NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equations

This paper introduces Non-Autonomous Input-Output Stable Network (NAIS-Net), a very deep architecture where each stacked processing block is derived from a time-invariant non-autonomous dynamical system. Non-autonomy is implemented by skip connections from the block input to each of the unrolled processing stages and allows stability to be enforced so that blocks can be unrolled adaptively to a pattern-dependent processing depth. NAIS-Net induces non-trivial, Lipschitz input-output maps, even for an infinite unroll length. We prove that the network is globally asymptotically stable so that for every initial condition there is exactly one input-dependent equilibrium assuming tanh units, and multiple stable equilibria for ReL units. An efficient implementation that enforces the stability under derived conditions for both fully-connected and convolutional layers is also presented. Experimental results show how NAIS-Net exhibits stability in practice, yielding a significant reduction in generalization gap compared to ResNets.Comment: NIPS 201

Nonempirical Range-separated Hybrid Functionals for Solids and Molecules

Dielectric-dependent hybrid (DDH) functionals were recently shown to yield accurate energy gaps and dielectric constants for a wide variety of solids, at a computational cost considerably less than that of GW calculations. The fraction of exact exchange included in the definition of DDH functionals depends (self-consistently) on the dielectric constant of the material. Here we introduce a range-separated (RS) version of DDH functionals where short and long-range components are matched using system dependent, non-empirical parameters. We show that RS DDHs yield accurate electronic properties of inorganic and organic solids, including energy gaps and absolute ionization potentials. Furthermore we show that these functionals may be generalized to finite systems.Comment: In press. 13 pages, 7 figures, 8 tables, Physical Review B 201

Kelo, Cuno, and the Broken Window

In June 2005, the Supreme Court made one of its least popular decisions in recent history. In Kelo v. New London, the Court missed a simple point: that local decision makers make local decisions.

The Impact of Immigration on the Structure of Male Wages: Theory and Evidence from Britain

Immigration to the UK has risen in the past 10 years and has had a measurable effect on the supply of different types of labour. But, existing studies of the impact of immigration on the wages of native-born workers in the UK (e.g. Dustmann, Fabbri and Preston, 2005) have failed to find any significant effect. This is something of a puzzle since Card and Lemieux, (2001) have shown that changes in the relative supply of educated natives do seem to have measurable effects on the wage structure. This paper offers a resolution of this puzzle - natives and immigrants are imperfect substitutes, so that an increase in immigration reduces the wages of immigrants relative to natives. We show this using a pooled time series of British cross-sectional micro data of observations on male wages and employment from the mid-1970s to the mid-2000s. This lack of substitution also means that there is little discernable effect of increased immigration on the wages of native-born workers.Wages, wage inequality, immigration

Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods

The literature on Inverse Reinforcement Learning (IRL) typically assumes that humans take actions in order to minimize the expected value of a cost function, i.e., that humans are risk neutral. Yet, in practice, humans are often far from being risk neutral. To fill this gap, the objective of this paper is to devise a framework for risk-sensitive IRL in order to explicitly account for a human's risk sensitivity. To this end, we propose a flexible class of models based on coherent risk measures, which allow us to capture an entire spectrum of risk preferences from risk-neutral to worst-case. We propose efficient non-parametric algorithms based on linear programming and semi-parametric algorithms based on maximum likelihood for inferring a human's underlying risk measure and cost function for a rich class of static and dynamic decision-making settings. The resulting approach is demonstrated on a simulated driving game with ten human participants. Our method is able to infer and mimic a wide range of qualitatively different driving styles from highly risk-averse to risk-neutral in a data-efficient manner. Moreover, comparisons of the Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL framework more accurately captures observed participant behavior both qualitatively and quantitatively, especially in scenarios where catastrophic outcomes such as collisions can occur.Comment: Submitted to International Journal of Robotics Research; Revision 1: (i) Clarified minor technical points; (ii) Revised proof for Theorem 3 to hold under weaker assumptions; (iii) Added additional figures and expanded discussions to improve readabilit

Remarks on step cocycles over rotations, centralizers and coboundaries

By using a cocycle generated by the step function $\varphi_{\beta, \gamma} = 1_{[0, \beta]} - 1_{[0, \beta]} (. + \gamma)$ over an irrational rotation $x \to x + \alpha \mod 1$, we present examples which illustrate different aspects of the general theory of cylinder maps. In particular, we construct non ergodic cocycles with ergodic compact quotients, cocycles generating an extension $T_{\alpha, \varphi}$ with a small centralizer. The constructions are related to diophantine properties of $\alpha, \beta, \gamma$

ReConvNet: Video Object Segmentation with Spatio-Temporal Features Modulation

We introduce ReConvNet, a recurrent convolutional architecture for semi-supervised video object segmentation that is able to fast adapt its features to focus on any specific object of interest at inference time. Generalization to new objects never observed during training is known to be a hard task for supervised approaches that would need to be retrained. To tackle this problem, we propose a more efficient solution that learns spatio-temporal features self-adapting to the object of interest via conditional affine transformations. This approach is simple, can be trained end-to-end and does not necessarily require extra training steps at inference time. Our method shows competitive results on DAVIS2016 with respect to state-of-the art approaches that use online fine-tuning, and outperforms them on DAVIS2017. ReConvNet shows also promising results on the DAVIS-Challenge 2018 winning the $10$-th position.Comment: CVPR Workshop - DAVIS Challenge 201

The Impact of Immigration on the Structure of Male Wages: Theory and Evidence from Britain

Immigration to the UK has risen over time. Existing studies of the impact of immigration on the wages of native-born workers in the UK have failed to find any significant effect. This is something of a puzzle since Card and Lemieux, (2001) have shown that changes in the relative supply of educated natives do seem to have measurable effects on the wage structure. This paper offers a resolution of this puzzle - natives and immigrants are imperfect substitutes, so that an increase in immigration reduces the wages of immigrants relative to natives. We show this using a pooled time series of British cross-sectional micro data of observations on male wages and employment from the mid-1970s to the mid-2000s. This lack of substitution also means that there is little discernable effect of increased immigration on the wages of native-born workers, but that the only sizeable effect of increased immigration is on the wages of those immigrants who are already here.Wages, Wage Inequality, Immigration

Self-consistent hybrid functional for condensed systems

A self-consistent scheme for determining the optimal fraction of exact exchange for full-range hybrid functionals is presented and applied to the calculation of band gaps and dielectric constants of solids. The exchange-correlation functional is defined in a similar manner to the PBE0 functional, but the mixing parameter is set equal to the inverse macroscopic dielectric function and it is determined self-consistently by computing the optimal dielectric screening. We found excellent agreement with experiments for the properties of a broad class of systems, with band gaps ranging between 0.7 and 21.7 eV and dielectric constants within 1.23 and 15.9. We propose that the eigenvalues and eigenfunctions obtained with the present self-consistent hybrid scheme may be excellent inputs for G$_0$W$_0$ calculations.Comment: Reprint of PRB articl

M\"obius function of semigroup posets through Hilbert series

In this paper, we investigate the M{\"o}bius function $\mu\_{\mathcal{S}}$ associated to a (locally finite) poset arising from a semigroup $\mathcal{S}$ of $\mathbb{Z}^m$. We introduce and develop a new approach to study $\mu\_{\mathcal{S}}$ by using the Hilbert series of $\mathcal{S}$. The latter enables us to provide formulas for $\mu\_{\mathcal{S}}$ when $\mathcal{S}$ belongs to certain families of semigroups. Finally, a characterization for a locally finite poset to be isomorphic to a semigroup poset is given.Comment: 11 page