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Earth's tropics are characterized by quasi-steady precipitation with small oscillations about a mean value, which has led to the hypothesis that moist convection is in a state of quasi-equilibrium (QE). In contrast, very warm simulations of Earth's tropical convection are characterized by relaxation-oscillator-like (RO) precipitation, with short-lived convective storms and torrential rainfall forming and dissipating at regular intervals with little to no precipitation in between. We develop a model of moist convection by combining a zero-buoyancy model of bulk-plume convection with a QE heat engine model, and we use it to show that QE is violated at high surface temperatures. We hypothesize that the RO state emerges when the equilibrium condition of the convective heat engine is violated, i.e., when the net cooling times a thermodynamic efficiency exceeds the work that can be performed. We test our hypothesis against one- and three-dimensional numerical simulations and find that it accurately predicts the onset of RO convection. The proposed mechanism for RO emergence from QE breakdown is agnostic of the condensing component, and can be applied to any planetary atmosphere undergoing moist convection. To date, RO states have only been demonstrated in three-dimensional convection-resolving simulations, which has made it seem that the physics of the RO state requires simulations that can explicitly resolve the three-dimensional interaction of cloudy plumes and their environment. We demonstrate that RO states also exist in single-column simulations of radiative-convective equilibrium with parameterized convection, albeit in a different surface temperature range and with much longer storm-free intervals., Comment: 30 pages, 9 figures, and 1 table

The Akaike information criterion (AIC) is a common tool for model selection. It is frequently used in violation of regularity conditions at parameter space singularities and boundaries. The expected AIC is generally not asymptotically equivalent to its target at singularities and boundaries, and convergence to the target at nearby parameter points may be slow. We develop a generalized AIC for candidate models with or without singularities and boundaries. We show that the expectation of this generalized form converges everywhere in the parameter space, and its convergence can be faster than that of the AIC. We illustrate the generalized AIC on example models from phylogenomics, showing that it can outperform the AIC and gives rise to an interpolated effective number of model parameters, which can differ substantially from the number of parameters near singularities and boundaries. We outline methods for estimating the often unknown generating parameter and bias correction term of the generalized AIC., Comment: 21 pages, 5 figures

This work proposes a method for using any generator network as the foundation of an Energy-Based Model (EBM). Our formulation posits that observed images are the sum of unobserved latent variables passed through the generator network and a residual random variable that spans the gap between the generator output and the image manifold. One can then define an EBM that includes the generator as part of its forward pass, which we call the Hat EBM. The model can be trained without inferring the latent variables of the observed data or calculating the generator Jacobian determinant. This enables explicit probabilistic modeling of the output distribution of any type of generator network. Experiments show strong performance of the proposed method on (1) unconditional ImageNet synthesis at 128x128 resolution, (2) refining the output of existing generators, and (3) learning EBMs that incorporate non-probabilistic generators. Code and pretrained models to reproduce our results are available at https://github.com/point0bar1/hat-ebm., Comment: NeurIPS 2022 camera ready

This work presents strategies to learn an Energy-Based Model (EBM) according to the desired length of its MCMC sampling trajectories. MCMC trajectories of different lengths correspond to models with different purposes. Our experiments cover three different trajectory magnitudes and learning outcomes: 1) shortrun sampling for image generation; 2) midrun sampling for classifier-agnostic adversarial defense; and 3) longrun sampling for principled modeling of image probability densities. To achieve these outcomes, we introduce three novel methods of MCMC initialization for negative samples used in Maximum Likelihood (ML) learning. With standard network architectures and an unaltered ML objective, our MCMC initialization methods alone enable significant performance gains across the three applications that we investigate. Our results include state-of-the-art FID scores for unnormalized image densities on the CIFAR-10 and ImageNet datasets; state-of-the-art adversarial defense on CIFAR-10 among purification methods and the first EBM defense on ImageNet; and scalable techniques for learning valid probability densities. Code for this project can be found at https://github.com/point0bar1/ebm-life-cycle.

Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference to be possible. As a step toward inferring a general species network, this work considers its tree of blobs, in which non-cut edges are contracted to nodes, so only tree-like relationships between the taxa are shown. An identifiability theorem, that most features of the unrooted tree of blobs can be determined from the distribution of gene quartet topologies, is established. This depends upon an analysis of gene quartet concordance factors under the model, together with a new combinatorial inference rule. The arguments for this theoretical result suggest a practical algorithm for tree of blobs inference, to be fully developed in a subsequent work., Comment: 18 pages, 8 figures

We present theories for the latitudinal extents of both Hadley cells throughout the annual cycle by combining our recent scaling for the ascending edge latitude (Hill et al. 2021) with the uniform Rossby number (Ro), baroclinic instability-based theory for the poleward, descending edge latitudes of Kang and Lu 2012. The resulting analytic expressions for all three Hadley cell edges are predictive except for diagnosed values of Ro and two proportionality constants. The theory captures the climatological annual cycle of the ascending and descending edges in an Earth-like simulation in an idealized aquaplanet general circulation model (GCM), provided the descending edge prediction is lagged by one month. In simulations in this and two other idealized GCMs with varied planetary rotation rate ($\Omega$), the winter, descending edge of the solsticial, cross-equatorial Hadley cell scales approximately as $\Omega^{-1/2}$ and the summer, ascending edge as $\Omega^{-2/3}$, both in accordance with our theory., Comment: 11 pages, 5 figures, 1 table, submitted to Journal of the Atmospheric Sciences

How far the Hadley circulation's ascending branch extends into the summer hemisphere is a fundamental but incompletely understood characteristic of Earth's climate. Here, we present a predictive, analytical theory for this ascending edge latitude based on the extent of supercritical forcing. Supercriticality sets the minimum extent of a large-scale circulation based on the angular momentum and absolute vorticity distributions of the hypothetical state were the circulation absent. We explicitly simulate this latitude-by-latitude radiative-convective equilibrium (RCE) state. Its depth-averaged temperature profile is suitably captured by a simple analytical approximation that increases linearly with $\sin\varphi$, where $\varphi$ is latitude, from the winter to the summer pole. This, in turn, yields a one-third power-law scaling of the supercritical forcing extent with the thermal Rossby number. In moist and dry idealized GCM simulations under solsticial forcing performed with a wide range of planetary rotation rates, the ascending edge latitudes largely behave according to this scaling., Comment: 15 pages, 7 figures, revised for Journal of the Atmospheric Sciences

The vulnerability of deep networks to adversarial attacks is a central problem for deep learning from the perspective of both cognition and security. The current most successful defense method is to train a classifier using adversarial images created during learning. Another defense approach involves transformation or purification of the original input to remove adversarial signals before the image is classified. We focus on defending naturally-trained classifiers using Markov Chain Monte Carlo (MCMC) sampling with an Energy-Based Model (EBM) for adversarial purification. In contrast to adversarial training, our approach is intended to secure pre-existing and highly vulnerable classifiers. The memoryless behavior of long-run MCMC sampling will eventually remove adversarial signals, while metastable behavior preserves consistent appearance of MCMC samples after many steps to allow accurate long-run prediction. Balancing these factors can lead to effective purification and robust classification. We evaluate adversarial defense with an EBM using the strongest known attacks against purification. Our contributions are 1) an improved method for training EBM's with realistic long-run MCMC samples, 2) an Expectation-Over-Transformation (EOT) defense that resolves theoretical ambiguities for stochastic defenses and from which the EOT attack naturally follows, and 3) state-of-the-art adversarial defense for naturally-trained classifiers and competitive defense compared to adversarially-trained classifiers on Cifar-10, SVHN, and Cifar-100. Code and pre-trained models are available at https://github.com/point0bar1/ebm-defense., Comment: ICLR 2021

Weak-temperature-gradient influences from the tropics and quasigeostrophic influences from the extratropics plausibly constrain the subtropical-mean static stability in terrestrial atmospheres. Because mean descent acting on this static stability is a leading-order term in the thermodynamic balance, a state-invariant static stability would impose constraints on the Hadley cells, which this paper explores in simulations of varying planetary rotation rate. If downdraft-averaged effective heating (the sum of diabatic heating and eddy heat flux convergence) too is invariant, so must be vertical velocity -- an "omega governor." In that case, the Hadley circulation overturning strength and downdraft width must scale identically -- the cell can strengthen only by widening or weaken only by narrowing. Simulations in two idealized, dry GCMs with a wide range of planetary rotation rates exhibit nearly unchanging downdraft-averaged static stability, effective heating, and vertical velocity, as well as nearly identical scalings of the Hadley cell downdraft width and strength. In one, eddy stresses set this scaling directly (the Rossby number remains small); in the other, eddy stress and bulk Rossby number changes compensate to yield the same, ({\sim}\Omega^{-1/3}) scaling. The consistency of this power law for cell width and strength variations may indicate a common driver, and we speculate that Ekman pumping could be the mechanism responsible for this behavior. Extending to moist atmospheres, in an idealized aquaplanet GCM the subtropical static stability is also insensitive to rotation rate but the effective heating and vertical velocity are not., Comment: 20 pages (6200 words) main text, 12 figures

The atmosphere of Venus is characterized by strong superrotation, in which the wind velocities at cloud heights are around 60 times faster than the surface rotation rate. The reasons for this strong superrotation are still not well understood. Motions in the atmosphere below the thick cloud deck are hard to determine remotely and in-situ measurements of the circulation below 40 km altitude are scarce. No model to date has been able to simulate superrotating winds with magnitudes comparable with those measured by entry probes, in the dense atmosphere between the surface and the clouds. However, important information on the dynamics and circulation of Venus' atmosphere can be determined by studying the atmosphere at cloud levels, where there are significantly more measurements than in the sub-cloud region, including the many recent observations made during the Venus Express and Akatsuki missions. In this work we describe a new Venus Middle atmosphere general circulation Model (VMM) to study the dynamics of the atmosphere at cloud altitudes. The model simulates the atmosphere from just below cloud deck to around 95 km altitude. We present simulations using the VMM with a simplified Newtonian cooling radiation scheme. Sensitivity studies have been performed to determine the most appropriate values for model parameters and the model has been validated by comparison with observations, including those from Venus Express and Akatsuki. The validated model provides some constraints on parameters which are poorly measured close to the boundary such as the mean winds and temperatures, and provides a basis for further investigations of the dynamics of Venus' cloud-level atmosphere. In future studies we will also investigate the influence of atmospheric waves, such as Kelvin and Rossby waves, to determine the role they play in generating the poorly-understood cloud-level structure at all latitudes., Comment: Updated references

We consider the relevance of known constraints from each of Hide's theorem, the angular momentum conserving (AMC) model, and the equal-area model on the extent of cross-equatorial Hadley cells. These theories respectively posit that a Hadley circulation must span: all latitudes where the radiative convective equilibrium (RCE) absolute angular momentum ($M_\mathrm{rce}$) satisfies $M_\mathrm{rce}>\Omega a^2$ or $M_\mathrm{rce}<0$ or where the RCE absolute vorticity ($\eta_\mathrm{rce}$) satisfies $f\eta_\mathrm{rce}<0$; all latitudes where the RCE zonal wind exceeds the AMC zonal wind; and over a range such that depth-averaged potential temperature is continuous and that energy is conserved. The AMC model requires knowledge of the ascent latitude $\varphi_\mathrm{a}$, which need not equal the RCE forcing maximum latitude $\varphi_\mathrm{m}$. Whatever the value of $\varphi_\mathrm{a}$, we demonstrate that an AMC cell must extend at least as far into the winter hemisphere as the summer hemisphere. The equal-area model predicts $\varphi_\mathrm{a}$, always placing it poleward of $\varphi_\mathrm{m}$. As $\varphi_\mathrm{m}$ is moved poleward (at a given thermal Rossby number), the equal-area predicted Hadley circulation becomes implausibly large, while both $\varphi_\mathrm{m}$ and $\varphi_\mathrm{a}$ become increasingly displaced poleward of the minimal cell extent based on Hide's theorem (i.e. of supercritical forcing). In an idealized dry general circulation model, cross-equatorial Hadley cells are generated, some spanning nearly pole-to-pole. All homogenize angular momentum imperfectly, are roughly symmetric in extent about the equator, and appear in extent controlled by the span of supercritical forcing., Comment: 18 pages, 9 figures, published

We present a bottom-up approach for the task of object instance segmentation using a single-shot model. The proposed model employs a fully convolutional network which is trained to predict class-wise segmentation masks as well as the bounding boxes of the object instances to which each pixel belongs. This allows us to group object pixels into individual instances. Our network architecture is based on the DeepLabv3+ model, and requires only minimal extra computation to achieve pixel-wise instance assignments. We apply our method to the task of person instance segmentation, a common task relevant to many applications. We train our model with COCO data and report competitive results for the person class in the COCO instance segmentation task.

The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as highlighted by recent work of Drton. Indeed, poor behavior of a $\chi^2$ for testing near singularities and boundaries is apparent in simulations, and can lead to conservative or anti-conservative tests. Here we develop a new distribution designed for use in hypothesis testing near singularities and boundaries, which asymptotically agrees with that of the likelihood ratio statistic. For two example trinomial models, arising in the context of inference of evolutionary trees, we show the new distributions outperform a $\chi^2$., Comment: 32 pages, 12 figures