On the Role of Theory and Modeling in Neuroscience

A pragmatic view: science as problem-solving

We propose that a pragmatic view of the scientific enterprise (James, 1907; Laudan, 1978; Ben-Ari, 2011; Douglas, 2014) is better suited to inform scientific practice. In this view, science is a process through which we solve empirical problems and answer questions about observable phenomena (Laudan, 1978; Nickles, 1981; Haig, 1987; Douglas, 2014; Firestein, 2015; Redish et al., 2018). Empirical problems can range from matters of basic scientific interest (for example, “How does the brain process visual signals?” or “How does an animal select between alternative choices?”), to those with more obvious applications (such as “Which brain functions are disrupted in schizophrenia?”). Like any other problem, a scientific problem can be seen as a search to achieve a desired goal, which is specified by the statement of the problem (Newell and Simon, 1972). However, scientific problems are often ill defined (Bechtel and Richardson, 2010), in part because the search space and solution criteria are not always explicitly stated and in part because they evolve with additional discoveries (Firestein, 2012). For example, the discovery of multiple memory and decision-making systems raises further questions of how those systems interact (Scoville and Milner, 1957; O'Keefe and Nadel, 1978; Squire, 1987; Nadel, 1994; Balleine and Dickinson, 1998; Schacter, 2001; Daw et al., 2005; Redish, 2013), while the question “How does the pineal gland generate consciousness?” (Descartes, 1637) is now considered outdated. Further, scientific problems are never definitively solved, but are only deemed “adequately solved” by a research community. What is seen as an adequate solution in one socio-historical context may not be in another: as new data become available, standards change, or alternative solutions are presented. While a continuously evolving landscape of problems and proposed solutions might seem to counter a notion of progress in science, scientific theories have been used to explain and control progressively more phenomena over the course of the scientific record (Laudan, 1978; Douglas, 2014). According to the pragmatic view, this progress results from community-maintained standards of explanation, under an overarching drive to better predict and control natural phenomena of potential relevance to society (Hacking, 1983; Douglas, 2014).

We can thus define a scientific explanation (Hempel and Oppenheim, 1948; Woodward, 2019) as a proposed solution to an empirical problem, and scientific theories to be the ideas we use to form explanations. Where traditional views have tried to specify the form theories take, the pragmatic view sees theory structure as closely tied to its function and context. As a result, a theory can include a wide and complex range of structural elements, including those that are not formalized (Winther, 2021). While theories may be spelled out in the scientific literature, they are more often used implicitly in the explanation of phenomena and design of experiments. By shifting theories from “proposals of truth to be falsified” to “proposed problem-solving tools,” the pragmatic view prompts us to assess a theory by its utility: what empirical problems it can solve, how easily it can be used to solve them, and how good its solutions are. It also requires criteria to evaluate the quality of solutions to a problem and a set of standards by which we measure the utility of the theory, such as accuracy, simplicity, falsifiability, generalizability, and reproducibility (Laudan, 1978; van Fraassen, 1980; Chang, 2007b, 2011; Schindler, 2018). Through competition to solve empirical problems, theories become more precise, provide clearer and more concise explanations, can be used to make more reliable and accurate predictions, and can be applied to larger domains.

Conceptual frameworks provide constructs and constraints

Assessing scientific explanations inevitably involves considerations that are not directly related to solution quality but are instead constraints on the form solutions can take. These constraints constitute a conceptual framework (Table 1): a language within which explanations are proposed. In effect, a conceptual framework is a set of foundational theories that provide a conceptual structure on which further theories within that program are built (Lakatos, 1978; Laudan, 1978; Kuhn, 2012).

The stability of such a framework allows its component theories to change without rebuilding their conceptual foundations. For example, under the modern framework of neuropsychiatry, psychiatric disorders are framed in terms of biophysical dysfunctions in neural structure. Current debates about the underpinnings of schizophrenia include hypotheses of dysfunction within dopaminergic or glutamatergic systems, dysfunctional pruning of dendrites, and dysfunctional oscillatory dynamics (Moghaddam and Javitt, 2012; Glausier and Lewis, 2013; Uhlhaas and Singer, 2015; Howes et al., 2017). However, they all lie within a general framework of biophysical changes in neural processes. The consistency of this founding idea allows us to modify theories without disrupting the foundational premise, which allows them to be directly compared and contrasted.

While explanations are naturally comparable within a framework, theories under different frameworks are composed of fundamentally different objects and describe the world in different terms, which makes them difficult to compare. For example, explanations under the traditional psychoanalytic framework (Luyten et al., 2015) are fundamentally different from those under the modern neuropsychiatry framework (American Psychiatric Association, 2013; Cuthbert and Insel, 2013; Insel and Cuthbert, 2015; World Health Organization, 2021). The two frameworks are composed of fundamentally different objects and are described in different terms: in contrast to the neuropsychiatric framework, psychoanalytic explanations for schizophrenia invoke unconscious conflicts and/or distorted ego functions as the key factors underlying psychosis (Luyten et al., 2015). Even the categorizations of psychiatric phenomena are different under these frameworks, making direct comparisons of explanations for the same phenomena across frameworks difficult (Feyerabend, 1993).

Despite the difficulties in directly comparing theories across frameworks, all frameworks are not equivalent. One can compare conceptual frameworks by asking how well their theories allow us to predict and control our environment (Lakatos, 1978). This is not to say that all research requires a direct application, but rather that consideration of practical components is necessary for a complete understanding of scientific progress (Laudan, 1978; Douglas, 2014). For example, the psychoanalytic framework implies treatment-based analytic therapy, while the modern neuropsychiatry framework suggests medication as a key component. Furthermore, under the new framework known as computational psychiatry, psychiatric disorders are attributed to computational “vulnerabilities” in the systems architecture of the brain (Redish, 2004; Redish et al., 2008; Montague et al., 2012; Huys et al., 2016; Redish and Gordon, 2016). Theories in this new framework suggest that such disorders would be treatable by changing information processing: by modifying the physical substrate (e.g., through electrical stimulation or pharmacological changes), enhancing compensation processes (e.g., through cognitive training), or changing the environment (e.g., by giving a student with ADHD extra time on a test). The pragmatic view suggests that the ultimate adoption (or not) of this framework will come down to how successfully it can be applied to unsolved problems.

Models as the interface between theories and phenomena

While “theoretical” work may appear further from “applied” science than its experimental counterpart, models can act as an interface between theory and phenomena. A model consists of a structure and an interpretation of how that structure relates to its target phenomena (Frigg and Hartmann, 2006), also known as the model's “construal” (Weisberg, 2013). For example, the equation τdV/dt=−V+Vrest is a mathematical structure that is interpreted to represent the temporal dynamics of the membrane potential, V, of a passive cell with time constant, τ, and resting potential, Vrest (Hodgkin and Huxley, 1952; Koch and Segev, 1989; Rall, 1992; Hille, 2001; Gerstner et al., 2014). Models whose structure consists of mathematical equations or computational processes are amenable to simulation and analytical treatment. Models can be constructed from many different kinds of interpreted structures, such as physical structures that are interpreted to represent the double helix of DNA (Watson and Crick, 1953) or diagrammatic structures that are interpreted to represent protein interactions involved in signaling cascades (Alon, 2006). Many “animal models” used in experimental neuroscience are physical structures interpreted to represent other phenomena, such as the 6-OHDA rat or the MPTP monkey, which are interpreted to represent the pathology of Parkinson's disease (Schultz et al., 1989; Dorval and Grill, 2014).

In creating a model, a researcher has to make foundational assumptions in the terms they use, the form those terms take, and the relationships between them. These assumptions instantiate aspects of a theory in an explicit expression with a well-defined form. The voltage equation above instantiates the theory that a neuron's electrical properties arise from a semipermeable membrane (Hodgkin and Huxley, 1952; Rall, 1992), while the 6-OHDA model instantiates the theory that Parkinson's disease arises from dopaminergic dysfunction (Langston and Palfreman, 2013). This explicit formulation of theories can force us to confront hidden assumptions (Marder, 2000), and provide useful insights for the design of experiments or potential engineering applications.

Further, in selecting some aspects of a phenomenon to include, and others to ignore, creating a model abstracts a multi-faceted phenomenon into a concise, but inevitably simplified, representation. Thus, models simultaneously act as an instantiation of a theory and an abstraction of a phenomenon (Rosenblueth and Wiener, 1945; Stafford, 2009). This dual role of models is the foundation of their use in explanation (Cartwright, 1997).

Descriptive explanations

The first problem often encountered in scientific research is: What is the phenomenon? Phenomena are not divided into discrete entities a priori, but instead appear as a continuous multifaceted stream with many possible methods of observation and many aspects that could be observed. Thus, the set of characteristics that define a phenomenon are often unclear. This problem is addressed with a descriptive explanation (Kaplan and Bechtel, 2011). For example, to explain the spikes observed from a hippocampal neuron we could use a theory of “place cells” (O'Keefe and Nadel, 1978): a collection of ideas that defines the relationship between neural activity in the hippocampus and an animal's position in an environment, which can be instantiated in a model that specifies that relationship in an equation (O'Keefe and Nadel, 1978; Redish, 1999; Colgin, 2020). Descriptive models are founded on basic assumptions of which variables to observe and how to relate them. At its heart, a descriptive explanation is simply a selective account of phenomenological data; indeed, descriptive models are often called phenomenological models (Craver, 2007; Kaplan, 2011) or, when they are well established, phenomenological laws (Cartwright, 1997).

Mechanistic explanations

After addressing the “what” question, one might ask: How does the phenomenon arise? This problem is addressed with a mechanistic explanation, which explains a phenomenon in terms of its component parts and their interactions (Machamer et al., 2000; Craver, 2007; Bechtel and Richardson, 2010). For example, to explain the activity of place cells, we can create explanations based on afferent information from other structures, internal connectivity patterns, and intraneuronal processing, which can be instantiated in a model that specifies how they interact to produce neural firing (Redish, 1999; Hartley et al., 2000; Barry et al., 2006; Fuhs and Touretzky, 2006; Solstad et al., 2006; Giocomo et al., 2011; Sanders et al., 2015). A mechanistic model is founded on an assumption of which parts and processes are relevant, and illustrates how their interaction can produce a phenomenon or, equivalently, how the phenomenon can emerge from these parts. Often these parts are considered to be causally relevant to the phenomenon, and a mechanistic explanation is often also referred to as a causal explanation (Machamer et al., 2000; Craver, 2007; Bechtel and Richardson, 2010).

Mathematical mechanistic models in neuroscience often take the form of a dynamical system (Koch and Segev, 1989; Ellner and Guckenheimer, 2006; Izhikevich, 2007; Ermentrout and Terman 2010; Gerstner et al., 2014; Börgers, 2017; Gabbiani and Cox, 2017), in which a set of variables represent the temporal evolution of component processes or their equilibrium conditions. For example, the classic Hodgkin–Huxley model uses a set of four coupled differential equations to represent the dynamics of membrane potential and voltage-dependent conductances, and shows how an action potential can emerge from their interaction by producing a precise prediction of the progression of the membrane potential in time (Hodgkin and Huxley, 1952). However, qualitative mechanistic models, in which complex processes are summarized in schematic or conceptual structures that represent general properties of components and their interactions, are also commonly used. For example, Hebb considered a conceptualization of neural processing in which coincident firing of synaptically connected neurons strengthened the coupling between them. From this model, Hebb was able to propose how memories could be retrieved by the completion of partial patterns and how these processes could emerge from synaptic plasticity, as cells that were coactive during a particular stimulus or event would form assemblies with the ability to complete partially activated patterns (Hebb, 1949).

Mechanistic models represent the (assumed) underlying processes that produce the phenomenon (Craver, 2007; Kaplan and Bechtel, 2011). They can be used to make predictions about situations where the same processes are presumed to operate (Ellner and Guckenheimer, 2006). This includes the effects of manipulations to component parts, and circumstances beyond the scope of data used to calibrate the model.

Normative explanations

In addition to the mechanistic question of “how,” we can also ask the question: Why does the phenomenon exist? This kind of problem is addressed with a normative explanation, which is used to explain a phenomenon in terms of its function (Barlow, 1961; Kording et al., 2007; Bialek, 2012). A normative explanation of place cells would appeal to an animal's need to accurately encode its location, and could instantiate that need in a model of a navigation task (O'Keefe and Nadel, 1978; McNaughton and Nadel, 1990; Redish, 1999; Zilli and Hasselmo, 2008). Appealing to a system's function serves as a guiding concept that can be a powerful heuristic to explain its behavior based on what it ought to do to perform its function (Dennett, 1989). This kind of explanation has a long history in the form of teleological explanation, which explains a thing by its “purpose” (Aristotle, no date), and is often used implicitly in biological sciences, for example, stating that the visual system is “for” processing visual information. In neuroscience, functions often come in the form of cognitive, computational, or behavioral goals.

When quantified, normative models formalize the goal of the phenomenon in an objective function (also known as a utility or cost function), which defines what it means for a system to perform “well.” These models are founded on an assumed statement of a goal and the constraints under which the system operates. For example, models of retinal function formalize the goal of visual processing using equations that represent the ability to reconstruct a sensory signal from neural responses, under the constraints of sensory degradation and a limited number of noisy neurons (Rieke et al., 1997; Field and Rieke, 2002; Doi and Lewicki, 2014). Such an approach also relies on an assumption of an underlying optimization process. This assumption is often justified by appealing to evolution, which might be expected to optimize systems (Barlow, 1961; Parker and Smith, 1990; Bialek and Setayeshgar, 2008). However, evolution does not guarantee optimality because of limitations of genetic search (Gould and Lewontin, 1979; Gould, 1983). Moreover, there are numerous processes in physical, biological, neurologic, and social systems that can drive phenomena toward a state that maximizes or minimizes some objective function; however, these processes each also have their own unique limitations. For example, physical processes that minimize surface-to-volume ratio create hexagonal tessellations in beehives, but this process is limited by the physical properties of construction (Thompson, 1992; Smith et al., 2021). Economic markets might be expected to optimize the balance between offer and selling price, but are limited by imperfect and unbalanced information and the limited decision-making abilities of agents (Akerlof, 1978; Kahneman et al., 1991; Shleifer, 2000; Fox, 2009; Gigerenzer and Gaissmaier, 2011). Similarly, supervised learning might be expected to optimize object discrimination, but its implementation in the brain would be limited by constraints, such as synaptic locality and the availability of credit signals and training data (McNaughton et al., 1978; Häusser and Mel, 2003; Takeuchi et al., 2014; Richards et al., 2019; Hamrick et al., 2020; Hunt et al., 2021). Where each of these processes might be expected to bring systems toward an optimal solution, the constraints under which they operate may themselves impose distinct signatures on the systems they optimize.

The descriptive/mechanistic/normative classification depends on context

Theories and models do not exist in isolation, but are embedded in scientific practice. As the descriptive/mechanistic/normative categorization reflects the problem being solved, it can be applied to both theories and models depending on the context (i.e., kind of explanation) in which they are being used. In general, this categorization is independent of whether an explanation is accepted by the scientific community. For instance, a mechanistic explanation does not cease to be mechanistic if it is not adopted (e.g., because some of its predictions are not experimentally corroborated). Further, models with the same structure can be used for different purposes, and can thus be assigned to a different category in different contexts. For example, the integrate-and-fire model can be used as a descriptive model for membrane potential dynamics, or as a mechanistic model for the neuronal input-output transformation; and while the Hodgkin–Huxley model was discussed above as a mechanistic model for the problem of spike generation, it was originally proposed to be “an empirical description of the time course of the changes in permeability to sodium and potassium” (Hodgkin and Huxley, 1952). Indeed, theories often start as an effort to solve one class of problem, and over time develop aspects to address related problems of different classes, resulting in a theory with descriptive, mechanistic, and normative aspects.

Descriptive models define abstractions at different levels

Abstraction is most obvious when we consider the construction of descriptive explanations. First, abstractions are made when researchers decide which aspects of a phenomenon not to include. For example, the cable equation which describes the relationship between axonal conductance and membrane potential (Rinzel and Ermentrout, 1989; Rall, 1992; Gerstner et al., 2014) does not include details about intracellular organelles, the dynamics of individual ion channels, or the impact of nearby neurons on the extracellular potential. Importantly, these models do not include many larger-scale effects (e.g., the neuron's embedding in a circuit, or the social dynamics of the agent) as well as smaller scale factors (Vinogradov et al., 2022). The process of abstraction thus applies to both phenomena at smaller scales (organelles) and at larger scales (social interactions of the agent) that are hypothesized to be unnecessary to address the question at hand. Each of these factors are abstracted away, leaving only the features chosen to be represented in a model's structure.

Second, the aspects that are included must be represented in an idealized form. For instance, ionic flux through the cell membrane is not a strictly linear current function of voltage and conductance, but we often idealize it as such for tractability (Koch and Segev, 1989; Rall, 1992; Hille, 2001). These idealizations are assumptions about a phenomenon which are, strictly speaking, false, but are used because they serve some purpose in creating the model (Potochnik, 2017).

Classic accounts of neuroscience emphasize analysis at different levels of abstraction (Wimsatt, 1976; Marr, 1982; Sejnowski et al., 1988; Churchland and Sejnowski, 1994; Shepherd, 1994; Craver, 2007) (Box 1). However, despite the ubiquity of level-based views of neuroscience and a number of proposed schemes, no consensus can be found on what the relevant levels of abstraction are, or even what defines a level (Guttinger and Love, 2019). Suggestions of different level schemes range from those of computational abstraction (Colburn and Shute, 2007; Wing, 2008), which simplifies a process to be independent of its specific implementation or physical substrate, to levels of conceptual abstraction, which delineate the degree of idealization versus relatability to data (O'Leary et al., 2015), and levels of physical abstraction, which are used to deal with different spatiotemporal scales (Churchland and Sejnowski, 1994). However, recent analyses suggest that natural phenomena are not organized into levels in a universally coherent manner (Potochnik and McGill, 2012; Potochnik, 2017, 2020). From a pragmatic view, levels of abstraction need not reflect discrete “levels” in nature but are indicative of our problem-solving strategies and constraints. Because different abstractions can facilitate different research aims (Potochnik, 2017), multiple descriptive models are needed to represent the same phenomenon but abstract different features to different degrees.

Mechanistic and normative models connect levels of abstraction

Without links between them, we would be left with a hodgepodge of different descriptions. However, unification has been noted as a strong desideratum for scientific theories (Keas, 2018; Schindler, 2018). The relationship between different descriptions of the same phenomena can often be expressed in terms of a mechanistic explanation. For example, we might describe single-neuron activity in terms of membrane currents, or by listing a set of spike times: a natural reduction in the dimensionality that can result from many possible combinations of currents (Golowasch et al., 2002; Prinz et al., 2004). A mechanistic model (e.g., Hodgkin and Huxley, 1952) that demonstrates how spike times emerge from currents connects the descriptions at the two levels and, in addition, does so asymmetrically, as it does not claim to be a mechanism by which currents emerge from spike times. By bridging descriptions that each abstract different features to different degrees, mechanistic explanations create a multilevel “mosaic unity” in neuroscience (Craver, 2007), in which descriptions are grounded through their interconnections, and more abstract features are grounded in their emergence from less abstract counterparts (Oppenheim and Putnam, 1958; Craver, 2002, 2007; Bechtel, 2008; Kaplan and Bechtel, 2011).

In contrast, a normative explanation connects descriptions by appealing to the ability of less abstract features to satisfy a description of more abstract goals. For example, the mammalian hypothalamus could be described as maintaining body temperature like a thermostat (Morrison and Nakamura, 2011; Tan and Knight, 2018) or as a circuit of interconnected neurons. A normative model connects the two descriptions by explaining the negative feedback loop in the circuit through its ability to achieve those thermostatic functions. Because functions exist over a range of levels, from cellular to behavioral or computational, we could imagine a “multilevel” approach to understanding the mammalian hypothalamus that in turn uses the goal of a negative feedback loop to explain the developmental processes that establish hypothalamic connectivity. Like their mechanistic counterparts, normative explanations establish links between descriptions, which each have their own utility for different problems by virtue of their unique abstractions.

Thus, the threefold division of explanatory labor in neuroscience falls naturally into the different roles a model can play in terms of levels of abstraction. Descriptive explanations define abstractions of phenomena at different levels, while mechanistic and normative explanations bridge levels of abstraction. Descriptive models, rather than “mere” descriptions of phenomena (as they are sometimes dismissed), are the necessary foundation of both normative and mechanistic models. In turn, mechanistic and normative explanations connect a description at a “source” level to a description at a higher or lower “target” level (Fig. 2). Each of the terms that represent the components of mechanistic models and the constraints of normative models are descriptive models at a lower level of abstraction, while those that represent the emergent properties of mechanistic models and the goals of normative models are descriptive models at a higher level of abstraction. Given their multilevel nature, a dialogue between descriptive, normative, and mechanistic models is needed for a theoretical account of any neuroscientific phenomenon.

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Figure 2.

Interactions between three explanatory processes and levels of abstraction. Descriptive explanations define an idealized abstraction of specific aspects of a phenomenon for discussion, measurement, and repeatability. Mechanistic explanations account for properties of a phenomenon by their emergence from less abstract phenomena, while normative explanations account for those properties by appealing to their ability to perform more abstract goals.

At what level of abstraction should a model be built?

As different abstractions trade-off advantages and disadvantages, the selection of which abstraction to use is highly dependent on the problem at hand (Herz et al., 2006). Current neuroscientific practice generally attempts two approaches for selecting the appropriate level of abstraction, which serve different purposes. The first approach is to try to find as low a level as possible that still includes experimentally supported details and accounts for the phenomenon. For example, one might explain the phenomenon of associative memories using compartmental models of pyramidal cell networks, including specific active conductances, dendritic compartments, pharmacological effects on different inputs arriving at different compartments and identifying the consequences for learning and recall (Hasselmo, 1993). The multiplicity of parameters and variables used in this approach provides many details that can be matched to observable features of a phenomenon and can capture unexpected properties that emerge from their interaction. However, these details need to be extensively calibrated to ensure the model is accurate, and can be very sensitive to missing, degenerate, or improperly tuned parameters (Traub et al., 1991, 1999). The second approach is to try to find the most abstract level that can still account for the phenomenon. For example, we might instead appeal to the classic Hopfield network, in which units are binary (+1, −1), connections are symmetrical, and are updated using a very simple asynchronous rule (Hopfield, 1982; Hertz et al., 1991). While more abstract models sacrifice the ability to make predictions about lower-level details, their insights are often more robust to specific (e.g., unobserved) physiological details, and by reducing a complicated system to a small number of effective parameters, they allow for powerful analysis on the influences to the system properties. Further, abstract models can provide conceptual benefits, such as intuition for how the system works and the ability to generalize to other systems that can be similarly abstracted (Gilead et al., 2012, 2019; O'Leary et al., 2015).

Another important consideration is the ability of models at different levels to interface with different experimental modalities or scientific fields. Every measurement is itself an abstraction, in that it is a reduced description of the part of the universe corresponding to the measurement (Chang, 2007b). For example, fMRI measures blood flow across wide swaths of cortex but abstracts away the interactions between individual neurons, while silicon probes measure extracellular voltage but abstract away intracellular processes, and calcium imaging measures neuronal calcium levels, but abstracts away the electrophysiology of neuronal spiking. All of these are discussed as “neural activity,” but they likely reflect different aspects of learning, performance, and dynamics. Moreover, subsequent processing abstracts these signals even further, such as correlation (functional connectomics) in fMRI, sorting voltage signals into putative cell “spiking” from silicon probes, and treating calcium transients as “events” from calcium imaging. The abstraction made by one measurement device might lend itself to explanations at a given level, but not others, and the measurements available are important considerations when selecting which abstractions to make in our models.

Similarly, models at different levels are often used by distinct scientific fields or communities. The existence of a literature with a rich body of relevant work can provide details and support for components of a model outside of the immediate problem of interest. Integrating theories and models across these different fields can be particularly beneficial for scientific progress (Grim et al., 2013; Wu et al., 2019); however, crossing levels can be a sociological problem as well as a methodological one because different fields of study often use different languages and operate under different conceptual frameworks.

In general, it is important that researchers spell out the abstractions being made in their models, including their purposes as well as their limitations. By being concrete about the abstractions made, researchers can increase the reliability of their theories. Importantly, as noted above, it is useful to acknowledge not only the simplifications made about smaller-scale phenomena, but also the simplifications made as to larger-scale interactions that have been abstracted away from a theory.

Linking theory and phenomena

The domain of a theory is the set of phenomena that it purports to explain (Mitchell et al., 1986; Redish, 1997; Kuhn, 2011, 2012). The domain is therefore a set of data-imposed constraints, and the theory should provide an explanation consistent with those constraints. Theoretical studies should be explicit about what phenomena do and do not lie in their intended domain. In practice, nascent theories are often evaluated not only by their ability to explain data in their proposed domain (Laudan, 1978; Feyerabend, 1993) but also by their potential to expand beyond the initial domain with further development (Lakatos, 1978). For example, the theory that action potentials arise from voltage-dependent changes in ionic permeability (Hodgkin and Huxley, 1952; Goldman and Morad, 1977; Katz, 1993; Hille, 2001) should apply to the domain of all action potentials in all neurons. Early theories of action potential function identified voltage-gated sodium currents as the primary depolarizing component and formalized their action in models that developed into the Hodgkin–Huxley framework (Hodgkin and Huxley, 1952). When some action potentials were later found to be independent of sodium concentrations, it was straightforward to incorporate other voltage-gated channels within the same framework (Koch and Segev, 1989; Hille, 2001; Gerstner et al., 2014).

By instantiating a theory in a specific structure (Rosenblueth and Wiener, 1945; Stafford 2009), models play a key role in connecting a theory to phenomena in its domain. However, no model is directly comparable to experimental data by virtue of its structure alone. As noted above, a model also consists of an interpretation of how that structure relates to its target phenomena (Weisberg, 2013). This interpretation is specified by a translation function: a statement of how the model's components map onto its target phenomena. A translation function may be as straightforward as “variable V represents the membrane potential in millivolts,” but it can also be less constrained, e.g., “variable V describes the slow changes in the membrane potential and ignores all spiking activity.” In other cases, the translation function can be complex, as parts of the model can have a loose correspondence to general features of large classes of data, and can represent highly abstract effective parameters or qualitative behaviors. For example, the units in Hopfield's attractor network models (Hopfield, 1982; Hopfield and Tank, 1985; Hertz et al., 1991) are not meant to directly correspond to measurable properties of biological neurons but are instead intended to reflect qualitative features, namely, that neural populations are “active” or not. In effect, the translation function spells out the abstractions made by the model. Specifying the translation function of a model is as important as defining its structure (Weisberg, 2013). While these descriptions are often provided for highly abstract models, models that describe finer spatiotemporal scales (e.g., detailed compartmental models of neurons) are often considered to be “biologically realistic” and assume a simple or obvious translation function. However, it is important to remember that these models are also abstractions, albeit at a different level, and a proper description of the abstractions made will help clarify both the uses and the limitations of such models. By specifying the intended correspondence between model terms and phenomena, the translation function operationalizes the concepts associated with those terms in the theory (Bridgman, 1927; Chang, 2007a).

Experiments ground model assumptions

With a well-defined translation function in hand, we can consider the ways in which models are informed by experimental data. As outlined above, the components of descriptive, mechanistic, and normative models are each based on a different set of foundational assumptions. These assumptions are not generally arbitrary but are informed by experimental observations and results.

Descriptive models are founded on an assumed relationship between variables, which is generally formulated to capture an observed regularity in experimental data. These initial observations often rely on “exploratory” experiments, which attempt to identify empirical regularities and the constructs with which to describe them (Steinle, 1997). In specifying the characteristic properties of a phenomenon, descriptive explanations delineate the attributes that are expected to be replicable in future experiments and play a foundational role in subsequent mechanistic and normative models. This is extremely important for the current replication controversy (Baker, 2016; Goodman et al., 2016; Fanelli, 2018; Redish et al., 2018). A recent National Academy report (National Academies of Sciences and Medicine, 2019) characterizes replicability as the ability to obtain consistent results across multiple studies, and contrasts it with reproducibility, defined as the ability to get the same results when applying the same analyses to the same data. Several authors have suggested that the replication crisis is indeed a crisis of theory development, as it is the scientific claims (not data) that should be replicable (Drugmonkey, 2018; Redish et al., 2018; Smaldino, 2019). We suggest that this crisis stems from three sources: (1) a failure to define domains correctly, assuming that limited observations correspond to a much larger range of phenomena than they actually do; (2) a failure to formalize observations in adequate descriptive models (e.g., an overreliance on correlation, or assumed simple relationships); and (3) a failure to connect those descriptive models with mechanistic or normative models that integrate descriptions at different levels of abstraction.

Mechanistic models are founded on a set of parts and interactions that are assumed to be relevant to a target phenomenon. The existence of candidate parts/interactions can be informed by experimental observations, and their relevance (or irrelevance) to a given target phenomenon is often derived from experimental or natural interventions (Pearl, 2009). Once the decision is made to include a part/interaction in a mechanistic model, its corresponding terms can be parameterized by virtue of the descriptive models at their source level of abstraction. For example, when trying to explain the phenomenon of burst spiking in thalamocortical neurons, we might observe the presence of a hyperpolarization-activated current (I_h) which, when blocked, disrupts burst spiking (McCormick and Pape, 1990). We can then calibrate the parameters used to model I_h with values acquired through slice experiments.

Experimental data can also inform the founding assumptions (goal/constraints) of normative models. For example, when trying to explain the responses of visual neurons, we might parameterize the constraints of an efficient coding model with data from retinal photoreceptors (Field and Rieke, 2002). As with mechanistic models, these normative parameters rely on the descriptive models we have for photoreceptor properties. However, grounding an assumed function (e.g., “vision”) in experimental data can be more challenging. This arises from a notable asymmetry between mechanistic and normative approaches: while the founding assumptions of a mechanistic model (parts/interactions) are less abstract than their target phenomena, the founding assumptions of normative approaches (a function/goal) are generally more abstract than the phenomenon they are used to explain. This often results in normative approaches being termed “top-down,” in contrast to “bottom-up” mechanistic modeling. In practice, functions are often operationalized via performance on a specified task, rendering them groundable in experimental data. For example, the assumed goal of primate facial recognition areas is grounded in the change in facial recognition abilities when those neural systems are manipulated or absent, neural responses to facial stimuli, and in the coupling of those areas with sensory and motor areas providing a behavioral circuit (Gross et al., 1969; Tsao et al., 2006; Grimaldi et al., 2016; Moeller et al., 2017).

Experiments assess solution quality

As has been noted by many previous authors, we cannot definitively “confirm” theories (Popper, 1959), nor can we definitively test/falsify the validity of a theory in isolation (Lakatos, 1980; Duhem, 1991). However, a theory's utility does not require absolute confidence in its validity, but only a track record of solving problems in its domain. By instantiating theories in a model with a well-defined translation function, we can assess the quality of solutions proposed with a given theory by comparing the behavior of those models to experimental observations.

In the case of descriptive models, model fitting can estimate confidence intervals and goodness of fit for the best-fitting parameter values, and can even be used to quantitatively compare candidate models to determine which can best explain experimental data with the fewest parameters. A researcher might build a mechanistic model with terms that correspond to the proposed parts to see if they are able to reproduce features of the data, or test the model's ability to predict the effect of experimental manipulations. Alternatively, a researcher can hypothesize that the system is performing some function, make a normative model that instantiates the goal, and see if properties of the data match those expected from a system optimizing that goal. In these “confirmatory” (theory-driven/hypothesis-testing) experiments, models are used to apply existing theories to account for observed phenomena, compare possible instantiations of a theory, or even compare theories with overlapping domains to see which better accounts for the phenomenon. In each case, the assumptions of the model act as a hypothesis and the degree of similarity between model and experimental data are used to assess the sufficiency of a theory (and its specific model instantiation) to account for a phenomenon.

However, the value of modeling is often in its ability to show insufficiency of a theory/model to account for experimental data. Rather than invalidating the theory, this can often prompt updates to the theory or a search for yet-unobserved relevant phenomena. For example, early models of head-direction tuning found that a mechanism based on attractor networks required recurrent connections not supported by anatomic data (Redish et al., 1996). This incompatibility led to subsequent analyses which found that the tuning curves were more complicated than originally described, matching those seen in the model without the recurrent connections (Blair et al., 1997). Similarly, the usefulness of normative models often lies in their ability to identify when a system is performing suboptimally (Parker and Smith, 1990). Such a finding can provide additional information about unexpected functions or constraints. When there is a mismatch between a normative model and observed phenomena, one could hypothesize that the agent is optimizing a different goal (Fehr and Schmidt, 1999; Binmore, 2005), new constraints that limit the processes available (Simon, 1972; Mullainathan, 2002), historical processes that could limit the optimization itself (Gould and Lewontin, 1979; Gould, 1983), or computational processes that limit the calculations available to the system (Nadel, 1994; Schacter, 2001; Redish, 2013; Webb et al., 2021). For instance, several studies have found that foraging subjects tend to remain at reward sites longer than needed (Camerer, 1997; Nonacs, 2001; Carter and Redish, 2016) and accept longer-delay offers than would be expected to maximize total reward (Wikenheiser et al., 2013; Sweis et al., 2018a,b; Schmidt et al., 2019). However, optimality could be restored by assuming an additional factor in the cost function (Simon, 1972) subsequently characterized as “regret”: an increased cost of making a mistake of one's own agency compared with equivalently poor outcomes that were not because of recognizable mistakes (Zeelenberg et al., 2000; Schmidt et al., 2005; Wikenheiser et al., 2013; Steiner and Redish, 2014; Sweis et al., 2018b, Coricelli et al., 2005). Similarly, Fehr and colleagues have found that normative explanations of behavior in a multiplayer game require an additional component with information about one's companion's success in addition to one's own, to account for the observed behavior (Fehr and Schmidt, 1999; Binmore, 2005; Fehr and Krajbich, 2014).

Modeling experiments explore theory implications

Confirmatory experiments can even be conducted without direct comparison to data, as phenomena at both the target and source levels of abstraction can be pure theoretical entities. Similar to their benchtop counterparts, we can treat different parameters or model instantiations as independent variables in the experiment, and test their sufficiency to account for different aspects of the phenomenon as the dependent variables (Omar et al., 2014; Gerkin et al., 2018). One can use these models as experiments to test the feasibility of theoretical claims in tractable idealized systems. For example, Hopfield's attractor network models (Hopfield, 1982; Hopfield and Tank, 1985) provided strong support for Hebb's theory (Hebb, 1949) that increased connectivity from coactive firing could create associative memory, by showing that strong connections between simple neuron-like entities were sufficient to produce cell assemblies that could be accessed through a pattern-completion process (Hertz et al., 1991).

Like their physical analogues (e.g., the 6-OHDA rat or the MPTP monkey), models can be used for exploratory experiments as well. Exploration of the Hopfield model (Kohonen, 1980, 1984; Hopfield, 1982; Hopfield and Tank, 1985) revealed novel properties of categorization, tuning curves, and pattern completion in the neuron-like entities, which were later identified experimentally (Rosch, 1983; Lakoff, 1990; Obermayer et al., 1992; Swindale and Bauer, 1998; Freedman et al., 2001, 2003; Obermayer and Sejnowski, 2001; Swindale, 2004; Wills et al., 2005; Yang and Shadlen, 2007; Colgin et al., 2010; de Villers-Sidani and Merzenich, 2011; Jezek et al., 2011; Nahum et al., 2013; Kelemen and Fenton, 2016). Exploratory modeling experiments can instantiate idealized aspects of a theory to help build intuition for the theory itself. Hopfield's model and its subsequent derivatives have provided researchers with a deeper understanding of how memories can be accessed by content through pattern-completion processes and given rise to concepts, such as “basins of attraction” (Hopfield, 1982; Hertz et al., 1991). These computational discoveries can help build understanding of the theory, and lead to predictions and ideas for new experiments.

Modeling experiments are especially useful in the context of theory development (Guest and Martin, 2020). When a phenomenon cannot be readily explained using an existing theory, assumptions can be made as the basis of a modeling experiment. The behavior of this model can then be used to evaluate the sufficiency of these assumptions to account for the phenomenon. Often, these modeling experiments precede a well-formed theory, and a theorist will perform numerous experiments with different models in the process of developing a theory (van Rooij and Baggio, 2020). Over time, specific successful model formulations can become closely associated with the theory and develop into its canonical instantiations that make the theory applicable to a wider range of problems and give more precise solutions.

In conclusion, a scientific theory is a thinking tool: a set of ideas used to solve specific problems. We can think of theoretical neuroscience as a field which approaches problems in neuroscience with the following problem-solving methodology: theories exist within conceptual frameworks and are instantiated in models which, by virtue of a translation function, can be used to assess a theory's ability to account for phenomena in the theory's domain or explore its further implications (Fig. 3).

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Figure 3.

How the various components discussed in this manuscript interact. The domain of a theory is the set of phenomena which it purports to explain. Theories are instantiated in models, which are an abstraction of phenomena in the domain, as specified by a translation function. By constraining the form solutions can take, a conceptual framework defines a way of looking at a problem, within which models and theories can be proposed. A given model can instantiate more than one theory, and a theory can be instantiated by more than one model.

We identified three kinds of explanations that play distinct roles in this process: those in which descriptive theories and models are used to define the abstractions by which we describe a phenomenon; those in which mechanistic theories and models are used to explain phenomena in terms of lower-level parts and their interactions; and those in which normative theories and models are used to explain phenomena in terms of a function at a higher level of abstraction.

These considerations lead to a more concrete view of theory in neuroscience under the pragmatic view: a theory is a set of assumptions available to be instantiated in models, whose adequacy for problems in their domain has been vetted via experimentation, and with a well-established translation function that defines their connection to phenomena. Over time and through the development of canonical model formulations, theories become more rigorous, such that researchers agree on how they should be implemented to explain specific domains. A theory in this sense is not a formal set of laws, but a continuously developing body of canonical models and model-phenomenon correspondences, bound together partly by history and partly by shared problem-solving methods and standards (Bechtel, 1993).

What recommendations can we take away from this perspective? First and foremost, scientists should be explicit about the underlying components of their theory. Reliability of theoretical work depends on being explicit about the domain that the theory purports to cover, the abstractions used (what has been ignored and left out), and the translation function to connect the theory to actual measurements. Furthermore, thinking of the pragmatic aspects suggests being explicit about what problems the work proposes to solve, what conceptual frameworks the theory fits in, and what the founding assumptions of the models are.

Finally, it is interesting to consider that we might apply our taxonomy to our own framework. The concept that “the ultimate goal of a theory is to provide tools that allow one to better explain and control one's environment” is a normative theory of the goal of scientific theories; the concept that “models instantiate theories and allow one to test their viability and their relationship to phenomena” is a mechanistic theory of how those theories achieve that goal; and the concept that “theories live within a framework that a community applies to them” is a descriptive theory of theories. One could imagine a metascientific research program which studies the available phenomena (e.g., the scientific literature) to test and further develop those theories, and even the use of models of the scientific process itself (e.g., Devezer et al., 2019). The benefits of such a research program could prove as impactful for scientific practice as other theories have proven for manipulation of phenomena in their domain.