Related papers: Complex Markov Logic Networks: Expressivity and Li…
The standard approach to verify representations learned by Deep Neural Networks is to use them in specific tasks such as classification or regression, and measure their performance based on accuracy in such tasks. However, in many cases, we…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
We consider the task of weighted first-order model counting (WFOMC) used for probabilistic inference in the area of statistical relational learning. Given a formula $\phi$, domain size $n$ and a pair of weight functions, what is the…
Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what…
The learned weights of a neural network are often considered devoid of scrutable internal structure. To discern structure in these weights, we introduce a measurable notion of modularity for multi-layer perceptrons (MLPs), and investigate…
We introduce a new approximate solution technique for first-order Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of first-order basis functions, we compute suitable weights by casting the…
Motivated by applications in large-scale knowledge base construction, we study the problem of scaling up a sophisticated statistical inference framework called Markov Logic Networks (MLNs). Our approach, Felix, uses the idea of Lagrangian…
We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these…
NLP tasks differ in the semantic information they require, and at this time no single se- mantic representation fulfills all requirements. Logic-based representations characterize sentence structure, but do not capture the graded aspect of…
Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify…
We introduce DeepPSL a variant of probabilistic soft logic (PSL) to produce an end-to-end trainable system that integrates reasoning and perception. PSL represents first-order logic in terms of a convex graphical model -- hinge-loss Markov…
Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order logic theory on a given finite domain. First-Order Logic theories that admit polynomial-time WFOMC w.r.t domain cardinality are called…
Estimating the difficulty of input questions as perceived by large language models (LLMs) is essential for accurate performance evaluation and adaptive inference. Existing methods typically rely on repeated response sampling, auxiliary…
For many fundamental physics applications, transformers, as the state of the art in learning complex correlations, benefit from pretraining on quasi-out-of-domain data. The obvious question is whether we can exploit Large Language Models,…
Interpretability has become a necessary feature for machine learning models deployed in critical scenarios, e.g. legal system, healthcare. In these situations, algorithmic decisions may have (potentially negative) long-lasting effects on…
This paper explores the complexity of deep feedforward networks with linear pre-synaptic couplings and rectified linear activations. This is a contribution to the growing body of work contrasting the representational power of deep and…
Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals. However, training them to capture fine details in multi-scale signals is difficult and…
We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more…
Large language models (LLMs) can be seen as atomic units of computation mapping sequences to a distribution over sequences. Thus, they can be seen as stochastic language layers in a language network, where the learnable parameters are the…
Lifted Relational Neural Networks (LRNNs) describe relational domains using weighted first-order rules which act as templates for constructing feed-forward neural networks. While previous work has shown that using LRNNs can lead to…