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arxiv: 2604.09833 · v1 · submitted 2026-04-10 · 💻 cs.NE · cs.ET

Recognition: unknown

Beyond Silicon: Materials, Mechanisms, and Methods for Physical Neural Computing

Stefan Fischer , Nihat Ay , Olaf Landsiedel , Esfandiar Mohammadi , Sebastian Otte , Bernd-Christian Renner , Nele Ru{\ss}winkel
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:08 UTC · model grok-4.3

classification 💻 cs.NE cs.ET
keywords physical neural computingneuromorphic systemsmemristorsphotonic neural networksbenchmarkingedge AImaterial substrates
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The pith

Physical neural computing substrates each occupy distinct performance regimes rather than one dominating all tasks.

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

This survey maps how materials beyond silicon, including memristors, photonic circuits, mechanical systems, and chemical networks, implement neural computation through their natural physical processes like charge flow or wave interference. It proposes a benchmarking method using common tasks and measurable dimensions to compare these approaches fairly. The key finding is that these systems complement each other, supporting uses from rapid signal handling to on-device learning in biology-like settings. This matters as traditional silicon chips struggle with energy costs for widespread AI deployment at the edge.

Core claim

By analyzing architectural paradigms and constraints across substrates, the paper establishes that no single physical neural system excels universally; instead, they fill complementary niches in speed, efficiency, and integration, as evidenced by evaluations on standardized static and dynamic tasks.

What carries the argument

A first-order benchmarking scheme using standardized static and dynamic tasks evaluated along physically interpretable dimensions such as scalability, precision, and interfacing overhead.

If this is right

  • Physical neural systems enable co-location of sensing, memory, and computation to minimize data movement in edge AI applications.
  • Applications in ultrafast signal processing can leverage photonic or mechanical substrates.
  • In-memory inference benefits from memristive devices.
  • Embodied control and biochemical decision making suit mechanical metamaterials and chemical reaction systems.
  • Engineering efforts should focus on addressing scalability, precision, and programmability for each substrate type.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Hybrid systems combining multiple substrates might achieve broader performance coverage than any single one.
  • The benchmarking approach could be extended to include more dynamic real-world tasks to refine the comparison.
  • Developers of edge AI devices may select substrates based on specific application requirements identified in the regimes.

Load-bearing premise

The first-order benchmarking scheme using standardized tasks and performance dimensions provides a fair comparison that does not miss critical platform-specific factors or selection biases.

What would settle it

An experimental result showing that one particular substrate, for example memristive devices, outperforms all others in every standardized task and across all considered performance dimensions would challenge the claim of complementary operating regimes.

Figures

Figures reproduced from arXiv: 2604.09833 by Bernd-Christian Renner, Esfandiar Mohammadi, Nele Ru{\ss}winkel, Nihat Ay, Olaf Landsiedel, Sebastian Otte, Stefan Fischer.

Figure 1
Figure 1. Figure 1: Landscape of physical substrates for computation and learning. The horizontal axis organizes approaches by the dominant coupling [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mechanisms of nucleic acid strand displacement. (A) Three-way branch migration: Two identical strands compete for binding to [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Architecture of a Chemical Reservoir Computer based on [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic of the closed-loop “Pong” experiment. Human [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Capacitive in-sensor tactile computing architecture. (a) [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Working principle of a 4-node self-learning magnetic [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Diffractive deep neural networks (D2NNs). (A) A D2NN uses multiple trainable diffractive layers with complex-valued trans￾mission or reflection coefficients to implement an optical function between input and output planes. Once the layer parameters have been optimized and the structure has been fabricated, inference is performed passively through wave propagation at the speed of light. (B) Example of a D2N… view at source ↗
Figure 8
Figure 8. Figure 8: Mechanical neural network (MNN) fabricated for the [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Physical reservoir computing using a soft silicone arm. [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Artificial Hodgkin-Huxley-like neuron based on 2D ionic [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
read the original abstract

Physical implementations of neural computation now extend far beyond silicon hardware, encompassing substrates such as memristive devices, photonic circuits, mechanical metamaterials, microfluidic networks, chemical reaction systems, and living neural tissue. By exploiting intrinsic physical processes such as charge transport, wave interference, elastic deformation, mass transport, and biochemical regulation, these substrates can realize neural inference and adaptation directly in matter. As silicon GPU-centered AI faces growing energy and data-movement constraints, physical neural computation is becoming increasingly relevant as a complementary path beyond conventional digital accelerators. This trend is driven in particular by pervasive intelligence, i.e., the deployment of on-device and edge AI across large numbers of resource-constrained systems. In such settings, co-locating computation with sensing and memory can reduce data shuttling and improve efficiency. Meanwhile, physical neural approaches have emerged across disparate disciplines, yet progress remains fragmented, with limited shared terminology and few principled ways to compare platforms. This survey unifies the field by mapping neural primitives to substrate-specific mechanisms, analyzing architectural and training paradigms, and identifying key engineering constraints including scalability, precision, programmability, and I/O interfacing overhead. To enable cross-domain comparison, we introduce a first-order benchmarking scheme based on standardized static and dynamic tasks and physically interpretable performance dimensions. We show that no single substrate dominates across the considered dimensions; instead, physical neural systems occupy complementary operating regimes, enabling applications ranging from ultrafast signal processing and in-memory inference to embodied control and in-sample biochemical decision making.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. This survey unifies physical neural computing across substrates including memristive devices, photonic circuits, mechanical metamaterials, microfluidic networks, chemical reaction systems, and living neural tissue. It maps neural primitives to intrinsic physical mechanisms (charge transport, wave interference, elastic deformation, mass transport, biochemical regulation), reviews architectural and training paradigms, catalogs engineering constraints (scalability, precision, programmability, I/O overhead), and introduces a first-order benchmarking scheme using standardized static and dynamic tasks plus physically interpretable performance dimensions. The central claim is that no single substrate dominates; physical neural systems instead occupy complementary operating regimes suited to applications ranging from ultrafast signal processing and in-memory inference to embodied control and in-sample biochemical decision making.

Significance. If the benchmarking scheme is shown to be robust and representative, the work provides a valuable unifying framework for a currently fragmented field. It offers practical guidance for selecting substrates in pervasive edge-AI settings where co-located sensing, memory, and computation can mitigate data-movement and energy costs, while highlighting application-specific strengths rather than a universal winner.

major comments (1)
  1. [Benchmarking scheme] Benchmarking scheme (as described in the abstract and used to reach the headline claim): the first-order scheme of standardized static/dynamic tasks and physically interpretable dimensions is load-bearing for the conclusion that substrates occupy complementary regimes. The abstract provides no quantitative evidence that the chosen tasks are representative across all listed substrates, nor any sensitivity analysis showing that omitted factors (long-term drift, fabrication yield, I/O energy, precision stability) do not alter the 'no single substrate dominates' verdict. Without such validation, task-selection or dimension-weighting bias could artificially support the complementary-regimes result.
minor comments (1)
  1. [Abstract] The abstract is information-dense; splitting the description of the benchmarking scheme and its results into separate sentences would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our survey and for the detailed, constructive feedback on the benchmarking scheme. We address the major comment point by point below and will make targeted revisions to clarify the scope and limitations of our first-order framework.

read point-by-point responses

  1. Referee: [Benchmarking scheme] Benchmarking scheme (as described in the abstract and used to reach the headline claim): the first-order scheme of standardized static/dynamic tasks and physically interpretable dimensions is load-bearing for the conclusion that substrates occupy complementary regimes. The abstract provides no quantitative evidence that the chosen tasks are representative across all listed substrates, nor any sensitivity analysis showing that omitted factors (long-term drift, fabrication yield, I/O energy, precision stability) do not alter the 'no single substrate dominates' verdict. Without such validation, task-selection or dimension-weighting bias could artificially support the complementary-regimes result.

    Authors: We agree that the benchmarking scheme is central to our headline claim and that the abstract does not supply quantitative evidence or sensitivity analysis. As this is a survey unifying a fragmented literature rather than a primary empirical study, the scheme is explicitly positioned as first-order and conceptual: tasks (static classification and dynamic sequence processing) and dimensions (scalability, precision, programmability, I/O overhead) were selected because they recur across published work on memristive, photonic, mechanical, microfluidic, chemical, and biological substrates. No new cross-substrate experiments were performed. We will revise the abstract, introduction, and benchmarking section to state these qualifications more prominently and to add a dedicated limitations subsection. That subsection will discuss how omitted factors such as long-term drift, fabrication yield, I/O energy, and precision stability could affect the complementary-regimes conclusion under alternative weightings, citing relevant substrate-specific studies. These changes will make the evidential basis and potential biases explicit without altering the survey's scope. revision: partial

Circularity Check

0 steps flagged

No circularity: survey applies externally sourced literature via introduced scheme

full rationale

This is a survey paper reviewing physical neural substrates drawn from external literature across disciplines. It introduces a first-order benchmarking scheme of standardized static/dynamic tasks and interpretable dimensions, then applies the scheme to the reviewed body of work to reach the conclusion that no single substrate dominates and systems occupy complementary regimes. The scheme is not defined in terms of the conclusion, nor does any derivation reduce by construction to fitted parameters, self-citations, or renamed inputs; the central mapping and comparison rest on external references rather than internal self-reference. No load-bearing self-citation chains, ansatz smuggling, or uniqueness theorems from the authors' prior work appear in the derivation. The paper is therefore self-contained against external benchmarks with independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This being a survey paper based on the abstract, no specific free parameters, axioms, or invented entities are introduced in the provided text; the work relies on established concepts from physics, materials science, and computer science as described in the cited literature.

pith-pipeline@v0.9.0 · 5595 in / 1203 out tokens · 86650 ms · 2026-05-10T16:08:48.042678+00:00 · methodology

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Forward citations

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  2. Embedded DNA Inference in In-Body Nanonetworks: Detection, Delay, and Communication Trade-Offs

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Reference graph

Works this paper leans on

167 extracted references · 123 canonical work pages · cited by 2 Pith papers · 1 internal anchor

  1. [1]

    The future of computing beyond moore’s law,

    J. Shalf, “The future of computing beyond moore’s law,”Philosophical Transactions of the Royal So- ciety A: Mathematical, Physical and Engineering Sciences, vol. 378, no. 2166, p. 20190061, Jan. 2020,issn: 1364-503X.doi: 10.1098/rsta.2019.0061

    work page doi:10.1098/rsta.2019.0061 2020

  2. [2]

    Training of physical neural networks,

    A. Momeni et al., “Training of physical neural networks,”Nature, vol. 645, no. 8079, pp. 53–61, Sep. 2025.doi: 10.1038/s41586-025-09384-2

    work page doi:10.1038/s41586-025-09384-2 2025

  3. [3]

    Can programming be liberated from the von Neumann style? a functional style and its algebra of programs,

    J. Backus, “Can programming be liberated from the von Neumann style? a functional style and its algebra of programs,”Commun. ACM, vol. 21, no. 8, pp. 613–641, Aug. 1978,issn: 0001-0782.doi: 10.1145/359576.359579

    work page doi:10.1145/359576.359579 1978

  4. [4]

    Neuromorphic electronic systems

    C. Mead, “Neuromorphic electronic systems,”Pro- ceedings of the IEEE, vol. 78, no. 10, pp. 1629–1636, 1990.doi: 10.1109/5.58356

    work page doi:10.1109/5.58356 1990

  5. [5]

    The missing memristor found,

    D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, “The missing memristor found,” Nature, vol. 453, no. 7191, pp. 80–83, May 2008, issn: 1476-4687.doi: 10.1038/nature06932

    work page doi:10.1038/nature06932 2008

  6. [6]

    Adamatzky, B

    A. Adamatzky, B. D. L. Costello, and T. Asai, Reaction-Diffusion Computers. Oxford: Elsevier Science, 2005,isbn: 9780444520425.doi: 10.1016/ B978-0-444-52042-5.X5000-2

    2005

  7. [7]

    Capacitive in-sensor tactile com- puting,

    Y. Chen et al., “Capacitive in-sensor tactile com- puting,”Nat Commun, vol. 16, no. 1, p. 5691, Jul. 2025.doi: 10.1038/s41467-025-60703-7

    work page doi:10.1038/s41467-025-60703-7 2025

  8. [8]

    Intelligent molecular logic comput- ing toolkits: Nucleic acid-based construction, func- tionality, and enhanced biosensing applications,

    Y. Hu, J. Zhang, K. Shen, W. Shen, H. K. Lee, and S. Tang, “Intelligent molecular logic comput- ing toolkits: Nucleic acid-based construction, func- tionality, and enhanced biosensing applications,” Chem. Sci., vol. 16, pp. 20139–20180, 43 2025.doi: 10.1039/D5SC06176H

    work page doi:10.1039/d5sc06176h 2025

  9. [9]

    Simulating physics with computers,

    R. P. Feynman, “Simulating physics with comput- ers,”International Journal of Theoretical Physics, vol. 21, no. 6, pp. 467–488, Jun. 1982,issn: 1572- 9575.doi: 10.1007/BF02650179

    work page doi:10.1007/bf02650179 1982

  10. [10]

    “neural” com- putation of decisions in optimization problems,

    J. J. Hopfield and D. W. Tank, ““neural” com- putation of decisions in optimization problems,” Biological Cybernetics, vol. 52, no. 3, pp. 141–152, Jul. 1985.doi: 10.1007/BF00339943

    work page doi:10.1007/bf00339943 1985

  11. [11]

    Rolandi, P

    A. Rolandi, P. Abiuso, P. Lipka-Bartosik, M. Aifer, P. J. Coles, and M. Perarnau-Llobet,Energy-time- accuracy tradeoffs in thermodynamic computing, 2026.doi: 10.48550/arXiv.2601.04358

    work page doi:10.48550/arxiv.2601.04358 2026

  12. [12]

    Neural net- work computation with DNA strand displacement cascades,

    L. Qian, E. Winfree, and J. Bruck, “Neural net- work computation with DNA strand displacement cascades,”Nature, vol. 475, no. 7356, pp. 368–372, 2011.doi: 10.1038/nature10262

    work page doi:10.1038/nature10262 2011

  13. [13]

    Sohr,The Navier-Stokes Equations: An Ele- mentary Functional Analytic Approach(Birkhäuser Advanced Texts Basler Lehrbücher), 1st ed

    H. Sohr,The Navier-Stokes Equations: An Ele- mentary Functional Analytic Approach(Birkhäuser Advanced Texts Basler Lehrbücher), 1st ed. Basel: Birkhäuser Basel, 2001,isbn: 978-3-0348-8255-2. doi: 10.1007/978-3-0348-8255-2

    work page doi:10.1007/978-3-0348-8255-2 2001

  14. [14]

    Toward Realistic AI-Generated Student Questions to Support Instructor Training

    X. Wang, H. Borras, B. Klein, and H. Fröning, “Variance-aware noisy training: Hardening DNNs against unstable analog computations,” inMachine Learning and Knowledge Discovery in Databases. Research Track, R. P. Ribeiro et al., Eds., Cham: Springer Nature Switzerland, 2026, pp. 147–163, isbn: 978-3-032-06109-6.doi: 10.1007/978-3-032- 06109-6_9

    work page doi:10.1007/978-3-032- 2026

  15. [15]

    On computing in fine-grained com- partmentalised Belousov–Zhabotinsky medium,

    A. Adamatzky, J. Holley, L. Bull, and B. De Lacy Costello, “On computing in fine-grained com- partmentalised Belousov–Zhabotinsky medium,” Chaos, Solitons, and Fractals, vol. 44, no. 10, 30 pp. 779–790, Oct. 2011,issn: 0960-0779.doi: 10. 1016/j.chaos.2011.03.010

    2011

  16. [16]

    G., Onodera, T., Stein, M

    L. G. Wright et al., “Deep physical neural networks trained with backpropagation,”Nature, vol. 601, no. 7894, pp. 549–555, Jan. 2022,issn: 1476-4687. doi: 10.1038/s41586-021-04223-6

    work page doi:10.1038/s41586-021-04223-6 2022

  17. [17]

    Humble, Alexander McCaskey, Dmitry I

    M. Davies et al., “Loihi: A neuromorphic many- core processor with on-chip learning,”IEEE Micro, vol. 38, no. 1, pp. 82–99, 2018.doi: 10.1109/MM. 2018.112130359

    work page doi:10.1109/mm 2018

  18. [18]

    Truenorth: Design and tool flow of a 65 mw 1 million neuron programmable neu- rosynaptic chip,

    F. Akopyan et al., “Truenorth: Design and tool flow of a 65 mw 1 million neuron programmable neu- rosynaptic chip,”IEEE Transactions on Computer- Aided Design of Integrated Circuits and Systems, vol. 34, no. 10, pp. 1537–1557, 2015.doi: 10.1109/ TCAD.2015.2474396

    work page arXiv 2015

  19. [19]

    Life at low Reynolds number,

    E. M. Purcell, “Life at low Reynolds number,” American Journal of Physics, vol. 45, no. 1, pp. 3– 11, Jan. 1977,issn: 0002-9505.doi: 10.1119/1. 10903

    work page doi:10.1119/1 1977

  20. [20]

    Wolf, Experimental Studies of Magnetic Tricritic al Points: Problems and Progress

    C. Mead,Analog VLSI and neural systems. USA: Addison-Wesley Longman Publishing Co., Inc., 1989,isbn: 0201059924.doi: 10.1007/978-1-4613- 1639-8

    work page doi:10.1007/978-1-4613- 1989

  21. [21]

    DNA as a universal substrate for chemical kinetics,

    D. Soloveichik, G. Seelig, and E. Winfree, “DNA as a universal substrate for chemical kinetics,” Proceedings of the National Academy of Sciences, vol. 107, no. 12, pp. 5393–5398, 2010.doi: 10.1073/ pnas.0909380107

    2010

  22. [22]

    Chemical implementation of neural networks and Turing machines.,

    A. Hjelmfelt, E. D. Weinberger, and J. Ross, “Chemical implementation of neural networks and Turing machines.,”Proceedings of the National Academy of Sciences, vol. 88, no. 24, pp. 10983– 10987, 1991.doi: 10.1073/pnas.88.24.10983

    work page doi:10.1073/pnas.88.24.10983 1991

  23. [23]

    Pro- grammable mechanical metamaterials,

    B. Florijn, C. Coulais, and M. van Hecke, “Pro- grammable mechanical metamaterials,”Phys. Rev. Lett., vol. 113, p. 175503, 17 Oct. 2014.doi: 10. 1103/PhysRevLett.113.175503

    2014

  24. [24]

    Molecular computation of solu- tions to combinatorial problems,

    L. M. Adleman, “Molecular computation of solu- tions to combinatorial problems,”Science, vol. 266, no. 5187, pp. 1021–1024, Nov. 1994.doi: 10.1126/ science.7973651

    1994

  25. [25]

    Kirkpatrick and C

    S. Kirkpatrick, C. D. Gelatt Jr, and M. P. Vecchi, “Optimization by simulated annealing,”Science, vol. 220, no. 4598, pp. 671–680, May 1983.doi: 10.1126/science.220.4598.671

    work page doi:10.1126/science.220.4598.671 1983

  26. [26]

    Wave physics as an analog recurrent neural network,

    T. W. Hughes, I. A. D. Williamson, M. Minkov, and S. Fan, “Wave physics as an analog recurrent neural network,”Sci Adv, vol. 5, no. 12, eaay6946, Dec. 2019.doi: 10.1126/sciadv.aay6946

    work page doi:10.1126/sciadv.aay6946 2019

  27. [27]

    Pattern recognition in a bucket,

    C. Fernando and S. Sojakka, “Pattern recognition in a bucket,” inAdvances in Artificial Life, W. Banzhaf, J. Ziegler, T. Christaller, P. Dittrich, and J. T. Kim, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg, 2003, pp. 588–597,isbn: 978-3-540- 39432-7.doi: 10.1007/978-3-540-39432-7_63

    work page doi:10.1007/978-3-540-39432-7_63 2003

  28. [28]

    Information processing via physical soft body,

    K. Nakajima, H. Hauser, T. Li, and R. Pfeifer, “Information processing via physical soft body,” ScientificReports, vol. 5, no. 1, p. 10487, May 2015, issn: 2045-2322.doi: 10.1038/srep10487

    work page doi:10.1038/srep10487 2015

  29. [29]

    Experimental demonstration of reservoir computing on a silicon photonics chip,

    K. Vandoorne et al., “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nature Communications, vol. 5, no. 1, p. 3541, Mar. 2014,issn: 2041-1723.doi: 10.1038/ncomms4541

    work page doi:10.1038/ncomms4541 2014

  30. [30]

    Recent advances in physical reservoir computing: A review,

    G. Tanaka et al., “Recent advances in physical reservoir computing: A review,”Neural Networks, vol. 115, pp. 100–123, 2019,issn: 0893-6080.doi: https://doi.org/10.1016/j.neunet.2019.03.005

    work page doi:10.1016/j.neunet.2019.03.005 2019

  31. [31]

    Equilibrium propaga- tion: Bridging the gap between energy-based mod- els and backpropagation,

    B. Scellier and Y. Bengio, “Equilibrium propaga- tion: Bridging the gap between energy-based mod- els and backpropagation,”Front Comput Neurosci, vol. 11, p. 24, May 2017.doi: 10.3389/fncom.2017. 00024

    work page doi:10.3389/fncom.2017 2017

  32. [32]

    Supervised learning in physical networks: From machine learning to learning machines,

    M. Stern, D. Hexner, J. W. Rocks, and A. J. Liu, “Supervised learning in physical networks: From machine learning to learning machines,”Phys. Rev. X, vol. 11, p. 021045, 2 May 2021.doi: 10.1103/ PhysRevX.11.021045

    2021

  33. [33]

    Demonstration of decentralized physics-driven learning,

    S. Dillavou, M. Stern, A. J. Liu, and D. J. Durian, “Demonstration of decentralized physics-driven learning,”Phys. Rev. Appl., vol. 18, p. 014040, 1 Jul. 2022.doi: 10.1103/PhysRevApplied.18.014040

    work page doi:10.1103/physrevapplied.18.014040 2022

  34. [34]

    Neurons with graded response have collective computational properties like those of two-state neurons.,

    J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons.,”Proceedings of the National AcademyofSciences, vol. 81, no. 10, pp. 3088–3092, 1984.doi: 10.1073/pnas.81.10.3088

    work page doi:10.1073/pnas.81.10.3088 1984

  35. [35]

    The “echo state

    H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks,”GMD- Report 148, German National Research Institute for Computer Science, Jan. 2001.doi: 10.24406/ publica-fhg-291111

    2001

  36. [36]

    Nucleic acid strand displacement - from DNA nanotechnology to translational regula- tion,

    F. C. Simmel, “Nucleic acid strand displacement - from DNA nanotechnology to translational regula- tion,”RNA Biol, vol. 20, no. 1, pp. 154–163, Jan. 2023.doi: 10.1080/15476286.2023.2204565

    work page doi:10.1080/15476286.2023.2204565 2023

  37. [37]

    DNA strand displacement based computa- tionalsystemsandtheirapplications,

    C. Chen, J. Wen, Z. Wen, S. Song, and X. Shi, “DNA strand displacement based computa- tionalsystemsandtheirapplications,”FrontGenet, vol. 14, p. 1120791, Feb. 2023.doi: 10.3389/fgene. 2023.1120791

    work page doi:10.3389/fgene 2023

  38. [38]

    Backpropagation in molecular neural networks: Teaching DNA to solve machine learning tasks,

    A. A. Zagitov et al., “Backpropagation in molecular neural networks: Teaching DNA to solve machine learning tasks,”Preprints, Jan. 2026.doi: 10 . 20944/preprints202601.0088.v1

    work page arXiv 2026

  39. [39]

    Folding DNA to create nanoscale shapes and patterns,

    P. W. K. Rothemund, “Folding DNA to create nanoscale shapes and patterns,”Nature, vol. 440, no. 7082, pp. 297–302, 2006.doi: 10 . 1038 / nature04586

    2006

  40. [40]

    Recent advances in DNA origami- engineered nanomaterials and applications,

    P. Zhan et al., “Recent advances in DNA origami- engineered nanomaterials and applications,”Chem- ical Reviews, vol. 123, no. 7, pp. 3976–4050, 2023. doi: 10.1021/acs.chemrev.3c00028

    work page doi:10.1021/acs.chemrev.3c00028 2023

  41. [41]

    Design of a universal decoder model based on DNA winner-takes-all neural net- works,

    C. Huang et al., “Design of a universal decoder model based on DNA winner-takes-all neural net- works,”IEEE Transactions on Computers, vol. 74, 31 no. 4, pp. 1267–1277, 2025.doi: 10.1109/TC.2024. 3521230

    work page doi:10.1109/tc.2024 2025

  42. [42]

    Scaling up molecular pattern recognition with DNA-based winner-take- all neural networks,

    K. M. Cherry and L. Qian, “Scaling up molecular pattern recognition with DNA-based winner-take- all neural networks,”Nature, vol. 559, no. 7714, pp. 370–376, 2018.doi: 10.1038/s41586-018-0289-6

    work page doi:10.1038/s41586-018-0289-6 2018

  43. [43]

    Qian and E

    L. Qian and E. Winfree, “Scaling up digital circuit computation with DNA strand displacement cas- cades,”Science, vol. 332, no. 6034, pp. 1196–1201, 2011.doi: 10.1126/science.1200520

    work page doi:10.1126/science.1200520 2011

  44. [44]

    Deep convolutional and fully- connected DNA neural networks,

    X. Liu et al., “Deep convolutional and fully- connected DNA neural networks,”Nat Commun, vol. 16, no. 1, p. 10629, Nov. 2025.doi: 10.1038/ s41467-025-65618-x

    2025

  45. [45]

    Proceedings of the National Academy of Sci- ences79(8), 2554–2558 (Apr 1982)

    J. J. Hopfield, “Neural networks and physical sys- tems with emergent collective computational abil- ities.,”Proceedings of the National Academy of Sciences, vol. 79, no. 8, pp. 2554–2558, 1982.doi: 10.1073/pnas.79.8.2554

    work page doi:10.1073/pnas.79.8.2554 1982

  46. [46]

    IEEE Transactions on Neural Networks and Learning Systems35(11), 15170–15181 (2023) https://doi.org/10.1109/tnnls

    J. Sun, H. Wang, Y. Yue, D. Ling, and Y. Wang, “Design of Hopfield neural network based on DNA strand displacement circuits and its application in sudoku conjecture,”IEEE Transactions on Neural Networks and Learning Systems, vol. 36, no. 10, pp. 18889–18899, 2025.doi: 10.1109/TNNLS. 2025.3576888

    work page doi:10.1109/tnnls 2025

  47. [47]

    Photocleavable Ortho- Nitrobenzyl-Protected DNA architectures and their applications,

    M. P. O’Hagan et al., “Photocleavable Ortho- Nitrobenzyl-Protected DNA architectures and their applications,”Chem. Rev., vol. 123, no. 10, pp. 6839–6887, May 2023.doi: 10 . 1021 / acs . chemrev.3c00016

    2023

  48. [48]

    Supervised learning in DNA neural networks,

    K. M. Cherry and L. Qian, “Supervised learning in DNA neural networks,”Nature, 2025.doi: 10. 1038/s41586-025-09479-w

    2025

  49. [49]

    Multi-threshold and multi-input DNA logic design style for profiling the microrna biomarkers of real cancers,

    M. Sanjabi and A. Jahanian, “Multi-threshold and multi-input DNA logic design style for profiling the microrna biomarkers of real cancers,”IET Nanobiotechnology, vol. 13, no. 7, pp. 665–673, 2019.doi: https://doi.org/10.1049/iet-nbt.2018. 5275

    work page doi:10.1049/iet-nbt.2018 2019

  50. [50]

    Nonlinear decision-making with enzymatic neural networks,

    S. Okumura et al., “Nonlinear decision-making with enzymatic neural networks,”Nature, vol. 610, no. 7932, pp. 496–501, Oct. 2022.doi: 10.1038/ s41586-022-05218-7

    2022

  51. [51]

    Harnessing DNA computing and nanopore decoding for practical applications: From informatics to microRNA-targeting diagnos- tics,

    S. Takiguchi et al., “Harnessing DNA computing and nanopore decoding for practical applications: From informatics to microRNA-targeting diagnos- tics,”Chem. Soc. Rev., vol. 54, pp. 8–32, 1 2025. doi: 10.1039/D3CS00396E

    work page doi:10.1039/d3cs00396e 2025

  52. [52]

    Synthetic neuromorphic computing in livingcells,

    L. Rizik, L. Danial, M. Habib, R. Weiss, and R. Daniel, “Synthetic neuromorphic computing in livingcells,”NatureCommunications,vol.13,no.1, p. 5602, Sep. 2022.doi: 10.1038/s41467-022-33288- 8

    work page doi:10.1038/s41467-022-33288- 2022

  53. [53]

    CRISPR-based neuromor- phic computing for solving regression and classifi- cation,

    C. M. Leon, Y. Wang, F. B. Bisso, A. Mehta, and C. C. Samaniego, “CRISPR-based neuromor- phic computing for solving regression and classifi- cation,”bioRxiv, 2025.doi: 10.64898/2025.12.03. 692209

    work page doi:10.64898/2025.12.03 2025

  54. [54]

    Journal of the Ameri- can Chemical Society144(15), 6625–6639 (2022) https://doi.org/10.1021/JACS

    C. Sun, X. Liu, J. Zhong, Q. Zhou, and J. Cheng, “Reusable noncomplementary DNA-based neural network,”J Am Chem Soc, vol. 147, no. 38, pp. 34339–34349, Aug. 2025.doi: 10.1021/jacs. 5c04886

    work page doi:10.1021/jacs 2025

  55. [55]

    Heat-rechargeable compu- tation in DNA logic circuits and neural networks,

    T. Song and L. Qian, “Heat-rechargeable compu- tation in DNA logic circuits and neural networks,” Nature, vol. 646, pp. 315–322, 2025.doi: 10.1038/ s41586-025-09570-2

    2025

  56. [56]

    Towards on-chip chemical computing: The oscillating Belousov- Zhabotinsky reaction in silicon microchips,

    S. Agostini, V. Zarth, et al., “Towards on-chip chemical computing: The oscillating Belousov- Zhabotinsky reaction in silicon microchips,” inSCS Fall Meeting 2025 Abstract Catalogue, Poster PC- 101, IBM Research, SCS, 2025

    2025

  57. [57]

    Chemical reservoir computation in a self-organizing reaction network,

    M. G. Baltussen, T. J. de Jong, Q. Duez, W. E. Robinson, and W. T. S. Huck, “Chemical reservoir computation in a self-organizing reaction network,” Nature, vol. 631, no. 8021, pp. 549–555, Jul. 2024. doi: 10.1038/s41586-024-07567-x

    work page doi:10.1038/s41586-024-07567-x 2024

  58. [58]

    Autonomous soft robots: Self-regulation, self- sustained, and recovery strategies,

    C. Zhu, B.-Y. Liu, L.-Z. Zhang, and L. Xu, “Autonomous soft robots: Self-regulation, self- sustained, and recovery strategies,”Chinese Jour- nal of Polymer Science, vol. 43, no. 4, pp. 535–547, Apr. 2025.doi: 10.1007/s10118-025-3284-z

    work page doi:10.1007/s10118-025-3284-z 2025

  59. [59]

    Study on the anti-interference characteristics of neuronal networks: A compar- ative study of chemical synapses and electri- cal synapse,

    X. Li and M. Lu, “Study on the anti-interference characteristics of neuronal networks: A compar- ative study of chemical synapses and electri- cal synapse,”Frontiers in Neuroscience, vol. 19, p. 1581347, 2025.doi: 10.3389/fnins.2025.1581347

    work page doi:10.3389/fnins.2025.1581347 2025

  60. [60]

    Logic gates in excitable media,

    A. Toth and K. Showalter, “Logic gates in excitable media,”Journal of Chemical Physics, vol. 103, pp. 2058–2066, 1995.doi: 10.1063/1.469732

    work page doi:10.1063/1.469732 2058

  61. [61]

    Reservoir computing with bio- compatible organic electrochemical networks for brain-inspired biosignal classification,

    M. Cucchi et al., “Reservoir computing with bio- compatible organic electrochemical networks for brain-inspired biosignal classification,”Science Ad- vances,vol.7,no.34,eabh0693,2021.doi:10.1126/ sciadv.abh0693

    2021

  62. [62]

    A tissue- like printed material,

    G. Villar, A. D. Graham, and H. Bayley, “A tissue- like printed material,”Science, vol. 340, no. 6128, pp. 48–52, Apr. 2013.doi: 10.1126/science.1229495

    work page doi:10.1126/science.1229495 2013

  63. [63]

    M. U. Gaimann and M. Klopotek,Robustly optimal dynamics for active matter reservoir computing, 2025.doi: 10.48550/arXiv.2505.05420

    work page doi:10.48550/arxiv.2505.05420 2025

  64. [64]

    Neural Ordinary Differential Equations

    R. T. Q. Chen, Y. Rubanova, J. Bettencourt, and D. Duvenaud, “Neural ordinary differential equa- tions,”arXiv preprint arXiv:1806.07366, 2018.doi: 10.48550/arXiv.1806.07366

    work page internal anchor Pith review doi:10.48550/arxiv.1806.07366 2018

  65. [65]

    SPIN-ODE: Stiff physics-informed neural ODE for chemical reaction rate estimation,

    W. Peng, Z.-S. Liu, and M. Boy, “SPIN-ODE: Stiff physics-informed neural ODE for chemical reaction rate estimation,” inECAI 2025 – 28th European Conference on Artificial Intelligence, in- cluding14thConferenceonPrestigiousApplications of Intelligent Systems (PAIS 2025) – Proceedings, I. Lynce et al., Eds., ser. Frontiers in Artificial Intelligence and App...

    work page doi:10.3233/faia251040 2025

  66. [66]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

    M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learn- ing framework for solving forward and inverse prob- lems involving nonlinear partial differential equa- tions,”Journal of Computational Physics, vol. 378, pp. 686–707, 2019.doi: 10.1016/j.jcp.2018.10.045

    work page doi:10.1016/j.jcp.2018.10.045 2019

  67. [67]

    A programmable chemical computer with memory and pattern recognition,

    J. M. Parrilla-Gutierrez et al., “A programmable chemical computer with memory and pattern recognition,”Nat. Commun., vol. 11, no. 1, p. 1442, Mar. 2020.doi: 10.1038/s41467-020-15190-3

    work page doi:10.1038/s41467-020-15190-3 2020

  68. [68]

    Navigat- ing complex labyrinths: Optimal paths from chemi- cal waves,

    O. Steinbock, A. Tóth, and K. Showalter, “Navigat- ing complex labyrinths: Optimal paths from chemi- cal waves,”Science, vol. 267, no. 5199, pp. 868–871, Feb. 1995.doi: 10.1126/science.267.5199.868

    work page doi:10.1126/science.267.5199.868 1995

  69. [69]

    Maze solving by chemotactic droplets,

    I. Lagzi, S. Soh, P. J. Wesson, K. P. Browne, and B. A. Grzybowski, “Maze solving by chemotactic droplets,”J. Am. Chem. Soc., vol. 132, no. 4, pp. 1198–1199, Feb. 2010.doi: 10.1021/ja9076793

    work page doi:10.1021/ja9076793 2010

  70. [70]

    Organoid intelligence (OI) - the ultimate functionality of a brain microphysiological system,

    L. Smirnova, I. E. Morales Pantoja, and T. Har- tung, “Organoid intelligence (OI) - the ultimate functionality of a brain microphysiological system,” ALTEX, vol. 40, no. 2, pp. 191–203, 2023.doi: 10. 14573/altex.2303261

    2023

  71. [71]

    A synthetic oscilla- tory network of transcriptional regulators,

    M. Elowitz and S. Leibler, “A synthetic oscilla- tory network of transcriptional regulators,”Nature, vol. 403, pp. 335–338, 2000.doi: 10.1038/35002125

    work page doi:10.1038/35002125 2000

  72. [72]

    Tamsir, A., Tabor, J

    A. Tamsir, J. J. Tabor, and C. A. Voigt, “Robust multicellular computing using genetically encoded NOR gates and chemical wires,”Nature, vol. 469, pp. 212–215, 2011.doi: 10.1038/nature09565

    work page doi:10.1038/nature09565 2011

  73. [73]

    A synchronized quorum of genetic clocks,

    T. Danino, O. Mondragón-Palomino, L. Tsimring, and J. Hasty, “A synchronized quorum of genetic clocks,”Nature, vol. 463, pp. 326–330, 2010.doi: 10.1038/nature08753

    work page doi:10.1038/nature08753 2010

  74. [74]

    Stains,et al., Anatomy of STEM Teaching in American Universities: A Snapshot from a Large-Scale Observation Study.Science359(6383), 1468–1470 (2018), doi:10.1126/science

    A. Tero et al., “Rules for biologically inspired adap- tive network design,”Science, vol. 327, no. 5964, pp. 439–442, Jan. 2010.doi: 10.1126/science. 117789

    work page doi:10.1126/science 2010

  75. [75]

    Adamatzky,Physarum Machines

    A. Adamatzky,Physarum Machines. World Scien- tific, 2010.doi: 10.1142/7968

    work page doi:10.1142/7968 2010

  76. [76]

    Brain organoid reservoir computing forartificialintelligence,

    H. Cai et al., “Brain organoid reservoir computing forartificialintelligence,”NatureElectronics,vol.6, no. 12, pp. 1032–1039, Dec. 2023.doi: 10.1038/ s41928-023-01069-w

    2023

  77. [77]

    Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynap- tic cell type,

    G.-Q. Bi and M.-M. Poo, “Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynap- tic cell type,”Journal of Neuroscience, vol. 18, pp. 10464–10472, 1998.doi: https : / / www . jneurosci.org/content/18/24/10464

    1998

  78. [78]

    Synthetic analog computation in living cells,

    R. Daniel, J. Rubens, R. Sarpeshkar, and T. K. Lu, “Synthetic analog computation in living cells,” Nature, vol. 497, pp. 619–623, 2013.doi: 10.1038/ nature12148

    2013

  79. [79]

    Friston, The free-energy principle: a unified brain theory?, Nature Reviews Neuroscience 11 (2010) 127–138

    K. Friston, “The free-energy principle: A unified brain theory?”Nat Rev Neurosci, vol. 11, no. 2, pp. 127–138, Jan. 2010.doi: 10.1038/nrn2787

    work page doi:10.1038/nrn2787 2010

  80. [80]

    Srinivasan, K

    M. Obien, K. Deligkaris, T. Bullmann, D. Bakkum, and U. Frey, “Revealing neuronal function through microelectrode array recordings,”Frontiers in Neu- roscience, vol. 9, p. 423, 2015.doi: 10.3389/fnins. 2014.00423

    work page doi:10.3389/fnins 2015

Showing first 80 references.