Related papers: Galois Transformers and Modular Abstract Interpret…
Static analyses overwhelmingly trade precision for soundness and automation. For this reason, their use-cases are restricted to situations where imprecision isn't prohibitive. In this paper, we propose and specify a static analysis that…
Reactive synthesis is the process of generating correct controllers from temporal logic specifications. Classical LTL reactive synthesis handles (propositional) LTL as a specification language. Boolean abstractions allow reducing LTLt…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Static analysis is sound in theory, but an implementation may unsoundly fail to analyze all of a program's code. Any such omission is a serious threat to the validity of the tool's output. Our work is the first to measure the prevalence of…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
Abstraction is an important and useful concept in the field of artificial intelligence. To the best of our knowledge, there is no syntactic method to compute a sound and complete abstraction from a given low-level basic action theory and a…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
Transformers (Vaswani et al., 2017) have brought a remarkable improvement in the performance of neural machine translation (NMT) systems but they could be surprisingly vulnerable to noise. In this work, we try to investigate how noise…
We consider Galois/monodromy groups arising in computer vision applications, with a view towards building more efficient polynomial solvers. The Galois/monodromy group allows us to decide when a given problem decomposes into algebraic…
We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines. To demonstrate the technique and support our claim, we transform…
Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al.…
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Model finding, as embodied by SAT solvers and similar tools, is used widely, both in embedding settings and as a tool in its own right. For instance, tools like Alloy target SAT to enable users to incrementally define, explore, verify, and…
Accounts of semantic phenomena often involve extending types of meanings and revising composition rules at the same time. The concept of monads allows many such accounts -- for intensionality, variable binding, quantification and focus --…
Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations…
To a "stable homotopy theory" (a presentable, symmetric monoidal stable $\infty$-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…
Automating string transformations has been one of the killer applications of program synthesis. Existing synthesizers that solve this problem produce programs in domain-specific languages (DSL) that are engineered to help the synthesizer,…