Related papers: The Pattern Basis Approach to Circuit Complexity
In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
We formalise the essential data of objective functions as equality constraints on composites of learners. We call these constraints "tasks", and we investigate the idealised view that such tasks determine model behaviours. We develop a…
We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…
Creating quantum algorithms is a difficult task, especially for computer scientist not used to quantum computing. But quantum algorithms often use similar elements. Thus, these elements provide proven solutions to recurring problems, i.e. a…
We propose a relax-and-round approach combined with a greedy search strategy for performing complex lattice basis reduction. Taking an optimization perspective, we introduce a relaxed version of the problem that, while still nonconvex, has…
The description complexity of a model is the length of the shortest formula that defines the model. We study the description complexity of unary structures in first-order logic FO, also drawing links to semantic complexity in the form of…
We say that a circuit $C$ over a field $F$ functionally computes an $n$-variate polynomial $P$ if for every $x \in \{0,1\}^n$ we have that $C(x) = P(x)$. This is in contrast to syntactically computing $P$, when $C \equiv P$ as formal…
Patterns describe proven solutions for recurring problems. Typically, patterns in a particular domain are interrelated and organized in pattern languages. As real-world problems often require patterns of multiple domains, different pattern…
Several paradigms for declarative problem solving start from a specification in a high-level language, which is then transformed to a low-level language, such as SAT or SMT. Often, this transformation includes a "grounding" step to remove…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
A fundamental question in interpretability research is to what extent neural networks, particularly language models, implement reusable functions through subnetworks that can be composed to perform more complex tasks. Recent advances in…
The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for…
A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the…
This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix. This representation turns…