The crisis of epistemic overload in modern scientific inquiry has exposed a critical deficiency in how truth claims are assessed, validated, and integrated across time and domain. The exponential growth in peer-reviewed publications, accompanied by inconsistent replication rates, entrenched citation biases, and the sociological entanglements of scientific authorship, has rendered traditional mechanisms of epistemic filtering increasingly obsolete. Simultaneously, artificial intelligence--while having demonstrated capacity in data correlation and language generation--remains fundamentally ill-equipped to perform rigorous epistemic reasoning. This gap is not merely technical but conceptual: current AI systems lack any principled framework for evaluating the truth-promoting value of claims, discerning authoritative sources, or understanding belief as a structured probabilistic relation between agents, claims, and contexts. The present work introduces a formal architecture--Bayesian Epistemology with Weighted Authority (BEW A)--which systematically encodes the logic of belief formation, update, and decay, guided by the core axioms of Bayesian rationality, tempered by structural mechanisms for authority weighting, replication scoring, and temporal reassessment.

This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction reduces the sample complexity of distributed simple binary hypothesis testing. In this paper, we show that sequential interaction does not help. The second problem suggests tightening existing sample complexity bounds for communication-constrained simple binary hypothesis testing. We derive optimally tight bounds for this setting and resolve this problem. Our main technical contributions are: (i) a one-shot lower bound on the Bayes error in simple binary hypothesis testing that satisfies a crucial tensorisation property; (ii) a streamlined proof of the formula for the sample complexity of simple binary hypothesis testing without constraints, first established in arXiv:2403.16981; and (iii) a reverse data-processing inequality for Hellinger-$λ$ divergences, generalising the results from arXiv:1812.03031 and arXiv:2206.02765.

Determining whether an algorithmic decision-making system discriminates against a specific demographic typically involves comparing a single point estimate of a fairness metric against a predefined threshold. This practice is statistically brittle: it ignores sampling error and treats small demographic subgroups the same as large ones. The problem intensifies in intersectional analyses, where multiple sensitive attributes are considered jointly, giving rise to a larger number of smaller groups. As these groups become more granular, the data representing them becomes too sparse for reliable estimation, and fairness metrics yield excessively wide confidence intervals, precluding meaningful conclusions about potential unfair treatments. In this paper, we introduce a unified, size-adaptive, hypothesis-testing framework that turns fairness assessment into an evidence-based statistical decision. Our contribution is twofold. (i) For sufficiently large subgroups, we prove a Central-Limit result for the statistical parity difference, leading to analytic confidence intervals and a Wald test whose type-I (false positive) error is guaranteed at level $α$. (ii) For the long tail of small intersectional groups, we derive a fully Bayesian Dirichlet-multinomial estimator; Monte-Carlo credible intervals are calibrated for any sample size and naturally converge to Wald intervals as more data becomes available. We validate our approach empirically on benchmark datasets, demonstrating how our tests provide interpretable, statistically rigorous decisions under varying degrees of data availability and intersectionality.

Unsupervised machine learning is widely used to mine large, unlabeled datasets to make data-driven discoveries in critical domains such as climate science, biomedicine, astronomy, chemistry, and more. However, despite its widespread utilization, there is a lack of standardization in unsupervised learning workflows for making reliable and reproducible scientific discoveries. In this paper, we present a structured workflow for using unsupervised learning techniques in science. We highlight and discuss best practices starting with formulating validatable scientific questions, conducting robust data preparation and exploration, using a range of modeling techniques, performing rigorous validation by evaluating the stability and generalizability of unsupervised learning conclusions, and promoting effective communication and documentation of results to ensure reproducible scientific discoveries. To illustrate our proposed workflow, we present a case study from astronomy, seeking to refine globular clusters of Milky Way stars based upon their chemical composition. Our case study highlights the importance of validation and illustrates how the benefits of a carefully-designed workflow for unsupervised learning can advance scientific discovery.

This paper proposes a framework for semantic hypothesis testing tailored to imaging inverse problems. Modern imaging methods struggle to support hypothesis testing, a core component of the scientific method that is essential for the rigorous interpretation of experiments and robust interfacing with decision-making processes. There are three main reasons why image-based hypothesis testing is challenging. First, the difficulty of using a single observation to simultaneously reconstruct an image, formulate hypotheses, and quantify their statistical significance. Second, the hypotheses encountered in imaging are mostly of semantic nature, rather than quantitative statements about pixel values. Third, it is challenging to control test error probabilities because the null and alternative distributions are often unknown. Our proposed approach addresses these difficulties by leveraging concepts from self-supervised computational imaging, vision-language models, and non-parametric hypothesis testing with e-values. We demonstrate our proposed framework through numerical experiments related to image-based phenotyping, where we achieve excellent power while robustly controlling Type I errors.

Ratio statistics--such as relative risk and odds ratios--play a central role in hypothesis testing, model evaluation, and decision-making across many areas of machine learning, including causal inference and fairness analysis. However, despite privacy concerns surrounding many datasets and despite increasing adoption of differential privacy, differentially private ratio statistics have largely been neglected by the literature and have only recently received an initial treatment by Lin et al. [1]. This paper attempts to fill this lacuna, giving results that can guide practice in evaluating ratios when the results must be protected by differential privacy. In particular, we show that even a simple algorithm can provide excellent properties concerning privacy, sample accuracy, and bias, not just asymptotically but also at quite small sample sizes. Additionally, we analyze a differentially private estimator for relative risk, prove its consistency, and develop a method for constructing valid confidence intervals. Our approach bridges a gap in the differential privacy literature and provides a practical solution for ratio estimation in private machine learning pipelines.

The predominant de facto paradigm of testing ML models relies on either using only held-out data to compute aggregate evaluation metrics or by assessing the performance on different subgroups. However, such data-only testing methods operate under the restrictive assumption that the available empirical data is the sole input for testing ML models, disregarding valuable contextual information that could guide model testing. In this paper, we challenge the go-to approach of data-only testing and introduce Context-Aware Testing (CAT) which uses context as an inductive bias to guide the search for meaningful model failures. We instantiate the first CAT system, SMART Testing, which employs large language models to hypothesize relevant and likely failures, which are evaluated on data using a self-falsification mechanism. Through empirical evaluations in diverse settings, we show that SMART automatically identifies more relevant and impactful failures than alternatives, demonstrating the potential of CAT as a testing paradigm.

Automated scientific discovery promises to accelerate progress across scientific domains, but evaluating an agent's capacity for end-to-end scientific reasoning is challenging as running real-world experiments is often prohibitively expensive or infeasible. In this work we introduce DiscoveryWorld, a virtual environment that enables benchmarking an agent's ability to perform complete cycles of novel scientific discovery in an inexpensive, simulated, multi-modal, long-horizon, and fictional setting.DiscoveryWorld consists of 24 scientific tasks across three levels of difficulty, each with parametric variations that provide new discoveries for agents to make across runs. Tasks require an agent to form hypotheses, design and run experiments, analyze results, and act on conclusions. Task difficulties are normed to range from straightforward to challenging for human scientists with advanced degrees. DiscoveryWorld further provides three automatic metrics for evaluating performance, including: (1) binary task completion, (2) fine-grained report cards detailing procedural scoring of task-relevant actions, and (3) the accuracy of discovered explanatory knowledge.While simulated environments such as DiscoveryWorld are low-fidelity compared to the real world, we find that strong baseline agents struggle on most DiscoveryWorld tasks, highlighting the utility of using simulated environments as proxy tasks for near-term development of scientific discovery competency in agents.

The prevailing model for disseminating scientific knowledge relies on individual publications dispersed across numerous journals and archives. This legacy system is ill suited to the recent exponential proliferation of publications, contributing to insurmountable information overload, issues surrounding reproducibility and retractions. We introduce the Discovery Engine, a framework to address these challenges by transforming an array of disconnected literature into a unified, computationally tractable representation of a scientific domain. Central to our approach is the LLM-driven distillation of publications into structured "knowledge artifacts," instances of a universal conceptual schema, complete with verifiable links to source evidence. These artifacts are then encoded into a high-dimensional Conceptual Tensor. This tensor serves as the primary, compressed representation of the synthesized field, where its labeled modes index scientific components (concepts, methods, parameters, relations) and its entries quantify their interdependencies. The Discovery Engine allows dynamic "unrolling" of this tensor into human-interpretable views, such as explicit knowledge graphs (the CNM graph) or semantic vector spaces, for targeted exploration. Crucially, AI agents operate directly on the graph using abstract mathematical and learned operations to navigate the knowledge landscape, identify non-obvious connections, pinpoint gaps, and assist researchers in generating novel knowledge artifacts (hypotheses, designs). By converting literature into a structured tensor and enabling agent-based interaction with this compact representation, the Discovery Engine offers a new paradigm for AI-augmented scientific inquiry and accelerated discovery.

Creative processes are typically divided into three types: combinatorial, exploratory, and transformational. Here, we provide a graphical theory of transformational scientific creativity, synthesizing Boden's insight that trans-formational creativity arises from changes in the "enabling constraints" of a conceptual space (Boden 1992) and Kuhn's structure of scientific revolutions as resulting from paradigm shifts (Kuhn 1962). We prove that modifications made to axioms of our graphical model have the most transformative potential and then illustrate how several historical instances of transforma-tional creativity can be captured by our framework.