The process of developing theories and models and testing them with experiments is fundamental to the scientific method. Automating the entire scientific method then requires not only automation of the induction of theories from data, but also experimentation from design to implementation. This is the idea behind a robot scientist -- a coupled system of AI and laboratory robotics that has agency to test hypotheses with real-world experiments. In this chapter we explore some of the fundamentals of robot scientists in the philosophy of science. We also map the activities of a robot scientist to machine learning paradigms, and argue that the scientific method shares an analogy with active learning. We demonstrate these concepts using examples from previous robot scientists, and also from Genesis: a next generation robot scientist designed for research in systems biology, comprising a micro-fluidic system with 1000 computer-controlled micro-bioreactors and interpretable models based in controlled vocabularies and logic.

Automated scientific discovery promises to accelerate progress across scientific domains. However, developing and evaluating an AI 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, the first virtual environment for developing and benchmarking an agent's ability to perform complete cycles of novel scientific discovery. DISCOVERYWORLD contains a variety of different challenges, covering topics as diverse as radioisotope dating, rocket science, and proteomics, to encourage development of general discovery skills rather than task-specific solutions. DISCOVERYWORLD itself is an inexpensive, simulated, text-based environment (with optional 2D visual overlay). It includes 120 different challenge tasks, spanning eight topics each with three levels of difficulty and several parametric variations. Each task requires an agent to form hypotheses, design and run experiments, analyze results, and act on conclusions. DISCOVERYWORLD further provides three automatic metrics for evaluating performance, based on (a) task completion, (b) task-relevant actions taken, and (c) the discovered explanatory knowledge. We find that strong baseline agents, that perform well in prior published environments, struggle on most DISCOVERYWORLD tasks, suggesting that DISCOVERYWORLD captures some of the novel challenges of discovery, and thus that DISCOVERYWORLD may help accelerate near-term development and assessment of scientific discovery competency in agents. Code available at: www.github.com/allenai/discoveryworld

Compound AI systems (CASs) that employ LLMs as agents to accomplish knowledge-intensive tasks via interactions with tools and data retrievers have garnered significant interest within database and AI communities. While these systems have the potential to supplement typical analysis workflows of data analysts in enterprise data platforms, unfortunately, CASs are subject to the same data discovery challenges that analysts have encountered over the years -- silos of multimodal data sources, created across teams and departments within an organization, make it difficult to identify appropriate data sources for accomplishing the task at hand. Existing data discovery benchmarks do not model such multimodality and multiplicity of data sources. Moreover, benchmarks of CASs prioritize only evaluating end-to-end task performance. To catalyze research on evaluating the data discovery performance of multimodal data retrievers in CASs within a real-world setting, we propose CMDBench, a benchmark modeling the complexity of enterprise data platforms. We adapt existing datasets and benchmarks in open-domain -- from question answering and complex reasoning tasks to natural language querying over structured data -- to evaluate coarse- and fine-grained data discovery and task execution performance. Our experiments reveal the impact of data retriever design on downstream task performance -- a 46% drop in task accuracy on average -- across various modalities, data sources, and task difficulty. The results indicate the need to develop optimization strategies to identify appropriate LLM agents and retrievers for efficient execution of CASs over enterprise data.

We propose two general methods for constructing robust permutation tests under data corruption. The proposed tests effectively control the non-asymptotic type I error under data corruption, and we prove their consistency in power under minimal conditions. This contributes to the practical deployment of hypothesis tests for real-world applications with potential adversarial attacks. One of our methods inherently ensures differential privacy, further broadening its applicability to private data analysis. For the two-sample and independence settings, we show that our kernel robust tests are minimax optimal, in the sense that they are guaranteed to be non-asymptotically powerful against alternatives uniformly separated from the null in the kernel MMD and HSIC metrics at some optimal rate (tight with matching lower bound). Finally, we provide publicly available implementations and empirically illustrate the practicality of our proposed tests.

Statistical methods have been widely misused and misinterpreted in various scientific fields, raising significant concerns about the integrity of scientific research. To develop techniques to mitigate this problem, we propose a new method for formally specifying and automatically verifying the correctness of statistical programs. In this method, programmers are reminded to check the requirements for statistical methods by annotating their source code. Then, a software tool called StatWhy automatically checks whether the programmers have properly specified the requirements for the statistical methods. This tool is implemented using the Why3 platform to verify the correctness of OCaml programs for statistical hypothesis testing. We demonstrate how StatWhy can be used to avoid common errors in a variety of popular hypothesis testing programs.

Quantum hypothesis testing (QHT) has been traditionally studied from the information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of samples of an unknown state. In this paper, we study the sample complexity of QHT, wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. By making use of the wealth of knowledge that already exists in the literature on QHT, we characterize the sample complexity of binary QHT in the symmetric and asymmetric settings, and we provide bounds on the sample complexity of multiple QHT. In more detail, we prove that the sample complexity of symmetric binary QHT depends logarithmically on the inverse error probability and inversely on the negative logarithm of the fidelity. As a counterpart of the quantum Stein's lemma, we also find that the sample complexity of asymmetric binary QHT depends logarithmically on the inverse type II error probability and inversely on the quantum relative entropy, provided that the type II error probability is sufficiently small. We then provide lower and upper bounds on the sample complexity of multiple QHT, with it remaining an intriguing open question to improve these bounds. The final part of our paper outlines and reviews how sample complexity of QHT is relevant to a broad swathe of research areas and can enhance understanding of many fundamental concepts, including quantum algorithms for simulation and search, quantum learning and classification, and foundations of quantum mechanics. As such, we view our paper as an invitation to researchers coming from different communities to study and contribute to the problem of sample complexity of QHT, and we outline a number of open directions for future research.

Large Language Models have recently gained significant attention in scientific discovery for their extensive knowledge and advanced reasoning capabilities. However, they encounter challenges in effectively simulating observational feedback and grounding it with language to propel advancements in physical scientific discovery. Conversely, human scientists undertake scientific discovery by formulating hypotheses, conducting experiments, and revising theories through observational analysis. Inspired by this, we propose to enhance the knowledge-driven, abstract reasoning abilities of LLMs with the computational strength of simulations. We introduce Scientific Generative Agent (SGA), a bilevel optimization framework: LLMs act as knowledgeable and versatile thinkers, proposing scientific hypotheses and reason about discrete components, such as physics equations or molecule structures; meanwhile, simulations function as experimental platforms, providing observational feedback and optimizing via differentiability for continuous parts, such as physical parameters. We conduct extensive experiments to demonstrate our framework's efficacy in constitutive law discovery and molecular design, unveiling novel solutions that differ from conventional human expectations yet remain coherent upon analysis.

Combining different forms of prompts with pre-trained large language models has yielded remarkable results on reasoning tasks (e.g. Chain-of-Thought prompting). However, along with testing on more complex reasoning, these methods also expose problems such as invalid reasoning and fictional reasoning paths. In this paper, we develop \textit{Hypothesis Testing Prompting}, which adds conclusion assumptions, backward reasoning, and fact verification during intermediate reasoning steps. \textit{Hypothesis Testing prompting} involves multiple assumptions and reverses validation of conclusions leading to its unique correct answer. Experiments on two challenging deductive reasoning datasets ProofWriter and RuleTaker show that hypothesis testing prompting not only significantly improves the effect, but also generates a more reasonable and standardized reasoning process.

Interpretability is the study of explaining models in understandable terms to humans. At present, interpretability is divided into two paradigms: the intrinsic paradigm, which believes that only models designed to be explained can be explained, and the post-hoc paradigm, which believes that black-box models can be explained. At the core of this debate is how each paradigm ensures its explanations are faithful, i.e., true to the model's behavior. This is important, as false but convincing explanations lead to unsupported confidence in artificial intelligence (AI), which can be dangerous. This paper's position is that we should think about new paradigms while staying vigilant regarding faithfulness. First, by examining the history of paradigms in science, we see that paradigms are constantly evolving. Then, by examining the current paradigms, we can understand their underlying beliefs, the value they bring, and their limitations. Finally, this paper presents 3 emerging paradigms for interpretability. The first paradigm designs models such that faithfulness can be easily measured. Another optimizes models such that explanations become faithful. The last paradigm proposes to develop models that produce both a prediction and an explanation.

Technological advancements have substantially increased computational power and data availability, enabling the application of powerful machine-learning (ML) techniques across various fields. However, our ability to leverage ML methods for scientific discovery, {\it i.e.} to obtain fundamental and formalized knowledge about natural processes, is still in its infancy. In this review, we explore how the scientific community can increasingly leverage ML techniques to achieve scientific discoveries. We observe that the applicability and opportunity of ML depends strongly on the nature of the problem domain, and whether we have full ({\it e.g.}, turbulence), partial ({\it e.g.}, computational biochemistry), or no ({\it e.g.}, neuroscience) {\it a-priori} knowledge about the governing equations and physical properties of the system. Although challenges remain, principled use of ML is opening up new avenues for fundamental scientific discoveries. Throughout these diverse fields, there is a theme that ML is enabling researchers to embrace complexity in observational data that was previously intractable to classic analysis and numerical investigations.