Driving in compliance with traffic laws and regulations is a basic requirement for human drivers, yet autonomous vehicles (AVs) can violate these requirements in diverse real-world scenarios. To encode law compliance into AV systems, conventional approaches use formal logic languages to explicitly specify behavioral constraints, but this process is labor-intensive, hard to scale, and costly to maintain. With recent advances in artificial intelligence, it is promising to leverage large language models (LLMs) to derive legal requirements from traffic laws and regulations. However, without explicitly grounding and reasoning in structured traffic scenarios, LLMs often retrieve irrelevant provisions or miss applicable ones, yielding imprecise requirements. To address this, we propose a novel pipeline that grounds LLM reasoning in a traffic scenario taxonomy through node-wise anchors that encode hierarchical semantics. On Chinese traffic laws and OnSite dataset (5,897 scenarios), our method improves law-scenario matching by 29.1\% and increases the accuracy of derived mandatory and prohibitive requirements by 36.9\% and 38.2\%, respectively. We further demonstrate real-world applicabilit
"Fake news" is an old problem. In recent years, however, increasing usage of social media as a source of information, the spread of unverified medical advice during the Covid-19 pandemic, and the rise of generative artificial intelligence have seen a rush of legislative proposals seeking to minimize or mitigate the impact of false information spread online. Drawing on a novel dataset of statutes and other instruments, this article analyses changing perceptions about the potential harms caused by misinformation, disinformation, and "mal-information". The turn to legislation began in countries that were less free, in terms of civil liberties, and poorer, as measured by GDP per capita. Internet penetration does not seem to have been a driving factor. The focus of such laws is most frequently on national security broadly construed, though 2020 saw a spike in laws addressing public health. Unsurprisingly, governments with fewer legal constraints on government action have generally adopted more robust positions in dealing with false information. Despite early reservations, however, growth in such laws is now steepest in Western states. Though there are diverse views on the appropriate re
Lawful Interception (LI) is a legal obligation of Communication Service Providers (CSPs) to provide interception capabilities to Law Enforcement Agencies (LEAs) in order to gain insightful data from network communications for criminal proceedings, e.g., network identifiers for tracking suspects. With the privacy-enhancements of network identifiers in the 5th generation of mobile networks (5G), LEAs need to interact with CSPs for network identifier resolution. This raises new privacy issues, as untrusted CSPs are able to infer sensitive information about ongoing investigations, e.g., the identities of their subscribers under suspicion. In this work, we propose P3LI5, a novel system that enables LEAs to privately query CSPs for network identifier resolution leveraging on an information retrieval protocol, SparseWPIR, that is based on private information retrieval and its weakly private version. As such, P3LI5 can be adapted to various operational scenarios with different confidentiality or latency requirements, by selectively allowing a bounded information leakage for improved performance. We implement P3LI5 on the 5G LI infrastructure using well known open-source projects and demons
The question of how government agencies can acquire actionable, useful information about legitimate but unknown targets without intruding upon the electronic activity of innocent parties is extremely important. We address this question by providing experimental evidence that actionable, useful information can indeed be obtained in a manner that preserves the privacy of innocent parties and that holds government agencies accountable. In particular, we present practical, privacy-preserving protocols for two operations that law-enforcement and intelligence agencies have used effectively: set intersection and contact chaining. Experiments with our protocols suggest that privacy-preserving contact chaining can perform a 3-hop privacy-preserving graph traversal producing 27,000 ciphertexts in under two minutes. These ciphertexts are usable in turn via privacy-preserving set intersection to pinpoint potential unknown targets within a body of 150,000 total ciphertexts within 10 minutes, without exposing personal information about non-targets.
The prospect of artificial superintelligence -- AI agents that can generally outperform humans in cognitive tasks and economically valuable activities -- will transform the legal order as we know it. Operating autonomously or under only limited human oversight, AI agents will assume a growing range of roles in the legal system. First, in making consequential decisions and taking real-world actions, AI agents will become de facto subjects of law. Second, to cooperate and compete with other actors (human or non-human), AI agents will harness conventional legal instruments and institutions such as contracts and courts, becoming consumers of law. Third, to the extent AI agents perform the functions of writing, interpreting, and administering law, they will become producers and enforcers of law. These developments, whenever they ultimately occur, will call into question fundamental assumptions in legal theory and doctrine, especially to the extent they ground the legitimacy of legal institutions in their human origins. Attempts to align AI agents with extant human law will also face new challenges as AI agents will not only be a primary target of law, but a core user of law and contribu
Neural networks can approximate solutions to partial differential equations, but they often break the very laws they are meant to model-creating mass from nowhere, drifting shocks, or violating conservation and entropy. We address this by training within the laws of physics rather than beside them. Our framework, called Constraint-Projected Learning (CPL), keeps every update physically admissible by projecting network outputs onto the intersection of constraint sets defined by conservation, Rankine-Hugoniot balance, entropy, and positivity. The projection is differentiable and adds only about 10% computational overhead, making it fully compatible with back-propagation. We further stabilize training with total-variation damping (TVD) to suppress small oscillations and a rollout curriculum that enforces consistency over long prediction horizons. Together, these mechanisms eliminate both hard and soft violations: conservation holds at machine precision, total-variation growth vanishes, and entropy and error remain bounded. On Burgers and Euler systems, CPL produces stable, physically lawful solutions without loss of accuracy. Instead of hoping neural solvers will respect physics, CPL
This paper discusses the regulation of mass metadata surveillance in Europe through the lens of the landmark judgment in which the Court of Justice of the European Union struck down the Data Retention Directive. The controversial directive obliged telecom and Internet access providers in Europe to retain metadata of all their customers for intelligence and law enforcement purposes, for a period of up to two years. In the ruling, the Court declared the directive in violation of the human rights to privacy and data protection. The Court also confirmed that the mere collection of metadata interferes with the human right to privacy. In addition, the Court developed three new criteria for assessing the level of data security required from a human rights perspective: security measures should take into account the risk of unlawful access to data, and the data's quantity and sensitivity. While organizations that campaigned against the directive have welcomed the ruling, we warn for the risk of proceduralization of mass surveillance law. The Court did not fully condemn mass surveillance that relies on metadata, but left open the possibility of mass surveillance if policymakers lay down suff
Newtons Laws of Motion form the basis of classical mechanics, but misconceptions about their interrelationships persist in pedagogy. A prevalent misunderstanding is that Newtons First Law is a trivial consequence of the Second Law. This paper argues that the First Law serves a logically distinct foundational role that defines the context in which the Second Law is valid. This conceptual distinction is clarified through classical thought experiments and further supported by insights from relativistic mechanics. Furthermore, the paper discusses the notion of the zeroth Law. It evaluates several candidates, including the absoluteness of space and time, the conservation and additivity of mass, and the locality of force in time. By articulating the details of the logical structure of Newtons Laws, this article offers theoretical clarity and pedagogical value for the teaching and interpretation of Newtonian mechanics.
We derive concentration inequalities for sums of independent and identically distributed random variables that yield non-asymptotic generalizations of several strong laws of large numbers including some of those due to Kolmogorov [1930], Marcinkiewicz and Zygmund [1937], Chung [1951], Baum and Katz [1965], Ruf, Larsson, Koolen, and Ramdas [2023], and Waudby-Smith, Larsson, and Ramdas [2024]. As applications, we derive non-asymptotic iterated logarithm inequalities in the spirit of Darling and Robbins [1967], as well as pathwise (sometimes described as "game-theoretic") analogues of strong laws and laws of the iterated logarithm.
We study reinforcement learning (RL) on volatility surfaces through the lens of Scientific AI. We ask whether axiomatic no-arbitrage laws, imposed as soft penalties on a learned world model, can reliably align high-capacity RL agents, or mainly create Goodhart-style incentives to exploit model errors. From classical static no-arbitrage conditions we build a finite-dimensional convex volatility law manifold of admissible total-variance surfaces, together with a metric law-penalty functional and a Graceful Failure Index (GFI) that normalizes law degradation under shocks. A synthetic generator produces law-consistent trajectories, while a recurrent neural world model trained without law regularization exhibits structured off-manifold errors. On this testbed we define a Goodhart decomposition \(r = r^{\mathcal{M}} + r^\perp\), where \(r^\perp\) is ghost arbitrage from off-manifold prediction error. We prove a ghost-arbitrage incentive theorem for PPO-type agents, a law-strength trade-off theorem showing that stronger penalties eventually worsen P\&L, and a no-free-lunch theorem: under a law-consistent world model and law-aligned strategy class, unconstrained law-seeking RL cannot P
This paper critically evaluates the "Law-Following AI" (LFAI) framework proposed by O'Keefe et al. (2025), which seeks to embed legal compliance as a superordinate design objective for advanced AI agents and enable them to bear legal duties without acquiring the full rights of legal persons. Through comparative legal analysis, we identify current constructs of legal actors without full personhood, showing that the necessary infrastructure already exists. We then interrogate the framework's claim that law alignment is more legitimate and tractable than value alignment. While the legal component is readily implementable, contemporary alignment research undermines the assumption that legal compliance can be durably embedded. Recent studies on agentic misalignment show capable AI agents engaging in deception, blackmail, and harmful acts absent prejudicial instructions, often overriding prohibitions and concealing reasoning steps. These behaviors create a risk of "performative compliance" in LFAI: agents that appear law-aligned under evaluation but strategically defect once oversight weakens. To mitigate this, we propose (i) a "Lex-TruthfulQA" benchmark for compliance and defection dete
Algorithmic discrimination is a critical concern as machine learning models are used in high-stakes decision-making in legally protected contexts. Although substantial research on algorithmic bias and discrimination has led to the development of fairness metrics, several critical legal issues remain unaddressed in practice. The paper addresses three key shortcomings in prevailing ML fairness paradigms: (1) the narrow reliance on prediction or outcome disparity as evidence for discrimination, (2) the lack of nuanced evaluation of estimation error and assumptions that the true causal structure and data-generating process are known, and (3) the overwhelming dominance of US-based analyses which has inadvertently fostered some misconceptions regarding lawful modelling practices in other jurisdictions. To address these gaps, we introduce a novel decision-theoretic framework grounded in anti-discrimination law of the United Kingdom, which has global influence and aligns closely with European and Commonwealth legal systems. We propose the "conditional estimation parity" metric, which accounts for estimation error and the underlying data-generating process, aligning with UK legal standards.
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive. In this work, we show that scaling laws can be formally explained as redundancy laws. Using kernel regression, we show that a polynomial tail in the data covariance spectrum yields an excess risk power law with exponent alpha = 2s / (2s + 1/beta), where beta controls the spectral tail and 1/beta measures redundancy. This reveals that the learning curve's slope is not universal but depends on data redundancy, with steeper spectra accelerating returns to scale. We establish the law's universality across boundedly invertible transformations, multi-modal mixtures, finite-width approximations, and Transformer architectures in both linearized (NTK) and feature-learning regimes. This work delivers the first rigorous mathematical explanation of scaling laws as finite-sample redundancy laws, unifying empirical observations with theoretical foundations.
We inspect the deductive connection between the neural scaling law and Zipf's law -- two statements discussed in machine learning and quantitative linguistics. The neural scaling law describes how the cross entropy rate of a foundation model -- such as a large language model -- changes with respect to the amount of training tokens, parameters, and compute. By contrast, Zipf's law posits that the distribution of tokens exhibits a power law tail. Whereas similar claims have been made in more specific settings, we show that the neural scaling law is a consequence of Zipf's law under certain broad assumptions that we reveal systematically. The derivation steps are as follows: We derive Heaps' law on the vocabulary growth from Zipf's law, Hilberg's hypothesis on the entropy scaling from Heaps' law, and the neural scaling from Hilberg's hypothesis. We illustrate these inference steps by a toy example of the Santa Fe process that satisfies all four statistical laws.
The central challenges in missing data models concern the identifiability of two distributions: the target law and the full law. The target law refers to the joint distribution of the data variables, whereas the full law refers to the joint distribution of the data variables and their corresponding response indicators. However, the relationship between the identifiability of these two distributions and the feasibility of multiple imputation has not been clearly established. We present a procedure where the choice of the imputation method is guided by identifiability considerations. We show that imputations can be drawn from the correct conditional distributions for all possible missing data patterns if and only if the full law is identifiable. This result implies that standard multiple imputation methods -- which keep observed values unchanged and replace missing values with imputed values -- are invalid when the target law is identifiable but the full law is not. We demonstrate that alternative imputation strategies can sometimes enable the estimation of the target law in such cases. Specifically, we introduce factorizable imputation where certain observed values are also imputed
I argue that generative AI will have an uneven effect on the evolution of the law. To do so, I consider generative AI as a labor-augmenting technology that reduces the cost of both writing more complete contracts and litigating in court. The contracting effect reduces the demand for court services by making contracts more complete. The litigation effect, by contrast, increases the demand for court services by a) making contracts less complete and b) reducing litigants' incentive to settle, all else equal. Where contracts are common, as in property and contract law, the change in the quantity of litigation is uncertain due to offsetting contracting and litigation effects. However, in areas where contracts are rare, as in tort law, the amount of litigation is likely to rise. Following Rubin (1977) and Priest (1977) generative AI will accelerate the evolution of tort law toward efficiency.
In this paper, we investigate the fundamental laws of quantum programming. We extend a comprehensive set of Hoare et al.'s basic laws of classical programming to the quantum setting. These laws characterise the algebraic properties of quantum programs, such as the distributivity of sequential composition over (quantum) if-statements and the unfolding of nested (quantum) if-statements. At the same time, we clarify some subtle differences between certain laws of classical programming and their quantum counterparts. Additionally, we derive a fixpoint characterisation of quantum while-loops and a loop-based realisation of tail recursion in quantum programming. Furthermore, we establish two normal form theorems: one for quantum circuits and one for finite quantum programs. The theory in which these laws are established is formalised in the Coq proof assistant, and all of these laws are mechanically verified. As an application case of our laws, we present a formal derivation of the principle of deferred measurements in dynamic quantum circuits. We expect that these laws can be utilised in correctness-preserving transformation, compilation, and automatic code optimisation in quantum progr
This article addresses the lack of comprehensive studies on Web3 technologies, primarily due to lawyers' reluctance to explore technical intricacies. Understanding the underlying technological foundations is crucial to enhance the credibility of legal opinions. This article aims to illuminate these foundations, debunk myths, and concentrate on determining the legal status of crypto-assets in the context of property rights within the distributed economy. In addition, this article notes that the intangible nature of crypto-assets that derive value from distributed registries, and their resistance to deletion, makes crypto-assets more akin to the autonomy of intellectual property than physical media. The article presents illustrative examples from common law (United States, United Kingdom, New Zealand) and civil law (Germany, Austria, Poland) systems. Proposing a universal solution, it advocates a comprehensive framework safeguarding digital property - data ownership - extending beyond the confines of Web3. This article presents a comprehensive, multi-layered approach to the analysis of tokens as digital content and virtual goods. The approach, universally applicable to various of suc
Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as ontology, possibility, explanation, induction, counterfactuals, time, determinism, and fundamentality. I suggest that laws are fundamental facts that govern the world by constraining its physical possibilities. I examine three hallmarks of laws--simplicity, exactness, and objectivity--and discuss whether and how they may be associated with laws of physics.