Self-supervised Learning in Symbolic Classification

Xenia Naidenova

and Sergey Kurbatov

Military medical academy, Lebedev Street, Saint Petersburg, Russia

Research Centre of Electronic Computer Engineering, Moscow, Russia

Keywords: Self-learning, intelligent agent, good classification test, internal learning context, external learning context.

Abstract: A new approach to modelling self-supervised learning for automated constructing and improving algorithms

of inferring logical rules from examples is advanced. As a concrete model, we consider the process of inferring

good maximally redundant classification tests or minimal formal concepts. The concepts of external and

internal learning contexts are introduced. A model of an intelligent agent capable of improving its learning

process is considered. It is shown that the same learning algorithm can be used in both external and internal

learning contexts.

INTRODUCTION

Self-learning embodies one of the essential properties

of the human intelligence related to an internal

evaluation of the quality of mental processes. Vukman

and Demetriou (2011, p. 37) suggest that the mind has

a three-level hierarchical structure. The first level

interfaces directly with the environment and it

includes several specialized capacity systems

addressed to representing and processing different

domains of the environment. The remaining two levels

cover goal elaborating mechanisms, assessments of

the proximity to the goal, algorithms defining the

ability to present and process information on the first

level, and (third level) the hypercognitive processes

related to self-consciousness and self- regulation.

Empirical research of Vukman and Demetriou

(2011, p. 38) has revealed that the first level covers 6

specific domains of thought: (1) the categorical

system (deals with similarity-difference relations and

classifications); (2) the quantitative system (deals

with quantitative variations and relations in the

environment); (3) the causal system for revealing

cause-effect relations; (4) the system for evaluating

spatial orientation and representation of the

environment in images; (5) the system of formal logic

(deals with the truth/falsity and the validity/invalidity

of the flow of information); (6) the system for

evaluating the social relations.

https://orcid.org/0000-0003-2377-7093

https://orcid.org/0000-0002-0037-9335

The second level is responsible for the complexity

and efficiency of information processing at the first

level at any given time. Operations of this level set

the speed of information processing, realize the

control of thinking processes, and direct the attention

to important stimulus and prohibit irrelevant ones.

This level also includes working memory.

The hypercognition includes self-awareness and

self-regulation of knowledge and strategies operating

as the interface between (a) mind and reality, and (b)

any of the various systems and processes of mind. The

hypercognitive level has two components: the

working hypercognition and the long term

hypercognition. The first component is responsible

for setting goals, planning, and monitoring the

achievement of goals, including responsibility for

updating goals and sub-goals. The self-consciousness

is an integral part of the hypercognitive system. The

component of long-term hypercognition involves the

internal representation of past cognitive experience.

Our analysis of modern research has been

implemented in the following directions: modeling of

self-learning (self-supervised learning) and learning

in robots and robotic systems. In artificial

intelligence, the theory of self-learning is still in the

formation, the practical results are obtained mainly in

the modeling of robot management. In the second

direction, it is particularly interesting the principles

and technologies of creating a robot that can move in

Naidenova, X. and Kurbatov, S.

Self-supervised Learning in Symbolic Classiﬁcation.

DOI: 10.5220/0010732700003101

In Proceedings of the 2nd International Conference on Big Data, Modelling and Machine Learning (BML 2021), pages 289-294

ISBN: 978-989-758-559-3

289

the environment, manipulate objects and avoid

obstacles (Pillai, 2017). The self-learning robot

should be aware of its own localization and have an

internal reflection of spatial situation. It is declared by

the author (Pillai & Leonard, 2017) that the robot

should be self-esteemed and self-managed on the

basis of previous experience. It must constantly adapt

its spatial and semantic models, improving the

performance of its tasks. Some concepts and

algorithms are proposed to evaluate the robot's own

movement (Self-Supervised Visual Ego Motion

Learning) (Sofman, Line et al., 2017). Note that such

a robot has not yet been implemented but the concept

of self-learning proposed by the author coincides with

the concept of self-learning offered by us.

In (Pathak, Agraval, et al., 2017), the role of

curiosity in self-learning is analyzed and the concept

of self-learning with the phenomenon of curiosity is

developed.

In (Shaukat, Burroughe & Gao, 2015), a robot’s

internal evaluation of its future path cost is proposed

on the basis of the probabilistic Bayesian method.

In some works, the authors propose the use of

robot’s manipulation reflection in learning algorithms

for improving and accelerating robot’s training. For

example, industrial Robot of Japanese Company

Fanuc uses a method known as "training with

reinforcement" to grab objects by a manipulator. In

this process, a robot fixes its work on video and uses

this video for correcting own activity. Domestic

development of robots is based on the use of artificial

neural networks (Pavlovsky & Savitsky, 2016;

Pavlovsky V.E. & Pavlovsky V.V., 2016; Pavlovsky

et al., 2016).

In paper (Bretan et al., 2019), the authors

introduce “Collaborative Network Training” – a self-

supervised method for training neural networks for

learning robots. This method covers task objective

functions, generates continuous-space actions, and

performs an optimization for achieving a desired task.

Also, the method allows learning parameters when a

process for measuring performance is available, but

labelled data is unavailable. The method involves

three randomly initialized independent networks that

use ranking to train one another on a single task.

Major improvements in time and data eﬃciency to

learn robot are achieved in (Berscheid, Rühr &

Kröger, 2019). Using a relatively small, fully-

convolutional neural network, it is possible predict

grasp and gripper parameters with great advantages in

training as well as inference performance. Motivated

by the small random grasp success rate of around 3%,

the grasp space was explored in a systematic manner.

The ﬁnal system was learned with 23000 grasp

attempts in around 60h, improving current solutions

by an order of magnitude. The authors measured a

grasp success rate of (96.6±1.0) %.

To model a self-learning process, we focus on the

logical or symbolic supervised methods of machine

learning. This mode of learning covers mining logical

rules and dependencies from data: “if-then” rules,

decision trees, functional, and associative

dependencies. This learning is also used for

extracting concept from data sets, constructing rough

sets, hierarchical classification of objects, mining

ontology from data, generating hypotheses, and some

others (Kotsiantis, 2007; Naidenova, 2012). It has

been proven in (Naidenova, 1996) that the tasks of

mining all logical dependencies from data sets are

reduced to approximating a given classification

(partitioning) on a given set of object descriptions.

The search for the best approximation of a given

object classification leads to the definition of a

concept of good classification (diagnostic) test firstly

introduced in (Naidenova & Polegaeva, 1986). A

good classification test has a dual nature. On the one

hand, it makes up a logical expression in the form of

implication, associative or functional dependency. On

the other hand, it generates the partition of a training

set of objects equivalent to a given classification

(partitioning) of this set or the partition that is the

nearest one to the given classification with respect to

the inclusion relation between partitions

(Cosmadakis, Kanellakis & Spiratos, 1986,

Naidenova, 2012). It means that inferring good

classification tests gives the least possible number of

functional or implicative dependencies.

Table 1: Example of dataset (adopted, (Ganascia, 1989)).

dex of object

Height

Color of

hair

Color o

eyes

Class

1 Low Blon

Blue 1

2 Low Brown Blue 2

3 Tall Brown Hazel 2

4TallBlon

Hazel 2

5TallBrown Blue 2

6 Low Blon

Hazel 2

7TallRe

Blue 1

8TallBlon

Blue 1

It means also that good classification tests have

the most possible generalization properties with

respect to object class descriptions. We consider two

ways for giving classifications: (1) by a target

attribute KL or (2) by value v of a target attribute. In

Table 1, an example of object classification is given.

The target attribute partitions a given set of

objects into disjoint classes the number of which is

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equal to the number of values of this attribute. The

target value of attribute partitions a given set of

objects into two disjoint classes: the objects in

description of which the target value appears (positive

objects); all the other objects (negative objects). The

problem of machine learning to approximate a given

classification consists in solving the following tasks:

Given attribute KL, to infer logical rules of the

form:

A B C → KL or D S → KL or …or A S Q V →

KL,

where A, B, C, D, Q, S, V – the names of

attributes.

Given value v of attribute KL, to infer logical rules

of the form:

if ((value of attribute А = “а”) & (value of

attribute В = “b”) & …, then (value of attribute KL =

“v”).

Rules of the first form are functional

dependencies as they are determined in the relational

data base theory. Rules of the second form are

implicative dependencies. The left parts of rules can

be considered as the descriptions of given

classifications or classes of objects. In our approach

to logical rules mining, the left parts of these rules

constitute classification tests. Implicative assertions

describe regular relationships connecting objects,

properties, and classes of objects. Knowing the

implication enables one to mine a whole class of

implicative assertions including not only simple

implication (a, b, c → d), but also forbidden assertion

(a, b, c → false (never)), diagnostic assertion (x, d →

a; x, b → not a; d, b → false), assertion of alternatives

(a or b → true (always); a, b → false), compatibility

(a, b, c → VA, where VA is the occurrence’s

frequency of rule).

We propose, in this paper, an idea of a deeper

level of self-learning allowing to manage the process

of inferring good tests in terms of its effectiveness

through an internal monitoring and evaluation of this

process and the development of rules for choosing the

best strategies (algorithms), and learning

characteristics.

Let's call a set of given objects with a class-

partitioning an external or application context. The

internal or reconfiguration level implements the

analysis and evaluation of the process of inferring

classification rules in the external context allowing to

identify the relationships between the external

contexts (sub-contexts) and the parameters of

learning process.

SOFTWARE AGENT CAPABLE

OF SELF-LEARNING

In the tasks of logical rule inference, the objects in the

external context (training samples) are described in

terms of their properties (features, attributes) and they

are specified by splitting into classes. The task of

learning is to find rules in each given context in order

to repeat the classification of objects represented by

splitting objects into disjoint classes. The learning

algorithms have a number of convenient properties

for self-monitoring the process of inferring tests

(Naidenova & Parkhomenko, 2020): a) external

context is decomposed into sub-contexts in which

good tests are inferred independently; b) sub-contexts

are chosen based on analysing their characteristics; c)

the choice of sub-context determines the speed and

efficiency of classification task. The strategies to

select sub-contexts and learning algorithms are easy

to describe with the use of special multi-valued

attributes.

Decomposition of context into sub-contexts

allows to reduce the problem of large dimension to

ones of smaller dimension and thereby to decrease the

computational complexity of the classification

problem.

Let us now introduce an intellectual agent

implementing the following functions.

First, the agent needs to memorize the situations

of learning and the activity associated with them (at

the application (external) level). Then the agent has to

evaluate the learning process in terms of its

effectiveness, temporal parameters, the number of

sub-contexts to be considered, the consistency

between the parameters of external contexts (sub-

contexts) and the parameters of the learning process.

Generalizing and simplifying the above, let's

assume

that the internal context necessarily contains:

Description of selected sub-context in terms

of its properties.

Description of selected learning steps.

Internal estimation of learning process with

the use of some given criteria of its efficiency.

THE STRUCTURE OF

INTERNAL CONTEXT

Let K be the descriptions of external sub-context via

its properties, А = {A1, A2, ….An} be the

descriptions of algorithms of good tests inferring via

their properties in this sub-context, R = {R1, R2,

….Rm} be the rules for selecting sub-contexts, and

Self-supervised Learning in Symbolic Classiﬁcation

291

V= {V1, V2, …, Vq) be the set of rule for evaluating

the process of good test inferring.

Then the internal context is described by the direct

product of sets K, A, R and its mapping on V: K × A×

R → V. A and R describe the learning process, V is an

internal evaluation of the learning process.

In order this assessment to be feasible as an

internal evaluation, the self-learning agent must have

some special functions of analysing the processes

taking place in it. One of these functions can be a

counter of the number of sub-contexts processed

during good test inferring, a counter of time requested

for processing sub-context, the calculator of the

relationship between the number of received good

tests in sub-context and some of its quantitative

characteristics (number of objects, number of

attributes, number of different attribute values), etc.

There are more simple variants of the internal

context:

K × A → V and K × R → V.

Now, to infer the logical rules for distinguishing

the variants of learning in the external context

evaluated as good ones from the variants evaluated as

not good ones, we can use any algorithms of inferring

good classification tests in the internal context.

A few algorithms for good test inferring have been

elaborated: ASTRA, DIAGARA, NIAGARA, and

INGOMAR (Naidenova, 2006; Naidenova &

Parkhomenko, 2020).

On the basis of internal learning, the agent can

select rules for more successful learning in solving

the main problem in the application context.

The internal context is a memory of the agent, the

rules extracted from the internal context represent the

agent's knowledge about the effectiveness of its

actions in the external context.

The practical implementation of self-learning in

this work is not developed. In the simplest case, we

can separate two processes in time: accumulating data

and forming an internal context (with an assessment

of the quality of learning) and building rules for

choosing sub-contexts by their characteristics. Once

these rules are received, they can be used to learn in

an external context and form a new internal one.

The internal context for choosing sub-contexts

can contain the following information:

The number of objects in sub-context.

The number of values of attributes in sub-

context.

The number of essential values of attributes

(Naidenova & Parkhomenko, 2020) in sub-

context.

The number of essential objects in sub- context

(1Naidenova & Parkhomenko, 2020).

The number of already obtained good tests

covered by sub-context.

The number of values of attributes (objects)

uncovered by already obtained good tests in sub-

context.

Some relationships between the characteristics of

sub-contexts listed above.

The strategies (rules) to select sub- contexts.

The evaluation of the process of external learning

(it gives the partition of accumulated data).

As a result of learning in this internal context we

obtain the rules revealing the connection between the

characteristics of sub-contexts and the strategies of

selecting them. Strategy can be: selecting sub-context

with the smallest number of essential values of some

attributes; selecting sub-context with the smallest

number of essential objects and some others.

Actions in the internal and external contexts can

be represented as actions of two agents functioning in

turn or in parallel and exchange data (Figure 1).

Figure 1. The interaction of two agents

Agent A1 transmits the data (the descriptions of

contexts, algorithms, rules for selecting sub-contexts)

to Agent A2. Agent A2 acts in the internal context

(obtained from agent A1) and passes to agent A1 the

rules, the latter applies these rules to select the best

variant of learning with each new external sub-

context.

For Agent A2, the internal context (memory)

should not be empty, but this agent (as well as Agent

A1) can work in an incremental mode of learning. A

few incremental algorithms for good test inferring in

symbolic contexts are proposed in (Naidenova, 2006;

Naidenova & Parkhomenko, 2020).

CONCLUSIONS

The results of this article are the following. A model

of self-learning was proposed allowing to manage the

process of inferring good tests in terms of its

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effectiveness through an internal evaluation of the

learning process and the development of rules for

choosing the best strategies, algorithms, and learning

characteristics. The concepts of internal and external

learning contexts were formulated. The structure of

the internal context was proposed. A model of

intelligent agent, capable of improving own learning

process of inferring good classification tests in the

external context was advanced.

It was shown that the same learning algorithm can

be used for supervised learning in the external and

internal contexts. The model of self-learning

proposed in this article is closely related to the

especially important research in artificial intelligence:

forming internal criteria of the learning process

efficiency, modelling on-line plausible deductive-

inductive reasoning on the level of self- learning.

ACKNOWLEDGEMENTS

The research was partially supported by Russian

Foundation for Basic Research, research project №

18-07-00098A

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