Related papers: The Safe Lambda Calculus

We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…

Interactive behaviors are ubiquitous in modern cryptography, but are also present in $\lambda$-calculi, in the form of higher-order constructions. Traditionally, however, typed $\lambda$-calculi simply do not fit well into cryptography,…

We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…

Balanced Singular Perturbation Approximation (SPA) is a model order reduction method for linear time-invariant systems that guarantees asymptotic stability and for which there exists an a priori error bound. In that respect, it is similar…

Science and technology have a growing need for effective mechanisms that ensure reliable, controlled performance from black-box machine learning algorithms. These performance guarantees should ideally hold conditionally on the input-that is…

We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of `safety' provides a fresh perspective on foundational issues in statistics, providing…

The $\lambda$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional…

A value of a CSP instance is typically defined as a fraction of constraints that can be simultaneously met. We propose an alternative definition of a value of an instance and show that, for purely combinatorial reasons, a value of an…

The good properties of Plotkin's call-by-value lambda-calculus crucially rely on the restriction to weak evaluation and closed terms. Open call-by-value is the more general setting where evaluation is weak but terms may be open. Such an…

Large language models (LLMs) often demonstrate strong safety performance in high-resource languages, yet exhibit severe vulnerabilities when queried in low-resource languages. We attribute this gap to a mismatch between language-agnostic…

Circumscription and logic programs under the stable model semantics are two well-known nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus…

Large language models (LLMs) employ safety mechanisms to prevent harmful outputs, yet these defenses primarily rely on semantic pattern matching. We show that encoding harmful prompts as coherent mathematical problems -- using formalisms…

Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class…

Ensuring that Large Language Models (LLMs) adhere to safety principles without refusing benign requests remains a significant challenge. While OpenAI introduces deliberative alignment (DA) to enhance the safety of its o-series models…

Fine-tuning safety-aligned large language models (LLMs) can substantially compromise their safety. Previous approaches require many safety samples or calibration sets, which not only incur significant computational overhead during…

Reinforcement learning algorithms typically necessitate extensive exploration of the state space to find optimal policies. However, in safety-critical applications, the risks associated with such exploration can lead to catastrophic…

Ensuring safety in industrial control systems usually involves imposing constraints at the design stage of the control algorithm. Enforcing constraints is challenging if the underlying functional form is unknown. The challenge can be…

Bender et al. (SPAA 2013) have proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be often calibrated. Given that calibration costs, it…

Languages with gradual information-flow control combine static and dynamic techniques to prevent security leaks. Gradual languages should satisfy the gradual guarantee: programs that only differ in the precision of their type annotations…

This paper presents the concept of an adaptive safe padding that forces Reinforcement Learning (RL) to synthesise optimal control policies while ensuring safety during the learning process. Policies are synthesised to satisfy a goal,…