Computational complexity as a potential limitation on brain-behaviour mapping

Abstract

Within the reductionist framework, researchers in the special sciences formulate key terms and concepts and try to explain them with lower-level science terms and concepts. For example, behavioural vision scientists describe contrast perception with a psychometric function, in which the perceived brightness increases logarithmically with the physical contrast of a light patch (the Weber-Fechner law). Visual neuroscientists describe the output of neural circuits with neurometric functions. Intuitively, the key terms from two adjacent scientific domains should map onto each other; for instance, psychometric and neurometric functions may map onto each other. Identifying such mappings has been the very goal of neuroscience for nearly two centuries. Yet mapping behaviour to brain measures has turned out to be difficult. Here, we provide various arguments as to why the conspicuous lack of robust brain-behaviour mappings is rather a rule than an exception. First, we provide an overview of methodological and conceptual issues that may stand in the way of successful brain-behaviour mapping. Second, extending previous theoretical work (Herzog, Doerig and Sachse, 2023), we show that brain-behaviour mapping may be limited by complexity barriers. In this case, reduction may be impossible.

Keywords: brain–behaviour mapping; cognitive ontology; computational complexity; localisationism; neural degeneracy.

FIGURE 1

(a) A hypothetical example of a psychometric function and the corresponding neuronal response (neurometric) function. As stimulus amplitude increases (x‐axis), detection improves, as evidenced by the logistic growth of the percent correct in a two‐alternative forced‐choice (2AFC) task (y‐axis, blue circular data points). The probability of the neuron that is selective to the stimulus responding follows a very similar function, as seen in the logistic curve of the percent unit response (y‐axis, orange square data points). In another neuron that is less selective for the given stimulus, detection is much weaker, requiring a larger stimulus amplitude to saturate to the maximal response (100%). Inspired by Figure 6 in Parker and Newsome (1998). (b) A caricature of the subpart coding framework. Low‐level features of the chair (lines) are processed in primary visual cortex (V1), more complex features (angles) are processed in secondary visual cortex (V2), shapes are processed in visual area V4, and the entire chair object is represented in inferotemporal cortex (IT). (c) Fourier transforms of the chair in B ‘coded’ by spatial frequencies rather than localised spatial features. (d) Inverted hourglass architecture of brain–behaviour mapping: an illustration of the relationship between the low‐dimensional physical level (e.g. a Vernier stimulus with the bottom line offset to the left or right of the top line), the high‐dimensional neural level (over 140 million neurons in V1 alone), and the low dimensional behavioural level (e.g. a 2AFC task to determine the Vernier offset direction).