Richard Granger

Sarah Oh, Elijah FW Bowen, Antonio Rodriguez et al.

Although perceptual (dis)similarity between sensory stimuli seems akin to distance, measuring the Euclidean distance between vector representations of auditory stimuli is a poor estimator of subjective dissimilarity. In hearing, nonlinear response patterns, interactions between stimulus components, temporal effects, and top-down modulation transform the information contained in incoming frequency-domain stimuli in a way that seems to preserve some notion of distance, but not that of familiar Euclidean space. This work proposes that transformations applied to auditory stimuli during hearing can be modeled as a function mapping stimulus points to their representations in a perceptual space, inducing a Riemannian distance metric. A dataset was collected in a subjective listening experiment, the results of which were used to explore approaches (biologically inspired, data-driven, and combinations thereof) to approximating the perceptual map. Each of the proposed measures achieved comparable or stronger correlations with subjective ratings (r ~ 0.8) compared to state-of-the-art audio quality measures.

Elijah Bowen, Antonio Rodriguez, Damian Sowinski et al.

Some biological mechanisms of early vision are comparatively well understood, but they have yet to be evaluated for their ability to accurately predict and explain human judgments of image similarity. From well-studied simple connectivity patterns in early vision, we derive a novel formalization of the psychophysics of similarity, showing the differential geometry that provides accurate and explanatory accounts of perceptual similarity judgments. These predictions then are further improved via simple regression on human behavioral reports, which in turn are used to construct more elaborate hypothesized neural connectivity patterns. Both approaches outperform standard successful measures of perceived image fidelity from the literature, as well as providing explanatory principles of similarity perception.

Richard Granger

The machinery of the human brain -- analog, probabilistic, embodied -- can be characterized computationally, but what machinery confers what computational powers? Any such system can be abstractly cast in terms of two computational components: a finite state machine carrying out computational steps, whether via currents, chemistry, or mechanics; plus a set of allowable memory operations, typically formulated in terms of an information store that can be read from and written to, whether via synaptic change, state transition, or recurrent activity. Probing these mechanisms for their information content, we can capture the difference in computational power that various systems are capable of. Most human cognitive abilities, from perception to action to memory, are shared with other species; we seek to characterize those (few) capabilities that are ubiquitously present among humans and absent from other species. Three realms of formidable constraints -- a) measurable human cognitive abilities, b) measurable allometric anatomic brain characteristics, and c) measurable features of specific automata and formal grammars -- illustrate remarkably sharp restrictions on human abilities, unexpectedly confining human cognition to a specific class of automata ("nested stack"), which are markedly below Turing machines.