On Logical Inference over Brains, Behaviour, and Artificial Neural Networks

Abstract

In the cognitive, computational, and neuro-sciences, practitioners often reason about what computational models represent or learn, as well as what algorithm is instantiated. The putative goal of such reasoning is to generalize claims about the model in question, to claims about the mind and brain, and the neurocognitive capacities of those systems. Such inference is often based on a model’s performance on a task, and whether that performance approximates human behavior or brain activity. Here we demonstrate how such argumentation problematizes the relationship between models and their targets; we place emphasis on artificial neural networks (ANNs), though any theory-brain relationship that falls into the same schema of reasoning is at risk. In this paper, we model inferences from ANNs to brains and back within a formal framework — metatheoretical calculus — in order to initiate a dialogue on both how models are broadly understood and used, and on how to best formally characterize them and their functions. To these ends, we express claims from the published record about models’ successes and failures in first-order logic. Our proposed formalization describes the decision-making processes enacted by scientists to adjudicate over theories. We demonstrate that formalizing the argumentation in the literature can uncover potential deep issues about how theory is related to phenomena. We discuss what this means broadly for research in cognitive science, neuroscience, and psychology; what it means for models when they lose the ability to mediate between theory and data in a meaningful way; and what this means for the metatheoretical calculus our fields deploy when performing high-level scientific inference.

What makes a good theory, and how do we make a theory good?

“…In terms of concepts with varying labels, similar care could be taken to make seemingly similar entities indeed sensible given divergent embeddings, especially if shared or borrowed from other fields. For example, the concept of biological plausibility makes sense in biology, but does not seem to stand up to further scrutiny in many situations; and in fact reducing to the absurd when discussing neurocognitive modelling at any level above that of biological neurons (Guest & Martin, 2023). A more appropriate concept, constraint, to make theories within the cognitive sciences relate to explananda and/or fall within certain classes of potential accounts is, e.g.…”

“…It is also related to the perspective on human (and other) cognitions granted by the Turing test (cf. Erscoi et al, 2023;Guest & Martin, 2023). In many ways, a metatheoretical calculus for reinforcement learning as used in AI (e.g.…”

“…Questions that could be answered comprise including when, how, and why behaviourism is seen as unethical (e.g. applied to treatment or education, Kirkham, 2017;Kumar & Kumar, 2019), or is not a useful framing of what is attempted to be scientifically understood (Guest & Martin, 2023), or is both (Erscoi et al, 2023). These parts of analysing a modern AI reinforcement learning paradigm only drop into place when seen through a genealogical lens.…”

“…Metatheoretical calculi are for understanding and improving the process of science, for making transparent what definitions and standards for "theory" and related terms are being used by practitioners to enable formal capture of that process (viz. Guest & Martin, 2023). Herein, theory is "a scientific proposition -described by a collection of natural-language sentences, mathematics, logic, and figures -that introduces causal relations with the aim of describing, explaining, and/or predicting a set of phenomena" (Guest & Martin, 2021, p. 794).…”

Toward an Atlas of Canonical Cognitive Mechanisms

“…Typically, showing that an algorithm derived from or linked to optimality principles can quantitatively account for behavioral data, is perceived as a superior explanation in Cognitive Science, spanning more than one levels of Marr's analyses, answering what, why, and how questions concerning cognitive capacities. However, a priori assuming that an "optimal" algorithm is the most satisfying computational account is unwarranted (Guest & Martin, 2021). Due to this misconception, the link between "optimal" algorithms and the empirical reality often ends up being loose.…”