Explainable Artiﬁcial Intelligence and Machine Learning: A

reality rooted perspective

Frank Emmert-Streib1,2, Olli Yli-Harja2, and Matthias Dehmer3

1Predictive Society and Data Analytics Lab, Faculty of Information Technology and Communication

Sciences, Tampere University, Tampere, Finland ∗

2Institute of Biosciences and Medical Technology, Tampere University of Technology, Tampere, Finland

3Institute for Intelligent Production, Faculty for Management, University of Applied Sciences Upper

Austria, Steyr Campus, 4040 Steyr, Austria

January 26, 2020

Abstract

We are used to the availability of big data generated in nearly all ﬁelds of science as

a consequence of technological progress. However, the analysis of such data possess vast

challenges. One of these relates to the explainability of artiﬁcial intelligence (AI) or machine

learning methods. Currently, many of such methods are non-transparent with respect to

their working mechanism and for this reason are called black box models, most notably deep

learning methods. However, it has been realized that this constitutes severe problems for a

number of ﬁelds including the health sciences and criminal justice and arguments have been

brought forward in favor of an explainable AI. In this paper, we do not assume the usual

perspective presenting explainable AI as it should be, but rather we provide a discussion

what explainable AI can be. The diﬀerence is that we do not present wishful thinking but

reality grounded properties in relation to a scientiﬁc theory beyond physics.

Introduction

Artiﬁcial intelligence (AI) and machine learning (ML) have achieved great successes in a number of

diﬀerent learning tasks including image recognition and speech processing [1–3]. However, many of

the best performing methods are too complex (abstract) prohibiting a straight forward explanation

of the obtained results in simple words. The reason therefore is that such methods process high-

dimensional input data in a non-linear and nested fashion to reach probabilistic decisions. This

convolutes a clear view, e.g., on what information in the input vector is actually needed to arrive

at certain decisions. As a result, such models are non-transparent or opaque and are typically

∗frank.emmert-streib@tuni.ﬁ

regarded as black box models [4]. Importantly, not only deep neural networks (DNNs) are suﬀering

from this shortcoming but also support vector machines (SVMs), random forests (RFs) or ensemble

models (e.g. Adaboost) [5–8].

This black box character establishes problems for a number of ﬁelds. For instance, when making

decisions in a hospital about the treatment of patients or at the court about the sentencing of

a defendant, such decisions should be explainable [9, 10].

In an endeavor to address this issue

the ﬁeld explainable AI (XAI) has recently re-emerged [11]. While previous work in this area

focused on speciﬁc problems of deep learning models, deﬁning explainable AI or the taxonomy of

XAI [12–14], our approach presents a diﬀerent perspective as follows. First, instead of describing AI

systems with desirable properties making them explainable, we present a reality rooted perspective

showing what XAI can deliver. Put simply, instead of presenting explainable AI as it should be

we show what explainable AI can be. Second, we derive thereof limitations of explainable AI.

Such limitations may be undesirable but they are natural and unavoidable. Third, we discuss

consequences of this for our way forward.

Our paper is organized as follows. In the next section, we brieﬂy describe the current state

of explainable AI. Then we present diﬀerent perspectives on learning methods and discuss the

deﬁnition of a scientiﬁc theory. This allows us to conclude some limitations of an even perfect

versions of explainable AI. Finally, we discuss reasons for the confusion about explainable AI and

present ways forward. The paper ﬁnishes with concluding remarks.

2 Current state of explainable AI

For our following discussion, it is important to know how explainable AI is currently deﬁned. Put

simply, one would like to have explanations of internal decisions within an AI system that lead

to an external result (output). Such explanations should provide insight into the rationale the AI

uses to draw conclusions [15].

A more speciﬁc deﬁnition of explainable AI was proposed in [16].

Deﬁnition 1 (explainable AI). 1) produce more explainable models while maintaining a high level

of learning performance (e.g., prediction accuracy), and 2) enable humans to understand, appro-

priately trust, and eﬀectively manage the emerging generation of artiﬁcially intelligent partners.

Another attempt of a deﬁnition of explainable AI is given in [13].

Deﬁnition 2 (explainable AI). Explainable Artiﬁcial Intelligence is a system that produces details

or reasons to make its functioning clear or easy to understand.

Furthermore,

it is argued that the goals of explainable AI are trustworthiness, causality,

transferability, informativeness, conﬁdence, fairness, accessibility, interactivity and privacy aware-

ness [13, 17].

In general, there is agreement that an explainable AI system should not be opaque (or a

black box) that hides its functional mechanism. Also, if a system is not opaque and one can even

understand how inputs are mathematically mapped to outputs then the system is interpretable [15].

Taken together, this implies model transparency. The terms interpretability and explainability

(and sometimes comprehensibility) are frequently used synonymously although the ML community

seems to prefer the former while the AI community prefers the latter [14].

From a problem-oriented view, in [18] diﬀerent types of interpretability, for instance perceptive

interpretability, interpretability via mathematical structure, data-driven interpretability or inter-

pretability by utilities, and explainability are discussed. They found that many journal papers in

the ML and AI community are algorithm-centric, whereas in medicine risk and responsibility re-

lated issues are more prevalent. Similar discussions for diﬀerent interpretations of interpretability

can be found in [19].

Overall, at to this point one can conclude the following. First, there is no single deﬁnition of

explainable AI available that would be generally accepted but many descriptions are overlapping

with each other in the above discussed ways. Second, the characterizations of explainable AI

state what XAI should be. That means they form desirable properties of such an AI system

without deriving these from higher principles. Hence, these characterizations can be seen as

wishful thinking. Before we can formulate reality rooted attainable goals of explainable AI, we

need to discuss diﬀerent perspectives on models and the general capabilities of a scientiﬁc theory.

3 Perspective of statistics

In statistics, one can distinguish between two main types of models. The ﬁrst type, called infer-

ential or explanatory model, provides a causal explanation of the data generation process whereas

the second type, called predictive model, just produces forecasts [20, 21]. Certainly, an inferential

model is more informative (i.e. theory-like, see below) than a predictive model because also an

explanatory model can be used to make predictions but the predictive model does not provide

(causal) explanations for such predictions. An examples for an explanatory model is a causal

Bayesian network whereas a random forest is a prediction model. Due to the complementary

capabilities of predictive and inferential models they are coexisting next to each other and each is

useful in its own right.

The general problem for creating causal models from data is that their inference from observa-

tional data is very challenging requiring usually also experimental data (generated by perturbations

of the system). Currently, most data in the health and social sciences are observational data ob-

tained from merely observing the behavior of the system because performing experiments is either

not straight forward or ethically prohibited.

4 Perspective of artiﬁcial intelligence

In [22] it was argued that explainable AI is not a new ﬁeld but has been already recognized and

discussed for expert systems in the 1980s. This is understandable considering that from about

the 1950s to the 1980s the dominant paradigm of AI was symbolic artiﬁcial intelligence (SAI) and

SAI used high-level and human-readable representations and rules for manipulating these, e.g.,

by using expert systems. Hence, not only the need for explainable systems has been realized but

some AI systems could also accomplish near optimal explainable goals due to the nature of SAI.

With the renewed interest in neural networks in recent years in the form of deep neural networks

(DNN), the question of explaining and interpreting models has been re-surfaced. One reason for

this is that deep neural networks, in contrast to methods used for SAI, are not symbol-based but

connectionist, i.e., they are learning (possibly high-dimensional) features from data and store them

in the weights of the network [23, 24]. Although, more powerful in practice the price payed for

this comes in form of a higher complexity of the representation used, which is no longer human-

readable. Recently, it has been argued that AI systems should not only solve pattern recognition

problems but provide causal models of the world that support explanation and understanding [25].

This demand connects directly to the statistics perspective because causal models are exploratory,

see above.

After clarifying how explainable models are understood by diﬀerent communities we take a

step back to see what would be the ultimate goal achievable of an explainable AI. For this reason,

we discuss the meaning of a theory.

5 What is a scientiﬁc theory?

In science, the formal deﬁnition of a theory is diﬃcult but commonly it refers to a comprehensive

explanation of a subﬁeld of nature that is supported by a body of evidence [26–28]. In physics,

the term theory is generally associated with a mathematical framework derived from a set of

basic axioms or postulates which allows to generate experimentally testable predictions for such a

subﬁeld of physics. Typically these systems are highly idealized, in that the theories describe only

certain aspects. Examples include classical ﬁeld theory and quantum ﬁeld theory. An important

aspect of a theory is that it is falsiﬁable [29]. That means experiments can be conducted for testing

the predictions made by a theory. As long as such experiments do not contradict the predictions

a theory is accepted, otherwise rejected.

With respect to the stringency with which theories have been quantitatively tested, theories in

physics, e.g., general relativity or quantum electrodynamics, are certainly what can be considered

the best scientiﬁc theories. This implies that such theories provide answers to all questions that can

be asked within the scope of the theory. Furthermore, the theory provides also an explanation of

the obtained results. However, these explanations do not come in the form of a natural language,

e.g., English, but are mathematical formulas. Hence, the mathematical formulas need to be

interpreted by means of a natural language as good as possible. This may seem as a minor issue

but the severity of this may be exempliﬁed by the interpretation of quantum mechanics because

so far there is no generally accepted interpretation, although the Copenhagen interpretation is

the most popular one [30]. Interestingly, the reason for this is ascribed to personal philosophical

prejudice [30]. The latter point hints to the incompleteness of any natural language in interpreting

a mathematical formalism of quantum mechanics. For completeness, we would like to mention

that even in physics not everything is covered by the existing theories because so far there is no

theory unifying gravity and quantum mechanics [31].

6 Expected limitations of an explainable AI

From this discussion, we can conclude some limitations even a perfect version of an explainable

AI will have. Considering that essentially all applications of AI and ML are beyond physics, e.g.,

in biology, medicine and health care, industrial production or human behavior, one cannot expect

to have a simpler theory for any of these ﬁelds than what we have for physics. Hence, even the

interpretability of such a theory is expected to be more problematic than an interpretation of, e.g.,

quantum mechanics.

In order to make this point more clear let’s consider a speciﬁc example. Suppose a theory of

cancer would be known, in the sense of a theory in physics discussed above. Then this cancer theory

would be highly mathematical in nature which would not permit a simple one-to-one interpretation

in any natural language. Hence, only highly trained theoretical cancer mathematicians (in analogy

to theoretical physicists) would be able to derive and interpret meaningful statements from this

theory. Regardless of the potential success of such a cancer theory, this implies that medical doctors

not trained as theoretical cancer mathematicians - could not understand nor interpret such a

theory properly and, hence, from their perspective the cancer theory would appear opaque or non-

explainable. Without our discussion, such a result would appear undesirable and unacceptable,

however, given the context we provided above this appears unavoidable and natural. A similar

discussion can be provided for any other ﬁeld than cancer showing that even a perfect version

of an explainable AI theory would not be interpretable or explainable for managers or general

practitioners for natural reasons.

The next optimistic but less ambitious assumption would be to suppose AI could provide

a description for ﬁelds outside of physics. Interestingly, physicists realized already decades ago

that such an expansion of a theory beyond the boundaries of physics is very challenging. For

instance, severe problems encountered are due to the arising of emergent properties and non-

equilibrium systems [32,33]. For this reason, phenomena outside of physics are usually addressed by

"approaches" collectively named as complex adaptive systems (CAS) [34,35]. We used intentionally

the word "approaches" and not "theories" because the used models and the obtained descriptions

are qualitatively very diﬀerent thereof. Whereas it is unquestionable that valuable insights have

been gained into complex phenomena from economy, society and sociology [36,37] a theory for such

ﬁelds is still absent and currently not in sight. Hence, it seems fair to conclude that even the most

powerful AI system of CAS would be far from being a theory and for this reason lack explanatory

capabilities. However, this translates directly into a principle incompleteness of questions such an

AI system could answer and reduces further what could be delivered by an explainable AI.

Finally, we come to the most realistic view on an AI system which views its purpose as a

system to analyze data. Depending on the AI system and the available data it is clear that the

understanding that can be obtained from such a system is even further limited in the answers that

can be provided as well as in the level of explanations it can give. This is also true if the AI system

would be based on a perfect method because the data represent only an incomplete sample of all

possible data and is as such inherently limited in the explanations it can provide translating in an

unavoidable uncertainty of statements about the population it studies.

In Fig. 1, we summarize the above discussion graphically. The shown coordinate systems

indicate the qualitative relation between the inﬂuence of the distance from a theory and the

comprehensiveness of the description (left) and the inﬂuence of the sample size on the uncertainty

of statements or explanations about the population (right). The yellow arrow on the left indicates

the distance from physical theories which corresponds also to the x-axis of the left coordinate

system. A similar meaning has the purple arrow on the right for the diameter of the random

sample and x-axis of the right coordinate system

7 Reasons for the confusion

It is interesting to ask how utopian, idealistic requirement for an explainable AI, as discussed in

Section 2 above, could be demanded when reality looks quite diﬀerently. We think the reason for

this is twofold. First, statistical models and machine learning methods have been introduced due to

the lack of general theories outside of physics because these allow a quantitative analysis studying

experimental evidence. Hence, even in this unsatisfactory situation, systematic and quantitative

approaches are available for extending our knowledge of complex phenomena. Second, in recent

Figure 1: An overview describing the limitations of explainable AI with respect to attainable

goals. Left: Diﬀerent scientiﬁc ﬁelds are arranged according to their increasing complexity [32]

starting from the best (most comprehensive) theories of physics in the center. The further the

distance from these theories the less comprehensive are the models describing subjects of CAS

(left coordinate system). Right: Any AI system analyzes a random sample of data drawn from a

population. One source of uncertainty is provided by the sample size of the data (right coordinate

system) that translates directly into uncertain statements about the population.

years we have been experiencing a data surge which gives the impression that every research

question should start with "data". This led even to the establishment of a new ﬁeld called data

science [38]. Taken together, this may have given the impression that AI and ML methods are

more powerful than physical theories because they can (approximately) reach areas - due to the

availability of methods and data - that are blocked for physics. However, these methods are

not intended as theories but merely as practical instruments to deal with complex phenomena.

Importantly, the questions that can be answered need to have answers that can be found within

the data. Every lack of such qualitative data, e.g., due to a limited sample size, translates directly

into a lack of answers and is for this reason an inherent uncertainty of any AI system.

8 Discussion

Having realized the limitations of explainable AI with respect to attainable goals, what does this

mean for the way to go forward? In the following, we present a discussion of practical remedies

that are based on the insights gained in the ﬁrst part of our paper. We want to emphasize that

these remedies do not bring us back to the delusional view of an idealized explainable AI but

provide means to realistically formulate achievable goals.

An AI system may not need to be explainable in a natural language as long as its generalization

error does not exceed an acceptable level. An example for such a practice are nuclear power plants.

PhysicsTheoryBiologyEconomySociologyCASQM: quantum mechanicsQFT: quantum field theoryapplications of AImodelsrandom sample of datapopulationmethod[ ]⇒uncertain statementsabout populationdistance from theorycomprehensiveness of the descriptionsample sizeuncertainty CAS: complex adaptive systemsSince nuclear power plants are based on physical laws (see the discussion of quantum mechanics

above) the functioning mechanisms of such plants are not explainable to members of the regulatory

management or politicians responsible for governing energy politics. Nevertheless, nuclear power

plants have been operated since many decades contributing to our energy supply. In a similar way,

one could envision an operational policy for medicine, e.g., utilizing deep learning methods.

Deep learning may not be necessary to analyze a given data set. Nowadays, many people

are using deep learning methods because they seem to think such methods are needed without

exploring alternative approaches. However, in this way problems regarding the interpretability

and explainability of the results are encountered. While it may be possible that future deep

learning methods may be less opaque, if currently available methods solve the same problems in

a satisfactory way and do not suﬀer from such limitations, e.g., decision trees, they should be

preferred and used.

The similarity (or diﬀerence) of the predictiveness of AI systems needs to be quantiﬁed in an

explainable way. This point is related to the previous one because if one can quantitatively assesses

the similarity (or the diﬀerence) between two AI systems one can compare an explainable with a

non-explainable AI system to evaluate one beneﬁt over the other. Hence, even if an explainable

AI system does not fully solve a given problem, e.g., compared to a deep learning approach, it

may be suﬃcient to use. Importantly, even when an AI system itself may not be explainable the

comparison of diﬀerent systems can be understandable. This way the lack of an explainability

maybe compensatable. A challenge of such an approach is that a quantiﬁcation should not only

be based on prediction errors [39] but an assessment of risk and utility [40]. This latter issue is

clear in a clinical context.

Partial insights into the interpretability and explainability of AI systems should be developed. It

may not be feasible to convert deep learning models into fully transparent systems, however, this

may be achievable in part. For instance, certain aspects of an analysis could be understandable

which are integrated to achieve the complete model. Given the fact that in general data science

problems present themselves as a process [41] there should be ample opportunity to identify

subproblems deemable as an explainable AI.

9 Conclusions

In this paper, we shed some light on the current state of explainable AI and derived limitations

with respect to attainable goals from clarifying diﬀerent perspectives and the capabilities of well

tested physical theories. The main results can be summarized as follows:

1. An AI system does not constitute a theory but an instrument (a model) to analyze data.

⇒

The comprehensiveness and the explainability of an even perfect AI system are inherently

limited by the random sample of data used.

2. The more comprehensive (i.e. theory-like) an AI system becomes in predicting CAS the more

complex becomes its underlying mathematics.

There is no simple one-to-one translation

⇒

into a natural language to explain the results or the working mechanism.

3. The most powerful but opaque AI systems (e.g. deep learning) should not be preferred and

applied by default but a comparison to alternative explainable methods should be conducted

and diﬀerences should be quantiﬁed.

⇒

An explainable and quantiﬁable reason can be

derived by integrating prediction error, risk and utility for weighing the pros and cons for

each model.

We hope our results can contribute to formulating realistic goals for an explainable AI that

are also attainable [42].

Conﬂict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or ﬁnancial

relationships that could be construed as a potential conﬂict of interest.

Author Contributions

All authors contributed to all aspects of the preparation and the writing of the manuscript.

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Sociology

Economy

Biology

Physics

Theory

QM: quantum mechanics

QFT: quantum field theory

CAS: complex adaptive systems

population

uncertainty

CAS

applications of AI

sample size

comprehensiveness of the

description

models

random sample of data

distance from theory

method[ ]

uncertain statements

about population

⇒