Classification and Geometry of General Perceptual Manifolds

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object recognition and discrimination requires classifying the manifolds in a manner that is insensitive to variability within a manifold. How neuronal systems give rise to invariant object classification and recognition is a fundamental problem in brain theory as well as in machine learning. Here we study the ability of a readout network to classify objects from their perceptual manifold representations. We develop a statistical mechanical theory for the linear classification of manifolds with arbitrary geometry revealing a remarkable relation to the mathematics of conic decomposition. Novel geometrical measures of manifold radius and manifold dimension are introduced which can explain the classification capacity for manifolds of various geometries. The general theory is demonstrated on a number of representative manifolds, including L2 ellipsoids prototypical of strictly convex manifolds, L1 balls representing polytopes consisting of finite sample points, and orientation manifolds which arise from neurons tuned to respond to a continuous angle variable, such as object orientation. The effects of label sparsity on the classification capacity of manifolds are elucidated, revealing a scaling relation between label sparsity and manifold radius. Theoretical predictions are corroborated by numerical simulations using recently developed algorithms to compute maximum margin solutions for manifold dichotomies. Our theory and its extensions provide a powerful and rich framework for applying statistical mechanics of linear classification to data arising from neuronal responses to object stimuli, as well as to artificial deep networks trained for object recognition tasks.Comment: 24 pages, 12 figures, Supplementary Material

Gravity Waves as a Probe of Hubble Expansion Rate During An Electroweak Scale Phase Transition

Just as big bang nucleosynthesis allows us to probe the expansion rate when the temperature of the universe was around 1 MeV, the measurement of gravity waves from electroweak scale first order phase transitions may allow us to probe the expansion rate when the temperature of the universe was at the electroweak scale. We compute the simple transformation rule for the gravity wave spectrum under the scaling transformation of the Hubble expansion rate. We then apply this directly to the scenario of quintessence kination domination and show how gravity wave spectra would shift relative to LISA and BBO projected sensitivities.Comment: 28 pages, 2 figures

The Neural Encoding of Cocaine-Induced Devaluation in The Ventral Pallidum

Cocaine experience affects motivation structures such as the nucleus accumbens (NAc) and its major output target, the ventral pallidum (VP). Previous studies demonstrated that both NAc activity and hedonic responses change reliably as a taste cue comes to predict cocaine availability. Here we extended this investigation to examine drug-experience induced changes in hedonic encoding in the VP. VP activity was first characterized in adult male Sprague–Dawley rats in response to intraoral infusions of palatable saccharin and unpalatable quinine solutions. Next, rats received 7 daily pairings of saccharin that predicted either a cocaine (20 mg/kg, ip) or saline injection. Finally, the responses to saccharin and quinine were again assessed. Of 109 units recorded in 11 rats that received saccharin–cocaine pairings, 71% of responsive units significantly reduced firing rate during saccharin infusions and 64% increased firing rate during quinine exposure. However, as saccharin came to predict cocaine, and elicited aversive taste reactivity, VP responses changed to resemble quinine. After conditioning, 70% of saccharin-responsive units increased firing rate. Most units that encoded the palatable taste (predominantly reduced firing rate) were located in the anterior VP, while most units that were responsive to aversive tastes were located in the posterior VP. This study reveals an anatomical complexity to the nature of hedonic encoding in the VP