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I wrote this paper because technology can really improve people's lives. With it, we can live longer in a healthy body, save time through increased efficiency and automation, and make better decisions. To get to the next level, we need to start looking at intelligence from a much broader perspective, and promote international interdisciplinary collaborations. Section 1 of this paper delves into sociology and social psychology to explain that the mechanisms underlying intelligence are inherently social. Section 2 proposes a method to classify intelligence, and describes the differences between weak and strong intelligence. Section 3 examines the Chinese Room argument from a different perspective. It demonstrates that a Turing-complete machine cannot have strong intelligence, and considers the modifications necessary for a computer to be intelligent and have understanding. Section 4 argues that the existential risk caused by the technological explosion of a single agent should not be of serious concern. Section 5 looks at the AI control problem and argues that it is impossible to build a super-intelligent machine that will do what it creators want. By using insights from biology, it also proposes a solution to the control problem. Section 6 discusses some of the implications of strong intelligence. Section 7 lists the main challenges with deep learning, and asserts that radical changes will be required to reach strong intelligence. Section 8 examines a neuroscience framework that could help explain how a cortical column works. Section 9 lays out the broad strokes of a road map towards strong intelligence. Finally, section 10 analyzes the impacts and the challenges of greater intelligence.

We consider random analytic functions given by a Taylor series with independent, centered complex Gaussian coefficients. We give a new sufficient condition for such a function to have bounded mean oscillations. Under a mild regularity assumption this condition is optimal. Using a theorem of Holland and Walsh, we give as a corollary a new bound for the norm of a random Gaussian Hankel matrix. Finally, we construct some exceptional Gaussian analytic functions which in particular disprove the conjecture that a random analytic function with bounded mean oscillations always has vanishing mean oscillations., Comment: 33 pages

We investigate the characteristic polynomials $\varphi_N$ of the Gaussian $\beta$-ensemble for general $\beta>0$ through its transfer matrix recurrence. Our motivation is to obtain a (probabilistic) approximation for $\varphi_N$ in terms of a Gaussian log--correlated field in order to ultimately deduce some of its fine asymptotic properties. We distinguish between different types of transfer matrices and analyze completely the hyperbolic regime of the recurrence. As a result, we obtain a new coupling between $\varphi_N(z)$ and a Gaussian analytic function with an error which is uniform for $z \in \mathbb{C}$ separated from the support of the semicircle law. We use this as input to give the almost sure scaling limit of the characteristic polynomial at the edge in arXiv:2009.05003. This is also required to obtain analogous strong approximations inside of the bulk of the semicircle law. Our analysis relies on moderate deviation estimates for the product of transfer matrices and this approach might also be useful in different contexts., Comment: Version 4. Implemented referee comments and added section on chaos convergence

We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$-face is included independently with probability p. Our main result is to exhibit a sharp threshold p=1/2 for homology vanishing as $n \to \infty$. This is a 2-dimensional analogue of the Burtin and Erd\H{o}s-Spencer theorems characterizing the connectivity threshold for random cubical graphs. Our main result can also be seen as a cubical counterpart to the Linial--Meshulam theorem for random 2-dimensional simplicial complexes. However, the models exhibit strikingly different behaviors. We show that if $p > 1 - \sqrt{1/2} \approx 0.2929$, then with high probability the fundamental group is a free group with one generator for every maximal $1$-dimensional face. As a corollary, homology vanishing and simple connectivity have the same threshold, even in the strong "hitting time" sense. This is in contrast with the simplicial case, where the thresholds are far apart. The proof depends on an iterative algorithm for contracting cycles -- we show that with high probability the algorithm rapidly and dramatically simplifies the fundamental group, converging after only a few steps., Comment: Third version. Presentation improvements

In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS$_3\times S^3\times T^4$ and the SCFT (on the moduli space of) the symmetric orbifold theory $Sym^N(T^4)$ as $N \rightarrow \infty$. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the $N\rightarrow \infty$ limit of the twisted gravitational theory. We emphasize the role of $\textit{Koszul duality}$---a ubiquitous mathematical notion to which we provide a friendly introduction---in field theory and string theory. After illustrating the appearance of Koszul duality in the "toy" example of holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul duality relates bulk and boundary operators in our twisted setup, and explain how one can compute algebra OPEs diagrammatically using this notion. Further details, results, and computations will appear in a companion paper., Comment: 80 pages, 9 figures

The Cometary Secondary Ion Mass Analyzer (COSIMA) onboard ESA's Rosetta orbiter has revealed that dust particles in the coma of Comet 67P/Churyumov-Gerasimenko are aggregates of small grains. We study the morphological, elastic, and electric properties of dust aggregates in the coma of Comet 67P/Churyumov-Gerasimenko using optical microscopic images taken by the COSIMA instrument. Dust aggregates in COSIMA images are well represented as fractals in harmony with morphological data from MIDAS (Micro-Imaging Dust Analysis System) and GIADA (Grain Impact Analyzer and Dust Accumulator) onboard Rosetta. COSIMA's images, together with the data from the other Rosetta's instruments such as MIDAS and GIADA do not contradict the so-called rainout growth of $10~\mu\mathrm{m}$-sized particles in the solar nebula. The elastic and electric properties of dust aggregates measured by COSIMA suggest that the surface chemistry of cometary dust is well represented as carbonaceous matter rather than silicates or ices, consistent with the mass spectra, and that organic matter is to some extent carbonized by solar radiation, as inferred from optical and infrared observations of various comets. Electrostatic lofting of cometary dust by intense electric fields at the terminator of its parent comet is unlikely, unless the surface chemistry of the dust changes from a dielectric to a conductor. Our findings are not in conflict with our current understanding of comet formation and evolution, which begin with the accumulation of condensates in the solar nebula and follow with the formation of a dust mantle in the inner solar system., Comment: 17 pages, 12 figures, 1 tables, to appear in Planetary and Space Science

We prove a formula for the speed of distance stationary random sequences generalizing the law of large numbers of Karlsson and Ledrappier. A particular case is the classical formula for the largest Lyapunov exponent of i.i.d.\ matrix products, but our result has applications in various different contexts. In many situations it gives a method to estimate the speed, and in others it allows to obtain results of dimension drop for escape measures related to random walks. We show applications to stationary reversible random trees with conductances, Bernoulli bond percolation of Cayley graphs, and random walks on cocompact Fuchsian groups., Comment: This article overlaps the (almost twice as long) preprint arXiv:1710.00733 which will remain unpublished. Compared with said preprint the results on hyperbolic Poisson-Delaunay random walks have been removed, the exposition of the abstract formula for speed has been improved, and new applications of it are given

In this note we apply mathematical results for the volume of certain symmetric spaces to the problem of counting flux vacua in simple IIB Calabi--Yau compactifications. In particular we obtain estimates for the number of flux vacua including the geometric factor related to the Calabi-Yau moduli space, in the large flux limit, for the FHSV model and some closely related models. We see that these geometric factors give rise to contributions to the counting formula that are typically not of order one and might potentially affect the counting qualitatively in some cases. We also note, for simple families of Calabi-Yau moduli spaces, an interesting dependence of the moduli space volumes on the dimension of the flux space, which in turn is governed by the Betti numbers of the Calabi-Yaus., Comment: 30 pages, 1 figure

Diplomacy is a seven-player non-stochastic, non-cooperative game, where agents acquire resources through a mix of teamwork and betrayal. Reliance on trust and coordination makes Diplomacy the first non-cooperative multi-agent benchmark for complex sequential social dilemmas in a rich environment. In this work, we focus on training an agent that learns to play the No Press version of Diplomacy where there is no dedicated communication channel between players. We present DipNet, a neural-network-based policy model for No Press Diplomacy. The model was trained on a new dataset of more than 150,000 human games. Our model is trained by supervised learning (SL) from expert trajectories, which is then used to initialize a reinforcement learning (RL) agent trained through self-play. Both the SL and RL agents demonstrate state-of-the-art No Press performance by beating popular rule-based bots., Comment: Accepted at NeurIPS 2019

In this work, we investigate the behavior of Al2O3/TiO2-x cross-point memristors in cryogenic environment. We report successful resistive switching of memristor devices from 300 K down to 1.5 K. The I-V curves exhibit negative differential resistance effects between 130 and 1.5 K, attributed to a metal-insulator transition (MIT) of the Ti4O7 conductive filament. The resulting highly nonlinear behavior is associated to a maximum ION/IOFF ratio of 84 at 1.5 K, paving the way to selector-free cryogenic passive crossbars. Finally, temperature-dependant thermal activation energies related to the conductance at low bias (20 mV) are extracted for memristors in low resistance state, suggesting hopping-type conduction mechanisms., Comment: 4 pages, 4 figures, IEEE 14th Nanotechnology Materials & Devices Conference (NMDC 2019)

We propose that a simple, Lagrangian 2d $\mathcal{N}=(0, 2)$ duality interface between the 3d $\mathcal{N}=2$ XYZ model and 3d $\mathcal{N}=2$ SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundary and 2d $\mathcal{N}=(0, 2)$ interfaces. In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3,3), (2,4), and (4,2) Pachner moves. We check these dualities using supersymmetric half-indices. We also describe how to produce stand-alone 2d theories (as opposed to interfaces) capturing the geometry of 4-simplices and Pachner moves by making additional field-theoretic choices, and find in this context that the Pachner moves recover abelian $\mathcal{N}=(0,2)$ trialities of Gadde-Gukov-Putrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4-manifold geometry that has been developed in recent years., Comment: 50 pages, 15 figures. v2: minor edits, references added

We propose potential-based analyses for first-order algorithms applied to constrained and composite minimization problems. We first propose ``idealized'' frameworks for algorithms in the strongly and non-strongly convex cases and argue based on a potential that methods following the framework achieve the best possible rate. Then we show that the geometric descent (GD) algorithm by Bubeck et al.\ as extended to the constrained and composite setting by Chen et al.\ achieves this rate using the potential-based analysis for the strongly convex case. Next, we extend the GD algorithm to the case of non-strongly convex problems. We show using a related potential-based argument that our extension achieves the best possible rate in this case as well. The new GD algorithm achieves the best possible rate in the nonconvex case also. We also analyze accelerated gradient using the new potentials. We then turn to the special case of a quadratic function with a single ball constraint, the famous trust-region subproblem. For this case, the first-order trust-region Lanczos method by Gould et al.\ finds the optimal point in an increasing sequence of Krylov spaces. Our results for the general case immediately imply convergence rates for their method in both the strongly convex and non-strongly convex cases. We also establish the same convergence rates for their method using arguments based on Chebyshev polynomial approximation. To the best of our knowledge, no convergence rate has previously been established for the trust-region Lanczos method.