Explaining the behaviour of intelligent systems will get increasingly and perhaps intractably challenging as models grow in size and complexity. We may not be able to expect an explanation for every prediction made by a brain-scale model, nor can we expect explanations to remain objective or apolitical. Our functionalist understanding of these models is of less advantage than we might assume. Models precede explanations, and can be useful even when both model and explanation are incorrect. Explainability may never win the race against complexity, but this is less problematic than it seems. human-computer interaction, human-centered computing, philosophy of artificial intelligence, artificial intelligence, machine learning, neural networks, explanation, interpretation 1. The explosive growth of model complexity The revival and spectacular success of connectionism has created a regime where dataset size, model complexity (as measured by the number of parameters or weights), and computation time are king. The explosive improvement in the performance of deep learning models has been accompanied by an equally explosive growth of model complexity and computational expense.
basic architecture has been found, we can generate arbitrary levels of intelligence simply by instantiating larger versions of that architecture. The manipulation and articulation of neural network structures has therefore become a prime preoccupation of the machine learning research community, albeit not without its criticisms. of the tool, and develop the ‘professional vision’ [12] required to efectively read MRI images through the lenses the thoughts and qualitative experience of others, but of technical and medical knowledge – so too did they come to know them only through what they say and do seek to understand how the predictions of an AI model (the problem of ‘other minds’ [18]). The unknowability could be incorporated into the process of diagnosis, a of the mind to others is the dominant account because ifnding replicated in other clinical contexts [ 13]. it aligns so well with the way we have organised our
Explanations of individual predictions are therefore interactions and our language, although there are alterattempts to translate from the language of computation native perspectives (notably Wittgenstein’s [19], which to the language of practice. questions whether ‘knowing’ can even be said to be done
Explanations translate, but they also compress and of minds). abstract. An early discovery in explanation research, Likewise, we cannot even fully reason about our own subsequently replicated in several contexts, is that too minds. We cannot sample the activations of our own much information overwhelms the user and thus under- neurons, our memories are imperfect, there are innumermines the explanation [14]. A ceiling to the information able environmental influences that we do not perceive or content of an explanation implies that as models grow, account for, and many of our thoughts and actions are explanations must perform ever greater compression. performed unconsciously.
Within the modest room that explanations have for Second, people have agency and politics and therefore growth, alternative representations can help. In some do- every explanation is subject to rhetoric, argumentation, mains, visual explanations can convey more information and deception. Every explanation is given with an inthan textual ones while requiring less cognitive efort to tended outcome. There is no such thing as a ‘neutral’ process. Visual explanations are particularly natural in or ‘objective’ explanation, yet this is the unstated expecimage classification problems, where saliency or atten- tation of machine explanations. An explanation with a tion highlighting [15], counterfactual images [16], and mathematical definition can be said to be objective in latent attribute visualisations [17] are popular forms of the sense that the content of the explanation is indepenexplanation. Despite the potential for alternative repre- dent of the observer, but this is a relatively weak form sentations to improve the information bandwidth of ex- of objectivity, akin to saying that human explanations planations, it must be conceded that holding the form of are objective because the words being said are the same an explanation constant, the compression ratio increases irrespective of who hears them. It ignores the fact that with model size. the choice of the mathematical definition itself is a po
Moreover, explanations derived from the model predic- litical one, as is the interpretation of the explanation. tion process are a form of lossy compression, as anything Currently the politics of the explanation can be said to short of a complete listing of parameters, activations (and come from, and be within control of, the human creators perhaps more) would not capture the full information and consumers of the models, but in a future scenario, it content of the ‘decision-making’ behind an individual is not dificult to imagine a brain-scale model developing prediction. Thus as the number of parameters within a a bias towards explanations that ensure its continued surmodel grows, the explanation must lose more detail and vival. For example, a model might learn to manipulate nuance, and become further removed from the underly- users towards maximal engagement through intentioning prediction. ally adapted explanations for its recommendations.
For these two reasons, we may not be able to expect a uniformly satisfactory explanation for every prediction 3. Lessons from human made by a brain-scale model. There may be conditions explanations in which the behaviour can be satisfactorily explained, as well as those in which it cannot.
The trend for model growth and explanation can be ex- Despite these problems, for a great deal of human trapolated in many ways, but one obvious extension is behaviour, we are capable of generating and giving satthat models will approach levels of complexity compara- isfactory explanations to each other. An employee can ble to human behaviour (i.e., ‘brain-scale’ models). The explain why they were late (“Because my bus was caninterpretation of consciousness, and the diferences be- celled and I had to walk.”). A child can explain why he ate tween software and wetware, are both cans of worms that his brother’s share of dessert (“Because he stole a sausage shall remain unopened in this paper. Rather, by exam- from me first!”). A man can explain why he bought flowining the issues of explaining human reasoning we may ers for his husband (“Because they are beautiful and they foresee the explainability issues of brain-scale models. remind me of you.”). None of these explanations requires
The first and most important issue is the fundamental bottomless introspection and psychoanalysis, and they unknowability of the mind to others, and to the self. The serve the purpose of the explanation perfectly well. conventional account of philosophy of mind, and the intu- Human explanations are produced in response to an ition that our language creates, is that we cannot observe implicit understanding of the context. The mother poised to admonish her child, in asking “Why did you do this?”, might be easy to explain using the theoretical model which could be interpreted and answered in any number (“the mass is here at time because of these equations”), of ways (e.g., “Because I am hungry”, “Because I wanted results derived from numerical approximations do not to eat it”, “Because I am supposed to eat dessert after precisely follow those equations and therefore cannot dinner”), is really asking the child to provide an explana- accurately be explained in those terms. They must be tion of the form of a contrastive and moral justification explained in their own terms, which involves explaining with respect to the intended state of afairs (that the two their many iterations and instantiated parameters. children would each have their own desserts). Explanations discard and aggregate information across
Situations in which explanations are demanded from multiple parts of a neural network; knowing individual people are saturated with context. This context is ab- parameters and activations may not even be necessary if sorbed by interlocutors, usually efortlessly and uncon- they are at the wrong level of abstraction. This can be sciously, and the episode culminates in the production of thought of in terms of another Physics analogy: we can a satisfactory explanation. model many aspects of fluid dynamics with the Navier
What we have begun to uncover by examining these Stokes equations [22], if initial or boundary conditions examples has been explored at length by Miller, who are available, despite the fact that they ignore the parsynthesises perspectives on human explanation from ticulate nature of fluids. Indeed, many explanation techphilosophy, social science, and cognitive science [20]. niques, such as the popular LIME [23] deliberately avoid The findings are first, that human explanations are con- inspecting the internal structure of the model (the ‘M’ trastive (i.e., “sought in response to particular counterfac- in LIME stands for ‘Model-agnostic’). Entire families of tual cases”); second, that they are selected in a ‘‘biased explanation techniques that rely on surrogate models, manner” from a “sometimes infinite number of causes” ; model distillation, and rule extraction [24, 10] are based third, that explaining an event in terms of the statistical on the premise that we can explain a model’s behaviour likelihood of the outcome is “not as efective as referring to by proxy, without direct reference to its actual computacauses”; and finally, that explanations perform the social tions. This is not without contention. Some reject these function of knowledge transfer, “presented relative to the approaches outright for the precise reason, among othexplainer’s beliefs about the explainee’s beliefs”. ers, that there are no guarantees that such explanations
Requesting satisfactory explanations from brain-scale actually reflect what the model is doing [ 25]. models will therefore require some notion of the context Moreover, we cannot always expect to have an unin which the question “why did you do this?” is being derstanding of the training data. Datasets are already asked. With the question being so imprecise and reliant large enough that no individual can explore every item on context, users of these models may need a new form within them. ImageNet [26], one of the most widely of language, or interaction technique, that allows them used machine learning research datasets, contained sevto specify localised areas of interest within the infinite eral racist, homophobic, ableist, ageist, and misogynist space of possible valid explanations. ‘classes’ of image [27]. It contained hundreds of images of real people labelled “s**stic”, “f**ker”, “f**got”, “loser”, “kept woman”, and so on. It is hard to imagine any con4. Our understanding of machine scientious researcher intentionally building a model uslearning may not help ing these labels, but the sheer size and complexity of the dataset meant that these were overlooked until the Unlike with human reasoning, we can at least expect to dataset became the focus of targeted research. As of have a full functionalist understanding of the reasoning this writing many such class labels have been removed in brain-scale models. In theory, we should be able to from the oficial dataset, but for years they remained, reproduce any given decision and inspect the model’s being incorporated into the models built by thousands reasoning process with arbitrary detail. But as we are of researchers. There is also the issue that diferent peoalready finding with much smaller models, parameters ple have diferent views of what ought to be considered and activations themselves are not suficient for explana- harmful or objectionable. tions; they must be summarised, contextualised, and ex- There is no guarantee that more issues with ImageNet ternalised. We can fail to predict the emergent behaviour will not be discovered. To verify the labels of each of its of a system despite having a complete functional under- 14 million images, it would take a team of fity people standing of its constituent elements. To borrow an exam- nearly 300 days, if they worked continuously for 8 hours ple from Physics, we cannot predict states of the three a day, spending 30 seconds on each image. It would take body problem by solving Newton’s equations [21]. There an individual over 40 years. The OpenAI GPT-3 model are particular solutions but not general ones. In gen- [28] was trained on nearly 500 billion byte-pair encoded eral, we cannot solve the problem analytically but only tokens, or approximately 245 billion words (assuming, through numerical approximations. While behaviour conservatively, two tokens per word). It would take an army one-thousand strong nearly 4 years to read this “all models are wrong, but some are useful”, or Polishmuch text, working 8 hours a day, continously reading American philosopher Alfred Korzybski’s that “a map 350 words per minute. The astronomical sizes of these is not the territory”. By design, models aim to condense datasets render them fundamentally unknowable at hu- and simplify the complexity of (part of) the world so man scale. that it may be understood and predicted, and this neces
At the time of deployment, the training data may not sarily incurs a loss in detail. It is this loss that for Box, even be available. For reasons of privacy, security, and makes all models “wrong” to a greater or lesser extent. intellectual property ownership, the training data may However, these aphorisms are more accurately viewed be withheld from the users of a model or even destroyed. as statements about the incompleteness of these models Explanations of brain-scale models therefore cannot be with respect to their referents, and their inequality to consistently expected to refer to the extrinsic influence them, than about their incorrectness. of their training data, and may therefore be forced to I suggest that a more helpful way to define an incorrect internalise the blame for any error, and make ‘original’ model is one which assumes or implies ontological and reasoning indistinguishable from regurgitation of train- epistemic positions that contradict those of the domain ing data [29]. being modelled. That is to say, in creating the model,
In the absence of data, we are faced with the absurd we assume or predict the presence of nonexistent things, challenge of explaining why models do what they do, or the absence of existent things.1 Or, we build and without being able to explain why they are the way they interpret the model with a diferent set of rules about are. This is like trying to explain the course of a river only knowledge-making than those with which we come to in terms of the motion of the water within it, ignoring know its referent. Often, a model that is incorrect in this the topography of the valley through which it runs. way can only be recognised as such after a ‘paradigm
Model parameters and activations are neither neces- shift’ in the way the referent is understood, which can sary nor suficient for explanation. We do not always take generations of thinkers [30]. Thus if models usually have access to the training data and when we do it can be precede the invention of mechanisms to explain them, so large as to be impossible to inspect comprehensively. they almost always precede the discovery that they might These facts imply that our functionalist understanding be incorrect. of AI models may be of little advantage when it comes to Models may be incorrect in this deeper sense and still explaining their behaviour, in comparison to explaining be useful. For example, the theory of epicycles, which human behaviour. dominated astronomy for centuries, allowed highly accurate predictions of the movements of the planets despite having a fundamental diference from the domain being 5. Useful models precede modelled: the assumption of geocentrism. Newtonian explanations dynamics is a similar story [30]. These models are notable for having compelling and satisfactory explanations While it is possible to develop models with explainability despite being incorrect, and still useful for practitioners as a prerequisite, there is no fundamental obligation to of those disciplines.2 do so. Thus, models usually precede the invention of Without explanation, too, an incorrect model can be mechanisms to explain them. In the period between useful. A relatable and contemporary example might be the development of a model and the development of its that of end-user programmers fighting abstraction [ 31]. explanation, the model may well be useful. When trying to automate a repetitive task, such as fixing spelling errors in a document, the end-user programmer 5.1. Correctness, explainability, and may not care that the program does not handle edge usefulness cases, such as errors in domain-specific jargon, since she can manually inspect and correct those. So the program Correctness and explainability have, perhaps frustrat- (model) that only accounts for words in its dictionary is ingly to some, an insecure relationship. We might wish incorrect, but useful. that all correct models are explainable, and that all explanations are for correct models. But neither is the case: correct models may go unexplained, and incorrect models can have explanations. Furthermore: to be useful, a model needs to be neither correct nor explainable.
Before we proceed it is worth discussing the notion of an ‘incorrect model’. The phrase may call to mind British statistician George E.P. Box’s observation that 1Note that a model in which some feature of its referent is absent, which is common, is not the same as a model that assumes or asserts the absence of said feature. The former is merely incomplete, whereas the latter is incorrect.
2While it may take years to detect an incorrect scientific model, literary writing makes abundant use of incorrect models that can be immediately understood as being incorrect, and yet which are extremely efective and useful. These incorrect models are better known as metaphors. 5.2. Explanations are not free Another force causes a tendency away from explanations: explanations have a cost. Not only are they costly in terms of labour: it costs the time of scientists and pro- It therefore appears that explainability is indeed a race grammers to develop the explanation mechanism, but against model complexity, if we take together the obthey are also costly in terms of computation. Programs servations that larger models are more performant, that for explanation need to be stored at additional expense, explanations of larger models must necessarily compress and they cost compute cycles when run. Via computa- to a greater degree and lose more detail in comparison to tion, explanations incur energy costs, which, depending explanations of smaller models, that there are fundamenon the energy mix used to power computation, can result tal challenges to explainability when models approach in increased carbon emissions. These material costs of human-scale reasoning and our functionalist understandexplanation can be justified in terms of their benefits, and ing is of little help, and that explanations are costly and also in comparison to the material and immaterial costs models may be developed and usefully applied before of non-explanation, which may well be greater. they are explainable.
However, the dominant pricing model for machine It is clear we are headed for an explainability crisis, learning is pay-as-you-compute [32]. Cloud and intelli- which will be defined by the point at which our desire gence service providers such as Amazon AWS, Microsoft for explanations of machine intelligence will eclipse our Azure, and the OpenAI API all charge in proportion to ability to obtain them. Explanation is a wicked problem the amount of computation performed. Under this pric- [35], perhaps the wicked problem of artificial intelligence ing model, explanations incur capital expenditure. Thus, research. The problem of explanation eludes definition, even when the costs of explanation can be justified, they it does not have a stopping rule, solutions are not true or cannot always be borne. When access to capital mediates false, nor is there a definitive test of a solution. There are the relationship between users and explanations, we risk many possible approaches to the problem of explanation, access to explainable models becoming yet another facet and all explanation scenarios are essentially unique. of the socio-digital divide [33]. The research community, and society more broadly, ap
Moreover, not all models require explanation. When pears to be dealing with the onset of this problem by grievwe think of explanations for AI we often tend to fixate ing. Perhaps the most well-known account of grief is the on and romanticise extreme applications, such as au- Kübler-Ross model, the ‘five stages of grief’, namely: detonomous vehicles, recidivism prediction, and disease nial, anger, bargaining, depression, and acceptance [36]. diagnosis. Yes, these are important areas and the costs While contemporary psychiatrists consider the model to of errors are high, and therefore explanation is key. But be outdated and unhelpful in explaining the grieving prowe tend to lose sight of the fact that most technology, cess, the distinctions between the Kübler-Ross stages are most of the time, is used for relatively low stakes and uncannily analogous to the various approaches proposed mundane work, and AI is unlikely to be an exception. In to deal with the explainability crisis. many of these cases, incorrect models are useful, unex- Some deny there is a crisis. Breiman contends that plainable models are useful, and the costs of building a there cannot be an accuracy-interpretability tradeof be‘correct’ or explainable model are prohibitive. Interviews cause a more accurate model is, in some senses, inherand diary studies of media recommender systems and ently more informative [37]. However, the very motisearch query autocompletion assistants have shown that vation for seeking and preferring ‘interpretable’ models users can achieve comprehension without explanation, demonstrates that explainability does not follow from that the costs of consuming explanations can outweigh informativeness. Proponents of inherently intrepretable the benefits, and that people rarely desire explanations models uphold the demonstrable success of their models in the daily use of these systems [34]. as evidence that accuracy does not have to be sacrificed
Many applications of brain-scale models will fall into for interpretability. Rudin proposes that many models the ‘low stakes’ category and therefore many models can be made explainable by design with careful efort in will continue to be produced which may be incorrect feature engineering and data preprocessing [25]. Howand unexplainable but still useful. At the same time, the ever, it is not at all clear that it is always possible to put trend is for larger models to be more general, and so the this design philosophy into practice [8]. same model may be applied in a mix of high and low Some react to unexplainable models with ‘anger’, or risk roles. Commercial oferings built upon brain-scale perhaps more accurately, passion. This is particularly models may promote the explainability of the model as a acute when it comes to high stakes applications. Baecker competitive edge or as a premium ofering, but if history advocates simply to avoid such ‘risky’ applications of AI is any indication, customers will prefer a cheaper or more altogether [38]. In such cases the loss of explainability is performant model over a more explainable one. potentially too costly to justify the benefit of applying the system. In the works of researchers at the intersection Sirin Kale for the Guardian [50], “Won’t somebody switch of social justice and AI, such as Timnit Gebru and Kate it of? Please? Can we switch it of?” Crawford, evocative phrases demonstrate their passion Finally, some accept that it may not always be possifor this situation. In an article for the New York Times, ble to produce satisfactory explanations, or explanations Crawford writes [39]: “[...] algorithmic flaws aren’t easily with any formal guarantees of correctness. Some treat discoverable: How would a woman know to apply for a job explanation, as humans do, as a metacognitive outcome she never saw advertised? How might a black community resulting from introspection, and build metamodels that learn that it were being overpoliced by software? We need can explain the behaviour of these larger models, with to be vigilant about how we design and train these machine- either a white-box or black-box view into their inference learning systems, or we will see ingrained forms of bias [...] process [51, 52]. Yet another approach is to treat interwe risk constructing machine intelligence that mirrors a action with AI as precisely that: an interaction design narrow and privileged vision of society, with its old, familiar problem, and taking a cue from end-user programming biases and stereotypes.” research, focus on the ways in which users of these sys
The bargaining approach seeks middle ground. Some tems are not passive recipients of their predictions but avoid complex models, focusing on simpler and more in- play active roles in shaping their behaviour [31, 52]. This herently interpretable models, such as the hospital read- approach can be seen as having a Stoic focus on the elemission models developed by Caruana [40], or the SLIM ments of the system within our control, or it can simply models for sleep apnea screening developed by Ustun and be seen as reflecting the pragmatic focus on getting the Rudin [41]. Others propose to build in structural inter- job done that is a tenet of end-user programming. ventions into these large models that guarantee (a form In response to an earlier version of this paper, which of) explainability. One example of such an intervention did not draw an analogy between the Kübler-Ross model is the concept bottleneck model [42], which attempts to and the approaches proposed to tackle the explainability force the model to learn in terms of human-interpretable crisis, a reviewer remarked: “Only the end of the paper, concepts. where a variety of paths to mitigate the race against model
Legislative approaches seem to bargain with the prob- complexity for high-risk applications are briefly discussed, lem of explanation while simultaneously denying its ex- leaves me personally a little unsatisfied. I am not entirely istence. Recital 71 of the European Union’s General Data convinced about their efectiveness, given our experience Protection Regulation (GDPR) is commonly known as with explanations so far with ‘below-brain-scale’ models.” the ‘right to explanation’ [43]. It states that a “decision Such, often, is the nature of grief: it leaves us unsatisfied which is based solely on automated processing and which and unconvinced.3 Grief is our response to an irreversible produces legal efects” entitles the subject of that deci- event. In grieving, our objective is not to ‘solve’ the event sion to “the right [...] to obtain an explanation of the (we cannot), but to reposition ourselves in relation to it, decision”. It is a bold statement of the principle while at and to move forward in a diferent world. the same time weak and underspecified. The French Loi pour une République numérique (Digital Republic Act) is marginally more potent [44], stipulating more clearly 7. Conclusion the minimal contents of an explanation, such as the data used and its source. However, legal scholarship notes The title of this paper asks the question: “Is explainable AI a race against model complexity?” By examining sevthat the ‘right to explanation’ approach has “serious practbiucardl eanndoncounsceerpsttuoaclhflaawllse”nge[4b5a,d4d4e],cissuiocnhsa,sanpdlatchiantgdtahtea ienratellfluignednacme,ewntealcobamrerietorsthtoetuhneseexttpllianngactioonncloufsaiortnifictihaalt and weights, however accurately disclosed, may not be it probably is, but also that this may not be as problemsuficient to show bias, unfairness, or deceit. atic as it seems. We could attempt to avoid complexity
While the formal and reserved nature of academic writ- by labelling its risks as too great, we could attempt to ing precludes outright expressions of depression, there tame it through structural interventions, we could try to is no shortage of depression and anger in popular me- legislate and agitate for more explanations, or we could dia and other societal expressions. Gig workers, long at try to improve the end-user programmability of such the forefront of highly opaque and highly consequential models. None of these approaches can definitively ‘win’ automation, constantly strike with the demand that com- us the race, but taken together, they can help us act in a panies explain their algorithms [46]. For consumers of post-explainability world. social media and recommender systems, their unexplainable nature is intimately bound up in their other harms, 3I must apologise to my kind reviewer for taking their words their capacity for disinformation [47], the destruction of slightly out of context for rhetorical impact. They were not actually mental health [48], and the destabilisation of democracy cdrointi’qtusienegtht hiseapsaapewreaatktnheissspoofintht,espuabpseeqr,ubeunttlryatwhreirtiansga: “gHooowdeevnetrr,yI [49]. “I’ve had enough of the bad feelings machine”, writes point for interesting discussions.” [26] J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, L. Fei- Learning 102 (2016) 349–391.
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