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Content and misrepresentation in hierarchical generative models

  • S.I. : Predictive Brains
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Abstract

In this paper, we consider how certain longstanding philosophical questions about mental representation may be answered on the assumption that cognitive and perceptual systems implement hierarchical generative models, such as those discussed within the prediction error minimization (PEM) framework. We build on existing treatments of representation via structural resemblance, such as those in Gładziejewski (Synthese 193(2):559–582, 2016) and Gładziejewski and Miłkowski (Biol Philos, 2017), to argue for a representationalist interpretation of the PEM framework. We further motivate the proposed approach to content by arguing that it is consistent with approaches implicit in theories of unsupervised learning in neural networks. In the course of this discussion, we argue that the structural representation proposal, properly understood, has more in common with functional-role than with causal/informational or teleosemantic theories. In the remainder of the paper, we describe the PEM framework for approximate Bayesian inference in some detail, and discuss how structural representations might arise within the proposed Bayesian hierarchies. After explicating the notion of variational inference, we define a subjectively accessible measure of misrepresentation for hierarchical Bayesian networks by appeal to the Kullbach–Leibler divergence between posterior generative and approximate recognition densities, and discuss a related measure of objective misrepresentation in terms of correspondence with the facts.

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Notes

  1. We also here include Fodor’s (1990) solution to the disjunction problem, based on asymmetries among nomic relations.

  2. Of course, we do not mean to rule out that parts may also be structured and function themselves as structural representations. Indeed, this is likely the case in hierarchically organized systems like those considered in this paper, but we lack space to consider this issue here.

  3. This way of putting things may go to the heart of some of the more radical formulations of the implications of PEM-style accounts for the nature of the mind-world relation—for example, claims that perception is “controlled hallucination” (Grush 2004). Similarly, Geoff Hinton (one of the originators of contemporary models of perceptual inference involving generative models) claims in essence that the contents of mental states are hypothetical worlds (Hinton 2005).

  4. There may be ways of resisting the conclusion in the case of misrepresentation by distinguishing types of misrepresentation, as discussed in Sect. 5 below. However, the point seems difficult to sidestep with respect to imagination.

  5. It should be noted that there are ‘wide’ versions of functional role semantics as well; see Harman (1973).

  6. We thank an anonymous reviewer for an earlier version of this paper for pressing this crucial point, as well as the issue concerning internalism just considered.

  7. This is a decidedly Kantian reading of these ideas, but we believe it would be more procrustean to attempt to defend the opposite view according to which all representation in imagination is really somehow representation of one’s physical environment. This is true even though actual sources of sensory input play an indispensable explanatory role within the PEM framework, and in fact are etiologically necessary to get any kind of representation off the ground.

  8. O’Brien and Opie (2004) distinguish strictly between functional role semantics and their preferred version of structural representation theory on the grounds that the former appeals to causal relations among vehicles while the latter appeals to physical relations. It is not obvious, however, why the latter category should preclude the former.

  9. Gładziejewski and Miłkowski (2017) draw a similar conclusion for different reasons.

  10. It is sometimes claimed that this notion of representation is also too liberal. The “exploitability” constraint mentioned earlier goes some way toward mitigating this. Also note that interesting, human-like cases at least are hard to come by: a system must, as a matter of empirical fact, be quite complex before it is able to structurally represent deeply hidden environmental causes.

  11. There is thus reason to think that perceptual systems employ generative models based on considerations about learning alone, in addition to the considerations about contextually biased interpretation of stimuli mediated by extra-classical receptive field effects.

  12. Though of course the system need not begin by representing such distinctions, for reasons discussed in Sect. 2.3.

  13. It should be stressed that the construction of the reliable information channel and the development of meaningful representations are constitutively related. These are two ways of describing the process whereby causal structure (which representation exploits) is set up within cortical hierarchies.

  14. We thank an anonymous reviewer for pressing us to clarify this distinction, which is also drawn by Gładziejewski (2016), who uses the “X”-on-a-map example referred to here.

  15. Clearly, if each generative model represents only the hypothetical world whose causal structure is isomorphic to it, there can be no misrepresentation, and thus arguably no genuine representation either. We need an independent standard of comparison to define misrepresentation, but note that this target need not be the actual world: it could be one specified by a fictional description, for example.

  16. In Friston’s model (2005), only the top-down connections introduce nonlinearities, but this is just a further way in which the two models diverge while still sharing structure. The whole point, of course, is that the recognition model is a (to some degree crude) approximation of the posterior under the generative model.

  17. The distribution c of course specifies the relevant natural scene statistics. NSS are therefore important in principle to understanding Bayesian models of perception, as Orlandi claims (see discussion in Sect. 2.3), even if such models are interpreted in representational terms.

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Acknowledgements

We wish to thank Michael Kirchhoff and two anonymous reviewers for comments. JH is supported by Australian Research Council Grants FT100100322 and DP160102770, and by the Research School Bochum and the Center for Mind, Brain and Cognitive Evolution, Ruhr-University Bochum.

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  1. City University of New York Graduate Center, New York, NY, USA

    Alex Kiefer

  2. Cognition & Philosophy Lab, Monash University, Melbourne, Australia

    Jakob Hohwy

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Kiefer, A., Hohwy, J. Content and misrepresentation in hierarchical generative models. Synthese 195, 2387–2415 (2018). https://doi.org/10.1007/s11229-017-1435-7

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