Studying the implementational level in decision-making

The previous sections have dealt with Marr’s first two levels of abstraction for information processing systems: the computational level and the algorithmic/representational level. Models from each level have been selected as experimental tools for studying the representation of choice options in the following chapters. For the implementational level, models are not so much relevant to the experimental work presented here so much as the techniques and methods used to gather and interpret neural data. Admittedly, there has been much work done at this level in pinpointing the exact biological mechanisms that carry out brain computations, as in studies of spike-timing dependent plasticity (STDP) (Sjöström & Gerstner, 2010), long-term depression (LTD) (Ito, 1989), short-term depression (STD) (Zucker, 1989), or N-methyl-D-aspartate (NMDA) receptor channels (Lisman, Fellous, & Wang, 1998). At the neuronal population level, an important class of models is known as neural networks (i.e., connectionist) which can be classified either as artificial neural networks (Hassabis, Kumaran, Summerfield, & Botvinick, 2017; Rumelhart, McClelland, & PDP Research Group, 1987) or biological neural networks (Dayan & Abbott, 2001). Although, one could argue that artificial neural networks are better suited for the algorithmic level, progress has been made in relating these models to brain biology (Scellier & Bengio, 2017). Although authors may classify these models at the algorithmic level, these types of discrepancies display that sometimes the same class of models can be reinterpreted at different levels. For example, the interactive word recognition model (McClelland & Rumelhart, 1981) – a connectionist model with interacting layers of representations – can be modified to perform Bayesian inference (Norris, 2013). Examples of other models that lie at the intersection between the algorithmic and computational levels are Bayesian explanations of inductive confirmation (Tentori, Crupi, & Russo, 2013) or probabilities with noise (Costello & Watts, 2014). Neural networks can illuminate the trade-off hypothesis between stimuli and goals given that they both seek to cluster similar stimuli together and to optimise a cost function at the same time (see Love, 2005 for a similar view). The scope of this area is vast but not relevant to this work. What is relevant here however are two methods that are closely related, one technological and the other analytical; functional magnetic resonance imaging and representational similarity analysis, respectively.

1.9.1 Brief overview of functional magnetic resonance imaging (fMRI)

When presented with a stimulus, a person’s nervous system will transform its physical presentation into a neuronal representation. What is the nature of a neural representation of a stimulus? Technological and methodological advances in cognitive neuroscience give the tools that are necessary in addressing this problem. Insight is gained into the neural representations of stimuli through fMRI. This technology can measure blood oxygen level dependent (BOLD) signals that vary with task demands and presentations of stimuli (Huettel, Song, & McCarthy, 2004). Such a signal is believed to correlate with population levels of neuronal activity (Goense, Merkle, & Logothetis, 2012). Although its temporal resolution is confined to be within just a few seconds, its spatial resolution operates on a millimetric scale with voxels being the standard representational unit for the images; well suited for localizing different brain functions and computations.4 _{This technique is used for both the top-down approach and the}

bottom-up approach in studying choice option representations (chapters 3 and 5, respectively). It is a technique that is well suited for many purposes such as: 1) validating cognitive models of decision-making and choice option representations, 2) localizing neuronal populations that correlate with cognitive operations in such models.

This technique gathers data in the form of voxels (mentioned above). A typical brain volume can be collected in matter of a few seconds and will be composed of approximately fifty thousand of these voluminous pixels for a typical experiment. The BOLD signal, which is intended to be recovered for each voxel from a series of brain volumes, varies on a time scale that is quite slow (around eight seconds to peak and fifteen seconds back to baseline). The typical analysis pipeline will seek to correct many artefacts in the data such as temporal drift, physiological noise like heart rate, and motions from the participant lying down in the fMRI scanner (Huettel, Song, & McCarthy, 2004). The canonical way of statistically analysing this data is through massive univariate general linear models (one for each voxel through time) (Monti, 2011). Other approaches include more global brain properties like independent component analysis (Calhoun, Liu, & Adali, 2009), principal component analysis (Smith, Hyvärinen, Varoquaux, Miller, & Beckmann, 2014), or multivariate pattern analyses (Norman, Polyn, Detre, & Haxby, 2006). For the work presented here, chapter 3 will make use of the

4 _{Although, the fact that fMRI can detect signals on such a coarse spatiotemporal scale reveals interesting}

canonical tradition of massive univariate analysis and chapter 5 will use both the univariate approach as well as the multivariate approach. A special case of the multivariate approach is known as representational similarity analysis, which is closely linked to the analysis of the neural similarity measures between choice options in chapter 5. It is important to note that inferences drawn from fMRI data are only indirectly related to neural activity through the BOLD signal. Deviations from baseline BOLD signal can be seen as averaging activity over tens of thousands of neurons. Thus, inferences in this space can only make claims at the level of summary statistics for neuronal populations. Inferring latent spaces from such summary statistics (i.e., dips and peaks with respect to baseline BOLD signal) will thus be constrained by the nature of the data, as will be displayed in chapter 5.

1.9.2 Representational similarity analysis (RSA)

As mentioned, different analysis pipelines have been proposed for analysing fMRI data. Multivariate pattern analyses (MVPA) such as representational similarity analysis (RSA) or machine learning classifiers such as linear support vector machines (SVM) have found great success for this purpose (Joern Diedrichsen & Kriegeskorte, 2016; Haxby, Connolly, & Guntupalli, 2014; Kriegeskorte, Mur, & Bandettini, 2008) (see Chapter 5 for an example of how these techniques may be used for inference on fMRI data). Indeed, RSA is a great starting point for understanding the nature of neural representations. This method is based on computing representational similarity matrices (RDM). These matrices are symmetrical and are constructed from all pairwise distances between stimuli for a given experiment. Each cell in one of these matrices represents a similarity between two different brain states (i.e. voxel activations). In the case of fMRI, a cell in this matrix could represent the distance between voxel activations for seeing the image of a hammer and voxel activations for seeing the image of a basketball. These brain states can represent the way the brain has reacted to a stimulus presentation or any other experimental event of interest. Computing the similarity between two different brain states can grant direct insight into the nature of endogenous choice option representations.