Balasubramanian, Vijay
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Publication Effect of Geometric Complexity on Intuitive Model Selection(2021-10-01) Piasini, Eugenio; Balasubramanian, Vijay; Gold, Joshua IOccam’s razor is the principle stating that, all else being equal, simpler explanations for a set of observations are to be preferred to more complex ones. This idea can be made precise in the context of statistical inference, where the same quantitative notion of complexity of a statistical model emerges naturally from different approaches based on Bayesian model selection and information theory. The broad applicability of this mathematical formulation suggests a normative model of decision-making under uncertainty: complex explanations should be penalized according to this common measure of complexity. However, little is known about if and how humans intuitively quantify the relative complexity of competing interpretations of noisy data. Here we measure the sensitivity of naive human subjects to statistical model complexity. Our data show that human subjects bias their decisions in favor of simple explanations based not only on the dimensionality of the alternatives (number of model parameters), but also on finer-grained aspects of their geometry. In particular, as predicted by the theory, models intuitively judged as more complex are not only those with more parameters, but also those with larger volume and prominent curvature or boundaries. Our results imply that principled notions of statistical model complexity have direct quantitative relevance to human decision-making.Publication Are Black Holes Really Two Dimensional?(2009-12-07) Balasubramanian, VijayPublication Helical Luttinger Liquids and Three-Dimensional Black Holes(2011-12-20) Balasubramanian, Vijay; GarcÃa-Etxebarria, Iñaki; Larsen, Finn; Simón, JoanWe use the AdS/CFT correspondence to discuss an equivalence between a helical, strongly coupled Luttinger liquid and a fermion propagating in the background of a topologically charged black hole in three dimensions. The Fermi level is set by the topological charges, thus surmounting difficulties in low dimensions of the standard approach using Coulomb charged black holes. The construction is fully embeddable in string theory, and the microscopic Lagrangian is explicitly known. The retarded Green function at low temperature and energy arises from the geometry very near the black hole horizon, a structure that is universal for all cold, charged liquids with a dual R×U(1)s invariant description in gravity. This explains a subtle relationship between Luttinger physics and the infrared behavior of higher dimensional non-Fermi liquids in the AdS/CFT correspondence.Publication How Occam’s Razor Guides Human Inference(2022-11-21) Piasini, Eugenio; Liu, Shuze; Chaudhari, Pratik; Balasubramanian, Vijay; Gold, Joshua IOccam’s razor is the principle stating that, all else being equal, simpler explanations for a set of observations are preferred over more complex ones. This idea is central to multiple formal theories of statistical model selection and is posited to play a role in human perception and decision-making, but a general, quantitative account of the specific nature and impact of complexity on human decision-making is still missing. Here we use preregistered experiments to show that, when faced with uncertain evidence, human subjects bias their decisions in favor of simpler explanations in a way that can be quantified precisely using the framework of Bayesian model selection. Specifically, these biases, which were also exhibited by artificial neural networks trained to optimize performance on comparable tasks, reflect an aversion to complex explanations (statistical models of data) that depends on specific geometrical features of those models, namely their dimensionality, boundaries, volume, and curvature. Moreover, the simplicity bias persists for human, but not artificial, subjects even for tasks for which the bias is maladaptive and can lower overall performance. Taken together, our results imply that principled notions of statistical model complexity have direct, quantitative relevance to human and machine decision-making and establish a new understanding of the computational foundations, and behavioral benefits, of our predilection for inferring simplicity in the latent properties of our complex world.Publication Momentum-space Entanglement and Renormalization in Quantum Field Theory(2012-08-06) Balasubramanian, Vijay; McDermott, Michael B; Van Raamsdonk, MarkThe degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation between this density matrix and the Wilsonian effective action obtained by integrating out degrees of freedom with spatial momentum above some scale. We argue that the entanglement entropy of and mutual information between subsets of field theoretic degrees of freedom at different momentum scales are natural observables in quantum field theory and demonstrate how to compute these in perturbation theory. The results may be understood heuristically based on the scale dependence of the coupling strength and number of degrees of freedom. We measure the rate at which entanglement between degrees of freedom declines as their scales separate and suggest that this decay is related to the property of decoupling in quantum field theory.Publication Why Do Axons Differ in Caliber?(2012-01-01) Perge, Janos A; Niven, Jeremy E; Balasubramanian, Vijay; Mugnaini, Enrico; Sterling, PeterCNS axons differ in diameter (d) by nearly 100-fold (∼0.1–10 μm); therefore, they differ in cross-sectional area (d2) and volume by nearly 10,000-fold. If, as found for optic nerve, mitochondrial volume fraction is constant with axon diameter, energy capacity would rise with axon volume, also as d2. We asked, given constraints on space and energy, what functional requirements set an axon's diameter? Surveying 16 fiber groups spanning nearly the full range of diameters in five species (guinea pig, rat, monkey, locust, octopus), we found the following: (1) thin axons are most numerous; (2) mean firing frequencies, estimated for nine of the identified axon classes, are low for thin fibers and high for thick ones, ranging from ∼1 to >100 Hz; (3) a tract's distribution of fiber diameters, whether narrow or broad, and whether symmetric or skewed, reflects heterogeneity of information rates conveyed by its individual fibers; and (4) mitochondrial volume/axon length rises ≥d2. To explain the pressure toward thin diameters, we note an established law of diminishing returns: an axon, to double its information rate, must more than double its firing rate. Since diameter is apparently linear with firing rate, doubling information rate would more than quadruple an axon's volume and energy use. Thicker axons may be needed to encode features that cannot be efficiently decoded if their information is spread over several low-rate channels. Thus, information rate may be the main variable that sets axon caliber, with axons constrained to deliver information at the lowest acceptable rate.Publication Thermalization of Strongly Coupled Field Theories(2011-05-09) Balasubramanian, Vijay; Bernamonti, Alice; de Boer, Johannes; Copland, Neil; Craps, Ben; Keski-Vakkuri, Esko; Müller, Berndt O.; Schäfer, Andreas; Shigemori, Masaki; Staessens, WielandUsing the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d = 2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.