Refined Kolmogorov complexity of analog, evolving and stochastic recurrent neural networks
Kolmogorov complexity measures the compressibility of real numbers. We provide a refined characterization of the hypercomputational power of analog, evolving, and stochastic neural networks based on the Kolmogorov complexity of their real weights, evolving weights, and real probabilities, respective...
Uloženo v:
| Vydáno v: | Information sciences Ročník 711; s. 122104 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
01.09.2025
|
| Témata: | |
| ISSN: | 0020-0255 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Kolmogorov complexity measures the compressibility of real numbers. We provide a refined characterization of the hypercomputational power of analog, evolving, and stochastic neural networks based on the Kolmogorov complexity of their real weights, evolving weights, and real probabilities, respectively. First, we retrieve the infinite hierarchy of complexity classes of analog networks, defined in terms of the Kolmogorov complexity of their real weights. This hierarchy lies between the complexity classes P and P/poly. Next, using a natural identification between real numbers and infinite sequences of bits, we generalize this result to evolving networks, obtaining a similar hierarchy of complexity classes within the same bounds. Finally, we extend these results to stochastic networks that employ real probabilities as randomness, deriving a new infinite hierarchy of complexity classes situated between BPP and BPP/log⁎. Beyond providing examples of such hierarchies, we describe a generic method for constructing them based on classes of functions of increasing complexity. As a practical application, we show that the predictive capabilities of recurrent neural networks are strongly impacted by the quantization applied to their weights. Overall, these results highlight the relationship between the computational power of neural networks and the intrinsic information contained by their parameters. |
|---|---|
| AbstractList | Kolmogorov complexity measures the compressibility of real numbers. We provide a refined characterization of the hypercomputational power of analog, evolving, and stochastic neural networks based on the Kolmogorov complexity of their real weights, evolving weights, and real probabilities, respectively. First, we retrieve the infinite hierarchy of complexity classes of analog networks, defined in terms of the Kolmogorov complexity of their real weights. This hierarchy lies between the complexity classes P and P/poly. Next, using a natural identification between real numbers and infinite sequences of bits, we generalize this result to evolving networks, obtaining a similar hierarchy of complexity classes within the same bounds. Finally, we extend these results to stochastic networks that employ real probabilities as randomness, deriving a new infinite hierarchy of complexity classes situated between BPP and BPP/log⁎. Beyond providing examples of such hierarchies, we describe a generic method for constructing them based on classes of functions of increasing complexity. As a practical application, we show that the predictive capabilities of recurrent neural networks are strongly impacted by the quantization applied to their weights. Overall, these results highlight the relationship between the computational power of neural networks and the intrinsic information contained by their parameters. |
| ArticleNumber | 122104 |
| Author | Cabessa, Jérémie Strozecki, Yann |
| Author_xml | – sequence: 1 givenname: Jérémie orcidid: 0000-0002-5394-5249 surname: Cabessa fullname: Cabessa, Jérémie email: jeremie.cabessa@uvsq.fr organization: Laboratoire DAVID, UVSQ – University Paris-Saclay, 78035 Versailles, France – sequence: 2 givenname: Yann orcidid: 0000-0002-0891-3766 surname: Strozecki fullname: Strozecki, Yann email: yann.strozecki@uvsq.fr organization: Laboratoire DAVID, UVSQ – University Paris-Saclay, 78035 Versailles, France |
| BookMark | eNp9kM1KAzEUhbOoYKs-gLs8gDPepJmf4EqKf1gQRDduQiZzU1OnSUmmo317p9S1qwMHvsO934xMfPBIyCWDnAErr9e58ynnwIuccc5ATMgUgEM2NsUpmaW0BgBRleWUfLyidR5b-hy6TViFGAZqwmbb4Y_r9zRYqr3uwuqK4hC6wfnVWLQ09cF86tQ7QyOaXYzoe-pxF3U3Rv8d4lc6JydWdwkv_vKMvN_fvS0es-XLw9PidpkZXrA-w6ZqRM1kI7istW5t0cjaclGXZg6AopKsbbQodY2C2UKgBGuqxrZcSjlvYH5G2HHXxJBSRKu20W103CsG6iBErdUoRB2EqKOQkbk5MjgeNjiMKhmH3mDrxn961Qb3D_0LWLdutQ |
| Cites_doi | 10.1007/BF02478259 10.1037/h0042519 10.1142/S0129065714500294 10.1016/j.neunet.2020.05.006 10.1109/18.605580 10.1073/pnas.2001893117 10.1006/jcss.1995.1013 10.1006/inco.1996.0062 10.1016/j.neunet.2014.09.003 10.1006/jcom.1999.0505 10.1016/j.jcss.2004.04.001 10.1162/089976698300017359 10.1016/0304-3975(94)90178-3 10.1145/235809.235811 10.1006/jcss.1999.1693 10.1142/S0129054107004772 10.1016/0893-6080(95)00095-X 10.1126/science.268.5210.545 10.1016/j.neunet.2020.03.019 10.1162/089976699300016656 10.1162/neco.1996.8.1.1 10.1016/j.tcs.2003.12.014 10.1016/j.neunet.2018.08.025 10.1016/j.jcss.2018.11.003 10.1109/TNNLS.2016.2582924 10.1016/j.neunet.2019.04.019 10.1126/science.1091277 10.1007/s11047-011-9291-8 10.1016/j.cosrev.2009.03.005 |
| ContentType | Journal Article |
| Copyright | 2025 Elsevier Inc. |
| Copyright_xml | – notice: 2025 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.ins.2025.122104 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Library & Information Science |
| ExternalDocumentID | 10_1016_j_ins_2025_122104 S0020025525002361 |
| GroupedDBID | --K --M --Z -~X .DC .~1 0R~ 1B1 1OL 1RT 1~. 1~5 29I 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AAEDT AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AATTM AAXKI AAXUO AAYFN AAYWO ABAOU ABBOA ABEFU ABFNM ABJNI ABMAC ABUCO ABWVN ABXDB ACDAQ ACGFS ACNNM ACRLP ACRPL ACZNC ADBBV ADEZE ADGUI ADJOM ADMUD ADNMO ADTZH ADVLN AEBSH AECPX AEIPS AEKER AENEX AFFNX AFJKZ AFTJW AFXIZ AGCQF AGHFR AGQPQ AGRNS AGUBO AGYEJ AHHHB AHJVU AHZHX AIALX AIEXJ AIGVJ AIIUN AIKHN AITUG AKRWK ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU AOUOD APLSM APXCP ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC BNPGV CS3 DU5 EBS EFJIC EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HAMUX HLZ HVGLF HZ~ H~9 IHE J1W JJJVA KOM LG9 LY1 M41 MHUIS MO0 MS~ N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SBC SDF SDG SDP SDS SES SEW SPC SPCBC SSB SSD SSH SST SSV SSW SSZ T5K TN5 TWZ UHS WH7 WUQ XPP YYP ZMT ZY4 ~02 ~G- 77I 9DU AAYXX ACLOT ACVFH ADCNI AEUPX AFPUW AIGII AKBMS AKYEP CITATION EFKBS EFLBG ~HD |
| ID | FETCH-LOGICAL-c251t-eb7b4819b4298aadf5b98f2486c300e4791dba46a8e41f54e90fc7bfd29993b03 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001456228400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0020-0255 |
| IngestDate | Sat Nov 29 07:57:28 EST 2025 Sat May 24 17:06:04 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Recurrent neural networks Computability theory Computational power Echo state networks Kolmogorov complexity Quantization Analog computation Stochastic computation |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c251t-eb7b4819b4298aadf5b98f2486c300e4791dba46a8e41f54e90fc7bfd29993b03 |
| ORCID | 0000-0002-5394-5249 0000-0002-0891-3766 |
| ParticipantIDs | crossref_primary_10_1016_j_ins_2025_122104 elsevier_sciencedirect_doi_10_1016_j_ins_2025_122104 |
| PublicationCentury | 2000 |
| PublicationDate | September 2025 2025-09-00 |
| PublicationDateYYYYMMDD | 2025-09-01 |
| PublicationDate_xml | – month: 09 year: 2025 text: September 2025 |
| PublicationDecade | 2020 |
| PublicationTitle | Information sciences |
| PublicationYear | 2025 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Maass, Orponen (br0220) 1998; 10 Jin, Du, Huang, Liu, Luan, Wang, Xiong (br0440) 2024 Hebb (br0100) 1949 Copeland (br0400) 2004; 317 Šíma (br0240) 2019; 116 Churchland, Sejnowski (br0010) 2016 Păun (br0320) 2000; 61 Grigoryeva, Ortega (br0390) 2018; 108 Turing (br0070) 1948 Merrill, Weiss, Goldberg, Schwartz, Smith, Yahav (br0360) 2020 Minsky, Papert (br0110) 1969 Maass (br0270) 1999 Lukoševičius, Jaeger (br0380) 2009; 3 Minsky (br0040) 1967 Pollack (br0080) 1987 Omlin, Giles (br0060) 1996; 43 Greff, Srivastava, Koutnìk, Steunebrink, Schmidhuber (br0350) 2017; 28 Siegelmann, Sontag (br0140) 1995; 50 Horne, Hush (br0050) 1996; 9 Cabessa, Tchaptchet (br0300) 2020; 126 Kilian, Siegelmann (br0150) 1996; 128 Siegelmann (br0210) 1999; 15 Siegelmann, Sontag (br0170) 1994; 131 Maass (br0280) 1996; 8 Gheorghe, Stannett (br0340) 2012; 11 McCulloch, Pitts (br0020) 1943; 5 Neumann (br0130) 1958 Balcázar, Gavaldà, Siegelmann (br0260) 1997; 43 Gholami, Kim, Dong, Yao, Mahoney, Keutzer (br0430) 2021 Maass, Markram (br0450) 2004; 69 Maass (br0290) November 27-30, 1995 Maass, Sontag (br0230) 1999; 11 Bournez, Pouly (br0420) 2021 Siegelmann (br0160) 1999 Kleene (br0030) 1956 Schmidhuber (br0120) 2015; 61 Siegelmann (br0180) 1995; 268 Cabessa, Siegelmann (br0200) 2014; 24 Jaeger, Haas (br0370) 2004; 304 Šíma (br0250) 2020; 128 Arora, Barak (br0410) 2006 Cabessa, Finkel (br0190) 2019; 101 Păun, Pérez-Jiménez, Salomaa (br0330) 2007; 18 Rosenblatt (br0090) 1958; 65 Papadimitriou, Vempala, Mitropolsky, Collins, Maass (br0310) 2020; 117 Turing (10.1016/j.ins.2025.122104_br0070) 1948 Pollack (10.1016/j.ins.2025.122104_br0080) 1987 Minsky (10.1016/j.ins.2025.122104_br0040) 1967 Lukoševičius (10.1016/j.ins.2025.122104_br0380) 2009; 3 Maass (10.1016/j.ins.2025.122104_br0450) 2004; 69 Hebb (10.1016/j.ins.2025.122104_br0100) 1949 Minsky (10.1016/j.ins.2025.122104_br0110) 1969 Merrill (10.1016/j.ins.2025.122104_br0360) 2020 Siegelmann (10.1016/j.ins.2025.122104_br0180) 1995; 268 Arora (10.1016/j.ins.2025.122104_br0410) 2006 Churchland (10.1016/j.ins.2025.122104_br0010) 2016 Neumann (10.1016/j.ins.2025.122104_br0130) 1958 Balcázar (10.1016/j.ins.2025.122104_br0260) 1997; 43 Copeland (10.1016/j.ins.2025.122104_br0400) 2004; 317 Grigoryeva (10.1016/j.ins.2025.122104_br0390) 2018; 108 Maass (10.1016/j.ins.2025.122104_br0220) 1998; 10 Schmidhuber (10.1016/j.ins.2025.122104_br0120) 2015; 61 Siegelmann (10.1016/j.ins.2025.122104_br0160) 1999 Gholami (10.1016/j.ins.2025.122104_br0430) Gheorghe (10.1016/j.ins.2025.122104_br0340) 2012; 11 Kleene (10.1016/j.ins.2025.122104_br0030) 1956 Siegelmann (10.1016/j.ins.2025.122104_br0140) 1995; 50 Šíma (10.1016/j.ins.2025.122104_br0240) 2019; 116 Maass (10.1016/j.ins.2025.122104_br0280) 1996; 8 Cabessa (10.1016/j.ins.2025.122104_br0200) 2014; 24 Omlin (10.1016/j.ins.2025.122104_br0060) 1996; 43 Păun (10.1016/j.ins.2025.122104_br0330) 2007; 18 Bournez (10.1016/j.ins.2025.122104_br0420) 2021 Jaeger (10.1016/j.ins.2025.122104_br0370) 2004; 304 Maass (10.1016/j.ins.2025.122104_br0290) 1995 Rosenblatt (10.1016/j.ins.2025.122104_br0090) 1958; 65 Maass (10.1016/j.ins.2025.122104_br0270) 1999 Siegelmann (10.1016/j.ins.2025.122104_br0170) 1994; 131 Siegelmann (10.1016/j.ins.2025.122104_br0210) 1999; 15 Păun (10.1016/j.ins.2025.122104_br0320) 2000; 61 Jin (10.1016/j.ins.2025.122104_br0440) 2024 Kilian (10.1016/j.ins.2025.122104_br0150) 1996; 128 Maass (10.1016/j.ins.2025.122104_br0230) 1999; 11 Papadimitriou (10.1016/j.ins.2025.122104_br0310) 2020; 117 Cabessa (10.1016/j.ins.2025.122104_br0190) 2019; 101 McCulloch (10.1016/j.ins.2025.122104_br0020) 1943; 5 Horne (10.1016/j.ins.2025.122104_br0050) 1996; 9 Cabessa (10.1016/j.ins.2025.122104_br0300) 2020; 126 Šíma (10.1016/j.ins.2025.122104_br0250) 2020; 128 Greff (10.1016/j.ins.2025.122104_br0350) 2017; 28 |
| References_xml | – year: 1958 ident: br0130 article-title: The Computer and the Brain – volume: 8 start-page: 1 year: 1996 end-page: 40 ident: br0280 article-title: Lower bounds for the computational power of networks of spiking neurons publication-title: Neural Comput. – volume: 131 start-page: 331 year: 1994 end-page: 360 ident: br0170 article-title: Analog computation via neural networks publication-title: Theor. Comput. Sci. – volume: 11 start-page: 771 year: 1999 end-page: 782 ident: br0230 article-title: Analog neural nets with Gaussian or other common noise distributions cannot recognize arbitary regular languages publication-title: Neural Comput. – volume: 24 year: 2014 ident: br0200 article-title: The super-Turing computational power of plastic recurrent neural networks publication-title: Int. J. Neural Syst. – year: 1969 ident: br0110 article-title: Perceptrons: An Introduction to Computational Geometry – year: 1967 ident: br0040 article-title: Computation: Finite and Infinite Machines – year: 1999 ident: br0160 article-title: Neural Networks and Analog Computation: Beyond the Turing Limit – year: 1948 ident: br0070 – volume: 108 start-page: 495 year: 2018 end-page: 508 ident: br0390 article-title: Echo state networks are universal publication-title: Neural Netw. – volume: 43 start-page: 1175 year: 1997 end-page: 1183 ident: br0260 article-title: Computational power of neural networks: a characterization in terms of Kolmogorov complexity publication-title: IEEE Trans. Inf. Theory – start-page: 443 year: 2020 end-page: 459 ident: br0360 article-title: A formal hierarchy of RNN architectures publication-title: Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, ACL 2020, Online, July 5-10, 2020, Association for Computational Linguistics – start-page: 3 year: 1956 end-page: 41 ident: br0030 article-title: Representation of events in nerve nets and finite automata publication-title: Automata Studies – volume: 126 start-page: 312 year: 2020 end-page: 334 ident: br0300 article-title: Automata complete computation with Hodgkin-Huxley neural networks composed of synfire rings publication-title: Neural Netw. – volume: 116 start-page: 208 year: 2019 end-page: 223 ident: br0240 article-title: Subrecursive neural networks publication-title: Neural Netw. – volume: 10 start-page: 1071 year: 1998 end-page: 1095 ident: br0220 article-title: On the effect of analog noise in discrete-time analog computations publication-title: Neural Comput. – year: November 27-30, 1995 ident: br0290 article-title: On the computational power of noisy spiking neurons publication-title: Advances in Neural Information Processing Systems 8, NIPS Conference – volume: 117 start-page: 14464 year: 2020 end-page: 14472 ident: br0310 article-title: Brain computation by assemblies of neurons publication-title: Proc. Natl. Acad. Sci. – volume: 128 start-page: 48 year: 1996 end-page: 56 ident: br0150 article-title: The dynamic universality of sigmoidal neural networks publication-title: Inf. Comput. – volume: 11 start-page: 253 year: 2012 end-page: 259 ident: br0340 article-title: Membrane system models for super-Turing paradigms publication-title: Nat. Comput. – volume: 15 start-page: 451 year: 1999 end-page: 475 ident: br0210 article-title: Stochastic analog networks and computational complexity publication-title: J. Complex. – year: 2016 ident: br0010 article-title: The Computational Brain – start-page: 55 year: 1999 end-page: 85 ident: br0270 article-title: Computing with spiking neurons publication-title: Pulsed Neural Networks – volume: 43 start-page: 937 year: 1996 end-page: 972 ident: br0060 article-title: Constructing deterministic finite-state automata in recurrent neural networks publication-title: J. ACM – year: 1949 ident: br0100 article-title: The Organization of Behavior: A Neuropsychological Theory – volume: 61 start-page: 108 year: 2000 end-page: 143 ident: br0320 article-title: Computing with membranes publication-title: J. Comput. Syst. Sci. – volume: 28 start-page: 2222 year: 2017 end-page: 2232 ident: br0350 article-title: LSTM: a search space odyssey publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 65 start-page: 386 year: 1958 end-page: 408 ident: br0090 article-title: The perceptron: a probabilistic model for information storage and organization in the brain publication-title: Psychol. Rev. – volume: 5 start-page: 115 year: 1943 end-page: 133 ident: br0020 article-title: A logical calculus of the ideas immanent in nervous activity publication-title: Bull. Math. Biophys. – volume: 317 start-page: 251 year: 2004 end-page: 267 ident: br0400 article-title: Hypercomputation: philosophical issues publication-title: Theor. Comput. Sci. – volume: 268 start-page: 545 year: 1995 end-page: 548 ident: br0180 article-title: Computation beyond the Turing limit publication-title: Science – volume: 9 start-page: 243 year: 1996 end-page: 252 ident: br0050 article-title: Bounds on the complexity of recurrent neural network implementations of finite state machines publication-title: Neural Netw. – volume: 50 start-page: 132 year: 1995 end-page: 150 ident: br0140 article-title: On the computational power of neural nets publication-title: J. Comput. Syst. Sci. – volume: 304 start-page: 78 year: 2004 end-page: 80 ident: br0370 article-title: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication publication-title: Science – volume: 101 start-page: 86 year: 2019 end-page: 99 ident: br0190 article-title: Computational capabilities of analog and evolving neural networks over infinite input streams publication-title: J. Comput. Syst. Sci. – year: 1987 ident: br0080 article-title: On connectionist models of natural language processing – volume: 3 start-page: 127 year: 2009 end-page: 149 ident: br0380 article-title: Reservoir computing approaches to recurrent neural network training publication-title: Comput. Sci. Rev. – start-page: 173 year: 2021 end-page: 226 ident: br0420 article-title: A Survey on Analog Models of Computation – volume: 128 start-page: 199 year: 2020 end-page: 215 ident: br0250 article-title: Analog neuron hierarchy publication-title: Neural Netw. – year: 2006 ident: br0410 article-title: Computational Complexity: A Modern Approach – volume: 69 start-page: 593 year: 2004 end-page: 616 ident: br0450 article-title: On the computational power of circuits of spiking neurons publication-title: J. Comput. Syst. Sci. – volume: 61 start-page: 85 year: 2015 end-page: 117 ident: br0120 article-title: Deep learning in neural networks: an overview publication-title: Neural Netw. – volume: 18 start-page: 435 year: 2007 end-page: 455 ident: br0330 article-title: Spiking neural P systems: an early survey publication-title: Int. J. Found. Comput. Sci. – year: 2021 ident: br0430 article-title: A survey of quantization methods for efficient neural network inference – start-page: 12186 year: 2024 end-page: 12215 ident: br0440 article-title: A comprehensive evaluation of quantization strategies for large language models publication-title: Findings of the Association for Computational Linguistics – volume: 5 start-page: 115 year: 1943 ident: 10.1016/j.ins.2025.122104_br0020 article-title: A logical calculus of the ideas immanent in nervous activity publication-title: Bull. Math. Biophys. doi: 10.1007/BF02478259 – start-page: 3 year: 1956 ident: 10.1016/j.ins.2025.122104_br0030 article-title: Representation of events in nerve nets and finite automata – volume: 65 start-page: 386 issue: 6 year: 1958 ident: 10.1016/j.ins.2025.122104_br0090 article-title: The perceptron: a probabilistic model for information storage and organization in the brain publication-title: Psychol. Rev. doi: 10.1037/h0042519 – volume: 24 issue: 8 year: 2014 ident: 10.1016/j.ins.2025.122104_br0200 article-title: The super-Turing computational power of plastic recurrent neural networks publication-title: Int. J. Neural Syst. doi: 10.1142/S0129065714500294 – year: 1948 ident: 10.1016/j.ins.2025.122104_br0070 – year: 2006 ident: 10.1016/j.ins.2025.122104_br0410 – start-page: 12186 year: 2024 ident: 10.1016/j.ins.2025.122104_br0440 article-title: A comprehensive evaluation of quantization strategies for large language models – volume: 128 start-page: 199 year: 2020 ident: 10.1016/j.ins.2025.122104_br0250 article-title: Analog neuron hierarchy publication-title: Neural Netw. doi: 10.1016/j.neunet.2020.05.006 – start-page: 443 year: 2020 ident: 10.1016/j.ins.2025.122104_br0360 article-title: A formal hierarchy of RNN architectures – year: 1999 ident: 10.1016/j.ins.2025.122104_br0160 – year: 1987 ident: 10.1016/j.ins.2025.122104_br0080 – volume: 43 start-page: 1175 issue: 4 year: 1997 ident: 10.1016/j.ins.2025.122104_br0260 article-title: Computational power of neural networks: a characterization in terms of Kolmogorov complexity publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.605580 – volume: 117 start-page: 14464 issue: 25 year: 2020 ident: 10.1016/j.ins.2025.122104_br0310 article-title: Brain computation by assemblies of neurons publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.2001893117 – volume: 50 start-page: 132 issue: 1 year: 1995 ident: 10.1016/j.ins.2025.122104_br0140 article-title: On the computational power of neural nets publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.1995.1013 – volume: 128 start-page: 48 issue: 1 year: 1996 ident: 10.1016/j.ins.2025.122104_br0150 article-title: The dynamic universality of sigmoidal neural networks publication-title: Inf. Comput. doi: 10.1006/inco.1996.0062 – volume: 61 start-page: 85 year: 2015 ident: 10.1016/j.ins.2025.122104_br0120 article-title: Deep learning in neural networks: an overview publication-title: Neural Netw. doi: 10.1016/j.neunet.2014.09.003 – volume: 15 start-page: 451 issue: 4 year: 1999 ident: 10.1016/j.ins.2025.122104_br0210 article-title: Stochastic analog networks and computational complexity publication-title: J. Complex. doi: 10.1006/jcom.1999.0505 – volume: 69 start-page: 593 issue: 4 year: 2004 ident: 10.1016/j.ins.2025.122104_br0450 article-title: On the computational power of circuits of spiking neurons publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2004.04.001 – volume: 10 start-page: 1071 issue: 5 year: 1998 ident: 10.1016/j.ins.2025.122104_br0220 article-title: On the effect of analog noise in discrete-time analog computations publication-title: Neural Comput. doi: 10.1162/089976698300017359 – year: 1958 ident: 10.1016/j.ins.2025.122104_br0130 – volume: 131 start-page: 331 issue: 2 year: 1994 ident: 10.1016/j.ins.2025.122104_br0170 article-title: Analog computation via neural networks publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(94)90178-3 – start-page: 55 year: 1999 ident: 10.1016/j.ins.2025.122104_br0270 article-title: Computing with spiking neurons – year: 1995 ident: 10.1016/j.ins.2025.122104_br0290 article-title: On the computational power of noisy spiking neurons – year: 1949 ident: 10.1016/j.ins.2025.122104_br0100 – volume: 43 start-page: 937 issue: 6 year: 1996 ident: 10.1016/j.ins.2025.122104_br0060 article-title: Constructing deterministic finite-state automata in recurrent neural networks publication-title: J. ACM doi: 10.1145/235809.235811 – volume: 61 start-page: 108 issue: 1 year: 2000 ident: 10.1016/j.ins.2025.122104_br0320 article-title: Computing with membranes publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.1999.1693 – start-page: 173 year: 2021 ident: 10.1016/j.ins.2025.122104_br0420 – volume: 18 start-page: 435 issue: 3 year: 2007 ident: 10.1016/j.ins.2025.122104_br0330 article-title: Spiking neural P systems: an early survey publication-title: Int. J. Found. Comput. Sci. doi: 10.1142/S0129054107004772 – volume: 9 start-page: 243 issue: 2 year: 1996 ident: 10.1016/j.ins.2025.122104_br0050 article-title: Bounds on the complexity of recurrent neural network implementations of finite state machines publication-title: Neural Netw. doi: 10.1016/0893-6080(95)00095-X – volume: 268 start-page: 545 issue: 5210 year: 1995 ident: 10.1016/j.ins.2025.122104_br0180 article-title: Computation beyond the Turing limit publication-title: Science doi: 10.1126/science.268.5210.545 – volume: 126 start-page: 312 year: 2020 ident: 10.1016/j.ins.2025.122104_br0300 article-title: Automata complete computation with Hodgkin-Huxley neural networks composed of synfire rings publication-title: Neural Netw. doi: 10.1016/j.neunet.2020.03.019 – volume: 11 start-page: 771 issue: 3 year: 1999 ident: 10.1016/j.ins.2025.122104_br0230 article-title: Analog neural nets with Gaussian or other common noise distributions cannot recognize arbitary regular languages publication-title: Neural Comput. doi: 10.1162/089976699300016656 – volume: 8 start-page: 1 issue: 1 year: 1996 ident: 10.1016/j.ins.2025.122104_br0280 article-title: Lower bounds for the computational power of networks of spiking neurons publication-title: Neural Comput. doi: 10.1162/neco.1996.8.1.1 – year: 2016 ident: 10.1016/j.ins.2025.122104_br0010 – year: 1967 ident: 10.1016/j.ins.2025.122104_br0040 – ident: 10.1016/j.ins.2025.122104_br0430 – volume: 317 start-page: 251 issue: 1–3 year: 2004 ident: 10.1016/j.ins.2025.122104_br0400 article-title: Hypercomputation: philosophical issues publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2003.12.014 – volume: 108 start-page: 495 year: 2018 ident: 10.1016/j.ins.2025.122104_br0390 article-title: Echo state networks are universal publication-title: Neural Netw. doi: 10.1016/j.neunet.2018.08.025 – volume: 101 start-page: 86 year: 2019 ident: 10.1016/j.ins.2025.122104_br0190 article-title: Computational capabilities of analog and evolving neural networks over infinite input streams publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2018.11.003 – volume: 28 start-page: 2222 issue: 10 year: 2017 ident: 10.1016/j.ins.2025.122104_br0350 article-title: LSTM: a search space odyssey publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2016.2582924 – year: 1969 ident: 10.1016/j.ins.2025.122104_br0110 – volume: 116 start-page: 208 year: 2019 ident: 10.1016/j.ins.2025.122104_br0240 article-title: Subrecursive neural networks publication-title: Neural Netw. doi: 10.1016/j.neunet.2019.04.019 – volume: 304 start-page: 78 issue: 5667 year: 2004 ident: 10.1016/j.ins.2025.122104_br0370 article-title: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication publication-title: Science doi: 10.1126/science.1091277 – volume: 11 start-page: 253 issue: 2 year: 2012 ident: 10.1016/j.ins.2025.122104_br0340 article-title: Membrane system models for super-Turing paradigms publication-title: Nat. Comput. doi: 10.1007/s11047-011-9291-8 – volume: 3 start-page: 127 issue: 3 year: 2009 ident: 10.1016/j.ins.2025.122104_br0380 article-title: Reservoir computing approaches to recurrent neural network training publication-title: Comput. Sci. Rev. doi: 10.1016/j.cosrev.2009.03.005 |
| SSID | ssj0004766 |
| Score | 2.47147 |
| Snippet | Kolmogorov complexity measures the compressibility of real numbers. We provide a refined characterization of the hypercomputational power of analog, evolving,... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 122104 |
| SubjectTerms | Analog computation Computability theory Computational power Echo state networks Kolmogorov complexity Quantization Recurrent neural networks Stochastic computation |
| Title | Refined Kolmogorov complexity of analog, evolving and stochastic recurrent neural networks |
| URI | https://dx.doi.org/10.1016/j.ins.2025.122104 |
| Volume | 711 |
| WOSCitedRecordID | wos001456228400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0020-0255 databaseCode: AIEXJ dateStart: 19950101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0004766 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Nb9MwGLZKxwEOaBugjTHkA-IABKWOHTvHadoEmzQhNqTCJYq_9qHNmdquqvj1vKntJIxNYgcuUWS1byI_j948tt8PhN6KTGcmz3ViUpMl1FKeSKKLhGUWxKwkkiuxbDbBj47EeFx8HQyOYy7M_JI7JxaL4vq_Qg1jAHaTOvsAuFujMAD3ADpcAXa4_hPw34wF5ag_HNaXV_VpPannPm7cLEL0ReWaDZtmbg34pnnMUgQVqM6qqa_prELZpqbcJYDofLD4tC9lQyLTkj_hO9rq891KNq1VlhTxR_HhRP7qvCXS8WxS_zLKt83-UTnX34AgrI2w6hIC0qRZmvSdKg8u1LvFESGhy_BfHttvHlzAMqMpnk7Yp-63f1bHvvXVamMJY5jaRQkmysZE6U08QiuEs0IM0crOl73xQZcuy_0RdnzveNi9DPu79R53y5WeBDlZRc_C2gHveMzX0MC4dfS0V1FyHW2HPBT8DvfwwcGDP0c_Aztwxw7csQPXFnt2fMSRGzCgcccN3HIDe27gyI0X6Pv-3snu5yS010gUiNpZYiSXFAShBEkiqkpbJgthCRW5ytLUUF6MtKxoXglDR5ZRU6RWcWk1KJgik2n2Eg1d7cwGwsyAbCWWMMoVzbWRKTMiZzYHMSjAxCZ6H2exvPZVVMp7cdtENM5zGejr5V0JnLn_b68e8owt9KSj8ms0nE1uzDZ6rOaz8-nkTSDMb9cpfkc |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Refined+Kolmogorov+complexity+of+analog%2C+evolving+and+stochastic+recurrent+neural+networks&rft.jtitle=Information+sciences&rft.au=Cabessa%2C+J%C3%A9r%C3%A9mie&rft.au=Strozecki%2C+Yann&rft.date=2025-09-01&rft.issn=0020-0255&rft.volume=711&rft.spage=122104&rft_id=info:doi/10.1016%2Fj.ins.2025.122104&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ins_2025_122104 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-0255&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-0255&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-0255&client=summon |