Arguing Machines: Human Supervision of Black Box AI Systems That Make Life-Critical Decisions

We consider the paradigm of a black box AI system that makes life-critical decisions. We propose an "arguing machines" framework that pairs the primary AI system with a secondary one that is independently trained to perform the same task. We show that disagreement between the two systems, without any knowledge of underlying system design or operation, is sufficient to arbitrarily improve the accuracy of the overall decision pipeline given human supervision over disagreements. We demonstrate this system in two applications: (1) an illustrative example of image classification and (2) on large-scale real-world semi-autonomous driving data. For the first application, we apply this framework to image classification achieving a reduction from 8.0% to 2.8% top-5 error on ImageNet. For the second application, we apply this framework to Tesla Autopilot and demonstrate the ability to predict 90.4% of system disengagements that were labeled by human annotators as challenging and needing human supervision

The Impact of Type Ia Supernovae in Quiescent Galaxies: I. Formation of the Multiphase Interstellar medium

A cool phase of the interstellar medium has been observed in many giant elliptical galaxies, but its origin remains unclear. We propose that uneven heating from Type Ia supernovae (SNe Ia), together with radiative cooling, can lead to the formation of the cool phase. The basic idea is that since SNe Ia explode randomly, gas parcels which are not directly heated by SN shocks will cool, forming multiphase gas. We run a series of idealized high-resolution numerical simulations, and find that cool gas develops even when the overall SNe heating rate $H$ exceeds the cooling rate $C$ by a factor as large as 1.4. We also find that the time for multiphase gas development depends on the gas temperature. When the medium has a temperature $T = 3\times 10^6$ K, the cool phase forms within one cooling time \tc; however, the cool phase formation is delayed to a few times \tc\ for higher temperatures. The main reason for the delay is turbulent mixing. Cool gas formed this way would naturally have a metallicity lower than that of the hot medium. For constant $H/C$, there is more turbulent mixing for higher temperature gas. We note that this mechanism of producing cool gas cannot be captured in cosmological simulations, which usually fail to resolve individual SN remnants.Comment: 16 pages, 11 figures, published by ApJ. This work is part of the SMAUG project, see more information at https://www.simonsfoundation.org/flatiron/center-for-computational-astrophysics/galaxy-formation/smaug/papersplash

The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Supernova Feedback and the Hot Gas Filling Fraction of the Interstellar Medium

Supernovae (SN), the most energetic stellar feedback mechanism, are crucial for regulating the interstellar medium (ISM) and launching galactic winds. We explore how supernova remnants (SNRs) create a multiphase medium by performing 3D hydrodynamical simulations at various SN rates, $S$, and ISM average densities, $\bar{n}$. The evolution of a SNR in a self-consistently generated three-phase ISM is qualitatively different from that in a uniform or a two-phase warm/cold medium. By travelling faster and further in the low-density hot phase, the domain of a SNR increases by $>10^{2.5}$. Varying $\bar{n}$ and $S$, we find that a steady state can only be achieved when the hot gas volume fraction $f_{\rm{V,hot}}\lesssim 0.6 \pm 0.1$. Above that level, overlapping SNRs render connecting topology of the hot gas, and the ISM is subjected to thermal runaway. Photoelectric heating (PEH) has a surprisingly strong impact on $f_{\rm{V,hot}}$. For \bar{n}\gtrsim 3 \cm-3 , a reasonable PEH rate is able to suppress the thermal runaway. Overall, we determine the critical SN rate for the onset of thermal runaway to be S_{\rm{crit}} = 200 (\bar{n}/1\cm-3)^k (E_{\rm{SN}}/10^{51}\erg)^{-1} \kpc^{-3} \myr-1, where $k = (1.2,2.7)$ for $\bar{n} \leq 1$ and > 1\cm-3 , respectively. We present a fitting formula of the ISM pressure $P(\bar{n}$, $S$), which can be used as an effective equation of state in cosmological simulations. Despite the 5 orders of magnitude span of $(\bar{n},S)$, the average Mach number varies little: $\mathcal{M} \approx \ 0.5\pm 0.2, \ 1.2\pm 0.3,\ 2.3\pm 0.9$ for the hot, warm and cold phases, respectively.Comment: 57 pages, 16 figures, 3 tables. ApJ accepte

Gromov-Witten invariants of blow-ups along submanifolds with convex normal bundles

Given a submanifold Z inside X, let Y be the blow-up of X along Z. When the normal bundle of Z in X is convex with a minor assumption, we prove that genus-zero GW-invariants of Y with cohomology insertions from X, are identical to GW-invariants of X. Under the same hypothesis, a vanishing theorem is also proved. An example to which these two theorems apply is when the normal bundle is generated by global sections. These two main theorems do not hold for arbitrary blow-ups, and counter-examples are included.Comment: 34 page

VISUAL GROUP IN ONLINE COMMUNICATION AND COLLABORATION FACILITY MEETING OR WEBINAR

In a normal work mode, most of a company’s employees will be in an office. If those individuals would like to join a big event (such as an all-hands meeting) as a team or as a group, they are able to gather together in a telepresence (TP) room. Today, as a result of the coronavirus disease 2019 (COVID-19), many people have chosen a hybrid work mode. Under such a mode, it is not easy for all of a team’s members to gather together in the same TP room since, for example, some of the team members may work from home and other of the team members may work in an office. To address the challenge that was described above, techniques are presented herein that provide a means under which people may join a meeting or a webinar, as a visual group, from different locations in a hybrid work mode. Aspects of the presented techniques eliminate dependence on any devices