We study the interplay between memorization and generalization of overparametrized networks in the extreme case of a single training example. The learning task is to predict an output which is as similar as possible to the input. We examine both fully-connected and convolutional networks that are initialized randomly and then trained to minimize the reconstruction error. The trained networks take one of the two forms: the constant function ("memorization") and the identity function ("generalization"). We show that different architectures exhibit vastly different inductive bias towards memorization and generalization. An important consequence of our study is that even in extreme cases of overparameterization, deep learning can result in proper generalization.

Adaptive data analysis is frequently criticized for its pessimistic generalization guarantees. The source of these pessimistic bounds is a model that permits arbitrary, possibly adversarial analysts that optimally use information to bias results. While being a central issue in the field, still lacking are notions of natural analysts that allow for more optimistic bounds faithful to the reality that typical analysts aren't adversarial. In this work, we propose notions of natural analysts that smoothly interpolate between the optimal non-adaptive bounds and the best-known adaptive generalization bounds. To accomplish this, we model the analyst's knowledge as evolving according to the rules of an unknown dynamical system that takes in revealed information and outputs new statistical queries to the data. This allows us to restrict the analyst through different natural control-theoretic notions. One such notion corresponds to a recency bias, formalizing an inability to arbitrarily use distant information. Another complementary notion formalizes an anchoring bias, a tendency to weight initial information more strongly. Both notions come with quantitative parameters that smoothly interpolate between the non-adaptive case and the fully adaptive case, allowing for a rich spectrum of intermediate analysts that are neither non-adaptive nor adversarial. Natural not only from a cognitive perspective, we show that our notions also capture standard optimization methods, like gradient descent in various settings. This gives a new interpretation to the fact that gradient descent tends to overfit much less than its adaptive nature might suggest.

Although many fairness-promoting interventions have been proposed in the machine learning literature, unconstrainedlearning remains the dominant paradigm among practitioners for learning risk scores from data. Given a prespecified class of models, unconstrained learning simply seeks to minimize the average prediction loss over a labeled dataset, without explicitly correcting for disparity with respect to sensitive attributes, such as race or gender. Many criticize the practice of unconstrained machine learning for propagating harmful biases [Crawford, 2013, Barocas and Selbst, 2016, Crawford, 2017]. Others see merit in unconstrained learning for reducing bias in consequential decisions [Corbett-Davies et al., 2017b,a, Kleinberg et al., 2018]. In this work, we show that defaulting to unconstrained learning does not neglect fairness considerations entirely.Instead, it prioritizes one notion of "fairness" over others: unconstrained learning achieves calibration with respect to one or more sensitive attributes, as well as a related criterion called sufficiency [e.g., Barocas et al., 2018], at the cost of violating other widely used fairness criteria, separation and independence (see Section 1.2 for references therein). A risk score is calibrated for a group if the risk score obviates the need to solicit group membership forthe purpose of predicting an outcome variable of interest. The concept of calibration has a venerable history in statistics and machine learning [Cox, 1958, Murphy and Winkler, 1977, Dawid, 1982, DeGroot and Fienberg, 1983, Platt, 1999, Zadrozny and Elkan, 2001, Niculescu-Mizil and Caruana, 2005]. The appearance of calibration as a widely adopted and discussed "fairness criterion" largelyresulted from a recent debate around fairness in recidivism prediction and pretrial

Saliency methods have emerged as a popular tool to highlight features in an input deemed relevant for the prediction of a learned model. Several saliency methods have been proposed, often guided by visual appeal on image data. In this work, we propose an actionable methodology to evaluate what kinds of explanations a given method can and cannot provide. We find that reliance, solely, on visual assessment can be misleading. Through extensive experiments we show that some existing saliency methods are independent both of the model and of the data generating process. Consequently, methods that fail the proposed tests are inadequate for tasks that are sensitive to either data or model, such as, finding outliers in the data, explaining the relationship between inputs and outputs that the model learned, and debugging the model. We interpret our findings through an analogy with edge detection in images, a technique that requires neither training data nor model. Theory in the case of a linear model and a single-layer convolutional neural network supports our experimental findings.

Saliency methods have emerged as a popular tool to highlight features in an input deemed relevant for the prediction of a learned model. Several saliency methods have been proposed, often guided by visual appeal on image data. In this work, we propose an actionable methodology to evaluate what kinds of explanations a given method can and cannot provide. We find that reliance, solely, on visual assessment can be misleading. Through extensive experiments we show that some existing saliency methods are independent both of the model and of the data generating process. Consequently, methods that fail the proposed tests are inadequate for tasks that are sensitive to either data or model, such as, finding outliers in the data, explaining the relationship between inputs and outputs that the model learned, and debugging the model. We interpret our findings through an analogy with edge detection in images, a technique that requires neither training data nor model. Theory in the case of a linear model and a single-layer convolutional neural network supports our experimental findings.

Saliency methods have emerged as a popular tool to highlight features in an input deemed relevant for the prediction of a learned model. Several saliency methods have been proposed, often guided by visual appeal on image data. In this work, we propose an actionable methodology to evaluate what kinds of explanations a given method can and cannot provide. We find that reliance, solely, on visual assessment can be misleading. Through extensive experiments we show that some existing saliency methods are independent both of the model and of the data generating process. Consequently, methods that fail the proposed tests are inadequate for tasks that are sensitive to either data or model, such as, finding outliers in the data, explaining the relationship between inputs and outputs that the model learned, and debugging the model. We interpret our findings through an analogy with edge detection in images, a technique that requires neither training data nor model. Theory in the case of a linear model and a single-layer convolutional neural network supports our experimental findings.

Modern learning models are characterized by large hyperparameter spaces. In order to adequately explore these large spaces, we must evaluate a large number of configurations, typically orders of magnitude more configurations than available parallel workers. Given the growing costs of model training, we would ideally like to perform this search in roughly the same wall-clock time needed to train a single model. In this work, we tackle this challenge by introducing ASHA, a simple and robust hyperparameter tuning algorithm with solid theoretical underpinnings that exploits parallelism and aggressive early-stopping. Our extensive empirical results show that ASHA slightly outperforms Fabolas and Population Based Tuning, state-of-the hyperparameter tuning methods; scales linearly with the number of workers in distributed settings; converges to a high quality configuration in half the time taken by Vizier (Google's internal hyperparameter tuning service) in an experiment with 500 workers; and beats the published result for a near state-of-the-art LSTM architecture in under 2x the time to train a single model.

Consequential decision-making typically incentivizes individuals to behave strategically, tailoring their behavior to the specifics of the decision rule. A long line of work has therefore sought to counteract strategic behavior by designing more conservative decision boundaries in an effort to increase robustness to the effects of strategic covariate shift. We show that these efforts benefit the institutional decision maker at the expense of the individuals being classified. Introducing a notion of social burden, we prove that any increase in institutional utility necessarily leads to a corresponding increase in social burden. Moreover, we show that the negative externalities of strategic classification can disproportionately harm disadvantaged groups in the population. Our results highlight that strategy-robustness must be weighed against considerations of social welfare and fairness.

We prove stable recurrent neural networks are well approximated by feed-forward networks for the purpose of both inference and training by gradient descent. Our result applies to a broad range of non-linear recurrent neural networks under a natural stability condition, which we observe is also necessary. Complementing our theoretical findings, we verify the conclusions of our theory on both real and synthetic tasks. Furthermore, we demonstrate recurrent models satisfying the stability assumption of our theory can have excellent performance on real sequence learning tasks.

Fairness in machine learning has predominantly been studied in static classification settings without concern for how decisions change the underlying population over time. Conventional wisdom suggests that fairness criteria promote the long-term well-being of those groups they aim to protect. We study how static fairness criteria interact with temporal indicators of well-being, such as long-term improvement, stagnation, and decline in a variable of interest. We demonstrate that even in a one-step feedback model, common fairness criteria in general do not promote improvement over time, and may in fact cause harm in cases where an unconstrained objective would not. We completely characterize the delayed impact of three standard criteria, contrasting the regimes in which these exhibit qualitatively different behavior. In addition, we find that a natural form of measurement error broadens the regime in which fairness criteria perform favorably. Our results highlight the importance of measurement and temporal modeling in the evaluation of fairness criteria, suggesting a range of new challenges and trade-offs.