine map from reference to physical coordinates is learnable (Eq. 4, Sec 4.1, Appendix A).
  • controller weights theta_contr (two MLPs, 2x64 tanh) = Optimized values not reported
    Feedforward and feedback MLP controllers are trained as part of pretraining (Eq. 3, Sec 4.1).
  • RON reference hyperparameters (Delta_t, rho_w, nu, gamma, epsilon) = Values in Table 3 vary per task and dimension
    The digital reference is manually tuned per task to achieve high performance, then the physical reservoir is fit to it (Appendix C, Table 3). These are hand-chosen, task-specific free parameters that indirectly shape the downstream results.
assumptions (5)
  • domain assumption The planar PCS model with 3N n_pcs = n_y is a valid differentiable soft robot model whose generalized coordinates are measurable reservoir outputs.
    Sec 4.1 and Appendix D; the entire proof of concept is in this simulator, so its fidelity is load-bearing.
  • domain assumption Coriolis and centrifugal terms can be neglected without materially changing reservoir dynamics or PRC performance.
    Appendix D, justified by NRMSE comparison only for n_y=6,9 on Mackey-Glass, not for all settings.
  • ad hoc to paper Acceleration-level equation error over i.i.d. samples is a sufficient objective for downstream task transfer.
    Sec 3.4, Eq. 5-6; the paper validates this empirically, but it is a modeling bet that derivative matching suffices without temporal integration.
  • domain assumption The RON is a structurally compatible, high-performing reference for soft robot dynamics, and the affine map with n_y = n_Q is expressive enough.
    Sec 3.1 and Sec 4.1; reachability of the reference dynamics by the physical reservoir class is assumed.
  • domain assumption The robot is fully actuated in generalized coordinates, and controller capacity is sufficient to approximate the reference dynamics.
    Sec 4.1 and Appendix D actuation model; this allows the controller to potentially bypass the body dynamics, which is a key limitation.

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Cite this review

Pith. "Pith review of From Digital to Physical Reservoir Computing: Co-Optimizing Soft Robotic Reservoirs via Dynamics Matching." pith.science (2026). https://pith.science/paper/2FNIVNF4

@misc{pith2026260800484,
  author       = {Pith},
  title        = {Pith review of: From Digital to Physical Reservoir Computing: Co-Optimizing Soft Robotic Reservoirs via Dynamics Matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2FNIVNF4}},
  note         = {Machine review of arXiv:2608.00484}
}
read the original abstract

Soft robotic substrates are promising for Physical Reservoir Computing (PRC) because their compliant nonlinear dynamics can provide temporal memory, high-dimensional state transformations, and efficient inference. However, physical reservoirs are often adopted as-is rather than pretrained or co-optimized, potentially limiting soft robotic PRC performance relative to digital reservoirs. We investigate whether a physical reservoir can instead be pretrained against high-performing digital reference dynamics. Our formulation jointly optimizes physical parameters, a diffeomorphic physical-reference state map, and feedforward-feedback control using a differentiable physical model and an acceleration-level equation-error objective that avoids temporal integration. As a proof of concept, we instantiate the formulation with simulated soft robots, a Random Oscillators Network (RON) reference, and parallel multi-start gradient descent. We evaluate the optimized reservoirs on classification (sMNIST and ADIAC) and forecasting (Mackey-Glass and Lorenz96) tasks across four reservoir dimensions. Compared with unoptimized soft robot reservoirs, the optimized reservoirs achieve a mean relative improvement of 33.7% across all tasks and datasets, while remaining close to the digital reference. These results demonstrate the feasibility of dynamics-level co-optimization for the simulated soft robotic reservoirs considered here.

Figures

Figures reproduced from arXiv: 2608.00484 by the authors.

Figure 1
Figure 1. Traditional PRC (top) and the proposed pre [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Soft robot instantiation of the proposed pretraining formulation. The reference position [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Time evolution of the mapped physical coordinates [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Scalability of the results of the PRC benchmark experiments. Each plot shows the resulting performance vs the reservoir [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Schematic of how RC is used to perform the sMNIST classification task. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Visualization of Mackey–Glass dataset-sequence partition. In this specific example [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Soft robot strains in the physical reservoir during inference in the Mackey–Glass task with [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Digital inference cost comparison for the four benchmark tasks, separated into reservoir dynamics, task-specific [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

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Reference graph

Works this paper leans on

58 extracted references · 49 canonical work pages

  1. [1]

    2021 , doi =

    Reservoir Computing , subtitle =. 2021 , doi =

    work page 2021

  2. [2]

    , title =

    Landau, Yoan D. , title =. 1979 , series =

    work page 1979

  3. [3]

    and Jaeger, H

    Lukoševičius, M. and Jaeger, H. , title =. Computer Science Review , volume =. 2009 , doi =

    work page 2009

  4. [4]

    , year =

    Nakajima, K. , year =. Physical reservoir computing--–An introductory perspective , volume =. Japanese Journal of Applied Physics , doi =

    work page

  5. [5]

    and Amor, D

    Cordova-Cardenas, R. and Amor, D. and Gutiérrez, A. , year =. Edge AI in Practice: A Survey and Deployment Framework for Neural Networks on Embedded Systems , volume =. Electronics , doi =

    work page

  6. [6]

    and Füchslin, R

    Hauser, H. and Füchslin, R. and Nakajima, K. , booktitle =. Morphological Computation---The Body as a Computational Resource , isbn =. 2014 , pages =

    work page 2014

  7. [7]

    Füchslin, R. M. and Dzyakanchuk, A. and Flumini, D. and Hauser, H. and Hunt, K. J. and Luchsinger, R. H. and Reller, B. and Scheidegger, S. and Walker, R. , title =. Artificial Life , volume =. 2013 , issn =

    work page 2013

  8. [8]

    and Ijspeert, A

    Hauser, H. and Ijspeert, A. J. and Füchslin, R. M. and Pfeifer, R. and Maass, W. , title =. Biological Cybernetics , year =. doi:10.1007/s00422-012-0471-0 , issn =

    doi:10.1007/s00422-012-0471-0

Show all 58 references
  1. [9]

    and van der Zant, T

    Ishii, K. and van der Zant, T. and Becanovic, V. and Ploger, P. , booktitle =. Identification of motion with echo state network , year =

  2. [10]

    2023 , school =

    Zardini, Gioele , title =. 2023 , school =

    2023

  3. [11]

    Bodily, D. M. and Allen, T. F. and Killpack, M. D. , booktitle =. Multi-objective design optimization of a soft, pneumatic robot , year =

  4. [12]

    The Eleventh International Conference on Learning Representations , year =

    Curriculum-based Co-design of Morphology and Control of Voxel-based Soft Robots , author =. The Eleventh International Conference on Learning Representations , year =

  5. [13]

    Proceedings of The 27th International Conference on Artificial Intelligence and Statistics , year =

    Random Oscillators Network for Time Series Processing , author =. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics , year =

  6. [14]

    2026 , url =

    SoRoMoX: Soft Robot Models in JAX , author =. 2026 , url =

    2026

  7. [15]

    and Boyer, F

    Renda, F. and Boyer, F. and Dias, J. and Seneviratne, L. , journal =. Discrete Cosserat Approach for Multisection Soft Manipulator Dynamics , year =

  8. [16]

    and Dickstein, J

    Dinh, L. and Dickstein, J. S. and Bengio, S. , title =. 5th International Conference on Learning Representations,

  9. [17]

    and Yamane, T

    Tanaka, G. and Yamane, T. and Héroux, J. B. and Nakane, R. and Kanazawa, N. and Takeda, S. and Numata, H. and Nakano, D. and Hirose, A. , title =. Neural Networks , volume =. 2019 , issn =

    2019

  10. [18]

    and Kwon, J

    Lee, T. and Kwon, J. and Wensing, P. M. and Park, F. C. , title =. Annual Review of Control, Robotics, and Autonomous Systems , year =. doi:doi.org/10.1146/annurev-control-061523-102310 , publisher =

    doi

  11. [19]

    arXiv preprint arXiv:2505.03761 , year =

    Soft yet effective robots via holistic co-design , author =. arXiv preprint arXiv:2505.03761 , year =

    arXiv

  12. [20]

    , journal =

    Werbos, P.J. , journal =. Backpropagation through time: what it does and how to do it , year =

  13. [21]

    Reservoir Computing: Theory, Physical Implementations, and Applications , editor =

    Hauser, Helmut , title =. Reservoir Computing: Theory, Physical Implementations, and Applications , editor =. 2021 , pages =. doi:10.1007/978-981-13-1687-6_8 , isbn =

    2021 doi

  14. [22]

    and Miller, J

    Dale, M. and Miller, J. F. and Stepney, S. and Trefzer, M. A. , editor =. Reservoir Computing in Material Substrates , booktitle =. 2021 , publisher =

    2021

  15. [23]

    , title =

    Van der Sande, Guy and Brunner, Daniel and Soriano, Miguel C. , title =. Nanophotonics , volume =. doi:https://doi.org/10.1515/nanoph-2016-0132 , year =

    2016 doi

  16. [24]

    and Avizienis, Audrius V

    Stieg, Adam Z. and Avizienis, Audrius V. and Sillin, Henry O. and Aguilera, Renato and Shieh, Hsien-Hang and Martin-Olmos, Cristina and Sandouk, Eric J. and Aono, Masakazu and Gimzewski, James K. , editor =. Self-organization and Emergence of Dynamical Structures in Neuromorph...

    2014

  17. [25]

    and Deligkaris, Kosmas and Bullmann, Torsten and Bakkum, Douglas J

    Obien, Marie Engelene J. and Deligkaris, Kosmas and Bullmann, Torsten and Bakkum, Douglas J. and Frey, Urs , title =. Frontiers in Neuroscience , volume =. 2015 , doi =

    2015

  18. [26]

    Harnessing disordered quantum dynamics for machine learning , volume =

    Fujii, Keisuke and Nakajima, Kohei , year =. Harnessing disordered quantum dynamics for machine learning , volume =. Physical Review Applied , doi =

  19. [27]

    Edge of Chaos

    Takemura, Hiroki and Mizumoto, Takahiro and Banerjee, Amit and Hirotani, Jun and Tsuchiya, Toshiyuki , booktitle =. Physical Reservoir Computing Using Nonlinear MEMS Resonator Having High Memory Capacity at "Edge of Chaos" , year =

  20. [28]

    and Cacucciolo, V

    Renda, F. and Cacucciolo, V. and Dias, J. and Seneviratne, L. , booktitle =. Discrete Cosserat approach for soft robot dynamics: A new piece-wise constant strain model with torsion and shears , year =

  21. [29]

    Proceedings of the 13th International Conference on Artificial Intelligence and Statistics , pages =

    Understanding the difficulty of training deep feedforward neural networks , author =. Proceedings of the 13th International Conference on Artificial Intelligence and Statistics , pages =. 2010 , editor =

    2010

  22. [30]

    Mackey and Leon Glass , title =

    Michael C. Mackey and Leon Glass , title =. Science , volume =. 1977 , doi =

    1977

  23. [31]

    and Ba, Jimmy , title =

    Kingma, Diederik P. and Ba, Jimmy , title =. International Conference on Learning Representations (ICLR) , year =

  24. [32]

    DeepMind and Babuschkin, Igor and Baumli, Kate and Bell, Alison and Bhupatiraju, Surya and Bruce, Jake and Buchlovsky, Peter and Budden, David and Cai, Trevor and Clark, Aidan and Danihelka, Ivo and Dedieu, Antoine and Fantacci, Claudio and Godwin, Jonathan and Jones, Chris an...

    2020

  25. [33]

    2018 , note =

    James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Yash Katariya and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander. 2018 , note =

    2018

  26. [34]

    Proceedings of The 6th Conference on Robot Learning , pages =

    Rethinking Optimization with Differentiable Simulation from a Global Perspective , author =. Proceedings of The 6th Conference on Robot Learning , pages =. 2023 , editor =

    2023

  27. [35]

    Patrick Kidger , year =

  28. [36]

    and Inoue, K

    Horii, Y. and Inoue, K. and Nishikawa, S. and Nakajima, K. and Niiyama, R. and Kuniyoshi, Y. , title =. ALIFE 2021: The 2021 Conference on Artificial Life , year =

    2021

  29. [37]

    and Hauser, H

    Nakajima, K. and Hauser, H. and Li, T. and Pfeifer, R. , title =. Scientific Reports , year =. doi:10.1038/srep10487 , issn =

    doi

  30. [38]

    Echo State

    Jaeger, Herbert , year =. The “Echo State” Approach to Analysing and Training Recurrent Neural Networks , institution =

  31. [39]

    Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the echo state network approach , institution =

    Jaeger, Herbert , year =. Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the echo state network approach , institution =

  32. [40]

    2004 , url =

    Liebald, Benjamin , title =. 2004 , url =

    2004

  33. [41]

    Optimization and Applications of Echo State Networks with Leaky-Integrator Neurons , journal =

    Jaeger, Herbert and Luko. Optimization and Applications of Echo State Networks with Leaky-Integrator Neurons , journal =. 2007 , volume =

    2007

  34. [42]

    2007 , type =

    Siewert, Udo and Wustlich, Welf , title =. 2007 , type =

    2007

  35. [43]

    and Stroobandt, Dirk , title =

    Schrauwen, Benjamin and Wardermann, Marion and Verstraeten, David and Steil, Jochen J. and Stroobandt, Dirk , title =. Neurocomputing , year =

  36. [44]

    and Browne, Matthew , title =

    Mayer, Norbert M. and Browne, Matthew , title =. Biologically Inspired Approaches to Advanced Information Technology , series =. 2004 , pages =

    2004

  37. [45]

    Parallel Problem Solving from Nature -- PPSN X , series =

    Jiang, Fei and Berry, Hugues and Schoenauer, Marc , title =. Parallel Problem Solving from Nature -- PPSN X , series =. 2008 , pages =

    2008

  38. [46]

    , title =

    Lorenz, Edward N. , title =. Proceedings of the Seminar on Predictability , volume =. 1996 , address =

    1996

  39. [47]

    Proceedings of the IEEE , volume =

    Gradient-based learning applied to document recognition , author =. Proceedings of the IEEE , volume =. 1998 , publisher =

    1998

  40. [48]

    arXiv preprint arXiv:1504.00941 , year =

    A simple way to initialize recurrent networks of rectified linear units , author =. arXiv preprint arXiv:1504.00941 , year =

    arXiv

  41. [49]

    and Rus, Daniela and Gan, Chuang , booktitle =

    Wang, Tsun-Hsuan and Ma, Pingchuan and Spielberg, Andrew Everett and Xian, Zhou and Zhang, Hao and Tenenbaum, Joshua B. and Rus, Daniela and Gan, Chuang , booktitle =. 2023 , url =. 2303.09555 , eprinttype =

    2023 arXiv

  42. [50]

    2024 , howpublished =

    Archetype Computing and Adaptive System (. 2024 , howpublished =

    2024

  43. [51]

    Advances in Neural Information Processing Systems 32 (NeurIPS 2019) , pages =

    PyTorch: An Imperative Style, High-Performance Deep Learning Library , author =. Advances in Neural Information Processing Systems 32 (NeurIPS 2019) , pages =

    2019

  44. [52]

    IEEE control systems magazine , volume =

    Model-based control of soft robots: A survey of the state of the art and open challenges , author =. IEEE control systems magazine , volume =. 2023 , publisher =

    2023

  45. [53]

    and Whitney, Donald R

    Mann, Henry B. and Whitney, Donald R. , title =. The Annals of Mathematical Statistics , year =

  46. [54]

    NIPS Deep Learning and Representation Learning Workshop , year =

    Hinton, Geoffrey and Vinyals, Oriol and Dean, Jeff , title =. NIPS Deep Learning and Representation Learning Workshop , year =. 1503.02531 , eprinttype =

    arXiv

  47. [55]

    and Rajan, Kanaka and Escola, G

    DePasquale, Brian and Cueva, Christopher J. and Rajan, Kanaka and Escola, G. Sean and Abbott, L. F. , title =. PLOS ONE , year =

  48. [56]

    2019 9th International

    He, Xu and Liu, Tianlin and Hadaeghi, Fatemeh and Jaeger, Herbert , title =. 2019 9th International. 2019 , pages =

    2019

  49. [57]

    and Wilkinson, Michael H

    Jalba, Andrei C. and Wilkinson, Michael H. F. and Roerdink, Jos B. T. M. and Bayer, Michael M. and Juggins, Stephen , title =. Machine Vision and Applications , volume =. 2004 , publisher =

    2004

  50. [58]

    IEEE/CAA Journal of Automatica Sinica , volume =

    Dau, Hoang Anh and Bagnall, Anthony and Kamgar, Kaveh and Yeh, Chin-Chia Michael and Zhu, Yan and Gharghabi, Shaghayegh and Ratanamahatana, Chotirat Annand and Keogh, Eamonn , title =. IEEE/CAA Journal of Automatica Sinica , volume =. 2019 , publisher =

    2019

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.