The generalization error (risk) of a supervised statistical learning algorithm quantifies its prediction ability on previously unseen data. Inspired by exponential tilting, Li et al. (2021) proposed the tilted empirical risk as a non-linear risk metric for machine learning applications such as classification and regression problems. In this work, we examine the generalization error of the tilted empirical risk. In particular, we provide uniform and information-theoretic bounds on the tilted generalization error, defined as the difference between the population risk and the tilted empirical risk, with a convergence rate of $O(1/\sqrt{n})$ where $n$ is the number of training samples. Furthermore, we study the solution to the KL-regularized expected tilted empirical risk minimization problem and derive an upper bound on the expected tilted generalization error with a convergence rate of $O(1/n)$.
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The meteoric rise in power and popularity of machine learning models dependent on valuable training data has reignited a basic tension between the power of running a program locally and the risk of exposing details of that program to the user. At the same time, fundamental properties of quantum states offer new solutions to data and program security that can require strikingly few quantum resources to exploit, and offer advantages outside of mere computational run time. In this work, we demonstrate such a solution with quantum one-time tokens. A quantum one-time token is a quantum state that permits a certain program to be evaluated exactly once. One-time security guarantees, roughly, that the token cannot be used to evaluate the program more than once. We propose a scheme for building quantum one-time tokens for any randomized classical program, which include generative AI models. We prove that the scheme satisfies an interesting definition of one-time security as long as outputs of the classical algorithm have high enough min-entropy, in a black box model. Importantly, the classical program being protected does not need to be implemented coherently on a quantum computer. In fact, the size and complexity of the quantum one-time token is independent of the program being protected, and additional quantum resources serve only to increase the security of the protocol. Due to this flexibility in adjusting the security, we believe that our proposal is parsimonious enough to serve as a promising candidate for a near-term useful demonstration of quantum computing in either the NISQ or early fault tolerant regime.
Recent work in database query optimization has used complex machine learning strategies, such as customized reinforcement learning schemes. Surprisingly, we show that LLM embeddings of query text contain useful semantic information for query optimization. Specifically, we show that a simple binary classifier deciding between alternative query plans, trained only on a small number of labeled embedded query vectors, can outperform existing heuristic systems. Although we only present some preliminary results, an LLM-powered query optimizer could provide significant benefits, both in terms of performance and simplicity.
Compromise estimation entails using a weighted average of outputs from several candidate models, and is a viable alternative to model selection when the choice of model is not obvious. As such, it is a tool used by both frequentists and Bayesians, and in both cases, the literature is vast and includes studies of performance in simulations and applied examples. However, frequentist researchers often prove oracle properties, showing that a proposed average asymptotically performs at least as well as any other average comprising the same candidates. On the Bayesian side, such oracle properties are yet to be established. This paper considers Bayesian stacking estimators, and evaluates their performance using frequentist asymptotics. Oracle properties are derived for estimators stacking Bayesian linear and logistic regression models, and combined with Monte Carlo experiments that show Bayesian stacking may outperform the best candidate model included in the stack. Thus, the result is not only a frequentist motivation of a fundamentally Bayesian procedure, but also an extended range of methods available to frequentist practitioners.
Modern optimizers such as AdamW, equipped with momentum and adaptive learning rate, are designed to escape local minima and explore the vast parameter space. This exploration is beneficial for finding good loss basins when training from scratch. It is not necessarily ideal when resuming from a powerful foundation model because it can lead to large deviations from the pre-trained initialization and, consequently, worse robustness and generalization. At the same time, strong regularization on all parameters can lead to under-fitting. We hypothesize that selectively regularizing the parameter space is the key to fitting and retraining the pre-trained knowledge. This paper proposes a new weight decay technique, Selective Projection Decay (SPD), that selectively imposes a strong penalty on certain layers while allowing others to change freely. Intuitively, SPD expands and contracts the parameter search space for layers with consistent and inconsistent loss reduction, respectively. Experimentally, when equipped with SPD, Adam consistently provides better in-distribution generalization and out-of-distribution robustness performance on multiple popular vision and language benchmarks. Code available at~\url{//github.com/GT-RIPL/Selective-Projection-Decay.git}
The widespread use of machine learning and data-driven algorithms for decision making has been steadily increasing over many years. The areas in which this is happening are diverse: healthcare, employment, finance, education, the legal system to name a few; and the associated negative side effects are being increasingly harmful for society. Negative data \emph{bias} is one of those, which tends to result in harmful consequences for specific groups of people. Any mitigation strategy or effective policy that addresses the negative consequences of bias must start with awareness that bias exists, together with a way to understand and quantify it. However, there is a lack of consensus on how to measure data bias and oftentimes the intended meaning is context dependent and not uniform within the research community. The main contributions of our work are: (1) The definition of Uniform Bias (UB), the first bias measure with a clear and simple interpretation in the full range of bias values. (2) A systematic study to characterize the flaws of existing measures in the context of anti employment discrimination rules used by the Office of Federal Contract Compliance Programs, additionally showing how UB solves open problems in this domain. (3) A framework that provides an efficient way to derive a mathematical formula for a bias measure based on an algorithmic specification of bias addition. Our results are experimentally validated using nine publicly available datasets and theoretically analyzed, which provide novel insights about the problem. Based on our approach, we also design a bias mitigation model that might be useful to policymakers.
Continual learning with deep neural networks presents challenges distinct from both the fixed-dataset and convex continual learning regimes. One such challenge is plasticity loss, wherein a neural network trained in an online fashion displays a degraded ability to fit new tasks. This problem has been extensively studied in both supervised learning and off-policy reinforcement learning (RL), where a number of remedies have been proposed. Still, plasticity loss has received less attention in the on-policy deep RL setting. Here we perform an extensive set of experiments examining plasticity loss and a variety of mitigation methods in on-policy deep RL. We demonstrate that plasticity loss is pervasive under domain shift in this regime, and that a number of methods developed to resolve it in other settings fail, sometimes even performing worse than applying no intervention at all. In contrast, we find that a class of ``regenerative'' methods are able to consistently mitigate plasticity loss in a variety of contexts, including in gridworld tasks and more challenging environments like Montezuma's Revenge and ProcGen.
Solving societal problems on a global scale requires the collection and processing of ideas and methods from diverse sets of international experts. As the number and diversity of human experts increase, so does the likelihood that elements in this collective knowledge can be combined and refined to discover novel and better solutions. However, it is difficult to identify, combine, and refine complementary information in an increasingly large and diverse knowledge base. This paper argues that artificial intelligence (AI) can play a crucial role in this process. An evolutionary AI framework, termed RHEA, fills this role by distilling knowledge from diverse models created by human experts into equivalent neural networks, which are then recombined and refined in a population-based search. The framework was implemented in a formal synthetic domain, demonstrating that it is transparent and systematic. It was then applied to the results of the XPRIZE Pandemic Response Challenge, in which over 100 teams of experts across 23 countries submitted models based on diverse methodologies to predict COVID-19 cases and suggest non-pharmaceutical intervention policies for 235 nations, states, and regions across the globe. Building upon this expert knowledge, by recombining and refining the 169 resulting policy suggestion models, RHEA discovered a broader and more effective set of policies than either AI or human experts alone, as evaluated based on real-world data. The results thus suggest that AI can play a crucial role in realizing the potential of human expertise in global problem-solving.
Despite extensive efforts to create fairer machine learning (ML) datasets, there remains a limited understanding of the practical aspects of dataset curation. Drawing from interviews with 30 ML dataset curators, we present a comprehensive taxonomy of the challenges and trade-offs encountered throughout the dataset curation lifecycle. Our findings underscore overarching issues within the broader fairness landscape that impact data curation. We conclude with recommendations aimed at fostering systemic changes to better facilitate fair dataset curation practices.
The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.
We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.
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