Related papers: {\L}ukasiewicz Logic with Actions for Neural Netwo…

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…

The backpropagation algorithm is an invaluable tool for training artificial neural networks; however, because of a weight sharing requirement, it does not provide a plausible model of brain function. Here, in the context of a two-layer…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…

Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…

Perceptrons are the basic computational unit of artificial neural networks, as they model the activation mechanism of an output neuron due to incoming signals from its neighbours. As linear classifiers, they play an important role in the…

While feed-forward neurons in pre-trained language models (PLMs) can encode knowledge, past research targeted a small subset of neurons that heavily influence outputs. This leaves the broader role of neuron activations unclear, limiting…

We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate…

We present a method for learning multi-stage tasks from demonstrations by learning the logical structure and atomic propositions of a consistent linear temporal logic (LTL) formula. The learner is given successful but potentially suboptimal…

We introduce a novel neuromorphic network architecture based on a lattice of exciton-polariton condensates, intricately interconnected and energized through non-resonant optical pumping. The network employs a binary framework, where each…

In this paper, a simple, general method of adding auxiliary stochastic neurons to a multi-layer perceptron is proposed. It is shown that the proposed method is a generalization of recently successful methods of dropout (Hinton et al.,…

Human beings naturally utilize multiple reasoning modalities to learn and solve logical problems, i.e., different representational formats such as natural language, code, and symbolic logic. In contrast, most existing LLM-based approaches…

Extensive research on formal verification of machine learning systems indicates that learning from data alone often fails to capture underlying background knowledge, such as specifications implicitly available in the data. Various neural…

Predictive modeling on sequential event data is critical for fraud detection and healthcare monitoring. Existing data-driven approaches learn correlations from historical data but fail to incorporate domain-specific sequential constraints…

The rising popularity of neural networks (NNs) in recent years and their increasing prevalence in real-world applications have drawn attention to the importance of their verification. While verification is known to be computationally…

Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge…

In this study we explore the spontaneous apparition of visible intelligible reasoning in simple artificial networks, and we connect this experimental observation with a notion of semantic information. We start with the reproduction of a DNN…

Evaluation of multimodal reasoning models is typically reduced to a single accuracy score, implicitly treating reasoning as a unitary capability. We introduce MathLens, a benchmark of textbook-style geometry problems that exposes this…

A fuzzy multipreference semantics has been recently proposed for weighted conditional knowledge bases, and used to develop a logical semantics for Multilayer Perceptrons, by regarding a deep neural network (after training) as a weighted…

Declarative knowledge and procedural knowledge are two key parts in meta-cognitive theory, and these two hold significant importance in pre-training and inference of LLMs. However, a comprehensive analysis comparing these two types of…