We characterize learnability for quantum measurement classes by establishing matching necessary and sufficient conditions for their PAC learnability, along with corresponding sample complexity bounds, in the setting where the learner is given access only to prepared quantum states. We first probe the results from previous works on this setting. We show that the empirical risk defined in previous works and matching the definition in the classical theory fails to satisfy the uniform convergence property enjoyed in the classical setting for some learnable classes. Moreover, we show that VC dimension generalization upper bounds in previous work are frequently infinite, even for finite-dimensional POVM classes. To surmount the failure of the standard ERM to satisfy uniform convergence, we define a new learning rule -- denoised ERM. We show this to be a universal learning rule for POVM and probabilistically observed concept classes, and the condition for it to satisfy uniform convergence is finite fat shattering dimension of the class. We give quantitative sample complexity upper and lower bounds for learnability in terms of finite fat-shattering dimension and a notion of approximate finite partitionability into approximately jointly measurable subsets, which allow for sample reuse. We then show that finite fat shattering dimension implies finite coverability by approximately jointly measurable subsets, leading to our matching conditions. We also show that every measurement class defined on a finite-dimensional Hilbert space is PAC learnable. We illustrate our results on several example POVM classes.
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We propose a distributional framework for assessing socio-technical risks of foundation models with quantified statistical significance. Our approach hinges on a new statistical relative testing based on first and second order stochastic dominance of real random variables. We show that the second order statistics in this test are linked to mean-risk models commonly used in econometrics and mathematical finance to balance risk and utility when choosing between alternatives. Using this framework, we formally develop a risk-aware approach for foundation model selection given guardrails quantified by specified metrics. Inspired by portfolio optimization and selection theory in mathematical finance, we define a \emph{metrics portfolio} for each model as a means to aggregate a collection of metrics, and perform model selection based on the stochastic dominance of these portfolios. The statistical significance of our tests is backed theoretically by an asymptotic analysis via central limit theorems instantiated in practice via a bootstrap variance estimate. We use our framework to compare various large language models regarding risks related to drifting from instructions and outputting toxic content.
Systems for making determinations on socially-constructed and complex concepts at scale are increasingly being deployed. To make such fuzzy concepts tractable for training and evaluating AI, aligning model outputs, or human-in-the-loop workflows, the prevailing strategy involves developing `constitutions' in the form of rules, policies, or principles. However, high-level rules often fail to capture situational nuances or have differing interpretations, resulting in inconsistent decisions. In this work, we introduce case law grounding (CLG), a hybrid workflow inspired by case law in the legal realm where past judgments on specific cases inform new decisions. Evaluating on two task domains, we find that CLG can improve alignment of decisions (+9.6% and +10.9% accuracy) and consistency ($\Delta\bar{\kappa}$ of +0.263 and +0.433) of human decision-makers, while also providing auditable rationales. We also find similarly substantial alignment improvements for an LLM decision-maker (+25% and +23% accuracy).
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to be selected), various elections with diversity constraints, the model of public decisions (where decisions needs to be taken on a number of independent issues), and the model of collective scheduling. A critical property of voting is that it should be fair -- not only to individuals but also to groups of voters with similar opinions on the subject of the vote; in other words, the outcome of an election should proportionally reflect the voters' preferences. We formulate axioms of proportionality in this general model. Our axioms do not require predefining groups of voters; to the contrary, we ensure that the opinion of every subset of voters whose preferences are cohesive-enough are taken into account to the extent that is proportional to the size of the subset. Our axioms generalise the strongest known satisfiable axioms for the more specific models. We explain how to adapt two prominent committee election rules, Proportional Approval Voting (PAV) and Phragm\'{e}n Sequential Rule, as well as the concept of stable-priceability to our general model. The two rules satisfy our proportionality axioms if and only if the feasibility constraints are matroids.
Fine-tuning diffusion models through personalized datasets is an acknowledged method for improving generation quality across downstream tasks, which, however, often inadvertently generates unintended concepts such as watermarks and QR codes, attributed to the limitations in image sources and collecting methods within specific downstream tasks. Existing solutions suffer from eliminating these unintentionally learned implicit concepts, primarily due to the dependency on the model's ability to recognize concepts that it actually cannot discern. In this work, we introduce \methodname, a novel approach that successfully removes the implicit concepts with either an additional accessible classifier or detector model to encode geometric information of these concepts into text domain. Moreover, we propose \textit{Implicit Concept}, a novel image-text dataset imbued with three implicit concepts (\ie, watermarks, QR codes, and text) for training and evaluation. Experimental results demonstrate that \methodname not only identifies but also proficiently eradicates implicit concepts, revealing a significant improvement over the existing methods. The integration of geometric information marks a substantial progression in the precise removal of implicit concepts in diffusion models.
Policy gradient methods, where one searches for the policy of interest by maximizing the value functions using first-order information, become increasingly popular for sequential decision making in reinforcement learning, games, and control. Guaranteeing the global optimality of policy gradient methods, however, is highly nontrivial due to nonconcavity of the value functions. In this exposition, we highlight recent progresses in understanding and developing policy gradient methods with global convergence guarantees, putting an emphasis on their finite-time convergence rates with regard to salient problem parameters.
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently encountered in practice, the chain graph model has been largely under investigated in literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this paper, we first establish a set of novel identifiability conditions for the Gaussian chain graph model, exploiting a low rank plus sparse decomposition of the precision matrix. Further, an efficient learning algorithm is built upon the identifiability conditions to fully recover the chain graph structure. Theoretical analysis on the proposed method is conducted, assuring its asymptotic consistency in recovering the exact chain graph structure. The advantage of the proposed method is also supported by numerical experiments on both simulated examples and a real application on the Standard & Poor 500 index data.
Software Engineering concepts such as version control, continuous integration, and unit testing are often not presented in college computer science curriculums until the third year of study, after completing several semesters of programming courses. Throughout the summer of 2023, two high school students volunteered in our lab at Wayne State University where I'm a graduate research assistant and Ph.D. student in computer science. The students had taken AP Computer Science but had no prior experience with software engineering or software testing. This paper documents our experience devising a group project to teach the requisite software engineering skills to implement automated tests that meaningfully contribute to open-source scientific computing projects developed in connection with our lab. We describe the concepts covered, tools used, and software tests written in this early introduction to software engineering while maintaining shared emphases on education and the deployment of our work.
We provide a comprehensive theory of multiple variants of ordinal multidimensional scaling, including external and internal unfolding. We do so in the continuous model of Shepard (1966).
As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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