Ambiguity and diversity in human cognition can be regarded a final frontier in developing equivalent systems of artificial intelligence. Despite astonishing accomplishments, modern machine learning algorithms are still hardly more than adaptive systems. Deep neural networks, for example, represent complexity through complex connectivity but are not able to allow for abstraction and differentiation of interpretable knowledge, i.e., for key mechanisms of human cognition. Like support vector machines, random forests and other statistically motivated algorithms, they do neither reflect nor yield structures and strategies of human thinking. Therefore, we suggest to realign the use of existing machine learning tools with respect to the philosophical paradigm of constructivism, which currently is the key concept in human learning and professional teaching. Based on the idea that learning units like classifiers can be considered models with limited validity, we formulate five principles to guide a constructivist machine learning. We describe how to define such models and model limitations, how to relate them and how relationships allow to abstract and differentiate models. To this end, we propose the use of meta data for classifiers and other models. Moreover, we argue that such meta data-based machine learning results in a knowledge base that is both created by the means of automation and interpretable for humans.
Over the last decade, it has become widely accepted to
address computational systems intelligent. Not only
journalists, but also scientists have adapted this habit in their
publications. In fact, many classical engineering tasks like
monitoring or regulating have profited from the employment
of machine learning
A final frontier for learning systems, however, is the
variety of alternative cognitive functions observable in a
diverse set of individuals or from ambiguous stimuli
The main reason for this shortcoming is that so far both
algorithms and researchers have failed to incorporate a
constructivist point of view. Constructivism implies not only
cognition to be a highly individual phenomenon, but also
humans to take an active role in their perception of the world –
and that there is no such thing as a human-independent
reality
In the following, we introduce axioms that allow machine learning to follow constructivist principles. Key features of this approach are the use of modern tools from empirical sciences, model-oriented learning, the ability to handle ambiguity, the ability to integrate supervised and unsupervised learning into a unified framework, the ability to create an individual knowledge base and the ability to abstract, differentiate or discard learned knowledge automatically.
Since the introduction of artificial neural networks as a
theoretical concept
Functionalistic psychology explains cognitive functions
of humans by the concept of mental models
Philosophers, too, consider models an important tool in
human knowledge acquisition
Cybernetics, however, did neither reflect time-related
aspects nor issues involved with individual model subjects.
This matter was adressed by Herbert Stachowiak, who was
influenced by cybernetics when developing his General
Model Theory
Learning algorithms have been used for half a century
to transform sample data into models in a mathematical
sense, that is: into generalized mathematical relationships
between image and origin. The two major approaches or
objectives, known as supervised and unsupervised
learning, either do or do not require a given target parameter.
Artificial neural networks and their relatives are among the
most popular and prominent algorithms for learning with a
given target parameter
To some extent, machine learning parallels modern
education concepts. A construction process in the
constructivist sense may be matched by an unsupervised learning,
i.e., identifying clusterings or dimensionality reduction, and
can, e.g., be implemented with self-organizing maps,
kmeans, autoencoders or feature clustering
In order to automate and implement a deconstruction process, successfully learned models must be held available for comparison or re-training. More over, possible matchings with novel models must be identifiable in an unambiguous manner by calculation or logical operations, respectively. For Stachowiak models, features regarding validity limitations exist for any model employed, which allows to discriminate models. Here, we outline how such meta data can be identified for models created by machine learning.
Machine learning implies learning from examples termed training vectors. For a supervised training vector V resulting from sensor data, for instance, this implies
V = = (I; O) (i0; :::; im 1; o0; :::; on 1) with a m dimensional input I and a n dimensional output O.
A Stachowiak-like training vector V will, in addition, possess three pragmatic features: (1) (2) (3) (4) (5) (6) with
V = (V; TV ;
V ; ZV ) TV
V
=
ZV where TV is a point in time, and the infinite sets of model subjects Z
V and ZV are subsets of and of model purposes Z, respectively. When using sensor data as training data, T and for each vector may be given by sensor meta data and Z by the application context of the data collection.
If a machine learning-based model M is considered an approximation of n training vectors V with
M
fV0; :::; Vn 1g then meta data for a Stachowiak-like model M with = (M; TM;
M
can be derived from the underlying n Stachowiak-like
training vectors V
Vi ZM = [in=01ZVi (11) By extracting and administrating these meta data for every model a machine learning algorithm has learned, learned models become discriminable. Most importantly, overlaps or contradictions in model validity become thereby identifiable and may be resolved algorithmically.
4. Deconstructing models implies to either abstract, differentiate or discard them. Using the pragmatic features T , , Z of Stachowiak-like models as meta data, machine learning-generated models can be matched and discriminated automatically. In particular, this allows to implement learning through deconstruction of given models. With regard to the degree of meta data matching exposed by the respective models, four types of deconstruction operations will be distinguished here.
The degree of relationship between two given Stachowiak-like models Ma and Mb is termed 1. complete,
if TMa = TMb , Ma = 2. subjective-intentional ( Z),
if TMa 6= TMb , Ma = 3. temporal-intentional (T Z),
if TMa = TMb , Ma 6= 4. temporal-subjective (T ),
Mb , ZMa = ZMb .
Mb , ZMa = ZMb ;
Mb , ZMa = ZMb ; if TMa = TMb , Ma = Mb , ZMa 6= ZMb ;
The deconstruction of two completely related models can basically either confirm the congruency and validity of both models or render both invalid, which leads to both being discarded. As a third option, this deconstruction process allows to test whether the combination of both models may be split in two submodels of more limited temporal validity.
Two Z-related models Ma and Mb share a common set of model subjectives and model purposes, but differ in their temporal validity. Z deconstruction therefore builds and evaluates a temporal union of Ma and Mb; by this, the initial model is either replaced by a unified model with larger temporal validity – or left untouched.
Deconstruction of two T Z-related models Ma and Mb, which share a congruent temporal validity and a common set of model purposes but differ regarding their subjective validity, either promotes Ma to a model Mc of intersubjective validity – or leaves Ma untouched.
T deconstruction leaves two T -related models Ma and Mb untouched. Instead, it will construct novel models based on their outputs, yielding models of a higher level. This is possible only because Ma and Mb share a congruent temporal validity and a common set of model subjectives while differing in their model purpose. All together, a T deconstruction process can be regarded as a way of automated abstraction or generalization of knowledge. 5. A hierarchically ordered set of models constitutes an enriched knowledge base. Any set of models created by machine learning algorithms represents information inherited in the underlying training data and can therefore be considered a knowledge base. In a constructivist approach, however, each model of such a set possesses explicit validity limitations, which contributes additional knowledge and complexity. Temporal gaps in the knowledge base, e.g., can thereby be identified explicitly. A hierarchical ordering also indicates hot spots of abstraction, i.e., models of higher hierarchy levels.
The degree of abstraction and differentiation within such a knowledge base can be quantified by assessing the number of models, the average temporal validity, etc. Alternatively, this can be achieved by building and visualizing a meta databased ordering. Apart from their temporal validity, models of such a set can also be ordered according to their model purposes or level of abstraction, respectively. For uniform model subjects or identical learning algorithm, respectively, a three-dimensional plot may visualize both temporal extensions and the extend of successful abstraction.
Moreover, each individual model represents a supervised learning application, i.e., a classifier or regressor, and can be used as such after the knowledge base has been established. To this end, a hierarchically ordered set of models created by constructivist machine learning inherits not only structured, but also applicable knowledge. Models that match a given test sample – and are therein valid classifiers or regressors – can be identified by simply matching the meta data. Consequently, application of the knowledge base can be rejected in scenarios where no knowledge is available.
In the present work, we suggest principles for using existing machine learning algorithms with respect to constructivist theories of human learning. Based on five axioms introduced here, a constructivist approach of creating explainable knowledge can be implemented. This approch allows, in particular, to create an ambiguity-free knowledge base. While there is no restriction regarding potential applications for constructivist machine learning, it is likely that tasks where ambiguous knowledge and results need to be avoided will profit most from this learning paradigm. Future work on this approach will focus on parallelization strategies for constructivist machine learning and on developing task-oriented comparisons with human cognitive functionality.