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1Mixed Materials
Additional Titles: Recent advancements in Transformer-based architectures have led to impressive breakthroughs in natural language processing tasks, with models such as GPT-4, Claude, and Gemini demonstrating human-level reasoning abilities. However, despite their high performance, concerns remain about the inherent limitations of these models, especially when it comes to learning basic logical functions. While complexity-theoretic analyses indicate that Transformers can represent simple logic functions (e.g., $\mathsf{AND}$, $\mathsf{OR}$, and majority gates) by its nature of belonging to the $\mathsf{TC}^0$ class, these results assume ideal parameter settings and do not account for the constraints imposed by gradient descent-based training methods. In this work, we investigate whether Transformers can truly learn simple majority functions when trained using gradient-based methods. We focus on a simplified variant of the Transformer architecture and consider both $n=\mathrm{poly}(d)$ and $n=\exp(Ω(d))$ number of training samples, where each sample is a $d$-size binary string paired with the output of a basic majority function. Our analysis demonstrates that even after $\mathrm{poly}(d)$ gradient queries, the generalization error of the Transformer model still remains substantially large, growing exponentially with $d$. This work highlights fundamental optimization challenges in training Transformers for the simplest logical reasoning tasks and provides new insights into their theoretical limitations.
Authors: Chen, Bo, Shi, Zhenmei, Song, Zhao, Zhang, Jiahao
Index Terms: Machine Learning, Artificial Intelligence, Computational Complexity, text
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2Conference
Source: 2014 37th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO) Information and Communication Technology, Electronics and Microelectronics (MIPRO), 2014 37th International Convention on. :856-860 May, 2014
Relation: 2014 37th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO)
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3Book
Additional Titles: During the production and processing of food, large quantities of waste are generated which need to be properly stored and, at best, found new use and utilized. An extremely large problem worldwide is certainly the large amount of agroindustrial waste that is generated on a daily and especially annual basis. If agroindustrial waste is directly stored in the environment, it causes a greenhouse effect and is a large-scale environmental problem. However, agroindustrial waste has recently been regarded as an extremely valuable raw material that can be converted into an added-value raw material by applying different biotechnological approaches. Accordingly, this doctoral dissertation deals with the global problem of utilization and quality improvement of various agro-industrial wastes through the application of biotechnology. Modification and improvement of quality is achieved by growing the production microorganism on a solid surface, that is, agroindustrial waste. This is a rather new method which involves the use of cheap materials but they usually contain large amount of protein, sugar and mineral as well as bioactive compounds such as polyphenols, carotenoids and dietary fibers. Accordingly, the first part of this doctoral dissertation is the selection of the microorganism producer. During the selection, a rich collection of various commercial and natural bacterial strains was utilized, which is available at the Department of Biochemical Engineering and Biotechnology, Faculty of Technology and Metallurgy. Various strains have been tested for the ability to produce α-amylase, cellulase, pectinase and protease using selective medium on agar plates. In this way, one of the Bacillus strains was found to be particularly prominent in the production of targeted enzymes. Due to the fact that this strain is a natural isolate, identification by sequencing 16SrRNA encoding gene and subsequent analysis of the obtained sequence using the BLAST (Basic Logical Alignment Search Too
Authors: Knežević-Jugović, Zorica, Mojović, Ljiljana, Antov, Mirjana, Luković, Nevena, Šekuljica, Nataša, Salim, Abdalla Ali
Index Terms: hydrolytic enzymes production, soli-state ferementation, agroindustrial waste, antinutritional factors, biological activity, proizvodnja hidrolitičkih enzima, fermentacija na čvrstoj podlozi, agroindustrijski otpad, antinutritivni faktori, biološka aktivnost, doctoralThesis
URL:
https://uvidok.rcub.bg.ac.rs/bitstream/handle/123456789/3854/Referat.pdf https://eteze.bg.ac.rs/application/showtheses?thesesId=8746 https://fedorabg.bg.ac.rs/fedora/get/o:26334/bdef:Content/download https://plus.cobiss.net/cobiss/sr/sr/bib/70924297 https://nardus.mpn.gov.rs/handle/123456789/20632 http://nardus.mpn.gov.rs/bitstream/id/145484/Izvestaj_Komisije_12451.pdf http://nardus.mpn.gov.rs/bitstream/id/145483/Disertacija_12451.pdf https://hdl.handle.net/21.15107/rcub_nardus_20632 -
4Periodical
Authors: Chavdarov, Anatoliy V, primary
Source: JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES. 2020/06/28
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5Academic Journal
Source: Cognitive Science. 47(2)
Subject Terms: 5204 Cognitive and Computational Psychology (for-2020), 52 Psychology (for-2020), Basic Behavioral and Social Science (rcdc), Behavioral and Social Science (rcdc), Humans (mesh), Problem Solving (mesh), Logic (mesh), Learning (mesh), Logic, Rule-learning, Pattern recognition, Hierarchical reasoning, Bayesian modeling, Logic, Rule-learning, Pattern recognition, Hierarchical reasoning, Bayesian modeling, Humans (mesh), Learning (mesh), Problem Solving (mesh), Logic (mesh), Bayesian modeling, Hierarchical reasoning, Logic, Pattern recognition, Rule-learning, Humans (mesh), Problem Solving (mesh), Logic (mesh), Learning (mesh), 0801 Artificial Intelligence and Image Processing (for), 1701 Psychology (for), 1702 Cognitive Sciences (for), Experimental Psychology (science-metrix), 5201 Applied and developmental psychology (for-2020), 5202 Biological psychology (for-2020), 5204 Cognitive and computational psychology (for-2020)
File Description: application/pdf
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6Academic Journal
Authors: Xu, Chaoyou, Wu, Wenshuo, Su, Jie ⁎, Guo, Fengxu, Wang, Yiran, Liu, Haoran, Zhang, Zhiheng, Xu, Ting ⁎
Linked Full TextSource: In Chemical Engineering Journal 15 October 2025 522
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7Academic Journal
Authors: H, Yoshida, M, Iwahashi, M, Tonoike, M, Yamaguchi, T, Hamada
Source: NeuroReport. 10:953-957
Subject Terms: Adult, Male, 0301 basic medicine, 0303 health sciences, Magnetoencephalography, Magnetic Resonance Imaging, Association, 03 medical and health sciences, Mental Processes, Acoustic Stimulation, Parietal Lobe, Evoked Potentials, Auditory, Reaction Time, Humans, Female
Access URL: https://pubmed.ncbi.nlm.nih.gov/10321466
Linked Full Text -
8Academic Journal
Authors: H, Yoshida, M, Iwahashi, M, Yamaguchi, M, Tonoike
Source: NeuroReport. 9:1261-1265
Subject Terms: Adult, Cerebral Cortex, Thinking, 0301 basic medicine, Brain Mapping, 0303 health sciences, 03 medical and health sciences, Acoustic Stimulation, Logic, Humans, Functional Laterality
Access URL: https://pubmed.ncbi.nlm.nih.gov/9631409
Linked Full Text -
9Academic Journal
Authors: Mine, Hisashi, Koga, Yoshiaki
Source: IEEE Transactions on Electronic Computers IEEE Trans. Electron. Comput. Electronic Computers, IEEE Transactions on. EC-16(3):282-289 Jun, 1967
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10Academic Journal
Authors: Veerasamy, B.Aff1, Vinoth Raj, R.Aff2, IDs10825026025758_cor1, Manikandan, S. P.Aff3, Poovannan, E.Aff3, Aff4
Source: Journal of Computational Electronics. 25(3)
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11Dissertation/ Thesis
Authors: Cesana Arlotti, Nicolò
Contributors: University/Department: Universitat Pompeu Fabra. Departament de Ciències Experimentals i de la Salut
Thesis Advisors: Bonatti, Luca
Source: TDX (Tesis Doctorals en Xarxa)
Subject Terms: Logic, Development, Infants, Eye-tracker, Cognition, Lógica, Desarrollo, Bebé, Cognición, Preverbal
File Description: application/pdf
Access URL: http://hdl.handle.net/10803/402199
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12Conference
Authors: Choudhary, Dinesh Kumar, Ajnar, D. S., Mahant, Rupali, Gurjar, R. C., Khatri, Rajesh, Yadav, Anand
Source: 2025 IEEE International Conference on Advances in Computing Research On Science Engineering and Technology (ACROSET) Advances in Computing Research On Science Engineering and Technology (ACROSET), 2025 IEEE International Conference on. :1-5 Sep, 2025
Relation: 2025 IEEE International Conference on Advances in Computing Research On Science Engineering and Technology (ACROSET)
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13Academic Journal
Authors: Santoianni, Flavia, Ciasullo, Alessandro, Sodano, Noemi
Source: RESEARCH TRENDS IN HUMANITIES Education & Philosophy; Vol. 8 (2021): RTH - Education & Philosophy; 13-30 ; RESEARCH TRENDS IN HUMANITIES Education & Philosophy; V. 8 (2021): RTH - Education & Philosophy; 13-30 ; 2284-0184
Subject Terms: spatial education, spatial skills training, basic logic theory, basic logical processing, cognitive processing, educazione spaziale, formazione di abilità spaziali, teoria delle logiche di base, elaborazione logica di base, elaborazione cognitiva
File Description: application/pdf
Relation: https://serena.sharepress.it/rth/article/view/7621/8474; https://serena.sharepress.it/rth/article/view/7621
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14Conference
Source: 2017 IEEE II International Conference on Control in Technical Systems (CTS) Control in Technical Systems (CTS), 2017 IEEE II International Conference on. :289-292 Oct, 2017
Relation: 2017 IEEE II International Conference on Control in Technical Systems (CTS)
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15Conference
Authors: Salazar, Manuel Ortiz, Torres-Trevino, Luis M.
Source: 2014 13th Mexican International Conference on Artificial Intelligence Artificial Intelligence (MICAI), 2014 13th Mexican International Conference on. :112-117 Nov, 2014
Relation: 2014 13th Mexican International Conference on Artificial Intelligence (MICAI)
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16Academic Journal
Authors: Flower, Nigel ⁎, Pylkkänen, Liina
Source: In Cognition May 2026 270
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17Conference
Source: 2024 IEEE 33rd Asian Test Symposium (ATS) Asian Test Symposium (ATS), 2024 IEEE 33rd. :1-6 Dec, 2024
Relation: 2024 IEEE 33rd Asian Test Symposium (ATS)
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18Academic Journal
Authors: Chen, Henghao, Chen, Hao, Chan, Erwin H.W. ⁎
Linked Full TextSource: In Optics and Laser Technology March 2024 170
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19Periodical
Alternate Title: Basic Dimensions and Future Prospects of Wushu Oral History Research from the Perspective of Digital Humanities.
Source: Journal of Beijing Sport University. 2026, Vol. 49 Issue 6, p137-145. 9p.
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20Academic Journal
Authors: Hijazeen, Rima A.1 r.hijazeen@ju.edu.jo, Yousef, Al-Motassem2 ayousef@ju.edu.jo, Almousa, Ahmed3 a.almousa@ju.edu.jo, Alzoghair, Aya N.4 ayaalzoghair3@gmail.com, Dwairi, Jude K.5 dwairi2002@yahoo.com, Sawaqed, Majd I.4 majdsawaqed@hotmail.com, Ryahneh, Ghaith F. Al4 Ghaithfadi02@gmail.com, Ali, Marwan H.4 marwanalsheikh9@gmail.com
Source: Pharmacy Practice (1886-3655). Apr-Jun2026, Vol. 24 Issue 2, p1-10. 10p.
Subject Terms: Generative artificial intelligence, Pharmacology, Intellect, Medical logic, Medical education, Data analysis, Descriptive statistics, Professional licensure examinations, Educational tests & measurements, Chi-squared test, Natural language processing, Data analysis software, Computer assisted testing (Education)