ADADELTA: An Adaptive Learning Rate Method

We present a novel per-dimension learning rate method for gradient descent called ADADELTA. The method dynamically adapts over time using only first order information and has minimal computational overhead beyond vanilla stochastic gradient descent. The method requires no manual tuning of a learning rate and appears robust to noisy gradient information, different model architecture choices, various data modalities and selection of hyperparameters. We show promising results compared to other methods on the MNIST digit classification task using a single machine and on a large scale voice dataset in a distributed cluster environment.Comment: 6 page

Future Generations: A Prioritarian View

Should we remain neutral between our interests and those of future generations? Or are we ethically permitted or even required to depart from neutrality and engage in some measure of intergenerational discounting? This Article addresses the problem of intergenerational discounting by drawing on two different intellectual traditions: the social welfare function (“SWF”) tradition in welfare economics, and scholarship on “prioritarianism” in moral philosophy. Unlike utilitarians, prioritarians are sensitive to the distribution of well-being. They give greater weight to well-being changes affecting worse-off individuals. Prioritarianism can be captured, formally, through an SWF which sums a concave transformation of individual utility, rather than simply summing unweighted utilities in utilitarian fashion. The Article considers the appropriate structure of a prioritarian SWF in intergenerational cases. The simplest case involves a fixed and finite intertemporal population. In that case, I argue, policymakers can and should maintain full neutrality between present and future generations. No discount factor should be attached to the utility of future individuals. Neutrality becomes trickier when we depart from this simple case, meaning: (1) “non-identity” problems, where current choices change the identity of future individuals; (2) population-size variation, where current choices affect not merely the identity of future individuals, but the size of the world’s future population (this case raises the specter of what Derek Parfit terms “the repugnant conclusion,” i.e., that dramatic reductions in the average level of individual well-being might be compensated for by increases in population size); or (3) an infinite population. The Article grapples with the difficult question of outfitting a prioritarian SWF to handle non-identity problems, population-size variation, and infinite populations. It tentatively suggests that a measure of neutrality can be maintained even in these cases

The Disquieted Heart and the Lighted Path: LeVar Burton’s Dedication Day Speech

This Saturday past brought with it an electric sort of chill, the kind fueled by a driving breeze that lifts your jacket, steals past your socks and up your legs, worms its way through gaps in scarves and gloves, and leaves you feeling naked and afraid and alive in ways that no one else can see. The kind of wind that whisks away complicity and surety, leaving you with nothing but a burning compulsion to do something that will reignite your humanity, your belief in goodness, your claim to a kind life. For those who attended, the Dedication Day ceremony in the National Cemetery trembled with the same terrible power. This year, there was something dreadfully eerie about coming together to honor men slain in the struggle to prove that a nation “conceived in liberty, and dedicated to the proposition that all men are created equal” could endure terrible division and betrayal between its countrymen. The speechmaking, no matter its tenor, could not escape the gravity of the question on everyone’s mind: what does the future hold for America, and how can we make sure it won’t undo the already unfinished work for which our forefathers died? [excerpt

Justice, Claims and Prioritarianism: Room for Desert?

Does individual desert matter for distributive justice? Is it relevant, for purposes of justice, that the pattern of distribution of justice’s “currency” (be it well-being, resources, preference-satisfaction, capabilities, or something else) is aligned in one or another way with the pattern of individual desert? This paper examines the nexus between desert and distributive justice through the lens of individual claims. The concept of claims (specifically “claims across outcomes”) is a fruitful way to flesh out the content of distributive justice so as to be grounded in the separateness of persons. A claim is a relation between a person and a pair of outcomes. If someone is better off in one outcome than a second, she has a claim in favor of the first. If she is equally well off in the two outcomes, she has a null claim between the two. In turn, whether one outcome is more just than a second depends upon the pattern of claims between them. In prior work, I have elaborated the concept of claims across outcomes, and have used it to provide a unified defense of the Pareto and Pigou-Dalton axioms. Adding some further, plausible, axioms, we arrive at prioritarianism. Here, I consider the possibility of desert-modulated claims—whereby the strength of an individual’s claim between two outcomes is determined not only by her well-being levels in the two outcomes, and her well-being difference between them, but also by her desert. This generalization of the notion of claims suggests a new axiom of justice: Priority for the More Deserving, requiring that, as between two individuals at the same well-being level, a given increment in well-being be allocated to the more deserving one. If individual desert is intrapersonally fixed, this new axiom, together with a desert-modulated version of the Pigou-Dalton principle, and the Pareto axioms, yields a desert-modulated prioritarian account of distributive justice. Trouble arises, however, if an individual’s desert level can be different in different outcomes. In this case of intrapersonally variable desert, Priority for the More Deserving can conflict with the Pareto axioms (both Pareto indifference and strong Pareto). This conflict, I believe, is sufficient reason to abandon the proposal to make claim strength a function of individual desert on top of well-being levels and differences. If distributive justice is truly sensitive to each individual’s separate perspective—if the justice ranking of outcomes is built up from the totality of individual rankings—we should embrace the Pareto axioms as axioms of justice and reject Priority for the More Deserving. In short: desert-modulated prioritarianism is a nonstarter. Rawls was right to sever distributive justice from desert

Why De Minimis?

De minimis cutoffs are a familiar feature of risk regulation. This includes the quantitative individual risk thresholds for fatality risks employed in many contexts by EPA, FDA, and other agencies, such as the 1-in-1 million lifetime cancer risk cutoff; extreme event cutoffs for addressing natural hazards, such as the 100 - year - flood or 475 - year - earthquake; de minimis failure probabilities for built structures; the exclusion of low - probability causal models; and other policymaking criteria. All these tests have a common structure, as I show in the Article. A de minimis test, broadly defined, tells the decisionmaker to determine whether the probability of some outcome is above a low threshold and makes this determination relevant, in some way, to her choice. De minimis cutoffs are deeply problematic, and have been generally misunderstood by scholars. First, they are warranted - if at all - by virtue of policymakers\u27 bounded rationality. If policymakers were fully rational, de minimis cutoffs would have no justification. (This is true, I suggest, across a wide range of normative theories, and for the full gamut of de minimis tests). Second, although it seems plausible that some de minimis tests are justified once bounded rationality is brought into the picture, it is not clear which those are, or even how we should go about identifying them

Burying Evidence\u27s Dead Hand

When the Rhode Island Rules of Evidence were adopted, they displaced all inconsistent case law existing at the time. Though the Rules retain a great deal of the evidence practice that preceded them, there is much in evidence practice that changed with their adoption. Rhode Island courts have consistently applied Rule 403 in a manner that comports with practice as it existed before the enactment of the Rhode Island Rules of Evidence. That practice, though, is inconsistent with the plain language of the Rule. These doctrines must be discarded