Related papers: Exploring Hidden Semantics in Neural Networks with…

In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning…

Symbolic techniques based on Satisfiability Modulo Theory (SMT) solvers have been proposed for analyzing and verifying neural network properties, but their usage has been fairly limited owing to their poor scalability with larger networks.…

Many machine learning strategies designed to automate mathematical tasks leverage neural networks to search large combinatorial spaces of mathematical symbols. In contrast to traditional evolutionary approaches, using a neural network at…

Recently, deep neural networks (DNNs) have achieved great success in semantically challenging NLP tasks, yet it remains unclear whether DNN models can capture compositional meanings, those aspects of meaning that have been long studied in…

Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of…

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures…

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…

One of the ultimate goals of Artificial Intelligence is to assist humans in complex decision making. A promising direction for achieving this goal is Neuro-Symbolic AI, which aims to combine the interpretability of symbolic techniques with…

Symbolic Regression aims to automatically identify compact and interpretable mathematical expressions that model the functional relationship between input and output variables. Most existing search-based symbolic regression methods…

We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…

A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed…

The analysis of biophysical neural networks (BNNs) has been a longstanding focus in computational neuroscience. A central yet unresolved challenge in BNN analysis lies in deciphering the correlations between neuronal and synaptic dynamics,…

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…

This work presents a novel spiking neural network (SNN) decoding method, combining SNNs with Hyperdimensional computing (HDC). The goal is to create a decoding method with high accuracy, high noise robustness, low latency and low energy…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer…

Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces…

Mathematical expressions play a central role in scientific discovery. Symbolic regression aims to automatically discover such expressions from given numerical data. Recently, Neural symbolic regression (NSR) methods that involve…

Sometimes the meaning conveyed by images goes beyond the list of objects they contain; instead, images may express a powerful message to affect the viewers' minds. Inferring this message requires reasoning about the relationships between…

In this paper, we propose a novel Explanation Neural Network (XNN) to explain the predictions made by a deep network. The XNN works by learning a nonlinear embedding of a high-dimensional activation vector of a deep network layer into a…