1,398 research outputs found
Mathematical Model of the Impulses Transformation Processes in Natural Neurons for Biologically Inspired Control Systems Development
Abstract. One of the trends in the development of control systems for autonomous mobile robots is the approach of using neural networks with biologically plausible architecture. Formal neurons do not take into account some important properties of a biological neuron, which are necessary for this task. Namely -a consideration of the dynamics of data changing in neural networks; difficulties in describing the structure of the network, which cannot be reduced to the known regular architectures; as well as difficulties in the implementation of biologically plausible learning algorithms for such networks. Existing neurophysiological models of neurons describe chemical processes occurring in a cell, which is too low level of abstraction. The paper proposes a neuron's model, which is devoid of disadvantages described above. The feature of this model is description cell possibility with treestructured architecture dendrites. All functional changes are formed by modifying structural organization of membrane and synapses instead of parametric tuning. The paper also contains some examples of neural structures for motion control based on this model of a neuron and similar to biological structures of the peripheral nervous system
Synthesis of neural networks for spatio-temporal spike pattern recognition and processing
The advent of large scale neural computational platforms has highlighted the
lack of algorithms for synthesis of neural structures to perform predefined
cognitive tasks. The Neural Engineering Framework offers one such synthesis,
but it is most effective for a spike rate representation of neural information,
and it requires a large number of neurons to implement simple functions. We
describe a neural network synthesis method that generates synaptic connectivity
for neurons which process time-encoded neural signals, and which makes very
sparse use of neurons. The method allows the user to specify, arbitrarily,
neuronal characteristics such as axonal and dendritic delays, and synaptic
transfer functions, and then solves for the optimal input-output relationship
using computed dendritic weights. The method may be used for batch or online
learning and has an extremely fast optimization process. We demonstrate its use
in generating a network to recognize speech which is sparsely encoded as spike
times.Comment: In submission to Frontiers in Neuromorphic Engineerin
Brain in the data : neurotechnology in AI systems and management applications
Article translated from Russian. First published in: ΠΠ³Π΅Π΅Π² Π.Π. ΠΠ΅ΠΉΡΠΎΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π² ΡΠΈΡΡΠ΅ΠΌΠ°Ρ
ΠΈΡΠΊΡΡΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ½ΡΠ΅Π»Π»Π΅ΠΊΡΠ° ΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ Π² ΡΡΠ΅ΡΠ΅ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ, Π² ΠΊΠ½ΠΈΠ³Π΅ Π‘ΠΎΡΠΈΠΎΠ³ΡΠΌΠ°Π½ΠΈΡΠ°ΡΠ½ΡΠ΅ Π°ΡΠΏΠ΅ΠΊΡΡ ΡΠΈΡΡΠΎΠ²ΡΡ
ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ°ΡΠΈΠΉ ΠΈΡΠΊΡΡΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ½ΡΠ΅Π»Π»Π΅ΠΊΡΠ° ΠΏΠΎΠ΄ ΡΠ΅Π΄Π°ΠΊΡΠΈΠ΅ΠΉ Π.Π. ΠΠ΅ΠΏΡΠΊΠΎΠ³ΠΎ, Π.Π. Π Π°ΠΉΠΊΠΎΠ²Π°. ΠΠΎΡΠΊΠ²Π°, ΠΠΎΠ³ΠΈΡΠΎ-Π¦Π΅Π½ΡΡ. 2022. 308 Ρ. (201-212). (V.E. Lepsky/ A.N. Raikov, Socio-humanitarian Aspects of Digital Transformations and Artificial Intelligence, Kogito Center, Moscow 2022, 201-212)
The Software Continuum Concept: Towards a Biologically Inspired Model for Robust E-Business Software Automation
This paper introduces a new concept, the software continuum concept based on the observation that exists a general parallelism between the software continuum from bits to business/Internet ecosystems and the natural continuum from particles to ecosystems. The general parallelism suggests that homeomorphisms may be identified and therefore some concepts, processes, and/or mechanisms in one continuum can be investigated for application in the other continuum. We argue that the homeomorphisms give rise to a biologically-inspired architectural framework for addressing robust control, robust intelligence, and robust autonomy issues in e-business software and other business-IT integration challenges. As application, we examine the mapping of a major enterprise-level architecture framework to the biologically-inspired framework. Design considerations for robust intelligence and autonomy in large-scale software automation and some major systemic features for flexible business-IT integration are also discussed
ΠΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΠΎΠΉ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π΅ΠΉΡΠΎΠ½Π° ΡΠΎ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠ΅ΠΉ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ
Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π²Π°ΡΠΈΠ°Π½ΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΠΎΠΉ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π΅ΠΉΡΠΎΠ½Π° Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡΡ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. ΠΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ Π°Π½Π°Π»ΠΈΠ· ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
Π½Π΅ΠΉΡΠΎΠ½Π½ΡΡ
ΡΠ΅ΡΠ΅ΠΉ. ΠΠ΅Π»Π°Π΅ΡΡΡ Π²ΡΠ²ΠΎΠ΄ ΠΎ ΠΊΡΠ°ΠΉΠ½Π΅ Π½ΠΈΠ·ΠΊΠΎΠΌ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅ ΡΠ°Π±ΠΎΡ ΠΏΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π½Π΅ΠΉΡΠΎΠ½Π°. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π΅ΠΉΡΠΎΠ½Π° Π΄Π»Ρ Π΄Π°Π½Π½ΠΎΠΉ ΡΠ°Π±ΠΎΡΡ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²ΡΠ²Π°Π΅ΡΡΡ Π²ΡΠ±ΠΎΡ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΠΎΠΉ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ. ΠΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΊΡΠ°ΡΠΊΠΎΠ΅ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΡΠ°ΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ, ΠΎΡΠΌΠ΅ΡΠ΅Π½Ρ Π΅Ρ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠ΅ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡ Π΅Ρ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠ΅ ΡΠ΅ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅. ΠΠΏΠΈΡΡΠ²Π°Π΅ΡΡΡ ΡΠΏΠΎΡΠΎΠ± ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΊΠΎ Π²Ρ
ΠΎΠ΄Π½ΠΎΠΌΡ ΠΏΠ°ΡΡΠ΅ΡΠ½Ρ ΠΈΠΌΠΏΡΠ»ΡΡΠΎΠ². ΠΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΎΠ±ΡΠ°Ρ ΡΡ
Π΅ΠΌΠ° ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
Π½Π΅ΠΉΡΠΎΠ½ΠΎΠ² Π² ΡΠ΅ΡΡ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΈΡΠ»ΠΎΠ²ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π² ΠΏΠ°ΡΡΠ΅ΡΠ½Ρ ΠΈΠΌΠΏΡΠ»ΡΡΠΎΠ² Π²ΡΠ±ΠΈΡΠ°Π΅ΡΡΡ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ΅ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΊΡΠ°ΡΠΊΠΈΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΠΏΠΎ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π½Π° ΠΎΠ±ΡΠ΅Π΄ΠΎΡΡΡΠΏΠ½ΡΡ
Π½Π°Π±ΠΎΡΠ°Ρ
Π΄Π°Π½Π½ΡΡ
(Iris, MNIST). ΠΠ΅Π»Π°Π΅ΡΡΡ Π²ΡΠ²ΠΎΠ΄ ΠΎ ΡΠΎΠΏΠΎΡΡΠ°Π²ΠΈΠΌΠΎΡΡΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠΌΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ. ΠΡΠΎΠΌΠ΅ ΡΠΎΠ³ΠΎ, ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΠΎΠ΅ ΠΏΠΎΡΠ°Π³ΠΎΠ²ΠΎΠ΅ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΠΏΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΠ΅Π»Π΅ΡΠΏΡΠ°Π²Π»ΡΠ΅ΠΌΠΎΠ³ΠΎ Π½Π΅ΠΎΠ±ΠΈΡΠ°Π΅ΠΌΠΎΠ³ΠΎ ΠΏΠΎΠ΄Π²ΠΎΠ΄Π½ΠΎΠ³ΠΎ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ°: ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡ ΡΠ°ΠΊΠΎΠ³ΠΎ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ° Π΄ΠΎ Π΄Π½Π° ΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ° Π΅Π³ΠΎ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠ΅ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΡΠ΅Π°Π»ΡΠ½ΠΎΠΌΡ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΠ΅Π»Π΅ΡΠΏΡΠ°Π²Π»ΡΠ΅ΠΌΠΎΠ³ΠΎ Π½Π΅ΠΎΠ±ΠΈΡΠ°Π΅ΠΌΠΎΠ³ΠΎ ΠΏΠΎΠ΄Π²ΠΎΠ΄Π½ΠΎΠ³ΠΎ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ°. Π‘Π΄Π΅Π»Π°Π½ Π²ΡΠ²ΠΎΠ΄ ΠΎ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π½Π΅ΠΉΡΠΎΠ½Π° Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡΡ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ ΠΏΡΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΈ Π·Π°Π΄Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠΈΠ΅ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΡΠ΅ ΠΏΡΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΈΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΡΡ
Π½Π° ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
ΠΌΠΎΠ΄Π΅Π»ΡΡ
Π½Π΅ΠΉΡΠΎΠ½Π°
ΠΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΠΎΠΉ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π΅ΠΉΡΠΎΠ½Π° ΡΠΎ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠ΅ΠΉ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ
The problem of classification using a compartmental spiking neuron model is considered. The state of the art of spiking neural networks analysis is carried out. It is concluded that there are very few works on the study of compartmental neuron models. The choice of a compartmental spiking model is justified as a neuron model for this work. A brief description of such a model is given, and its main features are noted in terms of the possibility of its structural reconfiguration. The method of structural adaptation of the model to the input spike pattern is described. The general scheme of the compartmental spiking neuronsβ organization into a network for solving the classification problem is given. The time-to-first-spike method is chosen for encoding numerical information into spike patterns, and a formula is given for calculating the delays of individual signals in the spike pattern when encoding information. Brief results of experiments on solving the classification problem on publicly available data sets (Iris, MNIST) are presented. The conclusion is made about the comparability of the obtained results with the existing classical methods. In addition, a detailed step-by-step description of experiments to determine the state of an autonomous uninhabited underwater vehicle is provided. Estimates of computational costs for solving the classification problem using a compartmental spiking neuron model are given. The conclusion is made about the prospects of using spiking compartmental models of a neuron to increase the bio-plausibility of the implementation of behavioral functions in neuromorphic control systems. Further promising directions for the development of neuromorphic systems based on the compartmental spiking neuron model are considered.Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π²Π°ΡΠΈΠ°Π½ΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΠΎΠΉ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π΅ΠΉΡΠΎΠ½Π° Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡΡ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. ΠΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ Π°Π½Π°Π»ΠΈΠ· ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
Π½Π΅ΠΉΡΠΎΠ½Π½ΡΡ
ΡΠ΅ΡΠ΅ΠΉ. ΠΠ΅Π»Π°Π΅ΡΡΡ Π²ΡΠ²ΠΎΠ΄ ΠΎ ΠΊΡΠ°ΠΉΠ½Π΅ Π½ΠΈΠ·ΠΊΠΎΠΌ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅ ΡΠ°Π±ΠΎΡ ΠΏΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π½Π΅ΠΉΡΠΎΠ½Π°. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π΅ΠΉΡΠΎΠ½Π° Π΄Π»Ρ Π΄Π°Π½Π½ΠΎΠΉ ΡΠ°Π±ΠΎΡΡ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²ΡΠ²Π°Π΅ΡΡΡ Π²ΡΠ±ΠΎΡ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΠΎΠΉ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ. ΠΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΊΡΠ°ΡΠΊΠΎΠ΅ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΡΠ°ΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ, ΠΎΡΠΌΠ΅ΡΠ΅Π½Ρ Π΅Ρ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠ΅ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡ Π΅Ρ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠ΅ ΡΠ΅ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅. ΠΠΏΠΈΡΡΠ²Π°Π΅ΡΡΡ ΡΠΏΠΎΡΠΎΠ± ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΊΠΎ Π²Ρ
ΠΎΠ΄Π½ΠΎΠΌΡ ΠΏΠ°ΡΡΠ΅ΡΠ½Ρ ΠΈΠΌΠΏΡΠ»ΡΡΠΎΠ². ΠΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΎΠ±ΡΠ°Ρ ΡΡ
Π΅ΠΌΠ° ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
Π½Π΅ΠΉΡΠΎΠ½ΠΎΠ² Π² ΡΠ΅ΡΡ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΈΡΠ»ΠΎΠ²ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π² ΠΏΠ°ΡΡΠ΅ΡΠ½Ρ ΠΈΠΌΠΏΡΠ»ΡΡΠΎΠ² Π²ΡΠ±ΠΈΡΠ°Π΅ΡΡΡ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ΅ ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΊΡΠ°ΡΠΊΠΈΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΠΏΠΎ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π½Π° ΠΎΠ±ΡΠ΅Π΄ΠΎΡΡΡΠΏΠ½ΡΡ
Π½Π°Π±ΠΎΡΠ°Ρ
Π΄Π°Π½Π½ΡΡ
(Iris, MNIST). ΠΠ΅Π»Π°Π΅ΡΡΡ Π²ΡΠ²ΠΎΠ΄ ΠΎ ΡΠΎΠΏΠΎΡΡΠ°Π²ΠΈΠΌΠΎΡΡΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠΌΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ. ΠΡΠΎΠΌΠ΅ ΡΠΎΠ³ΠΎ, ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΠΎΠ΅ ΠΏΠΎΡΠ°Π³ΠΎΠ²ΠΎΠ΅ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΠΏΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΠ΅Π»Π΅ΡΠΏΡΠ°Π²Π»ΡΠ΅ΠΌΠΎΠ³ΠΎ Π½Π΅ΠΎΠ±ΠΈΡΠ°Π΅ΠΌΠΎΠ³ΠΎ ΠΏΠΎΠ΄Π²ΠΎΠ΄Π½ΠΎΠ³ΠΎ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ°: ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡ ΡΠ°ΠΊΠΎΠ³ΠΎ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ° Π΄ΠΎ Π΄Π½Π° ΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ° Π΅Π³ΠΎ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠ΅ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΡΠ΅Π°Π»ΡΠ½ΠΎΠΌΡ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΠ΅Π»Π΅ΡΠΏΡΠ°Π²Π»ΡΠ΅ΠΌΠΎΠ³ΠΎ Π½Π΅ΠΎΠ±ΠΈΡΠ°Π΅ΠΌΠΎΠ³ΠΎ ΠΏΠΎΠ΄Π²ΠΎΠ΄Π½ΠΎΠ³ΠΎ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ°. Π‘Π΄Π΅Π»Π°Π½ Π²ΡΠ²ΠΎΠ΄ ΠΎ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π½Π΅ΠΉΡΠΎΠ½Π° Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡΡ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ ΠΏΡΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΈ Π·Π°Π΄Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠΈΠ΅ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΡΠ΅ ΠΏΡΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΈΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΡΡ
Π½Π° ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ½ΡΡ
ΡΠΏΠ°ΠΉΠΊΠΎΠ²ΡΡ
ΠΌΠΎΠ΄Π΅Π»ΡΡ
Π½Π΅ΠΉΡΠΎΠ½Π°
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