We applaud Lieder and Griffiths’ focus on resource-rational explanations. We also think that it is incomplete. Their proposed top-down method for analyzing rational process models is atomistic. That is, it starts with an individual process and determines the optimal tradeoffs between resource usage and other desiderata. Done well, this constrains the empirical search space to a class of algorithms or even a token algorithm. These analyses are valuable. Yet atomistic analyses cannot capture an important constraint on resource allocation, which is competition between different processes for shared resources (Klein Reference Klein2018). We suggest that holistic interactions between processes on at least three different timescales – episodic, developmental, and evolutionary – must be taken into account by a complete resource-bounded explanation.
First, consider interactions between processes on the timescale of task performance. We are capable multitaskers. Conversation while sight-reading is demanding but possible. But, some tasks that are trivial to do on their own interfere with one another when performed simultaneously. For example, it is difficult to simultaneously remember a three-digit number and do mental arithmetic. Connectionist models indicate that these limitations emerge from the multiplexed structure of control representations. Multiplexing refers to the strategy of using the same control representation across multiple task-domains, resulting in a limit in the number of tasks that can be performed at the same time (Botvinick & Cohen Reference Botvinick and Cohen2014; Cohen et al. Reference Cohen, Dunbar and McClelland1990). Importantly, the resource-bounds which drive the explanation of task conflict cannot be derived from considering either task in isolation. Only a holistic resource-rational analysis can show the tradeoffs between processes which compete for the same computational resources.
Analogous arguments apply at the learning and evolutionary timescales. Optimization of control processes occurs through learning over time. For example, native bilingual speakers use overlapping brain circuitry to support comprehension and production in both languages, and different contexts place different demands on these shared resources. Further, Green and Abutalebi (Reference Green and Abutalebi2013) demonstrate how control representations for language switching are parameterized over developmental time in a context-sensitive way. A child develops its capacity to switch between Spanish at school and English at home. These control processes will have to adapt as the child becomes more proficient in each language, and as they encounter new contexts with new demands. Crucially, this optimization cannot be performed for each developmental stage and context independently: efficient allocation of neural and computational resources must take into account inter-process interactions.
Higher-order optimization processes also occur on evolutionary timescales. Evolution puts harsh demands on possible forms. Evolution often satisfices rather than optimizes (Simon Reference Simon1996), and what can evolve often depends strongly on what already has evolved (Brown Reference Brown2013). This is a point which is made in the context of the re-use of information in gene regulatory networks (Calcott Reference Calcott2014) and the re-use and overlap of neural implementations (Anderson Reference Anderson2010). We suggest that it is equally well applied to the computational and algorithmic domains with which Lieder and Griffiths are concerned. For example, the problem of mobilizing cognitive control is thought to be solved by using reward-based learning algorithms (Botvinick & Braver Reference Botvinick and Braver2015). Given the phylogenetic breadth of reward learning, this may represent the re-use of an evolutionarily older algorithm. The search for particular first-order algorithms thus cannot be undertaken in isolation, but should be constrained by evolutionary considerations.
Science must start somewhere, and we think that the atomistic method proposed by Lieder and Griffiths is a useful way to begin empirical investigation. Yet, analyses which focus only on a single task must necessarily leave free parameters in order to incorporate potential resource competition. Thus, the pitfall of underdetermination, for which they rightly criticize others, can return for atomic resource explanations in a modified form. We believe that Lieder and Griffiths do have resources to tackle this problem, some of which are hinted at in their target article. To be fully satisfying, holistic attention to inter-process coordination will be especially important if the theory is to avoid vacuity.
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We applaud Lieder and Griffiths’ focus on resource-rational explanations. We also think that it is incomplete. Their proposed top-down method for analyzing rational process models is atomistic. That is, it starts with an individual process and determines the optimal tradeoffs between resource usage and other desiderata. Done well, this constrains the empirical search space to a class of algorithms or even a token algorithm. These analyses are valuable. Yet atomistic analyses cannot capture an important constraint on resource allocation, which is competition between different processes for shared resources (Klein Reference Klein2018). We suggest that holistic interactions between processes on at least three different timescales – episodic, developmental, and evolutionary – must be taken into account by a complete resource-bounded explanation.
First, consider interactions between processes on the timescale of task performance. We are capable multitaskers. Conversation while sight-reading is demanding but possible. But, some tasks that are trivial to do on their own interfere with one another when performed simultaneously. For example, it is difficult to simultaneously remember a three-digit number and do mental arithmetic. Connectionist models indicate that these limitations emerge from the multiplexed structure of control representations. Multiplexing refers to the strategy of using the same control representation across multiple task-domains, resulting in a limit in the number of tasks that can be performed at the same time (Botvinick & Cohen Reference Botvinick and Cohen2014; Cohen et al. Reference Cohen, Dunbar and McClelland1990). Importantly, the resource-bounds which drive the explanation of task conflict cannot be derived from considering either task in isolation. Only a holistic resource-rational analysis can show the tradeoffs between processes which compete for the same computational resources.
Analogous arguments apply at the learning and evolutionary timescales. Optimization of control processes occurs through learning over time. For example, native bilingual speakers use overlapping brain circuitry to support comprehension and production in both languages, and different contexts place different demands on these shared resources. Further, Green and Abutalebi (Reference Green and Abutalebi2013) demonstrate how control representations for language switching are parameterized over developmental time in a context-sensitive way. A child develops its capacity to switch between Spanish at school and English at home. These control processes will have to adapt as the child becomes more proficient in each language, and as they encounter new contexts with new demands. Crucially, this optimization cannot be performed for each developmental stage and context independently: efficient allocation of neural and computational resources must take into account inter-process interactions.
Higher-order optimization processes also occur on evolutionary timescales. Evolution puts harsh demands on possible forms. Evolution often satisfices rather than optimizes (Simon Reference Simon1996), and what can evolve often depends strongly on what already has evolved (Brown Reference Brown2013). This is a point which is made in the context of the re-use of information in gene regulatory networks (Calcott Reference Calcott2014) and the re-use and overlap of neural implementations (Anderson Reference Anderson2010). We suggest that it is equally well applied to the computational and algorithmic domains with which Lieder and Griffiths are concerned. For example, the problem of mobilizing cognitive control is thought to be solved by using reward-based learning algorithms (Botvinick & Braver Reference Botvinick and Braver2015). Given the phylogenetic breadth of reward learning, this may represent the re-use of an evolutionarily older algorithm. The search for particular first-order algorithms thus cannot be undertaken in isolation, but should be constrained by evolutionary considerations.
Science must start somewhere, and we think that the atomistic method proposed by Lieder and Griffiths is a useful way to begin empirical investigation. Yet, analyses which focus only on a single task must necessarily leave free parameters in order to incorporate potential resource competition. Thus, the pitfall of underdetermination, for which they rightly criticize others, can return for atomic resource explanations in a modified form. We believe that Lieder and Griffiths do have resources to tackle this problem, some of which are hinted at in their target article. To be fully satisfying, holistic attention to inter-process coordination will be especially important if the theory is to avoid vacuity.