Related papers: Abstract computation over first-order structures. …
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which has…
Mechanistic interpretability aims to reverse engineer neural networks by uncovering which high-level algorithms they implement. Causal abstraction provides a precise notion of when a network implements an algorithm, i.e., a causal model of…
In earlier work, the Abstract State Machine Thesis -- that arbitrary algorithms are behaviorally equivalent to abstract state machines -- was established for several classes of algorithms, including ordinary, interactive, small-step…
The emergence of systems with non-volatile main memory (NVM) increases the interest in the design of \emph{recoverable concurrent objects} that are robust to crash-failures, since their operations are able to recover from such failures by…
Inspired by Leivant's work on absolute predicativism, Bellantoni and Cook in 1992 introduced a structurally restricted form of recursion called predicative recursion. Using this recursion scheme on the inductive structures of natural…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice.…
There are several important abstract operator systems with the convex cone of positive semidefinite matrices at the first level. Well-known are the operator systems of separable matrices, of positive semidefinite matrices, and of block…
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
Human visual reasoning is characterized by an ability to identify abstract patterns from only a small number of examples, and to systematically generalize those patterns to novel inputs. This capacity depends in large part on our ability to…
We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
Motivated by a variety of representations of fractional powers of operators, we develop the theory of abstract Besov spaces $B^{ s, A }_{ q, X }$ for non-negative operators $A$ on Banach spaces $X$ with a full range of indices $s \in…
A growing body of work in economics and computation focuses on the trade-off between implementability and simplicity in mechanism design. The goal is to develop a theory that not only allows to design an incentive structure easy to grasp…
Neural networks are hypothesized to implement interpretable causal mechanisms, yet verifying this requires finding a causal abstraction -- a simpler, high-level Structural Causal Model (SCM) faithful to the network under interventions.…
The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function…