In a profound sense, the law is an applied field. It exists because society needs rules to function. Even if these rules are seemingly "bright line", in limit cases they require interpretation. Even more so if the rule in question confines itself to enunciate a normative program, and leaves its implementation to the administration and the judiciary. The traditional response is hermeneutical. The legislator translates the normative intention into words. That way, it implicitly delegates spelling out what these words mean to the parties and the authorities involved in dissolving the concrete conflicts of life. This sketch of the law’s mission explains the traditional character of legal research. If a researcher adopts an "inside view", she engages in a division of labor with practicing lawyers. The quintessential product of this research is a "commentary". The researcher summarizes the state of the art thinking about a statutory provision (and maybe proposes an alternative reading). Alternatively, the researcher adopts an "outside view". In the spirit of a social scientist, she treats the law as her object of study. Typical products are more precise definitions of and empirical investigations into a class of social problems that legal rules are meant to address; or attempts at finding traces of judicial policy in the jurisprudence of a court. Large language models have the potential to deeply affect all of these strands of legal research. As the potential is more easily discernible for the "outside view", the talk will only briefly illustrate in which ways LLMs are likely to fuel this strand of legal research. It will drill deeper into the "inside view", and explain how an important part of this research, the summarization of the jurisprudence on a statutory provision (the guarantee of freedom of assembly in the German Constitution) can already today be delegated to the LLM. It is not difficult to predict that, ten years from now, legal research will look radically different.

I will present two recent joint works done with Arnaud Sangnier and Nathalie Sznajder. We study networks of processes that all execute the same finite protocol and communicate synchronously in two different ways: a process can broadcast one message to all other processes or send it to at most one other process. We study two coverability problems with a parameterised number of processes (state coverability and configuration coverability). It is already known that these problem are Ackermann-hard (and decidable) in the general case. This already holds when the processes communicate only by broadcasts. We show that when forbidding broadcasts, the two problems are EXPSPACE-complete. We also study a restriction on the protocol: a Wait-Only protocol has no state from which a process can send and receive messages. We show that without broadcasts, both problems are PTIME-complete in this restriction, and with broadcasts, state coverability is PTIME-complete and configuration coverability PSPACE-complete.

Modern machine learning (ML) has largely been driven by neural networks, delivering outstanding results not only in traditional ML applications, but also permeating into classical sciences solving open problems in physics, chemistry, and biology. This success came at a cost, as typical neural network architectures are inherently complex and their reasoning processes opaque. In domains where insights weigh more than prediction, such as modeling of systems biology, or in high-stakes decision making, such as healthcare and finance, the reasoning process of a neural network however needs to be transparent. Recently, the mechanistic interpretation of this reasoning process has gained significant attention, which is concerned with understanding the *internal reasoning process* of a network, including what information particular neurons respond to and how these specific neurons are organized into larger circuits. In this talk, I will (1) gently introduce the topic of mechanistic interpretability in machine learning, (2) show how to discover mechanistic circuits within a neural network, (3) discuss the relevance of mechanistic interpretability in real-world applications, and (4) discuss what is still missing in the field.