Related papers: Tractable Boolean and Arithmetic Circuits
Probabilistic circuits (PCs) are powerful probabilistic models that enable exact and tractable inference, making them highly suitable for probabilistic reasoning and inference tasks. While dominant in neural networks, representation…
Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
Scores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential SHAP-score, a version of the Shapley value that can help explain…
We characterize three notions of explainable AI that cut across research fields: opaque systems that offer no insight into its algo- rithmic mechanisms; interpretable systems where users can mathemat- ically analyze its algorithmic…
End-to-end deep neural networks have achieved remarkable success across various domains but are often criticized for their lack of interpretability. While post hoc explanation methods attempt to address this issue, they often fail to…
A main open question in contemporary AI research is quantifying the forms of reasoning neural networks can perform when perfectly trained. This paper answers this by interpreting reasoning tasks as circuit emulation, where the gates define…
Transformer-based language models have achieved significant success; however, their internal mechanisms remain largely opaque due to the complexity of non-linear interactions and high-dimensional operations. While previous studies have…
*Automated circuit discovery* is a central tool in mechanistic interpretability for identifying the internal components of neural networks responsible for specific behaviors. While prior methods have made significant progress, they…
Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to…
Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…
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…
We present a comprehensive survey of the advancements and techniques in the field of tractable probabilistic generative modeling, primarily focusing on Probabilistic Circuits (PCs). We provide a unified perspective on the inherent…
The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neural networks which can reason through any Boolean task…
Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns…
Explainability has been an important goal since the early days of Artificial Intelligence. Several approaches for producing explanations have been developed. However, many of these approaches were tightly coupled with the capabilities of…
Black box neural networks are an indispensable part of modern robots. Nevertheless, deploying such high-stakes systems in real-world scenarios poses significant challenges when the stakeholders, such as engineers and legislative bodies,…
Parametrized Quantum Circuits (PQCs) enable a novel method for machine learning (ML). However, from a computational point of view they present a challenge to existing eXplainable AI (xAI) methods. On the one hand, measurements on quantum…
It is an intriguing concept to use oscillators as fundamental building blocks of electronic computers. The idea is not new, but is currently subject to intense research as a part of the quest for 'beyond Moore' electronic devices. In this…
A popular approach to neurosymbolic AI involves mapping logic formulas to arithmetic circuits (computation graphs consisting of sums and products) and passing the outputs of a neural network through these circuits. This approach enforces…